text:
User talk:Laleena/Workshop

I got to copy Wikipedia articles.

Denmark
Kongeriget Danmark Kingdom of Denmark Motto: none (Royal motto: Guds hjælp, Folkets kærlighed, Danmarks styrke "The Help of God, the Love of the People, the Strength of Denmark") Anthem: Der er et yndigt land (national) . Royal anthem Kong Christian (royal) Location of Denmark Location of Denmark  (orange)

– on the European continent (camel & white) – in the European Union (camel)                  [Legend] Capital (and largest city) 	Copenhagen 55°43′N, 12°34′E Official languages 	Danish1 Demonym 	Danish Government 	Parliamentary democracy and Constitutional monarchy - 	Monarch 	Margrethe II -  	Prime Minister 	Anders Fogh Rasmussen Consolidation 	(prehistoric) EU accession 	1 January 1973 Area - 	Total 	43,094 km² (134th²) 16,639² sq mi -  	Water (%) 	1.6² Population - 	2007 estimate 	5,470,919 (108th) - 	Density 	129.04/km² (78th²) 334.23/sq mi GDP (PPP) 	2006 estimate - 	Total 	$198.5 billion (45th) - 	Per capita 	$37,000 (6th) GDP (nominal) 	2006 estimate - 	Total 	$256.3 billion (27th) - 	Per capita 	$46,600 (6th) Gini (1997) 	24.7 (low) (1st) HDI (2004) 	0.943 (high) (15th) Currency 	Danish krone (DKK) Time zone 	CET² (UTC+1) - 	Summer (DST) 	CEST² (UTC+2) Internet TLD 	.dk2,3 Calling code 	+454 1 Co-official with Greenlandic in Greenland, and Faroese in the Faroe Islands. German is recognised as a protected minority language in the South Jutland (Sønderjylland) area of Denmark. Danish is recognized as a protected minority language in the Schleswig-Holstein region of Germany. ² For Denmark excluding the Faroe Islands and Greenland. ³ The TLD .eu is shared with other European Union countries. 4 The Faroe Islands use +298 and Greenland uses +299.

Denmark, officially (translated to English) the Kingdom of Denmark (Danish: Kongeriget Danmark (help·info), IPA: [ˈd̥ænmɑɡ̊], (archaic:) IPA: [ˈd̥anmɑːɡ̊]) is a nation situated in Scandinavia in northern Europe. It is the southernmost of the Nordic countries. The mainland is bordered to the south by Germany; Denmark is located to the southwest of Sweden and the south of Norway. Denmark borders both the Baltic and the North Sea.

The country consists of a large peninsula, Jutland (Jylland) and a large number of islands, most notably Zealand (Sjælland), Funen (Fyn), Vendsyssel-Thy, Lolland, Falster and Bornholm as well as hundreds of minor islands often referred to as the Danish Archipelago. Denmark has long controlled the approach to the Baltic Sea, and these waters are also known as the Danish straits. The Faroe Islands and Greenland are autonomous provinces of Denmark with home rule.

Denmark is a constitutional monarchy with a parliamentary system of government. It is a member of NATO and the European Union, having joined the European Economic Community in 1973. The national capital and the largest city is Copenhagen. Originally a seafaring nation relying on fishing, farming and trade, Denmark experienced steady industrialization in the 19th and 20th centuries and developed the Scandinavian model welfare state. In 2006 a survey found Denmark to be the happiest place in the world, based on standards of health, welfare, and education. In 2007 the country's capital was ranked the third most liveable city in the world by Monocle magazine[1] and ranked as the happiest nation in the world.[2]

Gazette Editorial Starters
When I work on this, I have to try to decide how to interpret different standards to fit in the mix. I don't see why we need to have to coordinate books with standards that may or may not be actually good. I can testify, for instance, how standards lead to very poor academics in school. They do not interest most students, and those that do get interested is because the teacher/s lead them into further exploration. So I say, why not arrange books by interest levels, not by standards? Seems most sensible. (got this one from a leading discussion over at Textbook Standards that I began. This is the opening comment.)
 * (Response by Chazz)I'm sorry, Laleena, but I can't really agree, much as I wish I could. What the standards provide is a minimum, a level of factuality and verifiability, so that an educator using our texts (or any text) will have a basic level of trust in the materials he or she is using to teach. We must write to that minimum standard to be accepted. Without that minimum, we cannot be used for teaching and the whole thing becomes a pointless exercise. However: Nothing says that we can't exceed that minimum, and it is there that we hopefully can do better than the main stream. All the same, a text, even as flexible and fluid a text as WB, cannot inspire the way a teacher can. WB can, under the hands of a suitable teacher, inspire a class to new heights as it researches outside the classroom to find material to add to the text, to make a palpable contribution to the next class and to the future. There is no text that can make a mediocre teacher any good. What we have to do is meet the standards, exceed them where possible, and we have no choice but to trust the teachers to make the magic from what we can provide.

