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A-level Mathematics/OCR/C4/Algebra and Graphs

Rational Expressions
A rational expression has a polynomial in the numerator and a polynomial in the denominator: $$\frac{f\left(x\right)}{g\left(x\right)}$$. In some cases rational functions can be simplified, which can make differentiation, integration and just solving the equation easier. There is a simple procedure to follow if you want to simplify a fraction. {(ix+j)\cancel{(x+g)}\cancel{(x+h)}}=\frac{(ex+f)}{(ix+j)}$$
 * 1) Fully factor the numerator and denominator.
 * $$\frac{ax^3+bx^2+cx+d}{ax^2+bx+c}=\frac{(ex+f)(x+g)(x+h)}{(ix+j)(x+g)(x+h)}$$
 * 1) If the same factor is in both the numerator and denominator you can cancel them out.
 * $$\frac{(ex+f)\cancel{(x + g)}\cancel{(x +h)}}
 * 1) If there multiple factors left you can recombine based on the situation.

Example
Simplify the following expression:$$\frac{5x^3+40x^2+75x}{x^2+12x+35}$$.
 * 1) Factor both the numerator and the denominator notice that a 5x can be removed in the numerator.
 * $$\frac{5x(x^2+8x+15)}{(x+5)(x+7)}=\frac{5x(x+5)(x+3)}{(x+5)(x+7)}$$
 * 1) Cancel out the same factors
 * $$\frac{5x(x+5)(x+3)}{(x+5)(x+7)}=\frac{5x(x+3)}{(x+7)}$$
 * 1) Recombine the factors
 * $$\frac{5x(x+3)}{(x+7)}=\frac{5x^2+15x}{x+7}$$

Division of Polynomials
In core four you will be expected to divide polynomials of up to the fourth degree by either a linear or quadratic polynomial. This only works if the numerator is greater than the denominator. The resultant will always be in the form;$$\frac{f(x)}{g(x)}=q(x) + \frac{r(x)}{g(x)}$$ where q(x)is the resulting polynomial and $$\frac{r(x)}{g(x)}$$ is the remainder.

Long Division
Long division of polynomials is very similar to regular long division. I will use a problem to demonstrate how long division works.

Divide $$x^3 + 8x^2 - 4x + 10$$ by $$x^2 + 3x -1$$.

The first step is to set up the equation. Make sure that it is in order from highest power of x to lowest power of x.

Then we divide the first term of the dividend by the first term of the divisor.

$$\frac {x^3}{x^2} = x$$

We place this resultant on top.

Then we multiply the resultant by the divisor and subtract it from the dividend.

$$x \left ( x^2 + 3x -1 \right )= x^3 + 3x^2 -x$$

What is left becomes the new dividend and we repeat the process again. We continue to do this until the first term has a degree less than the first term of the divisor. What is left is the remainder.

Example One
Divide $$2x^5 + 5x^2 - 10x^3 -30x - 171$$ by x-3.

The divisor is c. So in this case it will be 3.

Then we need to arrange our divisor in order from highest to lowest degree, if a degree is missing replace it with zero.

$$2x^5 + 0x^4 - 10x^3 + 5x^2 -30x - 171$$

We then only look at the coefficients.

2 + 0 - 10 + 5 - 30 - 171

Now we set up our division equation.

Next we carry up the first term of the divisior.

Then we multiply the resultant by the divisor and add it to the next term.

We continue to do this until we reach the end.

Now we need to read the variables. When we read the variables we go from highest degree -1 to lowest degree. The last number is the remainder.

$$2x^4 + 6x^3 + 8x^2 + 29x +57$$ remainder 0.

This is the answer to the problem.

Partial Fractions
Only proper fractions can be made into partial fractions. A proper fraction is a fraction where the numerator is of a smaller degree than the denominator. Partial Fractions can used to make differentiation, integration or work with series easier. The goal of partial fractions is to take a complex polynomial and make it several simpler polynomials. To create a partial fraction equation you need to:
 * 1) Factor the denominator and the numerator.
 * $$\frac{ax^2+bx+c}{ax^3+bx^2+cx+d}\equiv\frac{(ix+j)(kx+l)}{(ax+b)(cx+d)(ex+f)}$$
 * 1) Create the partial fraction by making each factor the denominator, with a unique variable for the numerator.
 * $$\frac{(ix+j)(kx+l)}{(ax+b)(cx+d)(ex+f)}\equiv\frac{A}{(ax+b)}+\frac{B}{(cx+d)}+\frac{C}{(ex+f)}$$
 * 1) Multiply every fraction by the denominator of original fraction.
 * $$\frac{(ix+j)(kx+l)(ax+b)(cx+d)(ex+f)}{(ax+b)(cx+d)(ex+f)}\equiv$$
 * $$\frac{A(ax+b)(cx+d)(ex+f)}{(ax+b)}+\frac{B(ax+b)(cx+d)(ex+f)}{(cx+d)}+\frac{C(ax+b)(cx+d)(ex+f)}{(ex+f)}$$
 * 1) Cancel all out all factors that are the same.
 * $$(ix+j)(kx+l)\equiv A(cx+d)(ex+f)+B(ax+b)(ex+f)+C(ax+b)(cx+d)$$
 * 1) Multiply all factors together.
 * $$ikx^2+ilx+jlx+jl \equiv$$
 * $$(Acex^2+Acfx+Adex+Adf)+(Baex^2+Bafx+Bbex+Bbf)+(Cacx^2+Cadx+Cbdx+Cbd)\,$$
 * 1) Group all terms with x to the same index together.
 * $$ikx^2+(il+kj)x+jl\equiv$$
 * $$(Ace+Bae+Cac)x^2+\left(Acf+Ade+Baf+Bbe+Cad+Cbd\right)x+\left(Adf+Bbf+Cbd\right)$$
 * 1) The co-efficient of x raised to the same index is the same on both sides of the identity. Using this fact solve for the variables in the numerator, using simultaneous equations. This is known as equating coefficients.
 * $$ik\equiv\left(Ace+Bae+Cac\right)$$
 * $$\left(il+kj\right)\equiv\left(Acf+Ade+Baf+Bbe+Cad+Cbd\right)$$
 * $$jl\equiv\left(Adf+Bbf+Cbd\right)$$
 * 1) In step 2 replace the variables A, B, C with the value of the variable obtained from the previous step.

Example One
Rewrite as a partial fraction the following expression: $$\frac{x^2+13x+40}{2x^3+27x^2+111x+140}$$.
 * 1) Using the knowledge from Further Pure 1: Roots of Polynomial Equations. We can factor the denominator as such.
 * $$\frac{x^2+13x+40}{2x^3+27x^2+111x+140} \equiv \frac{(x+5)(x+8)}{(2x+5)(x+7)(x+4)}$$
 * 1) Now we start making the partial fraction.
 * $$\frac{x^2+13x+40}{(2x+5)(x+7)(x+4)}\equiv\frac{A}{(2x+5)}+\frac{B}{(x+7)}+\frac{C}{(x+4)}$$
 * 1) Next we multiply everything by the denominator of the original expression.
 * $$\frac{x^2+13x+40(2x+5)(x+7)(x+4)}{(2x+5)(x+7)(x+4)}\equiv$$
 * $$\frac{A(2x+5)(x+7)(x+4)}{(2x+5)}+\frac{B(2x+5)(x+7)(x+4)}{(x+7}+\frac{C(2x+5)(x+7)(x+4)}{(x+4)}$$
 * 1) Now we cancel out terms.
 * $$(x+7)(x+8)\equiv A(x+7)(x+4)+B(2x+5)(x+4)+C(2x+5)(x+7)$$
 * 1) Then multiply all the factors together.
 * $$x^2+13x+40=Ax^2+11Ax+28A+2Bx^2+13Bx+20B+2Cx^2+19Cx+35C\,$$
 * 1) We then group the terms together.
 * $$x^2+13x+40=(A+2B+2C)x^2+(11A+13B+19C)x+(28A+20B+35C)\,$$
 * 1) Now we equate coefficients. Then we need to solve the simultaneous equations.
 * $$1\equiv(A+2B+2C)\equiv\,$$
 * $$13\equiv(11A+13B+19C)\,$$
 * $$40\equiv(28A+20B+35C)\,$$
 * 1) First we equate A
 * $$1\equiv(A+2B+2C)\equiv A=1-2B-2C\,$$
 * Then
 * $$13\equiv11(1-2B-2C)+13B+19C\equiv11-22B-22C+13B+19C\equiv11-9B-3C$$
 * $$9B\equiv3C+2$$
 * $$B\equiv-\frac{3C+2}{9}$$
 * 1) We can further equate A to
 * $$A\equiv1-2(-\frac{3C+2}{9})-2C$$
 * $$A\equiv\frac{13-12C}{9}$$
 * 1) Now we can solve for C
 * $$40\equiv(28(\frac{13-12C}{9})+20(-\frac{3C+2}{9})+35C)\,$$
 * $$40\equiv((\frac{364-336C}{9})+(-\frac{60C+40}{9})+35C)\,$$
 * $$40=36-9C\,$$
 * $$C=\frac{-4}{9}$$
 * 1) Now we can solve for the rest
 * $$A\equiv\frac{13-12\frac{-4}{9}}{9}=\frac{55}{27}$$
 * $$B\equiv-\frac{3C+2}{9}=\frac{-2}{27}$$
 * $$C\equiv\frac{-4}{9}$$
 * 1) Now we can write out our partial fraction:
 * $$\frac{x^2+13x+40}{(2x+5)(x+7)(x+4)}\equiv\frac{55}{27(2x+5)}-\frac{2}{27(x+7)}-\frac{4}{9(x+4)}$$


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Cookbook:Nutritional Yeast

Nutritional yeast is a versatile inactive type of yeast (unlike brewer's active yeast) usually grown on sugar beets and sugar cane. It is a dry, brownish powder that is not quite coarsely ground but not fine either. When used in vegan "cheeses", it gives a good texture and somewhat cheesy-earthy taste. It can also be added to foods as a vitamin supplement as it naturally contains many trace nutrients including magnesium and copper. However, some brands of nutritional yeast are fortified with extra vitamins, including vitamin B12.

Nutritional yeast is a cooking yeast derived from a fungus, saccharomyces cerevisiae. It is sold in in powder and flake form, and is used most often in vegetarian and vegan cuisine to simulate creamy sauces such as fake cheese, but is also used as a general condiment.

Nutritional yeast is high in B vitamins and folic acid, and tastes sweet, salty and slightly nutty.

Nutritional yeast flakes are most commonly found for sale in bulk at natural or health food stores.

