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Special Relativity/Dynamics

Introduction
The way that the velocity of a particle can differ between observers who are moving relative to each other means that momentum needs to be redefined as a result of relativity theory.

The illustration below shows a typical collision of two particles. In the right hand frame the collision is observed from the viewpoint of someone moving at the same velocity as one of the particles, in the left hand frame it is observed by someone moving at a velocity that is intermediate between those of the particles.

If momentum is redefined then all the variables such as force (rate of change of momentum), energy etc. will become redefined and relativity will lead to an entirely new physics. The new physics has an effect at the ordinary level of experience through the relation $$K = \gamma m c^2 - m c^2\,$$ whereby it is the tiny deviations in gamma from unity that are expressed as everyday kinetic energy so that the whole of physics is related to "relativistic" reasoning rather than Newton's empirical ideas.

Momentum
In physics momentum is conserved within a closed system, the law of conservation of momentum applies. Consider the special case of identical particles colliding symmetrically as illustrated below:

The momentum change by the red ball is:

$$2m\mathbf{u_{yR}}$$

The momentum change by the blue ball is:

$$-2m\mathbf{u_{yB}}$$

The situation is symmetrical so the Newtonian conservation of momentum law is demonstrated:

$$2m\mathbf{u_{yR}}=2m\mathbf{u_{yB}}$$

Notice that this result depends upon the y components of the velocities being equal, that is, $$\mathbf{u_{yR}}=\mathbf{u_{yB}}$$.

The relativistic case is rather different. The collision is illustrated below, the left hand frame shows the collision as it appears for one observer and the right hand frame shows exactly the same collision as it appears for another observer moving at the same velocity as the blue ball:

The configuration shown above has been simplified because one frame contains a stationary blue ball (ie: $$u_{xB}=0$$) and the velocities are chosen so that the vertical velocity of the red ball is exactly reversed after the collision ie:$$u_{yR}^' = u_{yB}^'$$. Both frames show exactly the same event, it is only the observers who differ between frames. The relativistic velocity transformations between frames is:

$$u_{yR}^' = \frac{u_{yR} \sqrt{1 - v^2/c^2}}{1 - u_{xR}v/c^2}$$

$$u_{yB}^' =\frac{u_{yB} \sqrt{1 - v^2/c^2}}{1 - u_{xB}v/c^2}= u_{yB} \sqrt{1 - v^2/c^2}$$ given that $$u_{xB}=0\,$$.

Suppose that the y components are equal in one frame, in Newtonian physics they will also be equal in the other frame. However, in relativity, if the y components are equal in one frame they are not necessarily equal in the other frame (time dilation is not directional so perpendicular velocities differ between the observers). For instance if $$u_{yR}^' = u_{yB}^'$$ then:

$$u_{yB} = \frac{u_{yR}}{1 - u_{xR}v/c^2}$$

So if $$u_{yR}^' = u_{yB}^'$$ then in this case $$u_{yR} \ne u_{yB}$$.

If the mass were constant between collisions and between frames then although $$2 mu_{yR}^' = 2mu_{yB}^'$$ it is found that:

$$2 mu_{yR} \ne 2mu_{yB}$$

So momentum defined as mass times velocity is not conserved in a collision when the collision is described in frames moving relative to each other. Notice that the discrepancy is very small if $$u_{xR}$$ and $$v$$ are small.

To preserve the principle of momentum conservation in all inertial reference frames, the definition of momentum has to be changed. The new definition must reduce to the Newtonian expression when objects move at speeds much smaller than the speed of light, so as to recover the Newtonian formulas.

The velocities in the y direction are related by the following equation when the observer is travelling at the same velocity as the blue ball ie: when $$ u_{xB} = 0\,$$:

$$u_{yB} = \frac{u_{yR}}{1 - u_{xR}v/c^2}$$

If we write $$m_B$$ for the mass of the blue ball) and $$m_R$$ for the mass of the red ball as observed from the frame of the blue ball then, if the principle of relativity applies:

$$2 m_R u_{yR} = 2 m_B u_{yB} \,$$

So:

$$m_R = m_B \frac{u_{yB}}{u_{yR}}$$

But:

$$u_{yB} = \frac{u_{yR}}{1 - u_{xR}v/c^2}$$

Therefore:

$$m_R = \frac{m_B}{1 - u_{xR}v/c^2}$$

This means that, if the principle of relativity is to apply then the mass must change by the amount shown in the equation above for the conservation of momentum law to be true.

The particle velocities were chosen so that $$u_{yR}^' = u_{yB}^'$$. $$v$$ was selected so that $$ v = u_{xR}^'$$. This allows $$v$$ to be expressed in terms of $$u_{xR}\,$$:

$$u_{xR}^' = \frac{u_{xR} - v}{1 - u_{xR}v/c^2} = v$$

and hence:

$$v = \frac{c^2}{u_{xR}}(1 - \sqrt{1-u_{xR}^2/c^2})$$

So substituting for $$v$$ in $$m_R = \frac{m_B}{1 - u_{xR}v/c^2}$$:

$$m_R = \frac{m_B}{\sqrt{1 - u_{xR}^2/c^2}}$$

The blue ball is at rest so its mass is sometimes known as its rest mass, and is given the symbol $$m$$. As the balls were identical at the start of the boost the mass of the red ball is the mass that a blue ball would have if it were in motion relative to an observer; this mass is sometimes known as the relativistic mass symbolised by $$M$$. These terms are now infrequently used in modern physics, as will be explained at the end of this section. The discussion given above was related to the relative motions of the blue and red balls, as a result $$u_{xR}$$ corresponds to the speed of the moving ball relative to an observer who is stationary with respect to the blue ball. These considerations mean that the relativistic mass is given by:

$$M = \frac{m}{\sqrt{1 - u^2/c^2}}$$

The relativistic momentum is given by the product of the relativistic mass and the velocity $$\mathbf{p}=M\mathbf{u}$$.

The overall expression for momentum in terms of rest mass is:

$$\mathbf{p} = \frac{m\mathbf{u}}{\sqrt{1-u^2/c^2}}$$

and the components of the momentum are:

$$p_x = \frac{mu_x}{\sqrt{1-u^2/c^2}}$$

$$p_y = \frac{mu_y}{\sqrt{1-u^2/c^2}}$$

$$p_z = \frac{mu_z}{\sqrt{1-u^2/c^2}}$$

So the components of the momentum depend upon the appropriate velocity component and the speed.

Since the factor with the square root is cumbersome to write, the following abbreviation is often used, called the Lorentz gamma factor:

$$ \gamma = \frac{1}{\sqrt{1-u^2/c^2}}$$

The expression for the momentum then reads $$ \mathbf{p} = m \gamma \mathbf{u} $$.

It can be seen from the discussion above that we can write the momentum of an object moving with velocity $$\mathbf{u} $$ as the product of a function $$ M(u) $$ of the speed $$ u $$ and the velocity $$ \mathbf{u} $$:

$$ M(u) \mathbf{u} $$

The function $$ M(u) $$ must reduce to the object's mass $$ m $$ at small speeds, in particular when the object is at rest $$ M(0) = m $$.

There is a debate about the usage of the term "mass" in relativity theory. If inertial mass is defined in terms of momentum then it does indeed vary as $$M = \gamma m$$ for a single particle that has rest mass, furthermore, as will be shown below the energy of a particle that has a rest mass is given by $$E=Mc^2$$. Prior to the debate about nomenclature the function $$ M(u) $$, or the relation $$M = \gamma m$$, used to be called 'relativistic mass', and its value in the frame of the particle was referred to as the 'rest mass' or 'invariant mass'. The relativistic mass, $$M = \gamma m$$, would increase with velocity. Both terms are now largely obsolete: the 'rest mass' is today simply called the mass, and the 'relativistic mass' is often no longer used since, as will be seen in the discussion of energy below, it is identical to the energy but for the units.

Force
Newton's second law states that the total force acting on a particle equals the rate of change of its momentum. The same form of Newton's second law holds in relativistic mechanics. The relativistic 3 force is given by:

$$ \mathbf{f} = d\mathbf{p}/dt$$

If the relativistic mass is used:

$$\frac{d\mathbf{p}}{dt}= \frac{d(m\mathbf{u})}{dt}$$

By Leibniz's law where $$d(xy)=xdy+ydx$$:

$$\mathbf{f} = \frac{d\mathbf{p}}{dt}= m\frac{d\mathbf{u}}{dt}+\mathbf{u}\frac{dm}{dt}$$

This equation for force will be used below to derive relativistic expressions for the energy of a particle in terms of the old concept of "relativistic mass".

The relativistic force can also be written in terms of acceleration. Newton's second law can be written in the familiar form

$$ \mathbf{F} = m \mathbf{a} $$

where $$ \mathbf{a} = d\mathbf{v}/dt $$ is the acceleration.

here m is not the relativistic mass but is the invariant mass.

In relativistic mechanics, momentum is $$ \mathbf{p} = m \gamma \mathbf{v} $$

again m being the invariant mass and the force is given by $$ \mathbf{F} = \frac{d\mathbf{p}}{dt} = m \frac{d(\gamma \mathbf{v})}{dt} $$

This form of force is used in the derivation of the expression for energy without relying on relativistic mass.

It will be seen in the second section of this book that Newton's second law in terms of acceleration is given by:

$$ \mathbf{F} = m \gamma( \mathbf{a} + \frac{\gamma^2 v}{c^2} \frac{dv}{dt} \mathbf{v}) $$

Energy
The debate over the use of the concept "relativistic mass" means that modern physics courses may forbid the use of this in the derivation of energy. The newer derivation of energy without using relativistic mass is given in the first section and the older derivation using relativistic mass is given in the second section. The two derivations can be compared to gain insight into the debate about mass but a knowledge of 4 vectors is really required to discuss the problem in depth. In principle the first derivation is most mathematically correct because "relativistic mass" is given by: $$M = \frac{m}{\sqrt{1 - u^2/c^2}}$$ which involves the constants $$m$$ and $$c$$.