title: User talk:Laleena/Workshop


text:
.NET Development Foundation/System Types Classes

System types and collections: Classes, interfaces and tools

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


text:
User talk:Thetatelugu~enwikibooks

Welcome!
Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard  | talk 21:07, 24 December 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Thetatelugu. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Thetatelugu~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:49, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:35, 19 April 2015 (UTC)

title: User talk:Thetatelugu~enwikibooks


text:
User talk:Mayankjohri

Welcome!
Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard  | talk 21:08, 24 December 2007 (UTC)

File:Microsoft Application Virtualization - An Introduction to Sequencing.pdf
I'm afraid this file is not available via an acceptable license and will soon be deleted. You've marked it as CC-BY-SA, but the document itself shows that it is CC-BY-NC-SA. The Wikimedia projects do not allow content that can only be used for noncommercial use. They want content to be free for any user, not just the nonprofit or educational user. If you upload a new version of the file with the CC-BY-SA tag shown within the document instead, I'll remove the notice on the image. Thanks. -- Adrignola talk contribs 13:06, 18 December 2009 (UTC)

title: User talk:Mayankjohri


text:
.NET Development Foundation/Hello world

System types and collections: Hello world example

Hello world example
Note: when you create a new console project in Visual studio, all the code is generated by default except for the 3 "Console" lines in the Main method. Just add those 3 lines and run the program.

We have discussed all the parts of that program except for the role of the Console which will be discussed in the input/output section (Stream). For now, lets say that it is a System class, in the System namespace (the "using System" instruction makes the "System." part of "System.Console.Writeline" optional) and that the WriteLine and ReadLine methods write and read strings to and from the console.

title: .NET Development Foundation/Hello world


text:
VHDL for FPGA Design/4-Bit Multiplier

Simulation Waveform

VHDL-kieli FPGA-suunnittelussa/4-bittinen kertolaskupiiri

title: VHDL for FPGA Design/4-Bit Multiplier


text:
.NET Development Foundation/Using collections

System types and collections: Using collections

Using Collections
Exam objective: Manage a group of associated data in a .NET Framework application by using collections.

(Refer System.Collections namespace - MSDN)

ArrayList class
see MSDN

The ArrayList class is used for arrays whose size will dynamically increase as required. An ArrayList is not necessarily sorted.

using System; using System.Collections;

public class Demo { public static void Main { ArrayList myArrayList = new ArrayList; myArrayList.Add("Testing"); myArrayList.Add("1...2...3"); } }

Collection interfaces

 * ICollection interface and IList interface

 * ICollection interface - MSDN

 * The ICollection interface is the base interface for classes in the System.Collections namespace.

 * The ICollection interface extends IEnumerable; IDictionary and IList are more specialized interfaces that extend ICollection. An IDictionary implementation is a collection of key/value pairs, like the Hashtable class. An IList implementation is a collection of values and its members can be accessed by index, like the ArrayList class.

 * Some collections that limit access to their elements, such as the Queue class and the Stack class, directly implement the ICollection interface.

 * If neither the IDictionary interface nor the IList interface meet the requirements of the required collection, derive the new collection class from the ICollection interface instead for more flexibility.

 * The following tables list the members exposed by the ICollection type.

 * Public Properties

Count - Gets the number of elements contained in the ICollection. IsSynchronized - Gets a value indicating whether access to the ICollection is synchronized (thread safe). SyncRoot - Gets an object that can be used to synchronize access to the ICollection.
 * Public Methods

CopyTo - Copies the elements of the ICollection to an Array, starting at a particular Array index.