Important things to remember are
 * 1) Nutritional yeast is not the same as brewer's yeast, though Brewer's Yeast Flakes is a brand of nutritional yeast
 * 2) The recommended daily value of nutritional yeast is two heaping tablespoons and no more.

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

title: Cookbook:Nutritional Yeast


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Cookbook:Mini Three-Cheese English Muffin Pizzas

| American cuisine

Ingredients

 * 6 large English muffins, split and buttered
 * Grated Parmesan cheese
 * 1½ cups (6 ounces) shredded cheddar cheese
 * 6 frankfurters
 * 1 can (10.5 ounces) pizza sauce
 * 1 cup (4 ounces) shredded mozzarella cheese

Equipment

 * Oven
 * Broiler

Procedure

 * 1) Preheat oven to 350°F.
 * 2) Sprinkle buttered muffins with Parmesan cheese.
 * 3) Toast under broiler until golden brown.
 * 4) Place 1½ tablespoons of shredded cheddar cheese on each muffin.
 * 5) Cut frankfurters crosswise in ¼-inch slices; arrange on muffins.
 * 6) Top each with about 2 tablespoons of pizza sauce, and sprinkle with 1 tablespoon of mozzarella cheese.
 * 7) Bake 12–15 minutes or until thoroughly heated.


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User:Jingshen

Hi I am new to Wikibooks, see my page under the same name in Wikipedia.

title: User:Jingshen


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Introduction to Chemical Engineering Processes/Basic Statistics and Data Analysis

Mean and Standard Deviation
A lot of the time, when you're conducting an experiment, you will run it more than once, especially if it is inexpensive. Scientists run experiments more than once so that the random errors that result from taking measurements, such as having to guess a length between two hash marks on a ruler, cancel themselves out and leave them with a more precise measurement. However, the question remains: how should you consolidate all of the data into something that's more manageable to use?

Mean
Suppose you have n data points taken under the same conditions and you wish to consolidate them to as few as feasibly possible. One thing which could help is is to use some centralized value, which is in some way "between" all of the original data points. This, in fact, is called the mean of the data set.

There are many ways of computing the mean of a data set depending on how it is believed to be distributed. One of the most common methods is to use the arithmetic mean, which is defined as:

Other types of mean include the Geometric mean, which should be used when the data are very widely distributed (ex. an exponential distribution) and the "log-mean" which occurs often in transport phenomena.

Standard Deviation
Having a value for the mean tells you what value the data points "cluster" around but it does not tell you how spread out they are from the center. A second statistical variable called the standard deviation is used for that. The standard deviation is essentially the average distance between the data points and their mean. The distance is expressed as a squared distance in order to prevent negative deviations from lessoning the effect of positive deviations.

The mathematical formulation for the standard deviation $$ \sigma $$ is:

The denominator is n-1 instead of n because statisticians found that it gives better results for small numbers of experiments; see Standard deviation for a more thorough explanation of this.

Putting it together
The standard deviation of a data set measured under constant conditions is a measure of how precise the data set is. Because this is true, the standard deviation of a data set is often used in conjunction with the mean in order to report experimental results. Typically, results are reported as:

$$ \bar{x} \pm \sigma $$

If a distribution is assumed, knowing both the mean and standard deviation can help us to estimate the probability that the actual value of the variable is within a certain range, if there is no systematic bias in the data. If there is (such as use of broken equipment, negligence, and so on) then no statistics could predict the effects of that.

Linear Regression
Suppose you have a set of data points ($$ \hat{x}_k, \hat{y}_k $$) taken under differing conditions which you suspect, from a graph, can be reasonably estimated by drawing a line through the points. Any line that you could draw will have (or can be written in) the following form:

$$ y = mx + b $$ where m is the slope of the line and b is the y-intercept.

We seek the best line that we could possibly use to estimate the pattern of the data. This line will be most useful for both interpolating between points that we know, and extrapolating to unknown values (as long as they're close to measured values). In the most usual measure, how "good" the fit is is determined by the vertical distance between the line and the data points ($$ R_k $$), which is called the residual:

$$ R_k = (m\hat{x}_k + b) - \hat{y}_k $$

In order to normalize the residuals so that they don't cancel when one's positive and one's negative (and thus helping to avoid statistical bias), we are usually concerned with the square of $$ R_k $$ when doing least-squares regression. We use squared terms and not absolute values so that the function is differentiable, don't worry about this if you haven't taken calculus yet.

In order to take into account all of the data points, we simply seek to minimize the sum of the squared residuals:

$$ \mbox{ minimize }\Sigma {R_k}^2 $$

Using calculus, we can take the derivative of this with respect to m and with respect to b and solve the equations to come up with the values of m and b that minimize the sum of squares (hence the alternate name of this technique: least-squares regression. The formulas are as follows, where n is the total number of data points you are regressing[1]:

Example of linear regression
The first thing we should do with any data like this is to graph it and see if a linear fit would be reasonable. Plotting this data, we can see by inspection that a linear fit appears to be reasonable.

Now we need to compute all of the values in our regression formulas, and to do this (by hand) we set up a table:

Now that we have this data we can plug it into our linear regression equation:

$$ m^* = \frac{n*\Sigma(\hat{x}_k*\hat{y}_k)-\Sigma(\hat{x}_k)*\Sigma(\hat{y}_k)} {n*\Sigma(\hat{x_k}^2) - (\Sigma(\hat{x}_k))^2} $$

$$ = \frac{5* 15931.13 - 15.1*4642.2}{5*56.35 - (15.1)^2} $$

$$ = 177.9 \mbox{ } \frac{yard}{min} $$

So $$ b = \frac{\Sigma(\hat{y}_k) - m^{*}*\Sigma(\hat{x}_k)} {n} $$

$$ = \frac{4642.2 - 177.9*15.1}{5} = 391.2 \mbox{ yards} $$

Hence the equation for the line of best fit is:

The graph of this plotted against the data looks like this:

How to tell how good your regression is
In the previous example, we visually determined if it would be reasonable to perform a linear fit, but it is certainly possible to have a less clear-cut case! If there is some slight curve to the data, is it still "close enough" to be useful? Though it will always come down to your own judgment after seeing the fit line graph against the data, there is a mathematical tool to help you called a correlation coefficient, r, which can be defined in several different ways. One of them is as follows [1]:

It can be shown that this value always lies between -1 and 1. The closer it is to 1 (or -1), the more reasonable the linear fit. In general, the more data points you have, the smaller r needs to be before it's a good fit, but a good rule of thumb is to look for high (higher than 0.85 or 0.9) values and then graph to see if the graph makes sense. Sometimes it will, sometimes it won't, the method is not foolproof.

In the above example we have:

$$ r = \frac{5*15931.13 - 15.1*4642.2}{\sqrt{5*56.35-(15.1)^2}*\sqrt{5*4655464-(4642.2)^2}} $$

$$ r = 0.992 $$

Hence the data correlates very well with a linear model.

In general
Whenever you have to fit a parameter or multiple parameters to data, it is a good idea to try to linearize the function first, because linear regression is much less intensive and more accurate than nonlinear regression. The goal with any linearization is to reduce the function to the form:

$$ Variable\mbox{ 1} = constant + constant*\mbox{ Variable 2} $$

The difference between this and "standard" linear regression is that Variable 1 and Variable 2 can be any functions of x and y, as long as they are not combined in any way (i.e. you can't have $$ln(x + y) $$ as one variable). The technique can be extended to more than two variables using a method called multiple linear regression but as that's more difficult to perform, this section will focus on two-dimensional regression.

Power Law
To see some of the power of linearization, let's suppose that we have two variables, x and y, related by a power law:

$$ y = A*x^b $$

where A and b are constants. If we have data connecting changes in y to changes in x, we would like to know the values of a and b. This is difficult to do if the equation is in its current form but we can change it into a linear-type function!

The trick here is we need to get rid of the exponent b, so in order to do that we take the natural log of both sides:

$$ ln\mbox{ y} = ln\mbox{ (A*x}^b) $$

Using laws of logarithms we can simplify the right-hand side to obtain the following:

The beauty of this equation is that it is, in a sense, linear. If we graph ln(y) vs. ln(x) obtain a straight line with slope b and y-intercept ln(A).

Exponentials
Another common use of linearization is with exponentials, where x and y are related by an expression of the form:

$$ y = A*b^x $$

This works for any base but the most common base encountered in practice is Euler's constant, e. Again, we take the natural log of both sides, in order to get rid of the exponent:

This time, Graph ln y vs. x to obtain a line with slope ln(b) and y-intercept ln(A).

Linear Interpolation
Often, when you look up properties on a chart, you will be looking them up at conditions in between two charted conditions. For example, if you were looking up the specific enthalpy of steam at 10 MPa and 430oC you would look in the steam tables and see something like this: [2]

How can you figure out the intermediate value for this? We can't exactly but we can assume that H(T) is a linear function. If we assume that it is linear, then we can easily find the intermediate value. First, we set up a table, including the unknown value like this:

Then since we're assuming the relationship between T and H is linear, and the slope of a line is a constant the slope between points 3 and 2 has to equal the slope between points 3 and 1.

Therefore, we can write that:

$$ \frac{2943.4-x}{450-430} = \frac{2943.4-2832.4}{450-400} $$

Solving gives x = 2899 kJ/kg

The same method can be used to find an unknown T for a given H between two tabulated values.

General formula
To derive a more general formula (though I always derive it from scratch anyways, it's nice to have a formula), lets replace the numbers by variables ad give them more generic symbols:

Setting the slope between points 3 and 2 equal to that between 3 and 1 yields:

This equation can then be solved for x* or y* as appropriate.

Limitations of Linear Interpolation
It is important to remember that linear interpolation is not exact. How inexact it is depends on two major factors:

 * 1) What the real relationship between x and y is (the more curved it is, the worse the linear approximation)
 * 2) The difference between consecutive x values on the table (the smaller the distance, the closer almost any function will resemble a line)

Therefore, it is not recommended to use linear interpolation if the spaces are very widely separated. However, if no other method of approximation is available, linear interpolation is often the only option, or other forms of interpolation (which may be just as inaccurate, depending on what the actual function is).

See also interpolation.


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Classical Nahuatl/Grammar

Classical Nahuatl grammar sketch

Syllable structure
Maximal syllable is CVC. Maximal consonant cluster is -CC- medially. Initial and final consonant clusters do not occur. Affixes have two forms, one before/after a vowel, and one before/after a consonant.