Derivation of relativistic energy using the relativistic momentum
In the following, modern derivation, m means the invariant mass - what used to be called the "rest mass". Energy is defined as the work done in moving a body from one place to another. We will make use of the relativistic momentum $$ p=\gamma mv $$. Energy is given from:

$$ dE = \mathbf{f}d\mathbf{x}$$

so, over the whole path:

$$ E = \int_{0}^{x} \mathbf{f}d\mathbf{x}$$

Kinetic energy (K) is the energy used to move a body from a velocity of 0 to a velocity $$\mathbf{u}$$. Restricting the motion to one dimension:

$$K = \int_{u=0}^{u=u} \mathbf{f} dx$$

Using the relativistic 3 force:

$$K = \int_{u=0}^{u=u} \frac{d(m\gamma u)}{dt}dx=\int_{u=0}^{u=u}m \frac{d(\gamma u)}{dt}dx= \int_{u=0}^{u=u} m d(\gamma u)\frac{dx}{dt}$$

substituting for $$d(\gamma u)$$ and using $$dx/dt=u$$:

$$K = \int_{u=0}^{u=u} m (\gamma du + ud\gamma) u$$

Which gives:

$$K = \int_{u=0}^{u=u} m (u\gamma du + u^2 d\gamma)$$

The Lorentz factor $$ \gamma $$ is given by:

$$\gamma = \frac{1}{\sqrt{1 - u^2/c^2}}$$

meaning that :

$$d\gamma = \frac{u}{c^2}\gamma^3du$$

$$du = \frac{c^2}{u\gamma^3}d\gamma$$

So that

$$K = \int_{\gamma=1}^{\gamma=\gamma} m (u\gamma \frac{c^2}{u\gamma^3}d\gamma + u^2 d\gamma) = \int_{\gamma=1}^{\gamma=\gamma} m (\frac{c^2}{\gamma^2} + u^2) d\gamma = \int_{\gamma=1}^{\gamma=\gamma} m c^2 d\gamma$$

Alternatively, we can use the fact that:

$$\gamma^2c^2 - \gamma^2u^2 = c^2\,$$

Differentiating:

$$2\gamma c^2d\gamma - \gamma^22udu -u^22\gamma d\gamma =0\,$$

So, rearranging:

$$\gamma u du + u^2 d\gamma = c^2 d\gamma\,$$

In which case:

$$K = \int_{u=0}^{u=u} m (u\gamma du + u^2 d\gamma) = \int_{u=0}^{u=u} m c^2 d\gamma \,$$

As $$ u $$ goes from 0 to $$ u $$, the Lorentz factor $$ \gamma $$ goes from 1 to $$ \gamma $$, so:

$$K = m c^2 \int_{\gamma=1}^{\gamma=\gamma} d\gamma \,$$

and hence:

$$K = \gamma m c^2 - m c^2\,$$

The amount $$\gamma mc^2$$ is known as the total energy of the particle. The amount $$m c^2$$ is known as the rest energy of the particle. If the total energy of the particle is given the symbol $$E$$:

$$ E = \gamma m c^2 = mc^2 + K \,$$

So it can be seen that $$m c^2$$ is the energy of a mass that is stationary. This energy is known as mass energy.

The Newtonian approximation for kinetic energy can be derived by using the binomial theorem to expand $$\gamma = (1-u^2/c^2)^{-\frac{1}{2}}$$.

The binomial expansion is:

$$(a + x)^n = a^n + na^{n-1}x + \frac{n(n-1)}{2!}a^{n-2}x^2 ....$$

So expanding $$(1-u^2/c^2)^{-\frac{1}{2}}$$:

$$K = \frac{1}{2} m u^2 + \frac{3m u^4}{8c^2} + \frac{5m u^6}{16c^4} + ...$$

So if $$u$$ is much less than $$c$$:

$$K = \frac{1}{2} m u^2 $$

which is the Newtonian approximation for low velocities.

Derivation of relativistic energy using the concept of relativistic mass
Energy is defined as the work done in moving a body from one place to another. Energy is given from:

$$ dE = \mathbf{F}d\mathbf{x}$$

so, over the whole path:

$$ E = \int_{0}^{x} \mathbf{F}d\mathbf{x}$$

Kinetic energy (K) is the energy used to move a body from a velocity of 0 to a velocity $$u$$. So:

$$K = \int_{u=0}^{u=u} F dx$$

Using the relativistic force:

$$K = \int_{u=0}^{u=u} \frac{d(Mu)}{dt}dx$$

So:

$$K = \int_{u=0}^{u=u} d(Mu)\frac{dx}{dt}$$

substituting for $$d(Mu)$$ and using $$dx/dt=u$$:

$$K = \int_{u=0}^{u=u} (Mdu + udM) u$$

Which gives:

$$K = \int_{u=0}^{u=u} (Mu du + u^2 dM)$$

The relativistic mass is given by:

$$M = \frac{m}{\sqrt{1 - u^2/c^2}}$$

Which can be expanded as:

$$M^2c^2 - M^2u^2 = m^2c^2$$

Differentiating:

$$2Mc^2dM - M^22udu -u^22MdM =0$$

So, rearranging:

$$Mu du + u^2 dM = c^2 dM$$

In which case:

$$K = \int_{u=0}^{u=u} (Mu du + u^2 dM)$$

is simplified to:

$$K = \int_{u=0}^{u=u} c^2 dM$$

But the mass goes from $$m$$ to $$M$$ so:

$$K = c^2 \int_{M=m}^{M=M} dM)$$

and hence:

$$K = Mc^2 - mc^2$$

The amount $$Mc^2$$ is known as the total energy of the particle. The amount $$mc^2$$ is known as the rest energy of the particle. If the total energy of the particle is given the symbol $$E$$:

$$E = mc^2 + K$$

So it can be seen that $$mc^2$$ is the energy of a mass that is stationary. This energy is known as mass energy and is the origin of the famous formula $$E=mc^2$$ that is iconic of the nuclear age.

The Newtonian approximation for kinetic energy can be derived by substituting the rest mass for the relativistic mass ie:

$$M = \frac{m}{\sqrt{1 - u^2/c^2}}$$

and:

$$K = Mc^2 - mc^2$$

So:

$$K = \frac{mc^2}{\sqrt{1-u^2/c^2}} - mc^2$$

ie:

$$K = mc^2 ((1-u^2/c^2)^{-\frac{1}{2}} -1)$$

The binomial theorem can be used to expand $$(1-u^2/c^2)^{-\frac{1}{2}}$$:

The binomial theorem is:

$$(a + x)^n = a^n + na^{n-1}x + \frac{n(n-1)}{2!}a^{n-2}x^2 ....$$

So expanding $$(1-u^2/c^2)^{-\frac{1}{2}}$$:

$$K = \frac{1}{2} mu^2 + \frac{3mu^4}{8c^2} + \frac{5mu^6}{16c^4} + ...$$

So if $$u$$ is much less than $$c$$:

$$K = \frac{1}{2} mu^2 $$

Which is the Newtonian approximation for low velocities.

Nuclear Energy
When protons and neutrons (nucleons) combine to form elements the combination of particles tends to be in a lower energy state than the free neutrons and protons. Iron has the lowest energy and elements above and below iron in the scale of atomic masses tend to have higher energies. This decrease in energy as neutrons and protons bind together is known as the binding energy. The atomic masses of elements are slightly different from that calculated from their constituent particles and this difference in mass energy, calculated from $$E=mc^2$$, is almost exactly equal to the binding energy.

The binding energy can be released by converting elements with higher masses per nucleon to those with lower masses per nucleon. This can be done by either splitting heavy elements such as uranium into lighter elements such as barium and krypton or by joining together light elements such as hydrogen into heavier elements such as deuterium. If atoms are split the process is known as nuclear fission and if atoms are joined the process is known as nuclear fusion. Atoms that are lighter than iron can be fused to release energy and those heavier than iron can be split to release energy.

When hydrogen and a neutron are combined to make deuterium the energy released can be calculated as follows:

The mass of a proton is 1.00731 amu, the mass of a neutron is 1.00867 amu and the mass of a deuterium nucleus is 2.0136 amu. The difference in mass between a deuterium nucleus and its components is 0.00238 amu. The energy of this mass difference is:

$$E = mc^2 = 1.66 \times 10^{-27} \times 0.00238 \times (3 \times 10^8)^2$$

So the energy released is $$3.57 \times 10^{-13}$$ joules or about $$2 \times 10^{11}$$ joules per gram of protons (ionised hydrogen).

(Assuming 1 amu = $$1.66 \times 10^{-27}$$ Kg, Avogadro's number = $$6 \times 10^{23}$$ and the speed of light is $$3 \times 10^8$$ metres per second)

Present day nuclear reactors use a process called nuclear fission in which rods of uranium emit neutrons which combine with the uranium in the rod to produce uranium isotopes such as 236U which rapidly decay into smaller nuclei such as Barium and Krypton plus three neutrons which can cause further generation of 236U and further decay. The fact that each neutron can cause the generation of three more neutrons means that a self sustaining or chain reaction can occur. The generation of energy results from the equivalence of mass and energy; the decay products, barium and krypton have a lower mass than the original 236U, the missing mass being released as 177 MeV of radiation. The nuclear equation for the decay of 236U is written as follows:

$$^{236}_{92}U \rightarrow ^{144}_{56}Ba + ^{89}_{36}Kr + 3n + 177 MeV $$

If a large amount of the uranium isotope 235U (the critical mass) is confined the chain reaction can get out of control and almost instantly release a large amount of energy. A device that confines a critical mass of uranium is known as an atomic bomb or A-bomb. A bomb based on the fusion of deuterium atoms is known as a thermonuclear bomb, hydrogen bomb or H-bomb.

title: Special Relativity/Dynamics


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Russian/Grammar/Nominative

The Nominative case is the most commonly used grammatical case in Russian. It is the default case for words, and so it is the case that words are written in the dictionaries.

What is a case?
The nature of cases in Russian is detailed more thoroughly on its dedicated page. A case tells you what a noun, pronoun, or adjective is doing in a sentence, and is denoted by a set of rules that change the end of the word. For instance, if a person or thing is the object of a sentence (the 'object' is the thing which is being verbed), then you place it in the accusative case; an example of a rule for this case states that words which usually end in а, such as книга ('book'), change the a to у (so книга becomes книгу). English relies on the order of words to convey this kind of meaning, but Russian does this with grammatical cases, so they use word order for different purposes.

So, cases have rules that change a word and tell you what it's doing in a sentence. A word in the accusative case is the thing being verbed ('the dog chased the cat ' ), the genitive case describes something being counted ('he has five apples ' ) or something owned ('the house of Sasha ', or ' Sasha's house'), and so on.

The nominative case is special, as there are few rules to learn. When you look up a word in the dictionary, it will be in its nominative form. Thus, you don't need any rules to change a word into the nominative case: it's already in it by default. The only rules that are used in the nominative case are those to turn a word into its plural form (each case has its own rules for converting a word into the singular of that case, and into that case's plural form).

Usage
The nominative case is used when no other case is being used. Its use is to denote a word as being the subject of a verb - that is, the thing that's doing the verb. For instance, in the sentence, "Peter is driving a car", 'Peter' is the subject of the verb 'to drive'. In Russian, then, the word 'Peter' would be placed in the nominative case. If you don't know what case to put a word in, use the nominative, and you'll probably be right.

One of the first things to learn in Russian is the idea of gender; this article will give a brief overview, but see the dedicated page for a more thorough treatment. Unlike French, where gender is arbitrary, you can work out a word's gender by its ending:
 * Most words are MASCULINE, and they end in a consonant in the nominative case: б, в, г, д, ж, з, й к, л, м, н, п, р, с, т, ф, х, ч, ц, ш, or щ. It is easiest to remember that a word that doesn't have a feminine or neuter ending is probably masculine, though you will soon learn to predict gender intuitively. Words which are masculine in meaning but feminine in grammar (such as 'uncle', дядя), are classed as masculine (for adjectives, pronouns, etc.), but conjugate as a feminine noun (дядя >> дядю, for instance). The soft sign, ь, can be on either masculine or feminine nouns. Examples of masculine nouns in the nominative case are стул ('chair'), музей ('museum'), and медведь' ('bear').
 * Most other words are FEMININE, and they end in а or я, or occasionally ь. Examples are корова ('cow'), змея ('snake'), and дочь ('daughter').
 * Then there are NEUTER words, which end in either o or e. Examples are письмо ('letter'), море ('sea'), and платье ('dress').