 * IList interface - MSDN

 * IComparer interface, IEqualityComparer interface, and IKeyComparer interface

 * IComparer interface - MSDN

 * IEqualityComparer interface - MSDN

 * IKeyComparer interface - IKeyComparer does not exist in .Net 2.0

 * IDictionary interface and IDictionaryEnumerator interface

 * IDictionary interface - MSDN

 * IDictionaryEnumerator interface - MSDN

 * IEnumerable interface and IEnumerator interface - MSDN and MSDN

{{dynamic navigation IEnumerator sample public class Person {   public Person(string fName, string lName) {       this.firstName = fName; this.lastName = lName; }   public string firstName; public string lastName; }
 * title=C# code sample
 * body=

public class PeopleEnum : IEnumerator {   public Person[] _people; //Enumerators are positioned before the first element //until the first MoveNext call. int position = -1; public PeopleEnum(Person[] list) {       _people = list; }   public bool MoveNext {       position++; return (position < _people.Length); }   public void Reset {       position = -1; }   public object Current {       get {           try {               return _people[position]; }           catch (IndexOutOfRangeException) {               throw new InvalidOperationException; }       }    } }

public class People : IEnumerable {   private Person[] _people; public People(Person[] pArray) {       _people = new Person[pArray.Length]; for (int i = 0; i < pArray.Length; i++) {           _people[i] = pArray[i]; }   }    public IEnumerator GetEnumerator {       return new PeopleEnum(_people); } }

Write down a handler for Practicing the above code.

protected void lnkEnumerator_Click(object sender, EventArgs e)   { Person[] peopleArray = new Person[] { new Person("Irfan", "Akhtar"), new Person("Hammad", "Anwar"), new Person("Majid", "Aalim")    }; PeopleEnum Prson = new PeopleEnum(peopleArray);

while (Prson.MoveNext ) {       Person P = (Person)Prson.Current; Response.Write("First Name : " + P.firstName + ", Last Name : " + P.lastName); }
 * One way of using IEnumerator.

People peopleList = new People(peopleArray); foreach (Person p in peopleList) Response.Write("First Name : " + p.firstName + ", Last Name : " + p.lastName); }}
 * One way of using IEnumerable.

 * IHashCodeProvider interface - MSDN - Interface is now obsolete (as of .NET 2.0)

Iterators
See MSDN

 * An iterator is effectively a lightweight version of the IEnumerable interface. It is primarily used with foreach statements.

 * You will normally implement the GetEnumerator method of the IEnumerable interface.

public class Colors : System.Collections.IEnumerable {    string [] colors = { "Red", "Green", "Blue" };

public System.Collections.IEnumerator GetEnumerator {        for ( int i = 0; i < colors.Length; i++) {            yield return colors[i]; }    } }

 * This enables the class to be accessed using a standard foreach statement. A class is not restricted to implementing only a single iterator. Multiple iterators can be supplied, for example to enable iteration in both ascending and descending order of a list. To call a named iterator, use the following syntax:

foreach ( int i in myList.NamedIterator) {    System.Console.WriteLine(i); }

 * The yield statement marks a point where execution of a iterator will resume on a subsequent iteration. This can be used to supply multiple yield statements:

public System.Collections.IEnumerator GetEnumerator {    yield return "Statement returned on iteration 1"; yield return "Statement returned on iteration 2"; }

 * To end the iteration programmatically, use the

yield break;

 * statement.

Hashtable class - MSDN

 * Used to represent a collection of key/value pairs.

CollectionBase class and ReadOnlyCollectionBase class

 * CollectionBase class - MSDN

 * ReadOnlyCollectionBase class -MSDN

DictionaryBase class and DictionaryEntry class

 * DictionaryBase class - MSDN

 * DictionaryEntry structure - MSDN

Comparer class - MSDN

Queue class - MSDN

SortedList class - MSDN

BitArray class - MSDN

Stack class - MSDN


text:
.NET Development Foundation/Using generic collections

System types and collections: Using generic collections

Using generic collections
Exam objective: Improve type safety and application performance in a .NET Framework application by using generic collections.

(Refer System.Collections.Generic namespace MSDN)

Collection.Generic interfaces

 * Generic IComparable interface - MSDN

 * Note that IComparable is a member of the System namespace.