Consonant mutations

 * l + tl > ll (cal- "house" + -tli Absolutive suffix = calli "house (Abs.)")
 * l + y >/ ll (cual- "good thing" + -yōtl abstract suffix = cuallōtl "goodness")
 * n + p > mp (on "deictic particle" + pa "locative" = ompa "there")
 * y wordfinally > x (nicchīya "I observed it" + past tense loss of final vowel = nicchīx "I observed it")

Morphology
The words of Nahuatl can be divided into three basic functional classes: verbs, nouns and particles. Adjectives exist, but they generally behave like nouns and there are very few adjectives that are not derived from either verbal or nominal roots. The few adverbs that can be said to exist fall into the class of particles.

The Noun
Nouns belong to one of two classes: animates or inanimates. Originally the grammatical distinction between these were that inanimate nouns had no plural forms, but in most modern dialects both animate and inanimate nouns are pluralizable. The noun is inflected for two basic contrasting categories: plural and possessedness. Nominal morphology is mostly suffixing. Some irregular formations exist.

In Nahuatl, nouns take a suffix called the "absolutive". This suffix takes the form -tl after vowels (ā-tl, "water") and -tli after consonants, which assimilates to a final /l/ (tōch-tli, "rabbit", but cal-li, "house"). Some nouns have an irregular form in -in (mich-in, fish). These suffixes are dropped in most derived forms: tōch-calli, "rabbit-hole", mich-matlatl, "fishing net".

 * The absolutive singular suffix has three basic forms: -tl/tli, -lin/-in, and some irregular nouns with no suffix.
 * The absolutive plural suffix has three basic forms: -tin, -meh, or just a final glottal stop -h. Some plurals are formed also with reduplication of the noun's first syllable.
 * The possessive singular suffix has two basic forms: -uh (on stems ending in a vowel) or -Ø (on stems ending in a consonant).
 * The possessive plural suffix has the form -huān.

The table below present some common nouns conjugated as examples.

Plural forms
Only animate nouns can take a plural form. These include most animate living beings, but also words like tēpetl ("mountain"), citlalli ("star") and some other phenomena. Plurals are formed in several ways:
 * The absolutive suffix is replaced with -h (glottal stop), -tin or -meh
 * Some nouns may have a reduplication of their first consonant and vowel, with the reduplicated vowel long.

The plural isn't totally stable and in many cases several different forms are attested.

Possessor prefixes
nocal "my house" mocal "your house" īcal "his/her/its house" tocal "our house" anmocal "Your house (pl.)" īncal "their house" tēcal "someone's house"
 * 1st Person Singular: no-
 * 2nd Person Singular: mo-
 * 3rd Person Singular: ī-
 * 1st Person Plural: to-
 * 2nd Person Plural: anmo-
 * 3rd Person Plural: īn-
 * Unknown owner: tē-

Some other categories can be inflected on the noun such as:
 * Honorific formed with the suffix -tzin.
 * cīhua "woman" + tzin+ tli absolutive = cīhuatzintli "woman (said with respect)"

Derivational Morphology

 * -tia derives from noun X a verb with an approximate meaning of "to provide with X " or "to become X".
 * -huia derives from noun X a verb with an approximate meaning of "to use X " or "to provide with X".
 * -yōtl derives from a noun X a noun with an abstract meaning of x-hood or x-ness.
 * -yoh derives from a noun X a noun with a meaning of "thing full of X" or "thing with a lot of X"

The Verb
The verb is marked with prefixes in order to agree with the person and number of the subject and the object of the sentence; additionally, verbs inflect for tense and aspect.

Subject prefixes and suffix
This set of prefixes are used to express the subject of transitive and intransitive verbs. They can also be prefixed to a noun, X, to make a predicative construction with the meaning "is X". nitlācatl I am a man", nicochi "I sleep", titlācatl "you are a man", ticochi "you sleep" tlācatl "he/she/it is a man", cochi "he/she/it sleeps" titlatlācah "we are men", ticochih"we sleep" antlatlācah "You are men", ancochih "You sleep" tlatlācah "they are men", cochih "they sleep"
 * 1st Person Singular: ni-
 * 2nd Person Singular: ti-
 * 3rd Person Singular: Ø- (none)
 * 1st Person Plural: ti + plural -h/-queh
 * 2nd Person Plural: an + plural -h/-queh
 * 3rd Person Plural: Ø- (none) + plural -h/-queh

Object prefixes
This set of prefixes is used to express the direct object of transitive verbs. nēchitta "he/she/it sees me", tinēchitta "you see me" mitzitta "he/she/it sees you", nimitzitta "I see you" quitta "he/she/it sees him/her/it" tēchitta "he/she/it sees us" amēchitta "he/she/it sees You (pl.)" quimitta "he/she/it sees them" tēitta "he/she/it sees someone" tlatta "he/she/it sees something"
 * 1st Person Singular: nēch
 * 2nd Person Singular:mitz
 * 3rd Person Singular: qui
 * 1st Person Plural: tēch
 * 2ndPerson Plural: amēch
 * 3rd Person Plural: quim
 * unknown animate object: tē
 * unknown inanimate object: tla

Temporal and aspectual suffixes

 * Present: has no suffix.
 * Perfect: -c/h/?/Ø niquittac "I saw him/her/it (preterit aspect) "
 * Future: -z niquittāz "I will see him/her/it "
 * Imperfect: -ya niquittāya "I saw him/her/it (imperfect aspect) "
 * Irrealis: -zquiya niquittāzquiya "I would have seen him/her/it"

Applicative
The applicative construction adds an argument to the verb. The role of the added argument can be benefactive, malefactive, indirect object or similar. It is formed by the suffix -lia.
 * niquittilia "I see it for him"

Causative
The causative construction adds an argument to the verb. This argument is an agent causing the object to undertake the action of the verb. It is formed by the suffix -tia.
 * niquittatia "I make him see it/I show it to him"

Unspecified Subject/Passive
The construction called "passive" by some grammarians and "unspecified subject construction" by others removes the subject from the valency of the verb, substituting it with a null reference, and promoting the argument marked by object prefixes to subject. The passive or unspecified subject construction uses one of two suffixes: -lo or -hua.
 * quitta "he sees it"+ -lo= quittalo "it is seen (by someone)"
 * miqui "he dies" + hua = micohua "there is dying/people are dying"

Directional Affixes
Deixis:
 * -on- "away from the speaker"
 * on+ tlahtoa "to speak" = ontlahtoa "he/she/it speaks towards there"
 * -huāl- " towards the speaker"
 * huāl+ tlahtoa "to speak" = huāllahtoa "he/she/it speaks towards here"

Introvert: Imperfective: -qui  "comes towards the speaker in order to X" qui + itta "to see" + qui ="quittaqui "he/she/it will come here to see it" Perfective: -co "has come towards the speaker in order to X" qui + itta "to see" + co =quittaco "he/she/it has come here to see it"

Extrovert: Imperfective: -tīuh "goes away from the speaker in order to X" qui + itta "to see" + tīuh ="quittatīuh "he/she/it will go there to see it" Perfective: -to " has gone away from the speaker in order to X" qui + itta "to see" + to =quittato "he/she/it has gone there to see it"

Derivational
A number of different suffixes exist to derive nouns from verbs:

tla "something" + ixca "roast" + l + tli = tlaxcalli "something roasted/ a tortilla"
 * -lli used to derive passivized nouns from verbs.

tla + ihcuiloa "write/draw" + l - tli = tlahcuilolli "scripture/ a drawing"

miqui "to die" + liztli = miquiliztli "death"
 * -liztli used to derive abstract nouns from verbs.

tlahcuiloa "to write something" + liztli = tlahcuiloliztli "the concept of writing or being a scribe"

ichtequi "to steal" + qui = ichtecqui "a thief"
 * -qui used to derive agentive nouns from verbs.

tlahuāna "to become drunk" + qui = tlahuānqui "a drunkard"

miqui "to die" +ni = miquīni "a mortal"
 * -ni used to derive habitual nouns from verbs.

cuacua "to bite" + ni = cuacuāni "someone that is known to be capable of or to habitually bite"

Verbal compounds
Two verbs can be compounded with the morpheme -ti-.

Relational Nouns and Locatives
Spatial and other relations are expressed with relational nouns. Some locative suffixes also exist.

Noun Incorporation
Noun incorporation is productive in Classical Nahuatl and different kinds of material can be incorporated.
 * Body parts
 * Instruments.
 * Objects.

Syntax
The particle in is important in Nahuatl syntax and is used as a kind of definite article and also as a subordinating particle and a deictic particle, in addition to having other functions.

Non-configurationality
Classical Nahuatl can be classified as a non-configurational language, allowing many different kinds of word orders, even splitting noun phrases.

VSO basic word order
The basic word order of Classical Nahuatl is verb initial and often considered to be VSO, although some scholars have argued for it being VOS. However, being non-configurational, all wordorders are allowed and are used to express different kinds of pragmatic relations, such as thematization and focus.

Numeral System
Classical nahuatl has a vigesimal numeral system.

Numbers

 * cē -1
 * ōme -2
 * yei -3
 * nāhui - 4
 * macuilli -5
 * chicuacēn - 6
 * chicuōme - 7
 * chicueyi - 8
 * chicunāhui - 9
 * matlactli - 10
 * caxtolli 15
 * cēmpōhualli - 20

Colour Terminology
The Nahuatl colour system lacks a separate term for blue, and instead uses a single term to cover both blue and green nuances. It has been argued that Nahuatl has no basic colour terms, (in the Berlin & Kay sense of the word) because they are all derived with a -tic suffix from verbs or nouns.

Basic Colour terms

 * īstac - white
 * tlīltic - black
 * chichiltic - red
 * costic - yellow
 * xoxoctic- green and blue
 * quiltic - green
 * tlilectic - dark

Kinship Terminology
The kinship system of Classical Nahuatl distinguishes older and younger siblings.

title: Classical Nahuatl/Grammar


text:
Jeep Liberty/Equipment

Equipment includes the tools and supplies necessary to survive on the trail. It has been classified below by level of preparedness: green for minimally prepared, blue for prepared, and red for well prepared. Many off-road events will require much of the green classified equipment. Items in angle brackets are superseded by the item to their left.

Recovery

 * Front and Rear Tow Hooks
 * Tow-Hitch and Shackle/Clevis
 * Spare Tire (Full Size)
 * Jumper Cables
 * Tow Strap without hooks (15,000 lb)

Safety

 * CB Radio
 * Fire Extinguisher (Class ABC)
 * First Aid Kit
 * GPS (Portable)
 * Water (1 gal)

Supplies

 * Electrical Crimp Connectors
 * Electrical Tape
 * Fluid (Brake)
 * Fluid (Power Steering)
 * Fluid (Transmission)
 * Grease (Bearing)
 * Lube (Gear)
 * Oil (Motor)
 * Spare Fuses
 * Solder

Tools

 * Adjustable Wrench
 * Multi-Purpose Tool
 * Screw Driver (Multi-Bit)
 * Screw Drivers (Individual)
 * Socket Set (1/4")
 * Socket Set (3/8")
 * Socket Set (1/2")
 * Socket Set (Deep Well)
 * Soldering Iron
 * Wrenches (Metric and SAE)

title: Jeep Liberty/Equipment


text:
Cookbook:Mapo Tofu

| Cuisine of China

Mápó dòufu (麻婆豆腐), also romanized as mapo tofu, is a classic spicy tofu and meat dish from the Szechuan province of China. It is a very flavourful, easy-to-prepare, and spicy dish.