You may have noticed that not all the letters in the Russian alphabet have been used here, such as ё, у, и, etc. This is because they don't occur on the ends of default, nominative, singular nouns, and instead are really only used as noun endings after conjugation (ы, for instance, is the common plural ending for nouns). Rarely, unusual or foreign words may end in these non-standard letters, such as такси ('taxi') - these have irregular genders, and are indeclinable (that is, they don't change according to case or number).

Finally, apart from denoting verbal subjects and helping us tell a word's gender, the nominative has one other, small use: it is used after some prepositions. Like other cases, there are prepositions that call the nominative case, though these are extremely rare nowadays, and are mostly used in sayings and idioms. They are:
 * За + nom, 'of', 'what kind of' - this preposition is used in sentences like, "What kind of X is Y?", and are constructed in Russian using the word что: "Что Y за X", with both X and Y being in the nominative. For example: What kind of woman is she? Что она за женщина?. What kind of worker is Ivan? Что Иван за работник?.
 * В + nom, 'became' - this is used only with plural nouns to denote joining a group: "I became a worker", Я в рабочие.

Nouns
As stated above, the nominative case is the default, dictionary, singular form of a noun, and is used to denote the subject of a verb. As such, there are no rules for working out how to conjugate a singular word into this case, as it's already in it by default. When learning about other cases, the rules will explain how to go from this nominative case, to the case in question. Examples of nouns in the nominative are:
 * The husband is talking - Муж говорит
 * The train is old - Поезд старый
 * The student is new - Студент новый

Plural Nouns
If you want to refer to a group of objects in the nominative, you use the plural, just like in English. Though there are no rules needed to form the nominative singular (just look the word up in the dictionary), there are rules for forming the plural. These are very simple to learn:
 * Masculine nouns add -ы to the end of the word, just like how we add 's' in English. For example, стол ('table') >> столы ('tables').
 * Feminine nouns that end in -а replace the vowel with -ы, while nouns that end in -я or -ь have -и. For example, машина ('car') >> машины ('cars'); свинья ('pig') >> свиньи ('pigs'); ночь ('night') >> ночи ('nights').
 * Neuter nouns that end in -о have -а in the nominative plural, while -е becomes -я: письмо ('letter') >> письма ('letters'); море ('sea') >> моря ('seas').

These are the basic rulers for making words plural. In other cases, there are different rules which must be learned. As with many things in Russian, there are exceptions. There are several words in Russian with exceptional nominative plurals:
 * Сын >> Сыновья ('son', 'sons')
 * Брат >> Братья ('brother', brothers')
 * Друг >> Друзья ('friend', 'friends')

Perhaps the most common exceptions are those that fall under the Seven-Letter Rule.

The 7-letter spelling rule
There is a spelling rule called the '7-letter spelling rule', so called because it comes into effect after seven letters: к, г, х, ш, щ, ж, and ч. When you remove the default ending from a word, you are left with the stem. If the stem ends in one of those seven letters, then you generally have to add an alternate ending. For example, книга, 'book', has the stem книг-, so it obeys the 7-letter rule. What to do when this spelling rule appears will be covered in each instance individually. However, the rule generally just requires the use of an 'alternate' noun ending.

For the nominative plural, if a masculine or feminine word ends in the 7-letter rule, you always use the ending -и, not -ы. So, although книга, 'book', ends in -а, its nominative plural is книги, as its stem ends in г.
 * These rabbits - Эти кролики
 * The mice are nice - Мыши симпатичные
 * These are my friends - Эти мои друзья - Note the exceptional ending -я

What follows is a summary table for the endings found on singular and plural nouns in the nominative case. Where there are multiple endings, refer to the rules above:

In the future, the plural case will be treated as a sort of 'fourth gender', and will be give its own column. Here, however, it has a separate row.

As with all things in Russian, there are some irregular, unpredictable exceptions to the above rules:
 * Some masculine nouns drop the last vowel before adding ы or и, such as подарок ('gift') >> подарки. Theses are known as 'fleeting vowels', and are generally found in dictionaries in parentheses: подар(о)к.
 * Some masculine nouns add a to form the nominative plural, such as дом ('house') >> дома ('houses').
 * As mentioned above, words of foreign origin ending in o, и, or у, don't change between singular and plural. So, радио means 'radio' or 'radios', and такси is both 'taxi' and 'taxis'.

Adjectives
Like nouns, adjectives change according to case, number, and gender. An adjective has no inherent gender, so it changes its ending to suit the gender (and case and number) of the noun it's modifying. An adjective modifying a singular, feminine noun in the instrumental case, is itself in the singular, feminine, instrumental case.

However, when you look up an adjective in the dictionary, what do you see? You see the default, nominative, masculine, singular form. For a more thorough treatment of adjectives, see their dedicated page. For our purposes, we only need to know two things: all adjectives end in either -ый, -ий, or -ой, and conjugating adjectives is as simple as removing these endings and adding the new ones. The ending you add is the one that corresponds to the noun.

Adjectives modifying masculine nouns in the nominative case keep their default endings: 'new pencil' is новый карандаш. For feminine nouns, the adjective takes on the ending -ая: 'new book' is новая книга. For neuter nouns, the ending is -ое: 'new letter' is новое письмо.

Adjectives also change according to number, so when modifying a plural noun, regardless of gender, they have the ending -ые: 'new books' is новые книги. However, like nouns, they obey the 7-letter spelling rule.

The 7-letter spelling rule
As mentioned earlier, if the stem of a noun ends in к, г, х, ш, щ, ж, and ч, then different endings from usual apply. The same is true for adjectives. Adjectives such as хороший ('good'), русский ('Russian'), and другой ('different'), take on alternate endings to other adjectives. In the nominative case, this only affects plural adjectives: instead of -ые, these adjectives have the ending -ие.
 * New books - Новые книги
 * Old books - Старые книги
 * Good books - Хорошие книги
 * Different books - Разные книги

In general, after these seven consonants, whenever you would normally see ы in an adjectival ending, you instead find и. This also applies to standard adjectival endings: after these seven letters, you always have the default ending ий. This can be useful in predicting or remembering the default endings of adjectives. Unlike nouns, adjectives are affected by a second spelling rule.

The 5-letter spelling rule
On top of the previous spelling rule, there's a second important rule: after the letters ш, щ, ж, ч, and ц, the first unstressed о in an ending becomes е. For nominative adjectives, this only affects neuter singular endings: we have -ее as the ending, not -ое.
 * Bad wine - Плохое вино
 * Good wine - Хорошее вино
 * Old letter - Старое письмо
 * Fresh letter - Свежее письмо

An easy way to remember this is that four of the five letters are the 'hushes', ш, щ, ж, and ч, and these are also four letters from the seven-letter spelling rule. Few adjectives end in цый, so you don't have to worry about this so much. As such, almost all adjectives that follow this rule also follow the 7-letter rule: хороший, хорошее письмо, хорошие письма.

Soft adjectives
The final nuance with Russian adjectives are the adjectives that have the so-called 'soft ending': -ний, such as синий ('dark blue'). These adjectives don't fall into the above two spelling rules, but still take on the exceptional endings. These are covered more thoroughly on their own page, but in the nominative case they have only one unique ending: the feminine singular ending for these adjectives is -яя, not -ая. They also take on the alternate neuter and plural endings we learned for the seven- and five-letter spelling rules: -ее for neuter nouns, and -ие for plural nouns.

So, a summary of adjectival endings in the nominative case is as follows:
 * 1For adjectives with the soft ending.
 * 2For adjectives ending in the five-letter rule, and those with the soft ending.
 * 3For adjectives ending in the seven-letter rule, and those with the soft ending.

Personal Pronouns
The personal pronouns (words used to denote the speaker) are:

They are more thoroughly discussed on their dedicated page.

Possessive pronouns
The possessive pronouns are as follows:

'His' and 'its' are его ('ye-voh'), 'her' is её ('ye-yoh'), and 'their' is их ('eekh'), and these do not change with the gender or number of the possessed object.

Demonstrative Pronouns
это translates to "this" or "these."

Note that it starts with э, not е or з.

When это is followed by a nominative case noun, это changes to match the gender of the noun, thus becoming a demonstrative adjective:

For example, Этот чемодан мой ("This suitcase is mine.").

However, when a possessive pronoun is between это and the noun, the possessive pronoun changes but это doesn't change. For example, Это мой чемодан ("This is my suitcase").

Also note that for neuter nouns, changing word order doesn't change это, and that эта and это are both pronounced [ˈɛtə], since their endings are both unstressed.

Demonstrative Adjectives

 * Next: Accusative case

 * Back to Table of Contents

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Russian/Grammar/Nominative


text:
User talk:RBlowes~enwikibooks

Runescape

 * Hmm I spend way too much time writing and editing for this game =p Wonder if anyone goes there anymore... --RBlowes 16:30, 17 January 2006 (UTC)

Your account will be renamed
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title: User talk:RBlowes~enwikibooks


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User:Ilmari Karonen

I'm mostly active on the English Wikipedia. Please see my user page there.

title: User:Ilmari Karonen


text:
Russian/Grammar/Accusative case

The Accusative case is the second most common grammatical case in Russian. It is mainly used to identify a word as being the object of a verb, such as the word 'him' in the sentence "She likes him". In English, this is denoted by the objective case. Other uses of the accusative case are after some common prepositions, such as в + acc, 'into', or на + acc, 'onto'.

Usage
As mentioned above, the primary use of the accusative case is to denote the object of a verb. The indirect object ('I write a letter to you ') is denoted by the dative case. English has a case called the objective case, so called because it denotes the object of verbs. However, words in the English objective case are largely the same as when they're the subject of a verb (i.e., in the subjective case). Thus, English uses word order to denote what's the subject and object of a verb: though 'cats' and 'dogs' remain the same in "cats hate dogs" and "dogs hate cats", word order denotes which is the subject and which is the object.

In Russian, there is a very definite case system which denotes what's what in a sentence. Since Russians don't have to rely as much on word order to convey grammatical information, they can move words around more freely than in English. Word order instead denotes emphasis; whatever is on the end of a sentence is what's being emphasized. That said, Russians typically use a 'Subject Verb Object' construct by default, placing emphasis on the verb. However, the order 'Subject Object Verb' is often used, especially when the object is a person; it places emphasis on the object, while in 'Subject Verb Object' the emphasis is generally on the subject. So you would often see the sentence "I speak to her" as Я ей говорю, even though other permutations like Ей говорю я or Я говорю ей are grammatically correct. While you can say "I love you" as Я люблю тебя and be grammatically correct, it is more commonly said as Я тебя люблю, since the emphasis is obviously on "you."

In practice, though you can use the 'Subject Verb Object' system of English and still be understood, it pays to be aware that Russians don't always construct sentences that way. Thus, a good understanding of the Russian case system is essential.