 * You use this interface when you create a class and you want it to be used with generic types that support ordering (ex. SortedList or List.Sort) without having to specify a comparer object. The only method of IComparable is CompareTo(T other). There is an example on MSDN.

 * The following example implements IComparable for a custom made Point class. The example uses a List instead of a SortedList or OrderedDictionnary because the comparaison is done based on the distance of the points from the origin which can give the same value for many points.

 * Generic ICollection interface and Generic IList interface

 * Generic ICollection interface - MSDN

 * Generic IList interface - MSDN

 * Generic IComparer interface and Generic IEqualityComparer interface

 * Generic IComparer interface - MSDN

 * Generic IEqualityComparer interface - MSDN

 * Generic IDictionary interface - MSDN

 * Generic IEnumerable interface and Generic IEnumerator interface

 * Generic IEnumerable interface - MSDN

 * see also ONDotnet

 * Generic IEnumerator interface - MSDN

 * IHashCodeProvider interface - MSDN - Interface is now obsolete (as of .NET 2.0)

Generic Dictionary

 * Generic Dictionary class and Generic Dictionary.Enumerator structure

 * Generic Dictionary class - MSDN

 * Generic Dictionary.Enumerator structure - MSDN

 * Generic Dictionary.KeyCollection class and Dictionary.KeyCollection.Enumerator structure

 * Generic Dictionary.KeyCollection class - MSDN

 * Dictionary.KeyCollection.Enumerator structure - MSDN

 * Generic Dictionary.ValueCollection class and Dictionary.ValueCollection.Enumerator structure

 * Generic Dictionary.ValueCollection class - MSDN

 * Dictionary.ValueCollection.Enumerator structure - MSDN

Generic Comparer class and Generic EqualityComparer class

 * Generic Comparer class - MSDN

 * The Comparer class serves as a base class to easily implement the IComparer interface.

 * The example is the same then for the IComparable except that now a Comparer derived object is given to the List.Sort method instead of implementing the IComparable interface on Point.

 * This way of preceding has 2 advantages:
 * It can be used even if you dont have access to the source code of Point
 * You can have more than one Comparer derived class for the same Point class

 * Generic EqualityComparer class - MSDN

Generic KeyValuePair structure

 * see MSDN

Generic List class, Generic List.Enumerator structure, and Generic SortedList class

 * Generic List class - MSDN
 * A generic list class instance is simply declared using the List syntax where T is the specific type.

 * Generic List.Enumerator structure - MSDN

 * Generic SortedList class - MSDN

Generic Queue class and Generic Queue.Enumerator structure

 * Generic Queue class - MSDN

 * Generic Queue.Enumerator structure - MSDN

Generic SortedDictionary class

 * See MSDN

 * For differences between SortedList and SortedDictionary are explained see MSDN

Generic LinkedList

 * A Generic Linked List represents a doubly linked list and is a general-purpose linked list. It supports enumerators and implements the ICollection interface, consistent with other classes in the .NET Framework.

 * Generic LinkedList class - MSDN

 * Generic LinkedList.Enumerator structure - MSDN

 * Generic LinkedListNode class - MSDN

Generic Stack class and Generic Stack.Enumerator structure

 * Generic Stack class - MSDN

 * Generic Stack.Enumerator structure - MSDN


text:
.NET Development Foundation/Other system classes

System types and collections: Other system classes

Using specialized collections
Exam objective: Manage data in a .NET Framework application by using specialized collections.

(Refer System.Collections.Specialized namespace)

Specialized String classes

 * StringCollection class - MSDN

 * StringDictionary class - MSDN

 * StringEnumerator class - MSDN

Specialized Dictionary classes

 * HybridDictionary class - MSDN

 * IOrderedDictionary interface and OrderedDictionary class

 * IOrderedDictionary Interface - MSDN

 * OrderedDictionary class - MSDN

 * ListDictionary class - MSDN

Named collections

 * NameObjectCollectionBase class - MSDN

 * NameObjectCollectionBase.KeysCollection class - MSDN

 * NameValueCollection class - MSDN

CollectionsUtil class
CollectionsUtil class - MSDN

BitVector32 structure and BitVector32.Section structure

 * BitVector32 structure - MSDN

 * BitVector32.Section structure - MSDN

Standard interfaces
Exam objective: Implement .NET Framework interfaces to cause components to comply with standard contracts.