Ingredients

 * 1 onion, sliced
 * 1 small piece of ginger, minced (about 2 tsp)
 * 1–2 tsp crushed dried chile pepper
 * 200 g (7 oz) minced beef, or pork
 * 4 cloves of garlic, minced
 * 500 g (1 lb) silken tofu, cubed
 * 2 tbsp chili bean paste (Doubanjiang)
 * 1 tbsp Szechuan pepper, roasted and ground
 * 1 tbsp soy sauce
 * 1 tbsp rice wine
 * 3–4 green onions, cut into 2 cm (1 inch) pieces
 * 2–3 mushrooms (tree ears preferred; optional)

Procedure

 * 1) If using dried mushrooms, soak them in hot water for 10 minutes while preparing the rest of the ingredients, then slice before adding later.
 * 2) Sauté onion with ginger and crushed chili.
 * 3) Add minced meat and garlic, and fry until brown.
 * 4) Mix in other ingredients (including sliced mushrooms), lower heat, and simmer for 5–10 minutes.
 * 5) Serve over steamed jasmine rice.

Notes, tips and variations

 * Some extra chili pepper can be substituted for Szechuan pepper, but the taste and feeling will be different. Szechuan pepper has a numbing sensation, not heat.
 * A little ground coriander and cumin is very nice in this dish, especially if you cannot find Szechuan pepper easily.
 * A red bell pepper, a tomato, and fresh coriander leaves are all welcome additions, though not traditional.
 * The meal is just as good with whole beans instead of tofu.
 * A vegan/vegetarian version of this meal can be made by substituting the meat with textured vegetable protein (TVP) or ground tofu (e.g. Shiok Food's Vegetarian Ma Po Tofu )

title: Cookbook:Mapo Tofu


text:
Cookbook:Szechuan Pepper

Szechuan Pepper is a peppery spice used frequently in food from Sichuan province, China, but also in the cuisines of Japan, Tibet, and other countries in Asia. It has a slightly lemony aroma, and has a reputation for creating numbness in the mouth (very useful when eating really spicy foods like Mapo Doufu).

The flavour and spice are in the husks of the seed, not the seed itself. The seeds are hard like little stones, and are discarded before roasting and grinding the husks.

Szechuan pepper is one of the ingredients in Chinese five spice.

title: Cookbook:Szechuan Pepper


text:
User:Skycfc

About me
I'm a student who lives in Taiwan.

Taiwan Ruby Users Group

 * Taiwan Ruby Users Group -- TWRUG

Contact me

 * E-mail: zusocfc  gmail.com
 * Skype: zusocfc
 * MSN: zusocfc  gmail.com

title: User:Skycfc


text:
Talk:Yet Another Haskell Tutorial/Type basics

ISSUE: The pronunciation of Boolean is correctly given; then, a statement is made that an alternative pronunciation has been heard.

PROBLEM: Simply because one has "heard" an improper pronunciation does not mean that one should adopt the incorrect pronunciation.

ANALOGY: Let's concentrate on base 10 arithmetic. In that system, 2 + 2 = 4 (but -- once or twice -- I've also seen that 2 + 2 = 5)

DISCUSSION: As a tutor, one need not (and I would stress that one SHOULD not) confuse a student by introducing erroneous alternatives. The fact that I may have seen (perhaps when correcting homework of another student) the answer to our equation given as "5" instead of "4" does not reasonably obligate me (as a tutor) to share what I know to be incorrect information.

Either/left/right exercise very unclear
I don't think you're giving the student enough information to know how to do the exercise where you want either a value, a pair, a triple, etc back. Looking at the solution doesn't help either (it also doesn't help in the PDF that the solution goes off to the right and you can't see it all).

It says something about how you will need to use the Either type to represent it, but you don't have to directly mention Either (unless you are entering the function's type signature), but you do have to somehow guess that every time you use alternation, you get something that is addressable with Left and Right. Nothing in the text prepares the reader for this. Either is introduced earlier as "another useful type", not something that is going to automatically apply every time I define a type with the | symbol. Is that what the | symbol means? That I'm using Either? I don't get it.

Msouth 18:41, 17 July 2007 (UTC)

 * I agree, and I've fixed the problem.
 * MichaelPloujnikov (talk) 20:07, 13 October 2008 (UTC)

How do I display my type?
I'm brand new to haskell, and after reading this page and the "advanced type" page, I can't figure out how to tell GHCI to display my new type.

How do I make my new data type a member of class Show?


text: Template:Empty template

title: Template:Empty template


text:
ERP Internals/Data Tables/Accounts Receivable Payment

This group of tables contains the following tables:
 * Header
 * Line


text:
User talk:Deviance99

Image Copyright
Thanks for uploading images on Wikibooks. However, the images may soon be deleted unless we can determine the copyright holder and copyright status. The Wikimedia Foundation is very careful about the images included in Wikibooks because of copyright law (see Wikibooks' Copyright policy).

The copyright holder is usually the creator, the creator's employer, or the last person who was transferred ownership rights. Copyright information on images is signified using copyright templates. The three basic license types on Wikibooks are open content, public domain, and fair use. Find the appropriate template in Image copyright tags and place it on the image page like this:.

Please signify the copyright information on all images you have uploaded or will upload. Remember that images without this important information or giving false information can be deleted by an administrator. If you have any questions, ask them at the Staff lounge. Thank you. Az1568(Talk) 17:39, 24 February 2007 (UTC)

title: User talk:Deviance99


text:
ERP Internals/Data Tables/Accounts Receivable Payment/Header

This table contains one record for every customer payment.

Used By: Accounts Receivable, Order Entry

Key: Customer Number, Payment Number

Fields:
 * Customer Number
 * Payment Number (a unique number assigned by the ERP package)
 * Type (Check/Credit/Debit/Cash)
 * Date
 * Amount
 * Currency
 * Check Number
 * Credit Card Type
 * Credit Card Number
 * Credit Card Expiry Date
 * Credit Card Name


text:
ERP Internals/Glossary/T-4

A form required by the Canadian federal government once a year that reports the employee's earnings and deductions for income tax and various social programs.

title: ERP Internals/Glossary/T-4


text:
ERP Internals/Glossary/Unallocated Cash

Customers occasionally send checks that cannot be linked to specific invoices. This cash is recorded in Unallocated Cash for that customer. When its use is determined, it is transferred from Unallocated Cash to specific invoice(s).

title: ERP Internals/Glossary/Unallocated Cash


text:
ERP Internals/Glossary/Amortization

The process of paying off a debt through payments that combine interest and payments of principal.

title: ERP Internals/Glossary/Amortization


text:
Biology, Answering the Big Questions of Life/Metabolism/Metabolism2

How are food molecules broken down to make energy?
The major food molecule in living organisms is a sugar called glucose. Most carbohydrates (sugars and starches) are converted into glucose before they are broken down in the cytosol to release energy. The series of steps where glucose is broken down to release energy begins with a metabolic pathway called glycolysis. Glycolysis is the "lysing" or cutting of glucose to release energy. The six carbon sugar, glucose, is cut in half and converted into two three-carbon sugars called pyruvate. What happens next depends on the presence or absence of oxygen.

If oxygen is present, then glucose can be broken all the way down into carbon dioxide and water. This process is called aerobic respiration because it requires air (oxygen). In the absence of oxygen, the cell uses a process called anaerobic fermentation. or simply fermentation. Fermentation doesn't break the sugar down any further, it simply helps reset the system so that more sugar can be broken down.

Because aerobic respiration breaks the sugar all the way down, it releases much more energy than fermentation.

What is the equation for aerobic respiration?
 C6H12O6 + 6 O2 → 6 CO2 + 6 H2O + energy

Glucose + Oxygen → Carbon dioxide + water + energy

How is energy stored in the cell?
In living cells, energy is stored in the form of high energy molecules. The most common is a molecule that we call ATP (Adenosine triphosphate). ATP is a nucleic acid containing three high energy phosphate groups. It breaks off these groups to release measured amounts of energy. When ATP loses one phosphate group, it becomes Adenosine diphosphate (ADP). When ATP loses two phosphate groups it becomes adenosine monophosphate (AMP).

Many reactions in the cell are directly run by ATP. ATP drives reactions as varied as moving flagella, pumping salt through pores, and making muscles move. Because ATP has so many uses, it has been called "the currency of the cell".

There are other energy storing molecules found in cells. For the most part, these molecules must be converted into ATP for the cell to use them. This occurs in the mitochondria by a process called oxidative phosphorylation.

Why do we need to breathe oxygen to live?
Very simple organisms (e.g. bacteria) do not need much energy to live. Humans, however, require large amounts of energy to run their bodies. Fermentation produces two ATP molecules for every glucose molecule consumed. Humans need more energy than can be provided simply by fermentation alone. Therefore, humans must use aerobic respiration which produces 36 or 38 ATP's for each glucose molecule consumed.

(See the advanced page for more information about why humans need oxygen to live.)

Easy

Advanced


text:
ERP Internals/Glossary/Full Time Equivalent

The percentage of full-time employment. A full-time employee is 1.0; a half-time employee is .50.


text:
ERP Internals/Glossary/Work Order

An order to perform a specified amount of work.

title: ERP Internals/Glossary/Work Order


text:
Biology, Answering the Big Questions of Life/Metabolism/Metabolism3

=Glucose Catabolism=

How many ATPs are generated by Aerobic respiration?
(Table modified from [] Oct 2007).

What is the purpose of anaerobic and aerobic respiration?
The sugar glucose is the major food molecule in the cell, but it is too energetic to use directly in most chemical reactions. To be useful, glucose is broken down into an energy storing molecule (ATP) that can be used throughout the cell.

Why do cells need to ferment if they already get 2 ATP from glycolysis?
Glycolysis yields 2 net ATPs and 2NADHs. NADH is another high energy molecule. (NAD has low energy, NADH has higher energy). NADH has many fewer uses in the cell than ATP. It is normally converted into ATP in the mitochondrial electron transport chain if oxygen is present.