 * I like dogs - Я люблю собак - English 'SVO' word order; usual Russian word order
 * I like dogs - Собак люблю я - Emphasis on 'I'
 * I like dogs - Я собак люблю - Emphasis on 'like'
 * I like  dogs - Я люблю собак - Emphasis on 'dogs'; same as English word order

The other use of the accusative case is with two major prepositions: в and на. When followed by the accusative case, в means 'to' or 'into', as in 'I walked into the house' (Я шёл в дом), and на means 'onto' or 'toward', as in 'I walked onto the street' (Я шёл на улицу). However, both prepositions can also use the prepositional case: в + prep means 'in' or 'at', as in 'I lived in London' (Я жил в Лондоне), and на + prep means 'upon' or 'at', as in 'It's on the table' (Оно на столе). The accusative and prepositional uses are similar, though generally the accusative case denotes direction ('I walked towards the hotel'), while the prepositional case denotes location ('I stayed at this hotel').

 * I walked towards the hotel. - Я шла в гостиницу. - note the use of the accusative ending -у
 * I lived at the hotel. - Я жила в гостинице. - note the use of the prepositional ending -е
 * He walked onto the roof. - Он шёл на крышу.
 * He is on the roof. - Он на крыше.

Nouns
The accusative case is a peculiar case in Russian, as it makes a distinction that other cases do not. Specifically, if a masculine word denotes an inanimate thing ('table', 'chair', etc), then it remains the same as the nominative. If, however, a masculine word denotes a person or animal ('man', 'son', 'cow', etc), then the case uses the endings of the genitive case. For plurals in the accusative, no matter what gender the word, they are also split: any plural word that's inanimate is identical to its nominative plural form, while animate plural words follow the rules for the genitive plural. Some examples highlighting this distinction are as follows:
 * This chair is brown. - Этот стул коричневый. - Nominative of an inanimate noun
 * I made a chair. - Я де́лал стул. - Accusative of the noun
 * This cat likes me. - Этот кот любит меня. - Nom. of an animate noun
 * I like this cat. - Я люблю этого кота. - Acc. of the noun
 * These women like me. - Эти женщины любят меня. - Nom. of an animate, plural, feminine noun
 * I like these women. - Я люблю этих женщин. - Acc. of the noun

So, masculine nouns denoting inanimate objects in the accusative case are the same as in the nominative case. If they're animated nouns, they follow the genitive rules, which are: add -а, and replace -й and -ь with -я.

Neuter nouns, regardless of animation, also keep their nominative forms in the accusative case.

Feminine words are the only words to have their own accusative ending: -а becomes -у, and -я becomes -ю. Feminine nouns ending in the soft sign -ь do not change.

To form the plural of an inanimate word, use the nominative rules: add or replace with -ы or -и, and neuter nouns change -o to -а and -e to -я. If the word is animate, regardless of gender, use the genitive plural: drop -а and -о, convert or append ending consonants with -ов, -ев, or -ей, and replace -я with -ь or -й.

This summary table splits the masculine and plural forms into two sections, the left being the inanimate form, the right being the animate form.

Examples:
 * Dogs hate cats. - Собаки ненавидят котов.
 * Cats hate dogs. - Коты ненавидят собак.
 * I drove to the museum. - Я поехал в музей.

Adjectives
Adjectives change to fit the noun they modify, taking on their noun's gender, number, and case. This also includes animation: adjectives modifying inanimate masculine nouns keep their nominative form (ый, ий, and ой), while animate masculine adjectives take on their genitive form (ого and его).

Neuter adjectives also keep their nominative form (ое and ее).

Feminine adjectives in the accusative case have the ending (ую and юю) - this is easy to remember, as it's the two endings of feminine nouns in the accusative.

Plural adjectives take on their nominative form (ые and ие) when modifying inanimate nouns, and their genitive form (ых and их) when modifying animate nouns, as you might have guessed.

Examples:
 * Я люблю этот коричневый стол. - I like this brown desk.
 * Он любит своего доброго брата. - He loves his kind brother.
 * Мы слушаем последнюю музыку. -  We are listening to the latest music.
 * Анна встретила новую учительницу. - Anna met the new teacher.
 * Они любят Каспийское море. -  They like the Caspian Sea.
 * Купи, пожалуйста, свежие фрукты.-  Please, buy fresh fruits.
 * Мужчины уважают этих талантливых женщин. - Men respect these talented women.

Personal Pronouns
Personal pronouns conjugate as follows:

Notice that the third-person singular masculine and neuter pronouns are the same word, его, and, like the genitive adjectival ending, it is pronounced ye- VOH . The third-person personal pronouns, его, её, and их, are the same as those in the genitive.

Possessive pronouns
Possessive pronouns act like adjectives, changing to suit the noun they modify, and thus, in the accusative case, make a distinction between animation. Like before, masculine and plural pronouns are split into inanimate forms on the left, and animate forms on the right.

For the third-person, the masculine and neuter possessive pronouns are the same as the personal pronouns: его. The feminine is её, and the third-person plural is их. These do not decline according to the gender or number of the modified noun.

Examples:
 * I want his cat - Я хочу его кота
 * I want his cats - Я хочу его котов

Prepositions
As well as the two major prepositions, в and на, there are a total of ten prepositions that can call the accusative case: в, на, за, под, по, с, про, о, сквозь, and через. Мany of these can also call other cases to denote other things.

Direction of motion, в, на, за, & под
Four prepositions refer to the direction of movement, and generally answer the directional question, Куда?, "Where (are you going)?". They can also call either the instrumental or prepositional case to answer the location question, Где?, "Where (are you)?". In depth, these four are:
 * В, 'into' - as discussed earlier, this preposition states that something is moving into something else, such as 'I walk into the building'. It can also call the prepositional case to say you are in somewhere, such as 'I'm in the theatre'.
 * На, 'onto' - as discussed earlier, this denotes onto which something is moving, such as 'I'm landing onto the roof'. Like в, if it calls the prepositional, it states what you are upon: 'I'm on the roof'.
 * За, 'behind' - this denotes that you are moving to the rear of something, as in 'I'm walking behind the building'. If it calls the instrumental case, it denotes that you are behind something, as in 'I'm behind the building'.
 * Под, 'under' - like за, this denotes that you are moving to the underside of something. By calling the instrumental case, it denotes that you are under something, as in 'I'm under the bridge'. Под also has three minor, unrelated uses for which it calls the accusative case: to denote something as being 'designated' for something else ('That bar is designated for celebrities'), to denote something fake ('artificial furniture', под обстановку), or to denote an approximate time ('around the evening', под вечер)

The remaining six: по, с, про, о, сквозь, через
The remaining six prepositions operate as follows:
 * Про, 'about' - this preposition means 'about', in the same way as о + prep does. So, 'Let's talk about me!' can be translated as either, Давайте говорить обо мне! (о + prep), or, Давайте говорить про меня! (про + acc).
 * С, 'about' - this preposition denotes an approximate number, as in 'I stayed there about a week'. When stating specific numbers, such as "I have five apples", Russians normally say, У меня есть пять яблок. To approximate the quantity, simply reverse the number and object: "I have about five apples" is У меня есть яблок пять. However, as Russian omit the word 'one', to say 'about one', you use с + acc: "I have about one apple" is У меня есть с яблоко.
 * По, 'up to' - this means 'up to' in the context of the extent of an object's involvement, relative to some other object. For example, 'I'm up to my neck in work' is Я по шею в работе. It is also used in the same way as по + dat to denote several verbal objects: "Dad gave the kids two apples each" - Папа дал детям по два яблока.
 * О, 'against' - this means 'against' in a physical sense, such as 'They hit their ball against the tree'. О + prep means 'about', in the same way as про + acc.
 * Сквозь, 'through' - this denotes the object through which another passes, as in 'The ball went through the window!'.
 * Через, 'through'/'across' - the final preposition has two main meanings. The first is synonymous with сквозь + acc, meaning 'through', and the second is to move 'across' something, as in 'I walked through the woods' - Я шёл через лес. The verbal prefix пере- is synonymous with this preposition, so через can be omitted when a verb with this prefix is used. For example, both of the following are grammatically correct: 'I crossed the street' - Я перешёл через улицу, Я перешёл улицу.

Most information on Russian accusative prepositions was derived from here.

 * Next: Instrumental case
 * Back to Table of Contents

title: Russian/Grammar/Accusative case


text:
Russian/Grammar/Prepositional case

The prepositional case is the sixth and final case in Russian, though due to its relative simplicity it is often learned before the more complex genitive, dative, and instrumental cases.

Usage
Words decline into a case for two broad reasons: because they match that case's primary function (the nominative denotes the verbal subject, the accusative denotes the verbal object, etc), or because they come after a preposition that governs that particular case (у governs the genitive, между governs the instrumental, etc). The prepositional case is so called because it is only ever used after prepositions. Historically, the prepositional case was called the locative case as its primary function was to denote the location of something. This use has been taken over by prepositions, so its name was changed accordingly. However, you may still hear it referred to by its old name, and some words still bear hallmarks of the old locative case.

Prepositions
The four prepositions that call this case are о/об/обо ('about'), при ('on') в ('in'), and на ('on'). Notice that these last two are locative in meaning when they call the prepositional case.

 * О/об/обо means 'about', and denotes the person or thing about which some verb is done ('they were talking about him', они говорили о нём).
 * When the following word begins with a vowel, о becomes об ('I heard about the bus', я послышал об автобусе).
 * Before awkward clusters of consonants, it becomes обо ('Boris read about me', Борис читал обо мне).

 * При means 'on' or 'on one's person' ('She has an umbrella on her', У неё есть зонтик при себе), and 'during' ('This happened during the reign of Peter I', Всё это случилось при Петре первом). As you might guess, this preposition is quite rare
 * В means 'in' or 'at', referring to the location of a person or thing ('I'm in Moscow', я в Москве).
 * На means 'on' or 'at', and like в refers to the location of something ('He's on the roof', Он на крыше).

At a place
The word 'at' is translated using в + prep', на + prep', and у + gen.

If you wish to say someone or something is at an enclosed building, such as 'He is at the theatre', use в + prep, as he is in that particular place: Он в театре. To say someone or something is at a particular street, such as 'She lives at Tverskaya street', use на + prep, as she is on something, rather than in it: Она живёт на Тверской улице. In general, if the place where someone or something is 'at' is an inanimate structure that humans normally go inside, use в + prep (e.g., 'They were at the theatre', 'He was at Moscow for the meeting'), otherwise use на + prep (e.g., 'They were at the field'). If the place is animate, instead use у + gen, meaning 'by someone's place' (e.g., 'They were at Sasha's')

В and на can also call the accusative case to refer to the direction towards which something is moving into or onto ('I'm walking into Moscow', 'He climbed onto the roof'). As a memory aid, recall that when в and на refer to the location of something, they use the prepositional case, which was once called the locative case. О/об/обо calls the accusative to mean 'against' or 'upon' something ('He leant upon the wall').

Examples:
 * Let's talk about the weather - Дава́йте говори́ть о пого́де
 * They'll read about Aeroflot tomorrow - Они́ прочита́ют об Аэрофло́те за́втра
 * She told a story about me - Она́ рассказа́ла расска́з обо́ мне
 * Boris lives in Liverpool - Бо́рис живёт в Ливерпул́е
 * Tatya is at work - Та́тя на рабо́те

Nouns
Forming the prepositional case is arguably easier than any other case.