(Refer System namespace)

IComparable interface - MSDN

 * The IComparable interface defines a comparison method that a value type or class implements to create a type-specific comparison method

IDisposable interface - MSDN

 * The IDispose interface can be used to explicitly release unmanaged resources in custom classes. The consumer of an object can call this method when the object is no longer needed.

 * The .Net garbage collector releases memory allocated to managed objects when they are no longer used, however, it is not possible to predict when garbage collection will occur and it has no knowledge of unmanaged resources such as window handles, or open files and streams.

IConvertible interface - MSDN

ICloneable interface - MSDN

INullableValue interface - MSDN

IEquatable interface - MSDN

IFormattable interface - MSDN


text:
User:Wimvandorst

See my profile on Wikipedia

title: User:Wimvandorst


text:
Linear Algebra/Direct Sum

Let V be a vector space, and let H1, H2, H3, ..., Hn are all subspaces of V. V is defined to be a direct sum of H1, H2, H3, ..., Hn when

 * 1) For every x within V, there is xn within Hn such that

$$x=\sum_{i=1}^n x_n$$
 * 1) When xn and yn is within Hn

$$\sum_{i=1}^n x_n=\sum_{i=1}^n y_n$$

implies that xn=yn.

The second condition can easily be proven to be equivalent to the following statement:

When xn are elements of Hn, then

$$x=\sum_{i=1}^n x_n=0$$

implies that all xn are also equal to 0.

Because of the second condition, the intersection of any two of the subspaces involved in a direct sum is the single element {0} where 0 is the 0 vector. This implies that all n dimension spaces are a direct sum of n one-dimension subspaces.

Theorem
If V is a vector space, then for any subspace H, there exists a subspace G such that V is a direct sum of H and G.

Proof
Let {e1, e2,..., ek} be a basis of H. This can be extended to a basis of V, say, {e1, e2,..., en}. Then the space G spanned by {ek+1, ek+2,..., en} is such that V is a direct sum of H and G.

General Sums
Given a vector space V, and H1, H2, H3, ..., Hn are all subspaces of V, then V is a sum of H1, H2, H3, ..., Hn are all subspaces of V when all elements of V can be expressed as a sum of elements in H1, H2, H3, ..., Hn.

Exercises

 * 1) Prove that the second condition is equivalent to the following statement:

When xn are elements of Hn, then

$$x=\sum_{i=1}^n x_n=0$$
 * 1) Prove that the intersection of of any two of the subspaces involved in a direct sum is the single element {0} where 0 is the 0 vector.

title: Linear Algebra/Direct Sum


text:
Linear Algebra/Quotient Space

Definition
Let V be a vector space over a field F, and let H be a subspace. Define an equivalence relation where x and y within V are said to be equivalent when x-y is an element of H. Define the sum of two equivalence classes X and Y to be the equivalence containing x+y when x is within X and y is within Y, and the scalar multiple aX where a is an element of F to be the equivalence class containing ax when x is an element of X.

Sums are well-defined because if x1 and x2 are within X and y1 and y2 are within Y, then x1+y1-(x2+y2)=(x1-x2)+(y1-y2) which is an element of H, so their sums are equivalent.

Scalar multiples are also well-defined because if x1 and x2 are within X and a is an element of F, then ax1-ax2=a(x1-x2) which is an element of H, so they are equivalent.

Given equivalence classes X and Y and an element x within X and y within Y and z within Z and an elements a and b within F, X+Y and Y+X both contain x+y and so are the same, (X+Y)+Z and X+(Y+Z) both contain x+y+z and so are the same, H is the identity for addition since any for any h within H, (x+h)-x=h which is within H, so X+H=X, and the equivalence class containing -x is the inverse of X, 1X contains 1x=x and so is the same as X, a(bX) and (ab)X both contain abx and so are the same, and (a+b)X and aX+bX are the same since they both contain ax+bx and a(X+Y) and aX+aY are the same since they both contain ax+ay.

The above paragraph establishes that the equivalence classes with addition and scalar multiplication as define also form a vector space, called the quotient space. This vector space is denoted V/H.