If no oxygen is present, then NADH builds up and the cell can run completely out of NAD. Without NAD glycolysis stops. NAD becomes a "limiting reagent" The chemical whose concentration determines whether the reaction will happen or not.

In the absence of Oxygen, the cell runs out of NAD and glycolysis is stopped until it can be regenerated. To regenerate NAD the cell uses a process called Fermentation.

In Fermentation, Pyruvate is transformed into another molecule using the energy provided by NADH. NADH gets converted to NAD so that it can be used again in glycolysis, and pyruvate becomes Lactic Acid in animal cells, or Ethanol + Carbon Dioxide in plants, yeast, and bacterial cells. (Lactic acid builds up in muscle cells and causes cramps. When oxygen is present again, lactic acid is converted back into pyruvate and broken down by aerobic respiration).

The anaerobic pathway is glycolysis + fermentation. This pathway recycles the NADH generated, so the only energy molecules made from the breakdown of sugar by this pathway is 2ATP for every glucose molecule. The molecules made by anaerobic fermentation still contain lots of energy in the form of chemical bonds. Anaerobic fermentation in not a very efficient pathway to yield energy from glucose.

What pathways make up aerobic respiration?
Aerobic respiration starts by breaking Glucose down into Pyruvate by glycolysis. Next in a preparatory step for the Krebs cycle, Coenzyme A joins to pyruvate causing a loss of one carbon and the generation of NADH. The acetyl-CoA formed enters the Krebs cycle and the acetyl group is transferred to a molecule of oxaloacetic acid making a molecule of citric acid. The Krebs cycle releases CO2 and the high energy molecules NADH, and FADH2 which are converted into ATP by the mitochondrial electron transport chain.

Why do we need oxygen to break down glucose completely by aerobic respiration?
Aerobic respiration requires oxygen because oxygen is the final electron acceptor of the electron transport chain in the mitochondria. If there is no oxygen to accept electrons, then the electron transport chain stops working and the high energy molecules NADH and FADH2 cannot be converted back into NAD and FAD. Without these molecules, the glucose biochemical pathway stops. These molecules become the limiting reagents needed for glucose break down to continue, and when they run out, the pathway stops.

How does the electron transport chain convert NADH and FADH2 into ATP?
In order to get the full amount of energy released by the breakdown of sugar, you must convert the high energy molecules NADH and FADH2 into ATP. This occurs in the inner membrane of the mitochondria.

Energy in the form of electrons is taken from these molecules and passed from molecule to molecule in a molecular game of "hot potato" until it is ultimately dumped on oxygen. The extra pair of electrons allows oxygen to make another chemical bond, and it makes a water molecule. This frees up the electron transport chain to take another pair of electrons from an FADH2 or a NADH.

The electron gradient
The mitochondria contains two compartments, the matrix which is the area inside of the inner membrane of the mitochondria, and the intermembrane space which lies between the inner and outer membranes of the mitochondria.

The Kreb's cycle occurs in the matrix of the mitochondria. This is where NADH and FADH2 are produced. They travel to the inner membrane and dump their electrons onto the membrane. This loss of electrons is a redox reaction and converts NADH back into NAD while FADH2 changes back into FAD.

The membrane proteins in the Electron Transport Chain are protein pumps. The passage of electrons across them makes them change shape and pump protons across the inner membrane from the matrix to the intermembrane space. Each NADH pumps three protons whereas each FADH2 pumps two protons.

NADH = 3ATP

FADH2 = 2ATP

This pumping of electrons across the inner membrane causes a concentration gradient of Hydrogen atoms across the membrane. By diffusion, the hydrogen ions will want to travel back into the matrix to reach equilibrium. They can do so by traveling through a special channel found in the membrane called ATP synthase. This channel uses the energy of the passage of the Hydrogen ions to make ATP. For each proton that passes, one ATP is made. This is why each NADH makes three ATP and each FADH2 makes 2 ATP.

Easy

Intermediate


text:
User talk:Rozzychan

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.– Mike.lifeguard  | talk 16:23, 11 October 2007 (UTC)

I will use this page to store notes from the book. If you want to make a comment make a new catagory and begin. Thanks.

April 2020
My current project is [| The Organ Systems]. Although it was written some years ago, we decided to update it. My class is adding new photos and FAQs. SO EXCITING!

Fermentation
How are grapes made into wine? What makes the holes in Swiss Cheese? What makes bread rise? Why do wine and beer always have about the same alcohol content? Why do humans have to breathe oxygen?

Why do leaves fall in the autumn? (plant Hormones)

WB:SLN
I moved your book request here since it's not really a book request. This is a good place for new users to get all kinds of help. – Mike.lifeguard  | talk 16:23, 11 October 2007 (UTC)

If you want to keep notes like the ones above, that's generally done on a subpage of your user: page. This User talk: page is usually reserved for communicating with fellow contributors. If you want help to move the page into your userspace, Please ask on WB:SLN or on my talk page. – Mike.lifeguard  | talk 16:25, 11 October 2007 (UTC)

If your interested in books about the mediawiki software, there are several on Wikibooks already. Using Wikibooks, Wiki Science and Editing Wikitext. --dark lama  22:07, 11 October 2007 (UTC)

Thanks Rozzychan 22:09, 11 October 2007 (UTC)

Page blanking
Please don't blank pages without putting a good reason in the edit summary. This is considered disruptive, and one of your recent edits was reverted because of this. – Mike.lifeguard  | talk 21:27, 14 January 2008 (UTC)
 * Sorry, it wasn't reverted since you're the only contributor to that page; do you want it deleted? – Mike.lifeguard  | talk 21:28, 14 January 2008 (UTC)

Yes. I made an error. I wanted to make a page called "About this book" in my book, but instead I accidentally started a new book called "about this book". This was a mistake. If you can, please remove it. Thanks. Rozzychan (talk) 21:32, 14 January 2008 (UTC)
 * ✅ - to request speedy deletion in the future, just add to the top of the page.  – Mike.lifeguard  | talk 22:21, 14 January 2008 (UTC)

 * I think this was supposed to be in your userspace, but it is a copyright violation regardless where it is. The other pages similarly. – Mike.lifeguard  | talk 20:45, 22 May 2008 (UTC)

Please
Hi, I'm Mirabelle.I could help with the chemistry is though.well it's good to know you're a high school teacher well I am a student and I am sure gonna be needing some from you during this holidays (don't know about you) and f don't mind, I am very intelligent you gotta trust me.So what do you say ma'am. Mirabelle heavens (discuss • contribs) 23:01, 9 April 2022 (UTC)

 * Hello Mirabelle. If you think you can add something to the book, go ahead. Nice to meet you.
 * Rozzychan (discuss • contribs) 03:50, 26 April 2022 (UTC)

title: User talk:Rozzychan


text:
User:Cocoaguy

Hi i am cocoaguy i have a account on english wikipedia here

title: User:Cocoaguy


text:
User talk:Sboot006

Hello and welcome to Wikibooks!

Here are some tips to help you get started:
 * You should sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:27, 24 February 2007 (UTC)

title: User talk:Sboot006


text:
User:Quartz25

This is Quartz25.

I know a few things about Python Programming, so I want to contribute.

title: User:Quartz25


text:
User talk:Sridd004

Hello and welcome to Wikibooks!

Here are some tips to help you get started:
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 * If you want to base your work here on materials from Wikipedia, please use WB:RFI to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:27, 24 February 2007 (UTC)

title: User talk:Sridd004


text:
User talk:Jrobi009

Hello and welcome to Wikibooks!

Here are some tips to help you get started:
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 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:28, 24 February 2007 (UTC)

title: User talk:Jrobi009


text:
User talk:Dgogg001

Hello and welcome to Wikibooks!

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 * Remember to maintain a Neutral point of view.
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You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:28, 24 February 2007 (UTC)

title: User talk:Dgogg001


text:
User talk:Stargaazr 7

Hello and welcome to Wikibooks!

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 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
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 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:29, 24 February 2007 (UTC)

title: User talk:Stargaazr 7


text:
User talk:Ecoar002

Hello and welcome to Wikibooks!

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 * Remember to conduct any editing experiments in the sandbox.
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 * If you want to base your work here on materials from Wikipedia, please use WB:RFI to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:29, 24 February 2007 (UTC)

title: User talk:Ecoar002


text:
User talk:Mgask002

Hello and welcome to Wikibooks!

Here are some tips to help you get started:
 * You should sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * If you're a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:30, 24 February 2007 (UTC)

title: User talk:Mgask002


text:
User talk:AmandaMichie

Hello and welcome to Wikibooks!

Here are some tips to help you get started:
 * You should sign your name on Talk and vote pages using four tildes, like this: ~~~~.
 * Remember to conduct any editing experiments in the sandbox.
 * If you're a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be an idea if you add this page to your "watchlist" so that you can see when any new information is posted there.

Good luck! Mattb112885 20:30, 24 February 2007 (UTC)

title: User talk:AmandaMichie


text:
A-level Chemistry/OCR (Salters)/Open-Book Paper

How to create diagrams
Diagrams are invaluable for conveying precise chemical information without encroaching on the word count. For two-dimensional diagrams such as skeletal formulae or flow charts, a molecule editor is your best bet.

For images of three-dimensional molecules, use molecular graphics software, such as Accelrys DS Visualizer, a free downloadable application for Windows. A tutorial on how to use DS Visualizer is available here.

Article 1: From Accident to Design: the progress of poly(ethene)

 * Discovery of poly(ethene)
 * Development of industrial production of poly(ethene)
 * Discovery of Ziegler-Natta catalysts

Article 2: Shaping up: the story of poly(propene)

 * /Stereochemistry in poly(propene)/
 * Development of Ziegler-Natta catalysts
 * /Discovery and development of metallocene catalysts/

Exemplar response
An exemplar response to the 2001 open paper exam is available here.


text:
How To Assemble A Desktop PC/Choosing the parts/CPU

The Central Processing Unit (CPU), also called a processor, is the heart of your computer. A processor takes software instructions (such as turn this 0 into a 1) from your computer (the operating system) and implements these instructions into your hardware. It performs nearly all the actual computation that takes place as the computer is used. The choice of a CPU will affect the ultimate speed of the computer more than any other single component (gaming systems excepted; there the GPU is usually the bottleneck).

Vocabulary
People who design a CPU have come up with a large number of terms to describe the inner workings of a CPU.

Before we can explain the differences between CPUs, you must be familiar with certain CPU terms.

Clock speed
Clock speed, measured in gigahertz (GHz) or megahertz (MHz) (1 GHz = 1000 MHz), is the number of calculation cycles that your CPU can perform per second. Therefore, a higher clock speed generally indicates a faster processor. But not all CPUs perform an equal amount of work per cycle, meaning two CPUs at the same clock speed can potentially perform at very different levels. Clock speeds should not be compared for CPUs from different architectures (e.g. AMD Ryzen versus Intel i7). Use reviews and benchmarks to judge relative performance.