Singular
To form the prepositional case, in general, you add е (pronounced yeh):
 * Masculine and neuter nouns ending in a consonant add e, and nouns ending in й, o, or ь, replace that letter with е. Nouns ending in ий instead become ии.
 * About the garden - Сад --> О саде
 * About the train - Поезд --> О поезде
 * About the museum - Музей --> О музее
 * About the letter - Письмо --> О письме

 * Feminine nouns ending in а or я replace that letter with е. Those ending in ь instead replace that letter with и. Feminine nouns that end in ия become ии.
 * About the book - Книга --> О книге
 * About the bird - Птица --> О птице
 * About the pig - Свинья --> О свинье
 * About mother - Мать --> О матери - note the addition of -ер- when мать declines

 * Neuter nouns ending in е are unchanged, unless they end in ие, in which case they become ии. Those that have the exceptional ending мя become ени (though this is fortunately quite rare).

Exceptions:
 * As you might have guessed from the above, always write ии instead of ие
 * Some nouns have a stressed у or ю after в + prep and на + prep, but not after о/об/обо + prep. This is the final hallmark of the old locative meaning of this case, as it can be seen as an ending that only occurs after locative prepositions ('in' and 'on'). See here for a list of such words.

In general, add or replace with е, but always have ии instead of ие.

Plural
The two plural endings, ах and ях, follow the same rules as the instrumental and dative plurals: after consonants, o, or а, use the ending ах. If such a noun has an irregular nominative plural ending in я (e.g., друг --> друзья), or if the noun ends in ь, й, е, or я, the ending is ях (e.g., друг --> друзья --> друзьях).
 * About the gardens - '''Сад --> Садах
 * About the trains - '''Поезд --> Поездах
 * About the museums - '''Музей --> Музеях
 * About the letters - '''Письмо - Письмах
 * About the books - '''Книга --> Книгах
 * About the birds - '''Птица --> Птицах
 * About the pigs - '''Свинья --> Свиньях
 * About the mothers - Мать --> Матерях

One exception is feminine nouns ending in мя, which instead take the ending енах. Again, this ending is fortunately quite rare.

Rules in italics are rare exceptions to the more general rules.

Adjectives
Adjectives modifying masculine or neuter nouns in the prepositional case usually end in ом. For adjectives with the soft ending (ний), or for those whose stem ends in the 5-letter rule (ш, щ, ч, ж, ц) and unstressed, the ending is ем.

For feminine adjectives, the endings are the same as those in the genitive, dative, and instrumental cases: ой, or for those with the soft ending or which end in the 5-letter rule, ей.

Like nouns, adjectives in the prepositional plural end in "х", and in fact take the same endings as the genitive plural: ых or, for those which normally end in ий, их.

 * I heard about your beautiful new wife - Я слышал о твое́й красивой новой жене
 * They're talking about those old Russian cars in the big red garage - Они говорят об этих старых русских машинах в большом красном гараже

Personal
The personal pronouns in the prepositional case are as follows: The third person singular personal pronoun нём is masculine and neuter, and ней is feminine.

Possessive
The possessive pronouns are as follows:

As ever, possessive pronouns conjugate almost exactly like adjectives. The possessive pronouns in the third person are его for masculine and neuter owners ('his' and 'its), её for feminine owners ('her'), and их for plural owners ('their'). These are the same in all cases.

Examples:
 * I am reading about them - Я чита́ю о них
 * I am reading about their children - Я чита́ю о их де́тях

This and that
Remember that о ('about') becomes об before the vowel э.

 * Back to Table of Contents

title: Russian/Grammar/Prepositional case


text:
Digital Signal Processing/Analog Filter Design

It may seem strange to have a section devoted to analog filter design in a digital signal processing book. However, there is a method to the madness. It turns out that digital filters can be modeled using analog filters, and analog techniques—which have been studied in depth for many years prior to digital systems—can be utilized to quickly and efficiently design digital filters.

The following chapters will show some of the techniques involved in designing analog filters, and transforming analog filters from one type to another. The section will culminate on a chapter on the bilinear transform, which transforms the mathematical representation for an analog filter into the equations for an equivalent digital filter.

Analog Design Process
Digital filters can be designed using analog design methods by following these steps:

 * 1) Filter specifications are specified in the digital domain. The filter type (highpass, lowpass,bandpass etc.) is specified.
 * 2) An equivalent lowpass filter is designed that meets these specifications.
 * 3) The analog lowpass filter is transformed using spectral transformations into the correct type of filter.
 * 4) The analog filter is transformed into a digital filter using a particular mapping.

There are many different types of spectral transformations and there are many mappings from analog to digital filters. the most famous mapping is known as the bilinear transform, and we will discuss that in a different chapter.

Butterworth
Butterworth ensures a flat response in the passband and an adequate rate of rolloff. A good "all rounder," the Butterworth filter is simple to understand and suitable for applications such as audio processing.

Chebyshev I
The Chebyshev 1 filter has ripple in the passband of the filter.

Chebyshev II
Chebyshev 2 has ripple in the stopband.

Elliptic
This filter has equiripple (the same amount of ripple in the passband and stopband).


text:
Russian/Grammar/Genitive case

The genitive case has four main uses: to denote possession ('Michael's car', meaning 'the car of Michael'), to denote number ('five apples'), in negative constructions ('there are no books'), and after several important prepositions ('without me').

Usage
The genitive case is the third most commonly used case, after the nominative and accusative, and has four main uses.

Counting
When denoting how many of something you have, we usually place the object in question in the genitive case. However, Russian has some key differences to English:
 * If the number is 1 or ends in один, use nominative singular:
 * There is one cat - Есть оди́н кот
 * He knows twenty-one words - Он зна́ет два́дцать одно́ сло́во

 * If the number ends in 2, 3 or 4 use the genitive singular:
 * Two roubles - Два рубля́
 * 22 kopecks - Два́дцать две копе́йки

 * If the number ends in 5, 6, 7, 8, 9, 0 or '-надцать' use the genitive plural:
 * Five roubles - Пять рубле́й
 * 25 kopecks - Два́дцать пять копе́ек

Notice that for the teens (11, 12, 13, 14, ... 19) ending on -надцать always the last rule is to be applied, no matter what digit they end on.

There are also other quantity words that take the genitive, either singular or plural according to meaning:
 * Мно́го - a lot, many, much
 * Не́сколько - a few, not many
 * Ма́ло - few, little
 * Ско́лько - how much? how many?

Examples:
 * A lot of money - Мно́го де́нег
 * Many apples - Мно́го я́блок
 * A few months - Не́сколько ме́сяцев
 * Few beers - Ма́ло пив
 * How many pounds? - Ско́лько фунтов?

The effective difference between не́сколько and ма́ло is like that between 'a few' and 'few' - one denotes a quantity that is just enough ('I have a few friends here'), while the other denotes an insufficient quantity ('I have few friends here'). That said, though, they are largely interchangeable.

Possession and Negation
To denote something as belonging to something else, you place the owner in the genitive case:
 * This is David's house - Э́то - дом Дэвида
 * This is Ivan's brother - Э́то - брат Ива́на

Note that (unlike English 's forms and Russian possessive adjectives and pronouns) Russian possessive genitives are usually postpositional.

Another use of the genitive is in the phrase "I have...". Though Russian does have the verb 'to have' (иметь), it is rarely used. Instead, Russians use the following construction to say "I have X": У меня есть Х. This literally means, 'By me exists X'. Since the preposition у calls the genitive case, the person or thing that has the object in question is placed in the genitive. The thing that is possessed remains in the nominative: У + gen + есть + nom To turn this into a question, place an inflection on есть, just as you place an inflection on the verb in a normal question.
 * Do you have a son? - У вас есть сын?
 * Yes, I have a son - Да, у меня есть сын.
 * Yes, I do - Да, есть.

Есть on its own can also be used to say 'There is...', 'There are...', or 'There exists...'. It is followed by the nominative case:
 * There are Frenchmen on this street - На э́той у́лице есть францу́зы
 * There are old buildings in Moscow - В Москве́ есть ста́рые зда́ния

Conversely, to say 'There isn't...', 'There aren't...', we use the word нет followed by the genitive case. Note that this use of the word нет is quite different from its usual meaning of 'no', and is closer to its original meaning as a contraction of не есть.
 * There are no restaurants - Нет рестора́нов
 * There are no old buildings in Moscow - В Москве́ нет ста́рых зда́ний

So, combining the above, to say 'I don't have...' is constructed as 'У меня нет...', followed by the genitive case.
 * Do you have a son? - У вас есть сын?
 * No, I don't have a son - У меня́ нет сы́на
 * My brother doesn't have any money - У моего́ бра́та нет де́нег

Prepositions
We've already seen how у commands the genitive case to roughly mean 'by', but many more prepositions use the genitive. The four most common, including у, are:
 * Для - for, for the benefit of
 * I want a present for my friend - Я хочу́ пода́рок для моего́ дру́га
 * He did this for her - Он э́то сде́лал для неё

 * У - by, near
 * I am standing by the fence - Я стою́ у забо́ра
 * She is sitting by the window - Она сидит у окна́
 * Your husband has one friend - У твоего́ му́жа есть оди́н друг

 * Без - without
 * He will drive without you - Он пое́дет без тебя́
 * Black coffee - Ко́фе без молока́

 * Из - from, out of (the opposite of в + acc, 'into')
 * I'm from England - Я из А́нглии
 * She's arrived from work - Она́ пришла́ с рабо́ты

 * От - away from
 * Get away from the grass - Отойти от травы

Singular
Masculine nouns:
 * if it ends in a consonant, add -а
 * if it ends in й, replace with я
 * if it ends in ь, replace with я

Neuter nouns:
 * if it ends in о, replace with а
 * if it ends in е, replace with я

Notice that these are the same rules for masculine animate nouns in the accusative case. Similarly, feminine nouns use the same rules as the nominative plural:
 * Replace -a with -ы.
 * Replace -я and -ь with -и.
 * If -а is preceded by one of the 'seven consonants', replace it instead with a -и.

Plural
The genitive plural is by far the most complicated ending in Russian, and is also the one with the most exceptions. However, as these rules are also the same for the accusative plural of animate nouns, they are also very commonly used:
 * Masculine nouns ending in a consonant add -ов in the genitive plural.
 * Table, five tables - Стол, пять столов

 * Nouns ending in -й or -ц are replaced by -ев.
 * Museum, six museums - Музе́й, шесть музе́ев

 * Nouns ending in -ь, -е, or one of the 'hushes' (-ш, -щ, -ж, -ч) add -ей.
 * Thing, ten things - Вещь, десять веще́й

 * Feminine nouns ending in a consonant and -я replace the -я with -ь. If they end in a vowel and -я, replace the -я with -й.
 * Week, seven weeks - Неде́ля, семь неде́ль

 * Feminine nouns lose their -a, and neuter nouns lose their -o.
 * Book, eight books - Кни́га, во́семь книг

In the case of awkward consonant clusters resulting from dropping ending vowels, it is common for o or e to be added between the consonants: марка - марок, англичанка - англичанок.