Theorem
If V has dimension d and H has dimension s, then V/H has dimension d-s.

title: Linear Algebra/Quotient Space


text:
Linear Algebra/Hyperplanes

A hyperplane H is any subspace of R^n$$$$ of dimension n-1. The orthogonal complement of H is a subspace of dimension 1 (i.e. a line through the origin). Assume H orthogonal is spanned by a vector v_1 then an equation of H is given by OP.v_1 = 0 where P is any point in H.

title: Linear Algebra/Hyperplanes


text:
Linear Algebra/Row and column spaces

Having gone over vector spaces, we now combine the ideas of bases and dimension with the vector spaces, and the ideas of linear dependence and rank applied earlier. We will apply these important ideas to the general solution of m linear equations of n variables.

Definitions
Suppose we have an a field F and an m×n matrix of elements of F, and let r be the rank of that matrix.

Consider the columns or rows of the matrix are elements of a vector space where addition and scalar multiplication were defined before. One can easily check that they form a vector space.

Let M be a minor of the matrix F with order r. This minor is called the basis minor, and the columns and rows of this minor are called the basis columns and basis rows. The column space and row space of a matrix are respectively the vector spaces spanned by the columns and rows of the matrix.

Theorem
The dimension of both the basis and column spaces of a matrix are both equal to r, the rank of the matrix, and the basis columns (or rows) form a basis for the column (or row) space.

Proof
Let 𝐴 be a 𝑚×𝑛 matrix with rank 𝑟. Consider a matrix 𝐿 𝑚×𝑟 which is formed by the 𝑟 columns of 𝐴 forming the bases (vectors). By construction of 𝐿, each column of 𝐴 can be written as a linear combination of the columns of 𝐿 i.e. there exist a matrix 𝑍 𝑟×𝑛 such that 𝐴=𝐿𝑍. This means that each row of 𝐴 can be written as a linear combination of the 𝑟 rows of 𝑍 i.e. the row space of 𝐴is spanned by the rows of 𝑍. That is, row rank of 𝐴 is bounded above by 𝑟. Also, 𝐴^𝑇=𝑍^𝑇𝐿^𝑇. Clearly, the range of 𝑍^𝑇𝐿^𝑇 is contained in the range of 𝑍^𝑇. So, the rank of 𝐴^𝑇 is at most the rank of 𝐴. This argument holds for any matrix. Using the above argument and a similar argument starting with 𝐴𝑇, we conclude that transposition does not change the rank of the matrix.

Corollaries

 * 1) Any n columns are linearly dependent when n>r.
 * 2) The columns (or rows) of a matrix are linearly dependent when the number of columns (or rows) is greater than the rank, and are linearly independent when the number of columns (or rows) is equal to the rank.
 * 3) The maximum number of linearly independent rows equals the maximum number of linearly independent columns.

title: Linear Algebra/Row and column spaces


text:
Linear Algebra/Homogeneous Systems

A homogeneous system of linear equations are linear equations of the form

$$a_{11}x_1+a_{12}x_2+a_{13}x_3+\ldots+a_{1n}x_n=0$$

$$a_{21}x_1+a_{22}x_2+a_{23}x_3+\ldots+a_{2n}x_n=0$$

$$a_{31}x_1+a_{32}x_2+a_{33}x_3+\ldots+a_{3n}x_n=0$$

$$\vdots$$

$$a_{m1}x_1+a_{m2}x_2+a_{m3}x_3+\ldots+a_{mn}x_n=0$$

The trivial solution is when all xn are equal to 0.

Consider the matrix of coefficients

$$A=\left(\begin{matrix} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{m1}&a_{m2}&\cdots&a_{mn} \end{matrix}\right)$$

A linear combination of the columns of A where the sum is equal to the column of 0's is a solution to this homogeneous system. A solution where not all xn are equal to 0 happens when the columns are linearly dependent, which happens when the rank of A is less than the number of columns. However, if the rank is equal to the number of columns, then all the columns are linearly independent, so then the only solution is the trivial one.