IPC
Instructions per cycle or IPC for short is the amount of work a CPU can do in a cycle. With modern processors this number is an average.

Multiple cores
Processors sold today typically include multiple cores. Each core gives the ability to send out 1 instruction, so 10 cores can send out 10 instructions at the same time. This improves performance while multitasking and when running software that supports multiple threads. This also saves money compared to the old way of having multiple cores, which was to install extra processors, which required special hardware and software.

Adding more cores can seriously improve performance to a point, but cores are not multipliers of performance. A processor with 8 cores will not be twice as fast as a processor with 4 cores running most software, all else being equal. You should look at the recommended requirements of the software you are using, and pick the number of cores based on what it supports - More cores are still better, but not if it requires a significant cost increase or trade-off in clock speed.

Interface (Socket/Slot)
CPUs plug into a socket on the motherboard. It is very important that your CPU is a COMPLETE MATCH to your motherboard CPU socket. Plugging a CPU into the wrong socket will never work and will usually break either the CPU, the socket, or both. Think of a socket as a Lego brick (or bread board) connection between the CPU to the motherboard.

Bit width
Modern processors are either 32-bit or 64-bit (this is a simplification; The Wikipedia article on 64-bit for details). For our purposes a processor can be called 64-bit if it supports running a 64-bit operating system. The x86-64 processors sold today are 64 bit, with compatibility for older 32 bit software.

Many complex applications benefit from using a 64 Bit processor, such as Mozilla Firefox. Some programs may only work with a 64 bit processor. A bit stands for a switch between 0 or 1. This is 2 options. 32 bit stands for 2^32. 64 bit means 2^64, which is the size of how much data you can fit into a given unit on the processor.

Simultaneous Multithreading
Some higher end processors feature simultaneous multithreading (SMT). Intel calls their SMT platform Hyper-threading which allows each processor core to simulate having two logical processors, effectively doubling the core count as far as the operating system is concerned. AMD Ryzen series CPU have a similar unbranded feature.

Cache
Cache is memory implemented directly on the CPU. Data which is being used in computations is stored in the cache as much as possible and can be retrieved from there much faster than the same data can be pulled through the northbridge from main memory. Generally, the larger the cache, the faster the system will run. Cache comes in (usually) three varieties, L1, L2, and L3. L1 being the smallest and fastest, and L3 being the largest and slowest. Usually only the L3 cache size will be shown, as L4 is rarely used in processor design, and L1 and L2 will often stay the same size throughout an entire processor product line. Note that L4 is only in special Intel Haswell high-end CPU's, which contain Iris Pro graphics. They contain an embedded 128MB DRAM inside, which is represented as L4.

Process size
The process size is a measurement of size of the components on a chip. In general, the smaller the process node, the better, as more components can be used on a chip, and those components can be made to consume less power. As of 2022 most processors use a 10 nm, 7nm, or 5nm process size, with nodes expected to shrink to 4nm and 3nm eventually.

PCI Express Lanes
Modern processors support a given generation of PCI Express, as well as the maximum number of lanes they support.

Memory Controller
Modern CPU designs integrate a memory controller into the CPU. This determines the type of memory supported, as well as how many channels can be used.

High end Intel processors and most AMD processors may support ECC memory, which can correct for errors. This memory is usually somewhat more expensive than regular RAM, and is typically found in workstations and mission critical computers, where crashes and failures must be kept to an absolute minimum. Regular memory is fine for most users.

ISA and Microarchitectures
A Instruction Set Architecture (ISA) determines the compatibility of the processor with software. Most desktop CPU models use the X86-64 ISA. Deeper than the ISA is the microarchitecture, which is what actually determines how the ISA is implemented. The microarchitecture of a processor determines many of it's qualities, which are listed above. Without using benchmarks it is only appropriate to compare processors based on specification if they are of the same microarchitecture, and even then there may be caveats.

How to choose CPU?
2023 Guides
 * tomshardware
 * digitaltrends
 * best CPU
 * YouTube search CPU 2023

Descriptions
Often in advertisements (especially for pre-built systems) a processor will be described briefly, like this:
 * AMD Ryzen 7 5700X at 3.4 GHz

But there’s more to it than that, a more detailed specification would read as follows:
 * AMD Ryzen 7 5700X eight core processor at 3.4GHz/4.6GHz, AM4 socket, 32MB L3 Cache, 4MB L2 Cache

Which parses out to: So we can see that while 3.4 GHz is a fast clock speed, this processor might not be as fast as, a higher end AMD Ryzen 9 5950X, which runs at the same 3.4 GHz base clock speed, but has 8 MB more L2 cache and an additional eight processing cores.
 * 1) Model: AMD Ryzen 7 5700X
 * 2) Base Clock Speed: 3.4 GHz (3400 MHz)
 * 3) Turbo Clock Speed: 4.6 GHz (4600 MHz)
 * 4) Socket: AM4
 * 5) L3 Cache: 32 MB, L2 Cache: 8 × 512 kB

For an Intel example ,
 * 1) Intel Core i5-13600K Processor 24M Cache, up to 5.10 GHz
 * 2) Model: Intel Core i5-13600K
 * 3) Cores: 14 (6P+8E)
 * 4) Base Clock Speed: 3.5 GHz (=3500 MHz)
 * 5) Turbo Clock Speed: 5.1 GHz (=5100 MHz)
 * 6) Interface: LGA 1700
 * 7) L2-Cache: 20 MB (=20480 kB)
 * 8) L3-Cache: 24 MB (=24576 kB)

Intel
Intel classifies its CPUs using a series of numbers. 2xxx, 3xxx, 4xxx, 5xxx, 6xxx, 7xxx, 8xxx, 9xxx, 10xxx, 11xxx, 12xxx, and 13xxx of which 13xxx denominates the latest generation. Generally, the higher the digit after generation, the faster the CPU and the more expensive. Many CPUs have suffixes: K denotes that the CPU is unlocked so can be overclocked; T denotes the low-power version; F denotes the CPUs without integrated graphics. Here is a list of most modern Intel Desktop CPUs: The Celeron series is a range of CPUs for budget computers and used to feature just one core. The last single core Celeron was released as part of the Sandy Bridge line-up, and since then all Celeron G-series processors have been dual-core.
 * Intel Celeron (Dual/Quad core)

The tablet-based Baytrail/Braswell Celeron have either 2 or 4 cores. However, due to their weak IPC , the performance does not match Core i CPU and single core performance is slightly below a Core 2 Duo with the same clockspeed. The Pentium series was part of Intel's most popular CPUs. Earlier Intels all featured just one core, although the newer Pentiums feature dual-core support, such as the Pentium D, the Pentium Dual-Core, and the Pentium G-series processors.
 * Intel Pentium (Dual core)

Baytrail/Braswell Pentium are generally quad-core. The weak IPC would generally mean that their multi-core performance would be around the range of a Core M, with half the single core performance.

Note that Intel Celeron and Pentium are being replaced by Intel Processor series.

These are low end processors that have hyperthreading enabled, allowing them to make use of multi-threaded software more efficiently. This CPU series is made for LGA 1156, 1155, 1150, 1151, 1200 and 1700, depending on generation. This processor lineup is adequate for most applications, including the majority of games. Since the 9th generation, they have Turbo Boost. These are mid range processors without hyperthreading(dual-core variants do have it). Like the rest of the 'i' lineup, they are made for LGA 1156,1155,1150,1151,1200 and 1700 depending on generation. This series can take almost any game without bottlenecking the graphics card. Turbo boost is included, which allows the processor to dynamically overclock to higher click speeds when power and thermal limits allow for. Intel's flagship line of consumer microprocessors, these CPUs all have 4 - 20 cores, feature Hyper Threading and feature higher amounts of cache and Intel's new "Turbo Boost" technology, which allows all cores to automatically clock themselves to appropriate frequencies in intervals of 133(Nehalem only)/100(Sandy Bridge and higher) MHz without stressing the processor and risking overheating. This feature is unavailable on LGA775-based Core 2, but most of them utilize a partial overclock by raising the multiplier by 0.5 when one core for every 2 cores is not in used. This means 2 cores can be turbo overclocked on a Core 2 Quad. It also support DDR4 and, since the 12th generation, DDR5, memory and does not use a FSB (Front Side Bus), but rather uses an Intel QuickPath interface. Turbo Boost is also available on i3 and i5.
 * Intel Core i3 (2 to 4 cores (desktop) / 2 to 10 cores (mobile))
 * Intel Core i5 (4 - 14 cores (desktop), 2 - 14 cores (mobile))
 * Intel Core i7 (4 - 20 cores (desktop), 2 - 20 cores (mobile))

In 2023 Intel announced that Intel is rebranding Intel Core series, removing i prefix. Currently the rebranding is for mobile CPUs only, like 16-core Intel Core Ultra 7 155H.

The Xeon brand was a brand of Intel x86/64 processors for workstations, servers, and embedded systems. The Xeon brand features single, dual, quad,, hexa(actually up to 288). core processors (although don't get excited - remember that these are for servers and similar systems, not your "Ultra-awesome high-tech bleeding-edge owns-everybody-else's computer" with a 790i Ultra SLi motherboard and 4 graphics cards)
 * Intel Core i9 (8 - 24 cores (desktop), 6 - 24 cores (mobile))
 * Intel Xeon (2 - 288 cores)

Additional Intel features
These features may not be there in every model.
 * 1) XD Technology: A CPU's model number followed by suffix J signifies XD (eXecute Disable) technology, which is an added security feature on Intel CPUs. Note that AMD processors have a similar technology dubbed EVP, or "Enhanced Virus Protection. Note that it is now included with every processor as it is required since Windows 8.
 * 2) VT-X In 2006, Intel and AMD introduced a feature known as hardware virtualization which boosts speeds when using more than 1 OS at the same time. This feature is available on some Intel Core 2 and most processors after that.

Naming schemes
Naming schemes determine how a CPU is named based on its performance, clockspeed and price. The consumer logic for processor speed may be misleading because many consumers think that clock speed, which is measured in gigahertz (GHz) or megahertz (MHz) is equal to system speed. While a higher clock speed will allow the CPU to do cycles more frequently and it does have a fundamental effect on speed, it is not the sole factor as the number of calculations (and data handled) per cycle is different for each different manufacturer and model. In addition, other factors, such as FSB speed will affect the CPU's ability to process data efficiently. If the FSB and RAM aren't able to get data to the CPU as quickly as the CPU can process it, then the CPU will spend some of the cycles doing nothing. A cycle during which the CPU does nothing is called a wasted cycle.