Usage
Adjectives take the number, gender, and case of the noun they modify. However, there is a peculiarity in Russian when counting: though we use the genitive singular on nouns that are numbered 2, 3, 4, 22, 23, 24, etc, we use the genitive plural for any adjectives attached to that noun:
 * Three bookshops - Три кни́жных магази́на
 * Five bookshops - Пять книжных магази́нов
 * He knows 102 Russian words - Он зна́ет сто два ру́сских сло́ва
 * He knows 106 Russian words - Он зна́ет сто шесть ру́сских слов

Conjugation
Like nouns, masculine and neuter adjectives have the same ending in the genitive singular, -ого, pronounced 'oh-vo'. If the adjectival stem ends in ж, ч, ш, щ, or ц, the ending is -его, pronounced 'ye-vo'. Notice that this is the same ending for masculine animate adjectives in the accusative case. Similarly, feminine adjectives in the genitive case have the same ending as the prepositional case: -ой, or, after the same five 'hush' consonants, -ей.
 * A kilogram of good Russian cheese - Кило́ хоро́шего ру́сского сы́ра
 * A kilogram of good Russian sausage - Кило́ хоро́шей ру́сской колбасы́

To form the plural, the ending for all genders is simply -ых, or, if the stem ends in к, г, х, ш, щ, ж, or ч, the ending is -их,
 * A kilogram of clean fresh apples - Кило́ чи́стых све́жих я́блок

Personal Pronouns
To use personal pronouns refer to the following table:

Notice that the genitive for 'of him' and 'of it' are the same: его́. Also, when the genitive is called by a preposition, его, её, and их have an н preceding them:
 * For him/it - Для него́
 * Without her - Без неё

Other pronouns are conjugated as follows:

Notice that, where available, variants of a word in the genitive are given in the order masculine/neuter, then feminine, and then plural.

Possessive Pronouns
Like personal pronouns, refer to this table for the possessive pronouns:

As ever, possessive pronouns conjugate almost exactly like adjectives. For third person possessive pronouns (of his, of her, of its, of their), use его, её, or их, regardless of the gender of the modified noun.

Examples:
 * The roof of my house - Крыша моего дома
 * The brother of his uncle - Брат его дяди
 * The sister of his aunt - Сестра́ его тёти
 * The brother of my wife - брат моей жены
 * The wife of my brother - жена моего брата
 * My brother is older than your sister - Мой брат старше твоей сестры
 * Without his chair - Без его сту́ла
 * Without his letter - Без его письма́

 * Next: Dative case
 * Back to Table of Contents

title: Russian/Grammar/Genitive case


text:
Russian/Grammar/Dative case

The dative case is traditionally the third grammatical case, and denotes the indirect object of a verb. This page assumes some familiarity with verbal aspect and the case system.

Usage
Remember that verbs generally have a subject and an object: the person or thing that performs the verb (the subject: ' He is reading a book'), and the person or thing that is receiving the action (the object: 'He is reading a book ' ). Just as the subject of a verb is in the nominative case, and the object of the verb is in the accusative case, there can be an indirect object of the verb that goes in the dative case.

The indirect object refers to objects that are not being directly acted upon. For example, 'I wrote a letter to you' - 'I' is the subject, 'a letter' is the object, and 'to you' is the indirect object. Thus, in Russian, instead of saying 'to you', they say the word 'you' in its dative form: Я пишу письмо вам. There are many common verbs that can have an indirect object, and most correspond with the English use of the word 'to':
 * To speak to... - Говорить/сказать + dat
 * To relate, tell to... - Рассказывать/рассказать + dat
 * To telephone (to)... - Звонить/позвонить + dat
 * To answer, reply to... - Отвечать/ответить + dat
 * To show (to)... - Показывать/показать + dat
 * To give (to)... - Давать/дать + dat

Some of these verbs don't use 'to' in English (e.g., 'I'll ring you' is, in Russian, is 'I'll ring to you'), while others can either use it or omit it (e.g., we can say both 'Give it to him' and 'Give him it'). In general, the object given or spoken about is in the accusative, while the person to whom the object is given or spoken about is in the dative case.

To give, давать/дать
One important verb that calls the dative is давать/дать, 'to give'. It is irregular, and conjugates as follows:

Prepositions
Like other cases, there are prepositions that require the following phrase to be place in the dative case. The two main prepositions are к(о) ('to', 'towards') and по ('along'). Of all Russian prepositions, по is the vaguest: it can call three different cases as a preposition, it's commonly seen as a prefix in the perfective aspect of verbs, and has seven broad categories of meaning when it calls the dative case:
 * Motion on/along/across a surface - the most common meaning is movement across (e.g., crossing the road), or along (e.g., walking along the street), or about (i.e., moving all around the entirety of a surface), or otherwise moving in some fashion on top of some surface.
 * We drove along the street - Мы поехали по улице
 * To travel across Russia - Ездить по России
 * Housework (work across the house) - Работа по дому - notice that 'across a surface' can be interpreted quite loosely, and can lead to idioms such as this.

 * Activity in identical places/times - some activity or verb is occurring in multiple instances of a place or time. Places visited multiple times, or things done at multiple times, use по.
 * She went around to many shops - Она шла по многим магазинам
 * She runs in the evenings - Она бегает по вечерам
 * They meet every Friday - Они встречаются по пятницам

 * Uniform distribution - commonly translated as 'apiece' or 'per', this use of по is used to denote a singular noun as being distributed one apiece. For example, in the sentence, 'He gave his boys one apple each', we could say по яблоку to mean 'one apple each'. If there are multiple objects being given out, (e.g., 'five apples each'), use по and the accusative case.
 * He gave his boys one apple each - Он дал его детям по яблоку - one item each, so по + dat; note that the dative is also used for 'his kids'.
 * He gave his boys two apples each - Он дал его детям по два яблока - two items each, so по + acc.

 * The thing struck - primarily used with the verb бить/побить ('to beat/strike'), this denotes something as being struck or hit or beat.
 * He hit the table with his shoe - Он бил ботинком по столу
 * Rain drummed against the window - Дождь барабанил по окну

 * Reason or cause of - the reason or cause of some event can be denoted using по and the dative case.
 * The woman drank the poison by mistake - Женщина выпила яд по ошибке

 * Your specialization - the trade or subject you specialize in, particularly with work, school, exams, etc. This typically translates as 'in'.
 * Russian exam (exam in Russian ) - экзамен по русскому языку
 * in my opinion (colloquially, 'in my') - По моему мнению ('по-моему')

 * In accordance with - this usage denotes one thing as being in line with, or in accord with, or in accordance with, another thing, such as a plane flying to schedule.
 * The plane flew according to plan - Самолёт летал по плану

По can also be used with the accusative case (meaning 'up to' or 'till', or, as discussed above, 'apiece'), and with the prepositional case (meaning 'after' or 'for'). К is relatively simpler, referring to or gesturing at the direction something is located.

Nouns
To decline masculine and neuter nouns into the dative case, replace the ending o with у, add у to a consonant, or replace й, е, or ь with a ю. Feminine nouns decline exactly as in the prepositional case: а and я become е, while ь becomes и.

The dative plural is formed using the same rules that govern the instrumental and prepositional plural, albeit with slightly different endings: all nouns which end in a consonant, an а, or an о, the plural ending is -ам. As a memory aid, try to link the a and ам. For those that end in a й, a я, or a е, and any noun with an irregular nominative plural ending in -я, the ending is -ям. Again, try to link the я and the ям. Examples:
 * The pen moved across the letter - Ручка пошла по письму
 * Why did he tell it to the policeman? - Почему он сказал это полицейскому?
 * She gave money to the museum - Она дала деньги музею
 * The ship traveled about the sea - Судно шлo по морю
 * Sasha is walking towards the school - Саша идёт к школе
 * Boris won, thanks to his friends - Борис побеждал благодаря его друзьям
 * Boris won, thanks to his friends - Борис побеждал благодаря его друзьям
 * Boris won, thanks to his friends - Борис побеждал благодаря его друзьям
 * Boris won, thanks to his friends - Борис побеждал благодаря его друзьям

Adjectives
Adjectives modifying masculine or neuter nouns in the dative case have the ending -ому. If they end in the 5-letter rule (ш, щ, ч, ж, or ц) or have the soft ending (-ний), their dative ending is -ему. Feminine adjectives have -ой or, after the 5-letter rule or soft ending, -ей. Essentially, these are the same as e prepositional endings, with masculine and neuter adjectives having an extra -у - the same ending most masculine and neuter nouns get.

To form the dative plural, the ending is -ым or, after the soft ending or the 7-letter rule (к, г, х, ш, щ, ч, or ж), -им.

 * She spoke to his good friend Sasha - Она сказала его хорошему другу Саше
 * Tanya will give the presents to the nice Russian man - Таня даст подарки симпатичному русскому человеку
 * They traveled across the large country - Они поехали по большей стране

Personal
The personal pronouns in the dative case are as follows: The third person singular personal pronoun ему is masculine and neuter, and ей is feminine.

personal pronouns quiz
Russian/Personal Pronouns/Quiz

Possessive
The possessive pronouns are as follows:

As ever, possessive pronouns conjugate almost exactly like adjectives. The third person pronouns are его for masculine and neuter owners, её for feminine owners, and иx for plural owners. These are the same in all cases.

Demonstrative Adjectives

 * Next: Accusative case
 * Back to Table of Contents

title: Russian/Grammar/Dative case


text:
Russian/Grammar/Instrumental case

The instrumental case is traditionally taught as the fourth case in Russian. It typically denotes an object as being the means by which some action is carried out (e.g., I ate with a fork).

Usage
The instrumental case is used to denote the means by which some actions is carried out. In the phrase, 'Boris wrote the school a letter with a pencil', there are four items:
 * 1) 'Boris' is the person who is doing, or did, or will do, the verb, so he is the subject of the verb. Thus, the word Бори́с is in its nominative form.
 * 2) 'A letter' is the thing that's being verbed, the direct object of the verb. Thus, the word письмо is in its accusative form.
 * 3) 'To school' is the thing that's being indirectly verbed, so it's the indirect object of the verb. Thus, the word школа is in its dative form, школе, and means 'to school'.
 * 4) 'With a pencil' is the thing that allows the verb to be done, or is the means by which it is done. Thus, the word карандаш is in its instrumental form, карандашо́м, and means 'with a pencil'
 * 5) Finally, the complete sentence is: Борис писал письмо школе карандашом. Notice that the words 'a', 'to', 'with', etc, are omitted in Russian and instead controlled by grammatical endings.

So the instrumental case is so called because it denotes the instrument by which some task is carried out, and this is its primary meaning. Thus, a word in the instrumental case can be translated by adding the words 'with' or 'by'.

Like the other cases, there are prepositions which can place whatever comes after them in the instrumental case. There are six in total: С(о), над, под, за, перед, and между.
 * C(o) + inst means 'with'. This may be confusing, as the primary meaning of the instrumental case on its own is also 'with'. There are two concepts that are both conveyed by the English word 'with', but are conveyed separately in Russian. 'With', as in 'by means of' ('He built it with his hands') is conveyed by the instrumental case on its own ('his hands' in their inst. form). 'With', as in 'accompanied with' ('He built it with her') is conveyed by c(o) followed by the instrumental case ('with her' is c + inst.). It can also be used to denote the manner in which something is done ('He built it with ease'). In both of these uses, c(o) inst is the antonym of без + gen ('without').
 * Над means 'over' or 'above', and под means 'under' or 'beneath'. Под + inst means 'under' if there is no motion involved - if there's motion, use под + acc instead ('The book is under the bed' - no movement, 'The book slid under the bed' - movement). Под + inst can also mean 'physically near', and под + acc can mean 'temporally near' or 'near in time' ('They live near the city' - physically near).
 * Перед means 'before' or 'in front of' in terms of positioning, and can also indicate responsibility ('The dog is in front of the house', 'The dog walked in front of the house', 'the family has a responsibility to the dog').
 * Между means 'between' or 'among', similar to среди + gen, 'among' (e.g., 'He stood between them').
 * За generally means 'behind' or 'beyond', but has a few nuances to it. Like под, when no motion is involved, the instrumental case is used. When motion is involved, however, the accusative case is used ('It's behind the house' - за + inst, 'It went behind the house' - за + acc).

Nouns
Nouns in the instrumental case decline unusually compared to other cases, using rules that aren't found elsewhere. While not as complex as the genitive plural, it still warrants extra attention.

Singular

 * Nouns ending in о or a consonant have -ом in the instrumental. However, if this ending syllable is both a) unstressed, and b) preceded by the five-letter rule (ч, ж, ш, щ, ц), then the ending becomes -ем.
 * Train - поезд --> поездом
 * Morning - утро --> утром
 * Pencil - карандаш --> карандашом - ends in ш, but ending syllable is stressed
 * Husband - муж - мужем - ends in ж and is unstressed

 * Nouns ending in й, е, or ь, have the ending -ем. If this ending is stressed, it becomes -ём. This applies mainly to masculine and neuter nouns; See below for feminine nouns ending in ь.
 * Museum - музей --> музеем
 * Sea - море --> морем
 * Dictionary - словарь --> словарём - ending is stressed
 * Day - день --> днём - e is a fleeting vowel, so vanishes when the word declines

 * Those ending in а of any gender have -ой. As above, if the ending is both unstressed and ends in the five-letter rule, the ending becomes -ей.
 * Book - книга --> книгой
 * Newspaper - газета --> газетой
 * Arm/hand - Рука --> Рукой
 * Chicken - курица --> курицей - untressed ending and stem ends in ц
 * Pear - груша --> грушей - unstressed ending and stem ends in ш

 * The ending я of any gender becomes -ей. If stressed, it becomes -ёй.
 * Week - неделя --> неделей
 * Surname - фамилия --> фамилией
 * Pig - свинья --> свиньёй - stress on end syllable

 * Feminine nouns ending in ь have -ью in the instrumental.
 * Square - площадь --> площадью
 * Horse - лошадь --> лошадью
 * Church - церковь --> церковью

So masculine and neuter nouns have the endings ом, ем, or ём, and feminine nouns have ой, ей, ёй, or ью.

Plural
There are two general endings for the instrumental plural: ами and ями. If the noun ends in a consonant, а, or о, the ending is ами. However, if such a noun has an irregular nominative plural that ends in я, use ями instead. If the noun ends in й, ь, я or е, use ями. In the following examples, the first word is the nom. sing., the last is the inst. pl., and the middle word (if one is given) is the nom. pl.:
 * House - дом --> домами
 * Book - книга --> книгами
 * Letter - письмо --> письмами
 * Museum - музей --> музеями
 * Day - день --> днями
 * Pig -  свинья  --> свиньями
 * Sea - море --> морями
 * Brother - брат --> братья --> братьями - note the irregular nominative plural
 * Friend - друг --> друзья --> друзьями - note the irregular nominative plural

There are three words which have the irregular instrumental plural ending ьми, (the three words given are the nom. sing., the nom. pl., and the inst. pl.):
 * Daughter - дочь --> дочери --> дочерьми
 * Mother - мать --> матери --> матерьми
 * Child - ребёнок --> дети --> детьми
 * Person - человек --> люди --> людьми

Adjectives
Adjectives modifying masculine or neuter nouns in the instrumental case have two endings: adjectives which have the default ending ый or ое have the instrumental ending ым, and those which end in ий or ее have им. Feminine adjectives have the same endings as the genitive, prepositional, and dative cases: ой, or, if the adjective's stem ends in the five letter rule (ц, ш, щ, ч, ж) or it has the soft ending (ний), the ending is ей.

The plural ending is ыми. For adjectives that end in ий, the ending is ими.

 * She walked to school with her new friends - Она шла в шко́лу с её но́выми друзья́ми
 * They live between the old Russian bookshops - Они живу́т ме́жду ста́рыми ру́сскими кни́жними магази́нами
 * Sasha was under the pink bed - Са́ша был под ро́зовой крова́тью

Pronouns

 * Next: Prepositional case
 * Back to Table of Contents

title: Russian/Grammar/Instrumental case


text: User talk:Vernon high school

title: User talk:Vernon high school


text:
Digital Signal Processing/DSP Programming

Digital Signal Processing units, on first glance, are very similar to other programmable microprocessors, microcontrollers, and FPGAs. However, DSP chips frequently have certain features and limitations involved that other categories of chips don't have. This chapter will attempt to explain, in broad language-neutral terms, some of the issues involved with DSP programming.

Saturation Arithmetic
Intel-compatible microprocessors, something that most programmers are familiar with, have several features that people have come to expect from programmable chips. In particular, Intel-compatible chips have an arithmetic mode known as "Roll-Over Arithmetic", also called modular arithmetic. Let's say that we have the integer number 250 (decimal) stored in a byte-sized register. If we add 10 to that number, the processor will overflow, and will roll-over the answer, giving us the answer 4. However, DSP chips frequently do not roll-over, and instead saturate to the maximum value.

Let's say we are processing a grayscale image. This image has byte-sized integer values of white/black value as such: Pure white is 255, and pure black is 0. Now, let's say we want to "brighten" every pixel by 10 points, to improve visibility. So we create a loop, and we go through each pixel in the image, adding 10 to the value at any particular point. But what happens if we add 10 to a pixel that is already pure white? In a regular Intel-compatible chip, the value 255 + 10 = 9. In effect, if we make the white pixels brighter, we are turning them black! now, to avoid this, DSP chips saturate, and will go up to the highest value (255), and won't roll over. So, on a DSP chip, white can't get any whiter. Here are some examples (using unsigned bytes):

 * $$255 + 10 = 255$$
 * $$0 - 10 = 0$$

Multiply and Accumulate (MAC)
In difference equations, we have seen that multiply and addition operations are the most common. Let's look at a general example:

 * $$A x_n + B x_{n-1} + C x_{n-2} + D x_{n-3} + ...$$

Now, we notice that each element in this equation is multiplied by a coefficient, and added to the total. DSP engineers have noticed this pattern, and have optimized DSP chips to be able multiply and add very quickly (at the expense of other operations missing or slow). In fact, many DSP chips will have instructions known as multiply and accumulate, which will perform both operations simultaneously, much quicker than a normal processor could do.


text:
Russian/Grammar/Introduction

Are you learning Russian to "get by" on a one-week business trip to Moscow? Or do you want to learn "good Russian"?

Russians will love you if you speak "good Russian." Educated Russians are extremely proud of their grammar skills, and rightly so. Russian grammar is unbelievably complex. The Russian word for "good" sounds like "horror show," and if you want to learn "horror show Russki" (good Russian) prepare for some scary stuff!

Pronouns ("I," "you," "they," etc.) are built into verbs, so Russians often drop pronouns without losing clarity. Thus Russian sentences are typically shorter and less ambiguous than English. The price you pay for this efficient, precise language is far more demanding grammar.

But to "get by" you need only basic grammar, but not the byzantine grammar of "good Russian." You could treat all nouns as if they were masculine, and all verbs as if you are the person doing the action, and Russians would usually understand your meaning. But you should read over the many grammar rules so that you have a clue what Russians are saying. E.g., you should be able to recognize when a Russian uses the prepositional case, even if you only use the nominative case.

Native speakers learn grammar as children by listening to adults talk, and by being corrected by their parents. A child who reads a lot and whose parents speak correctly doesn't need to learn grammar rules. As an adult learning Russian, you'll learn best if a native Russian listens to you and corrects your mistakes. But the grammar rules will act as shortcuts, to help you learn faster.

In learning some people are auditory learners, some are visual, and some are movement learners. (See ISBN 1573240648 "The Open Mind" by Dawna Markova, for more about this.) But all three learning styles are needed for organizing and committing to long-term memory. You may prefer to hear spoken Russian, or see written Russian, or (for movement learners) write a Russian word and then write how it sounds in English. You may need to do an activity, such as cooking dinner, to pay attention. But all of us need to do all of these things to learn well.

title: Russian/Grammar/Introduction


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Russian/Grammar/Pronouns

Pronouns are words which take the place of nouns (compare "Your husband drove to Florida" with "He drove to Florida"), which denote ownership ("My cat", "Your cat", etc), or which replace nouns with questions (compare "He drove" with "Who drove?" and "What drove?"). Russian has six categories of pronouns, the three most common of which are detailed further on their own pages: Personal, Possessive, Interrogative, Demonstrative, Reflexive, and Determinative. In Russian, the pronouns change according to the gender of the noun.

Formality
While most pronouns can be used just as they would in English, there's an important facet to them that English doesn't have: formality.

In modern English, there are two first-person personal pronouns, 'I' and 'we', four third-person pronouns, the singular ('he, 'she', and 'it') and the plural ('they'), and a single second-person pronoun, 'you'. That English has only one second-person personal pronoun, is a peculiarity of our language. In Russian, and indeed in most other languages, there is a distinction between two forms of 'you'.

Like first- and third-person pronouns, second-person pronouns have a singular and a plural form. To say 'you' and mean one person, say ты (ti). To refer to more than one person, use вы (vi). However, if you want to show respect, such as to a teacher or elder, or the person is someone you don't know, use вы instead of ты.
 * Where are you, brother? - Где ты, брат? - Notice the singular form ты
 * Where are you, teacher? - Где вы, учительница? - Notice the plural form вы

Interestingly, though English lost its second-person singular pronoun thou, some dialects have created a new plural one: Southern US English uses 'y'all' to refer to just that: 'you all'. But this isn't just a contraction, as it's used in a pronoun in its own right, giving us constructions like: "I want to talk to all y'all".

It is important to at least grasp this distinction, as it becomes important when learning about verbs: verbs have six basic forms of conjugation, one for each type of pronoun (1st/2nd/3rd person, and singular/plural).