Nehalem and higher(Core i architecture)
The Nehalem/Lynnfield/Sandy Bridge/Ivy Bridge/Haswell series line-up uses a different naming scheme as follows.
 * 1) Celeron/Pentium indicates a basic dual core. Pentiums usually have more cache and higher clockspeed than Celerons.
 * 2) i3 denotes 2 to 4 cores with hyperthreading (except 8th and 9th generations). Since 9th generation (9xxx), they have Turbo functionality.
 * 3) i5 usually denotes 4 to 14 cores with hyperthreading, for 10th to 13th generations, and all feature turbo functionality which allows the processor to raise its clockspeed under load. However, certain(2) earlier low wattage(35W) i5 were dual core hyperthreaded.
 * 4) i7 denotes 4 to 16 cores with hyperthreading except 9th generation, and all feature turbo functionality.
 * 5) i9 denotes 8 to 24 cores with hyperthreading, and all feature turbo functionality.

To find the generation and the socket for the processor, it is necessary to look at the numbering of the processors. The exception to this is the E(Extreme) series of the generation. For the budget Celeron/Pentium ,
 * 1) Any cpu that has the i designation and 3 digits is meant for LGA 1156(Nehalem.)
 * 2) Any cpu that has the ix-2xxx(Sandy Bridge) or ix-3xxx(Ivy Bridge) type naming is for LGA 1155.
 * 3) Any cpu that has the ix-4xxx(Haswell) or ix-5xxx(Broadwell) naming is for LGA 1150.
 * 4) Any CPU that has the ix-6xxx(Skylake) or ix-7xxx(Kaby Lake) naming is for LGA 1151.
 * 5) Any CPU that has the ix-8xxx(Coffee Lake) or ix-9xxx(Coffee Lake Refresh) is for LGA 1151v2.
 * 6) Any CPU that has the ix-10xxx(Comet Lake) or ix-11xxx(Rocket Lake) is for LGA 1200.
 * 7) Any CPU that has the ix-12xxx(Alder Lake), ix-13xxx(Raptor Lake) or ix-14xxx(Raptor Lake Refresh) is for LGA 1700.
 * 1) The i7-9xx series(Nehalem) use LGA 1366.
 * 2) The i7-3820/39x0 series(Sandy Bridge) and the i7-4820K/49x0 series(Ivy Bridge) use LGA 2011.
 * 3) The i7-5820K/59x0 series(Haswell) use LGA 2011-v3, which is incomparable with LGA 2011.
 * 1) Celeron G1101/Pentium G6950 is meant for LGA 1156
 * 2) Celeron G4xx and G5xx/Pentium G6xx and G8xx series are for LGA 1155
 * 3) Celeron G16xx/Pentium G2xxx are for LGA1155
 * 4) Celeron G18xx/Pentium G3xxx are for LGA 1150

Each processor has a letter after the model number which tells the type of CPU. To find out, use this:-

and for mobile processors , Note:- There are some exceptions to this. This applies only to Nehalem(1st generation i series and higher)
 * 1) T:- These types of processors use very less power than other variants(usually between 35-45 W). Some ultra-low power variants use 35 W, while others use 45W. Performance is usually somewhat reduced compared to other variants , especially for the i5/i7 35W variants.
 * 2) S:- These types of processors, while using more power that the T series , use less than their usual(no letter) variants. This is found only on i5 and i7 processors and use 65 W. Not present since Broadwell.
 * 3) No letter:- These types of processors use the full power. They range from 53 W(up to i5) till 84 W(i5, i7). Nehalem CPU's can use up to over 130 W. Skylake and later CPU's use only 65W, effectively replacing the S series.
 * 4) K/X:- These types of processors, only in i5, i7, i9 and Extreme series and the Pentium G3258 processors , can be overclocked beyond their normal clock speeds. They use between 53 W(Pentium) to over 165W(Extreme).
 * 5) R:- These processors(i5 - 4570R/4670R, i7-4770R , i5-5565R/5665R , i5-5775R) are not the ones you'll be building , as they are meant to be used in all-in-one PC types and they do not use the normal LGA1150 , they use BGA1164 socket. This variant has better graphics than the normal CPU's(Iris Pro). They use 65W of power. These processors cannot overclock(which the C series can).
 * 6) E:- Embedded processors. Not the ones you'll typically encounter.
 * 7) P:- Does not contain Intel's integrated graphics. Applies only to Sandy Bridge and Ivy Bridge. Exception:- i5-6402P
 * 8) C:- These are i5 and i7 processors(i5-5665C, i7-5775C) which contain Iris Pro , Intel's top of the line integrated graphics at that time. These processors can overclock and have a S series TDP(65 W). The main difference between it and the R series processors is that the C series uses the standard LGA 1150 socket , which the R series do not.
 * 1) Y:- Uses very little power, about 11.5(Haswell) to 13(Ivy Bridge)W.
 * 2) U:- Uses less power, from 15 to 28 W(though 15W is more common). This SKU is used in computers such as the MacBook Air and Surface Pro 3.
 * 3) M:- Uses about 37W, they are found in mainstream notebooks and some all-in-one PC's. i7 quad-core variants can use up to 47W depending on model. This type of CPU is easier to remove(Socket G1/PGA) , though not as easy as the desktop variants. Also you may have to find your desired replacement CPU on the Internet , as you would not find mobile Intel CPU's in most shops.
 * 4) E:- Embedded processors. Not the ones you'll typically encounter.
 * 5) Q:- Quad-core. Usually paired with H or Q to indicate a mobile quad-core processor. Example:- i7-4700MQ. Applies only to i7 and i5 since Skylake.
 * 6) H:- Used in all-in-one PC's and many laptops, uses about 47W of power(37 W for i3). This type of CPU cannot be easily removed(mostly soldered to the motherboard) because of the type of socket it uses(BGA).
 * 7) X:- Extreme series, they can be overclocked. Uses about 57W of power. These processors are very expensive and are found only in i7's. Exception - i7-6820HK , which is around the same price as a standard quad-core i7.
 * 8) C:- Special embedded processors.
 * 9) Core M - Considered as the successor of the Y series of Haswell, these processors are used in ultra-light tablets and notebooks. These processors have a TDP of 3.5-7 W that can be configured by the manufacturer if required. Some devices come without a fan at this level.(eg - MacBook)
 * 1) The i7-3820 processor is overclockable, but has a multiplier limitation of 43x which can be partially overcome by increasing the BCLK speeds. This processor is an Extreme i7 processor and uses 130W.
 * 2) Nehalem ultra low low-wattage mobile(18 W) CPU's are marked as 'UM' and not just as 'U' as in Sandy Bridge and later.
 * 3) Nehalem low wattage models(26 W) mobile CPU's are marked as 'LM'. Sandy Bridge and Ivy Bridge do not have this, and Haswell(28 W) are marked as 'U' only.
 * 4) i7-6820HK is overclockable.

AMD
Recent AMD Ryzen CPUs use a naming scheme that is different than, but similar to Intel's. AMD and Intel now both use the 3/5/7/9 series CPU classification, with AMD not using an "i" prefix. Ryzen processors increase in price as the last three numbers increase.

Zen 4

 * Ryzen 9 7950X3D 4.2/5.7 GHz 16c/32t
 * Ryzen 9 7950X 4.5/5.7 GHz 16c/32t
 * Ryzen 9 7900X3D 4.4/5.6 GHz 12c/24t
 * Ryzen 9 7900X 4.7/5.6 GHz 12c/24t
 * Ryzen 9 7900 3.7/5.4 GHz 12c/24t
 * Ryzen 7 7800X3D max 5.0 GHz 8c/16t
 * Ryzen 7 7700X 4.5/5.4 GHz 8c/16t
 * Ryzen 7 7700 3.8/5.3 GHz 8c/16t
 * Ryzen 5 7600X 4.7/5.3 GHz 6c/12t
 * Ryzen 5 7600 3.8/5.1 GHz 6c/12t

TDP(Thermal Design Power)
The TDP of a processor gives an idea of how much power would it consume in a standard heavy use scenario.

But note that it does not give the absolute maximum power it would consume. For instance, if you try to stress your CPU by running Prime95(a popular CPU stressing tool) or something of that sort , it is likely to exceed the TDP rating(atleast for a short period of time , this depends on the cooling efficiency.)

In some cases, it can nearly be the double. For instance, a MacBook Air with 15W TDP can hit up to 29W when running graphics-heavy workloads.

The TDP in a laptop is lower than a desktop, because laptops have space and battery requirements.

CPU cooling
CPU cooling is very important. A cool CPU temperature prolongs CPU life, sometimes by as much as 10 years, and allows your CPU to maintain a higher speed through Intel Turbo Boost or AMD Turbo Core. Conversely, high CPU temperatures can cause unreliable operation, such as computer freezes, or slow operation.

Extremely high temperatures can cause immediate CPU destruction by melting or burning the chip. Because of this, never switch on the computer if your CPU has no cooling at all. Trying to turn your computer on without a cooler installed "just to test whether my CPU works" is a bad idea and you may find that the CPU fries in less than 5 seconds and you will be out your money. If your computer turns off unexpectedly during use, it could be because of inefficient cooling. Modern CPU's automatically throttle when the temperature reaches its TJunction(usually 100C) and halts if it keeps on climbing.

Most CPU installations use forced-air cooling, but water cooling is another fairly common option. Convection cooling and even oil submersion cooling are more exotic options. For traditional forced-air cooling, the heat sink and fan (HSF) included with most retail CPUs is usually sufficient to cool the CPU at stock speed. Overclockers might want to use a more powerful after-market fan, or try water cooling to combat the increased heat caused by overclocking.

A small amount of thermally conductive compound is used in between the CPU and the heatsink to ensure optimal heat transfer. Many retail heatsinks have a thermal pad preinstalled. This pad is usable only once. If you wish to remove the fan from another CPU so that you can use it on your new one, or need to take it off for some reason, you will need to remove the pad and apply a thermal paste or another thermal pad. A poor quality thermal compound or application may result in less optimal performance, and a high quality compound and application may lower temperatures significantly on it's own. If you plan to do any high performance computing, or remove and replace the HSF often, a decent or high quality thermal paste is suggested. If you are planning on a long term installation a thermal pad is often best. Using one or the other is essential to ensure consistent heat conduction between the CPU and heatsink. Thermal compounds work optimally for a few years before they should be replaced.