Personal
Broadly speaking, sentences involve three people: the person speaking, the person being spoken to, and someone else not involved in the conversation. The person speaking is known as the 'first person' (think of first-person games that are viewed through the eyes of the player), the person spoken to is the 'second person', and the other person is the 'third person'. Each 'person' can be referred to as either singular ('I', 'he') or plural ('we', 'they'). Finally, note that third-person singular pronoun comes in three varieties that vary with gender: 'he', 'she', and 'it'. Russian pronouns are generally used the same as in English, with the exception of the above distinction between formal and informal 'you':
 * I see - Я ви́жу - ya VEE -zhoo
 * We see - Мы ви́дим - ''mi VEE -deem
 * You speak (sing. informal) - Tы говори́шь - ti ga-vo- REESH
 * You speak (sing. formal) - Вы говори́те - vi ga-vo- REE -tye
 * You speak (plural) - Вы говори́те - vi ga-vo- REE -tye
 * He/she/it reads - Он/Она́/Оно́ чита́ет - on/on- AH /on- OH chee- TA -yet
 * They read - Они́ чита́ют - on- EE chee- TA -yoot

Notice that though the verbs are the same in meaning, they change form: 'speak' changes from ты говоришь to вы говорите. Changing verbs like this is known as conjugation, and is covered more fully on its dedicated page. When nouns, pronouns, and adjectives change, it's called declension (this can also refer to verbs changing, however 'conjugation' refers specifically to verbs). Like most things in Russian, the personal pronouns change depending on which of the six cases they're in: Note that when some of these have several forms, these are clarified in the pages for that specific case. Also note that third-person singular pronouns have the suffice н- when preceded by a preposition: к ней, от неё, etc. This doesn't apply to the possessive pronouns, or in general any third-person pronoun that isn't directly called by the preposition.
 * I like you - Я тебя люблю
 * You talk to me - Вы мне говорите
 * You talk about me - Вы говорите обо мне
 * You talk with me - Вы говорите со мной

As the last example shows, the third-person singular pronouns он, она, and оно vary by gender in grammar, but not in meaning. The он in "Я сел на стул, и он развалился" (I sat on a chair, and it fell apart) is grammatically male to correspond with the table, but still translates to 'it' in English.

quiz
{Formal or informal? Вы говорите со мной + formal - informal
 * type=""}

{Formal or informal? Я тебя люблю - formal + informal
 * type=""}

{Formal or informal? Tы говори́шь - formal + informal
 * type=""}

Possessive
These pronouns act as adjectives and modify a noun, stating that it is owned by one of the three speakers (my cat, your cat, his cat). Unlike personal pronouns, but like adjectives, possessive pronouns also change to match the gender and number of the noun they modify. So in the following table, notice that the different gender and number of each type of pronoun refers to the object that's possessed, not the possessor. Since there are four pronouns that conjugate in four ways laterally and six ways vertically, shown here is only the forms for мой, 'my'. The rest are detailed on their own pages: The various forms given in the accusative case are detailed more thoroughly on that page. Third-person possessive pronouns are special: there are only three words, and each refers to the gender of the speaker, not the case, gender, or number of the object possessed. For masculine and neuter possessors, the word is его, 'his'/'its', pronouns ye-vo. For feminine possessors, use её. For plural possessors of any gender, use их.
 * My chair - Мой стул
 * My dog - Моя собака
 * My dress - Моё платье
 * My books - Мои книги
 * His chair - Его стул
 * His books - Его книги
 * Let's talk about his books - Давайте говорить о его книгах

quiz
{Gender? Мой стул +Masculine -Feminine -Neuter -Plural
 * type=""}

{Gender? Моя собака -Masculine +Feminine -Neuter -Plural
 * type=""}

{Gender? Моё платье -Masculine -Feminine +Neuter -Plural
 * type=""}

Demonstrative
There are many demonstrative pronouns in Russian. Here are a few:
 * такой
 * тот

Examples:
 * Взгляни на тот рисунок. = Look at that painting.
 * Он такой умный! = He is so smart!

title: Russian/Grammar/Pronouns


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Russian/Names

Russian names
Russians use three names: first name, or имя; middle or patronymic name, or отчество, which is their father's first name plus a suffix meaning "son of" (ович) or "daughter of" (овна); and the last name or family name, or фамилия. Women's last names add an а to the masculine form of the name.

To address a boss, a teacher, or somebody who is older or superior in rank use the person's first name and patronymic. For instance: Василий Иванович!

To address a military or police officer use the rank and the officer's family name. For instance: Рядовой Иванов (Private Ivanov). If you don't know the family name, use Товарищ and the rank. For instance Товарищ рядовой (Comrade private).

To address a suspect, a former spouse, and other types that don't deserve the title Comrade, use гражданин fem. гражданка (citizen). For instance: Гражданин, пройдёмте. (The citizen, follow me.)

The titles Господин fem. Госпожа (Mr. or Ms.) are reserved for wealthy foreigners. Ordinary citizens of foreign countries are your comrades. However, lately Russians have started to use Господин/Госпожа more frequently, especially in business circles.

Russians use relatively few first names. There are only a dozen or so men's first names, and maybe three dozen women's first names. Creativity in baby-naming isn't encouraged.

Russians also use diminutives or nicknames—lots! Each name typically has a version used by your best friend, another used by your other friends, another used by your teachers, another used by your grandmother, another used when you are scolded, etc. Some of the most common examples include Sasha for Alexander, Alyosha for Alexei, Misha for Mikhail, Dima for Dmitri, Lena for Elena, Olya for Olga, Natasha for Natalya and Katya for Ekaterina.

Girls first names
(Source: Wikipedia: Russian Names)

Back to Table of Contents

title: Russian/Names


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Digital Signal Processing/Digital Filters

Digital Filters can be very complicated devices, but they must be able to map to the difference equations of the filter design. This means that since difference equations only have a limited number of operations available (addition and multiplication), digital filters only have limited operations that they need to handle as well. There are only a handful of basic components to a digital filter, although these few components can be arranged in complex ways to make complicated filters.

Digital Filter Types
There are two types of filters in the digital realm: Finite Impulse Response (FIR) filters and Infinite Impulse Response (IIR) filters. They are very different in essence.

FIR Filters
FIR filters are specific to sampled systems. There is no equivalent in continuous-time systems. Therefore, only very specific analog filters are capable of implementing an FIR filter.

If we define the discrete time impulse function as

 * $$\delta [n] = \begin{cases} 1 & n = 0 \\ 0 & n \not = 0 \end{cases} \mbox{,} $$

the response of an FIR filter to δ[n], denoted as h[n], will decay to zero after a finite number of samples. The transfer function of an FIR filter contains only zeros and either no poles or poles only at the origin.

An FIR filter with symmetric coefficients is guaranteed to provide a linear phase response, which can be very important in some applications. However, FIR filters suffer from low efficiency, and creating an FIR to meet a given spec requires much more hardware than an equivalent IIR filter.

IIR Filters (infinite impulse response filter)
IIR filters are typically designed basing on continuous-time transfer functions. IIR filters differ from FIR filters because they always contain feedback elements in the circuit, which can make the transfer functions more complicated to work with.

The transfer function of an IIR filter contains both poles and zeros. Its impulse response never decays to zero (though it may get so close to zero that the response cannot be represented with the number of bits available in the system).

IIR filters provide extraordinary benefits in terms of computing: IIR filters are more than an order of magnitude more efficient than an equivalent FIR filter. Even though FIR is easier to design, IIR will do the same work with fewer components, and fewer components translate directly to less money.

Filtering a time-series in Octave/Sciplot
First create some points for a time series. In this case we'll create one second of random data sampled at 44 kHz.

sampling_t = 1/44000; t = 0:sampling_t:1; x = rand(size(t));

Have a look at the time series

plot(t,x);

Have a look at its spectrum (it is mostly uniform, what we would expect from noise)

specgram(x)

Now we'll use a built-in function to create a third order Butterworth low-pass filter with cutoff frequency pi*0.1 radians

[b,a] = butter(3,0.1)

Now filter the time series.

y = filter(b,a,x);

Have a look at the first 100 points of the filtered data.

hold on plot(y(1:100)) plot(x(1:100)) hold off

Check its spectrogram

specgram(y)

Now look at the magnitude of the FFT

plot(log(abs(fft(y))))

High-pass and Low-pass
High-Pass and Low-Pass filters are the simplest forms of digital filters, and they are relatively easy to design to specifications. This page will discuss high-pass and low-pass transfer functions, and the implementations of each as FIR and IIR designs.

Band-pass
Band-pass Filters are like a combination of a high-pass and a low-pass filter. Only specific bands are allowed to pass through the filter. Frequencies that are too high or too low will be rejected by the filter.

Stop-band
Notch filters are the complement of Band-pass filters in that they only stop a certain narrow band of frequency information, and allow all other data to pass without problem.

Notch
The direct complement of a bandpass filter is called a bandstop filter. A notch filter is essentially a very narrow bandstop filter.

Comb Filters
Comb Filters, as their name implies, look like a hair comb. They have many "teeth", which in essence are notches in the transfer function where information is removed. These notches are spaced evenly across the spectrum, so they are only useful for removing noise that appear at regular frequency intervals.

All-pass
The All-pass filter is a filter that has a unity magnitude response for all frequencies. It does not affect the gain response of a system. The All-pass filter does affect the phase response of the system. For example, if an IIR filter is designed to meet a prescribed magnitude response often the phase response of the system will become non-linear. To correct for this non-linearity an All-pass filter is cascaded with the IIR filter so that the overall response(IIR+All-pass) has a constant group delay.

Canonic and Non-Canonic
Canonic filters are filters where the order of the transfer function matches the number of delay units in the filter. Conversely, Noncanonic filters are when the filter has more delay units than the order of the transfer function. In general, FIR filters are canonic. Some IIR filter implementations are noncanonic.

Here is an example of a canonical, 2nd order filter:

Here is an example of a non-canonical 2nd order filter:

Notice that in the canonical filter, the system order (here: 2) equals the number of delay units in the filter (2). In the non-canonical version, the system order is not equal to the number of delays (4 delay units). Both filters perform the same task. The canonical version results in smaller digital hardware, because it uses fewer delay units. However, this drawback nearly disappears if several second order IIRs are cascaded, as they can share delay elements. In this case, the only "extra" delay elements are those on the input side of the first section.

Notations
There are some basic notations that we will be using:

 * ωp Pass-band cut off frequency
 * ωs Stop-band cut off frequency
 * δp Pass-band ripple peak magnitude
 * δs Stop-band ripple peak magnitude

- ← Digital Signal Processing →


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Digital Signal Processing/Infinite Input Filtering

Filtering a data input that is infinite in length can be a tricky task for any computer to manage, and DSP engineers have identified two techniques for breaking down an infinite input into manageable chunks for filtering.

"Infinite Input"
infinite input response (IIR) filters are structures that use a feedback element to help filter data. An IIR filter has a transfer function of the form:

 * $$G(z) = \frac{\prod(a_n - z^{-1})}{\prod(b_m - z^{-1})}$$

The constants an are known as the zeros of the transfer function, and the bm terms are known as the poles of the transfer function. FIR filters, by comparison do not have poles.

IIR filters are named as such because the filter does not stop responding once the input has stopped, but instead the feedback element will continue to input values into the filter structure for processing after the input has stopped.

IIR vs FIR Filters
An FIR filter will have an order that is a significantly higher than the order of an equivalent IIR filter. This means that FIR filters need more complexity and more components then IIR filters to complete the same task. However, IIR filters have a potential for instability, which requires more analysis.


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Gmail/The TO CC BCC Fields

An intuitive, selectable drop down list with matches from your contacts list is provided as a recipients are typed in. This includes those added explicitly to your contacts and those added automatically after a certain threshold of communications has been reached.

title: Gmail/The TO CC BCC Fields