Electrically insulating thermal pastes made up of silicon are the cheapest and safest, but silver-based thermal pastes sometimes perform better and carbon-based ones perform better still. When applied improperly both can be conductive, causing electrical shorts upon contact with the motherboard. A thin properly-applied layer will usually prevent this problem, although some pastes can become runny when they get hot. Users should also beware that many "silver" thermal pastes do not actually contain any silver metal.

For quiet operation, start with a low-heat (low wattage) CPU. You can also underclock your CPU, giving up some unneeded performance for some peace and quiet. Another option is to choose a large copper heat sink with an open fin pattern. However, true fanless operation is difficult to achieve in most case designs. You can position a case fan to blow across the heat sink, or mount a fan on the heat sink. With either choice, a large and slow fan will give better airflow and less noise than a small and fast fan.

Some low-noise CPU cooling fans require special mounting hardware on the motherboard. Be sure that the cooling systems you choose are compatible with your motherboard.

Overclocking
More details can be found here:- How To Assemble A Desktop PC/Overclocking

Desktop chips
Most desktop chips are locked to prevent overclocking.

Intel chips marked with a K have unlocked multipliers, allowing for easier overclocking. K series processors are usually priced slightly higher than locked CPU models.

AMD chips are typically unlocked, even on lower end chips.

The ability for a processor to overclock well is highly dependent on the individual CPU. This is due to minute differences caused during manufacturing, which are not noticeable at stock speeds, but can become problematic at higher speeds or when consuming more power. This so called "Silicon Lottery" could mean your chip under preforms or over preforms the typical overclocking potential of your specific processor.

There are external factors that affect the ability of a CPU to achieve a stable overclock, such as the power provided by a motherboard, or the cooling offered by the heatsink.

Mobile chips
If you have chosen to use a mobile processor in a desktop system, it is likely for their low power requirements and heat benefits. Overclocking basically nullifies these benefits, and is rarely supported on mobile chips anyway. However, there are some exceptions.

Intel mobile cpus marked with HK can be overclocked.

Privacy concerns
Modern CPU designs have raised a number of interesting privacy concerns. Both Intel and AMD CPUs have features designed for corperate users that are opaque to regular users, and have represented security risks in the past. The Intel Management Engine has been used on Intel chips since 2008. The AMD Platform Security Processor is similar to Intel's Management Engine and has been used on AMD chips since 2013.

A number of security vulnerabilities such as Meltdown and Spectre were found in the late 2010's. Sometimes, but not always, hardware vulnerabilities can be patched by microcode or handled by the operating system, but often at significant performance costs.

Unconventional CPU choices
For whatever reason, you may want to use an non Intel or AMD CPU for your system. These choices are unconventional on desktop computers for good reasons. Their linage typically stems from other use cases, such as embedded or mobile systems, and are often woefully under powered or based on cheaper obsolete manufacturing methods. They are typically available as a SOC only, and your choice in what GPU, RAM, or other hardware you end up using may be limited or non existent. Furthermore software support is limited, and you are typically left running some flavor of Linux or BSD, and even then the lack of support for that hardware may affect you.

Through a quirk of history, VIA makes some low powered x86 processors.

There are a few ATX form factor motherboards with standard expansion slots and integrated ARM or PowerPC processors intended for special use servers and workstations.

There are also a number of smaller boards of nonstandard sizes that use ARM or RISC-V processors. Intended for hobbyists and developers, these boards are cheap, but offer limited power and component flexibility.

Prices
Prices on CPUs vary, even of the same models, over locations.

Here are the general prices of the CPUs below:


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A-level Chemistry/OCR (Salters)/Open-Book Paper/Stereochemistry in poly(propene)

Isotactic
Isotactic polymers have all their R-groups pointing in the same direction.

Syndiotactic
Syndiotactic polymers have their R-groups pointing in alternating directions.

Atactic
Atactic polymers have no regularity in the direction of their R-groups.


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A-level Chemistry/OCR (Salters)/Open-Book Paper/Discovery and development of metallocene catalysts

= Ferrocene is planar =

= Zirconocenes are tilted =

= Specific zirconocenes produce stereospecific poly(propene) =


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User:Ben Mills

I'm Ben, a chemistry-focussed editor.

My user pages

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User talk:128.12.95.110

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.

Thanks very much for your contributions in Astronomy. Hope you enjoy it here.
 * --Brian 22:53, 24 February 2007 (UTC)

title: User talk:128.12.95.110


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User talk:59.101.56.27

Regarding edits made during February 24 2007
Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. If this is an IP address, and it is shared by multiple users, ignore this warning if you did not make any unconstructive edits. Az1568(Talk) 22:58, 24 February 2007 (UTC)

Please stop adding nonsense to Wikibooks. It is considered vandalism. If you would like to experiment, use the sandbox. Thank you. If this is an IP address, and it is shared by multiple users, ignore this warning if you did not make any unconstructive edits. Az1568(Talk) 23:00, 24 February 2007 (UTC)

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User talk:Bonchien

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.

Welcome, and thank you for contributing Astronomy/Life in the Solar System! Hope you enjoy it here.
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Introduction to Chemical Engineering Processes/Converting Information into Mass Flows

Converting Information into Mass Flows - Introduction
In any system there will be certain parameters that are easier (often considerably) to measure and/or control than others. When you are solving any problem and trying to use a mass balance or any other equation, it is important to recognize what pieces of information can be interconverted. The purpose of this section is to show some of the more common alternative ways that mass flow rates are expressed, mostly because it is easier to, for example, measure a velocity than it is to measure a mass flow rate directly.

Volumetric Flow rates
A volumetric flow rate is a relation of how much volume of a gas or liquid solution passes through a fixed point in a system (typically the entrance or exit point of a process) in a given amount of time. It is denoted as:

Why they're useful
Volumetric flow rates can be measured directly using flow meters. They are especially useful for gases since the volume of a gas is one of the four properties that are needed in order to use an equation of state (discussed later in the book) to calculate the molar flow rate. Of the other three, two (pressure, and temperature) can be specified by the reactor design and control systems, while one (compressibility) is strictly a function of temperature and pressure for any gas or gaseous mixture.

Limitations
Volumetric Flowrates are Not Conserved. We can write a balance on volume like anything else, but the "volume generation" term would be a complex function of system properties. Therefore if we are given a volumetric flow rate we should change it into a mass (or mole) flow rate before applying the balance equations.

Volumetric flowrates also do not lend themselves to splitting into components, since when we speak of volumes in practical terms we generally think of the total solution volume, not the partial volume of each component (the latter is a useful tool for thermodynamics, but that's another course entirely). There are some things that are measured in volume fractions, but this is relatively uncommon.

How to convert volumetric flow rates to mass flow rates
Volumetric flowrates are  related to mass flow rates by a relatively easy-to-measure physical property. Since $$ \dot{m} \dot= mass/time $$ and $$ \dot{V} \dot= volume/time $$,  we need a property with units of $$ mass/volume $$ in order to convert them. The density serves this purpose nicely!

The "i" indicates that we're talking about one particular flow stream here, since each flow may have a different density, mass flow rate, or volumetric flow rate.

Velocities
The velocity of a bulk fluid is how much lateral distance along the system (usually a pipe) it passes per unit time. The velocity of a bulk fluid, like any other, has units of:

By definition, the bulk velocity of a fluid is related to the volumetric flow rate by:

This distinguishes it from the velocity of the fluid at a certain point (since fluids flow faster in the center of a pipe). The bulk velocity is about the same as the instantaneous velocity for relatively fast flow, or especially for flow of gasses.

For purposes of this class, all velocities given will be bulk velocities, not instantaneous velocities.

Why they're useful
(Bulk) Velocities are useful because, like volumetric flow rates, they are relatively easy to measure. They are especially useful for liquids since they have constant density (and therefore a constant pressure drop at steady state) as they pass through the orifice or other similar instruments. This is a necessary prerequisite to use the design equations for these instruments.

Limitations
Like volumetric flowrates, velocity is not conserved. Like volumetric flowrate, velocity changes with temperature and pressure of a gas, though for a liquid, velocity is generally constant along the length of a pipe with constant cross-sectional area.

Also, velocities can't be split into the flows of individual components, since all of the components will generally flow at the same speed. They need to be converted into something that can be split (mass flow rate, molar flow rate, or pressure for a gas) before concentrations can be applied.

How to convert velocity into mass flow rate
In order to convert the velocity of a fluid stream into a mass flow rate, you need two pieces of information:

 * 1) The cross sectional area of the pipe.
 * 2) The density of the fluid.

In order to convert, first use the definition of bulk velocity to convert it into a volumetric flow rate:

$$ \dot{V}_n = v_n*A_n $$

Then use the density to convert the volumetric flow rate into a mass flow rate.

$$ \dot{m}_n = \dot{V}_n*{\rho}_n $$

The combination of these two equations is useful:

Molar Flow Rates
The concept of a molar flow rate is similar to that of a mass flow rate, it is the number of moles of a solution (or mixture) that pass a fixed point per unit time:

Why they're useful
Molar flow rates are mostly useful because using moles instead of mass allows you to write material balances in terms of reaction conversion and stoichiometry. In other words, there are a lot fewer unknowns when you use a mole balance, since the stoichiometry allows you to consolidate all of the changes in the reactant and product concentrations in terms of one variable.

Limitations
Unlike mass, total moles are not conserved. Total mass flow rate is conserved whether there is a reaction or not, but the same is not true for the number of moles. For example, consider the reaction between hydrogen and oxygen gasses to form water:

$$ H_2 + \frac{1}{2}O_2 \rightarrow H_2O $$

This reaction consumes 1.5 moles of reactants for every mole of products produced, and therefore the total number of moles entering the reactor will be more than the number leaving it.

However, since neither mass nor moles of individual components is conserved in a reacting system, it's better to use moles so that the stoichiometry can be exploited, as described later.

The molar flows are also somewhat less practical than mass flow rates, since you can't measure moles directly but you can measure the mass of something, and then convert it to moles using the molar flow rate.

How to Change from Molar Flow Rate to Mass Flow Rate
Molar flow rates and mass flow rates are related by the molecular weight (also known as the molar mass) of the solution. In order to convert the mass and molar flow rates of the entire solution, we need to know the average molecular weight of the solution. This can be calculated from the molecular weights and mole fractions of the components using the formula:

$$ \bar{MW}_n = [\Sigma({MW}_i*y_i)]_n $$

where i is an index of components and n is the stream number. $$ y_i $$ signifies mole fraction of each component (this will all be defined and derived later).

Once this is known it can be used as you would use a molar mass for a single component to find the total molar flow rate.


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Conphilosophy/Branches

 * /Metaphysics/
 * /Epistemology/
 * /Ethics/
 * /Philosophical logic/
 * /Mathematical logic/

title: Conphilosophy/Branches