title: Linear Algebra/Homogeneous Systems


text:
Linear Algebra/General Systems

Consider the system of m equations

$$a_{11}x_1+a_{12}x_2+a_{13}x_3+\ldots+a_{1n}x_n=b_1$$ $$a_{21}x_1+a_{22}x_2+a_{23}x_3+\ldots+a_{2n}x_n=b_2$$ $$a_{31}x_1+a_{32}x_2+a_{33}x_3+\ldots+a_{3n}x_n=b_3$$ $$\vdots$$ $$a_{m1}x_1+a_{m2}x_2+a_{m3}x_3+\ldots+a_{mn}x_n=b_m$$

and the matrices

$$A=\left(\begin{matrix} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{m1}&a_{m2}&\cdots&a_{mn} \end{matrix}\right)$$

$$A_1=\left(\begin{matrix} a_{11}&a_{12}&\cdots&a_{1n}&b_1\\ a_{21}&a_{22}&\cdots&a_{2n}&b_2\\ \vdots&\vdots&\ddots&\vdots\\ a_{m1}&a_{m2}&\cdots&a_{mn}&b_m \end{matrix}\right)$$

Kronecker-Capelli Theorem
The general system of linear equations has a solution if the rank of A is equal to the rank of A1, and has no solution if the rank of A is less than the rank of A1.

Proof
The system of linear equations has a solution only when the last column of A1 is a linear combination of the other columns. If that is so, then by a theorem proven earlier, the column span of A is the same as the column span of A1, so their ranks are the same. Now, suppose that their ranks are the same. Then the basis columns of A also form a basis column of A1 since they have column spans of the same dimension. Thus, their column spans are the same, and so the last column also belongs to the column span of A, and so is linearly dependent on the other columns, this linear dependence is the solution to this system of equations. Suppose that the rank of A1 is greater than A. This implies that Another proof is if we sopose that the rank of A is r, so if b is linear with {a1,a2....ar} it proof that the rank of {a1,a2...ar,b} is r,so the theorem is solved, But if the b is not combination with system (a1,a2.....ar),it means that the system (a1,a2...ar,b) is a base of system (a1....an,b), if we atach any ai/r<i<n,the system (a1,a2...ar,b,ai}is linear it mean that system (a1,a2.....ar,b)is a base of {a1,a2.....an.b),so the rank of (a1,a2.....an,b)is equal with Rank(A)+1. So we can not solve the system,

title: Linear Algebra/General Systems


text:
Linear Algebra/General Solutions

Suppose we have a general system of linear equations, and consider its basis columns by its coefficient matrix. Subtract the variables corresponding to those columns from both sides. The remaining variables can be solved using Cramer's rule using the determinants formed by its basis minor.

title: Linear Algebra/General Solutions


text:
Horticulture/Veratrum viride

Veratrum viride (Indian Poke, Indian Hellebore,  False Hellebore, Green False Hellebore) is a woodland herbaceous plant native to eastern and western (but not central) North America. It is extremely toxic, and is considered a pest plant by farmers with livestock. The species has acquired a large number of common names within its native range, including American False Hellebore, American White Hellebore, Bear Corn, Big Hellebore, Corn Lily, Devils Bite, Duck Retten, Indian Hellebore, Itch-weed, Itchweed, Poor Annie, and Tickleweed.

It is a herbaceous perennial plant reaching 0.7-2 m tall, with a solid green stem. The leaves are spirally arranged, 10–35 cm long and 5–20 cm broad, elliptic to broad lanceolate ending in a short point, heavily ribbed and hairy on the underside. The flowers are numerous, produced in a large branched inflorescence 30–70 cm tall; each flower is 5–12 mm long, with six green to yellow-green tepals. The fruit is a capsule 1.5–3 cm long, which splits into three sections at maturity to release the numerous flat 8–10 mm diameter seeds. The plant reproduces through rhizome growth as well as seeds.

There are two varieties:
 * Veratrum viride var. viride. Eastern North America. Side branches of inflorescence erect or spreading.
 * Veratrum viride var. eschscholzianum (Roemer & Schultes) Breitung. Western North America. Side branches of inflorescence drooping.

The related western North American ../Veratrum californicum/ (White False Hellebore) can be distinguished from sympatric var. eschscholzianum by its whiter flowers, with erect side branches of the inflorescence.

Distribution and habitat
In eastern North America, var. viride occurs from southwestern Labrador and southern Quebec south to northern Georgia. In the west, var. eschscholzianum occurs from Alaska and Northwest Territory south through Yukon, British Columbia, Alberta, Washington, Idaho, Montana, and Oregon to northern California.

It is found in wet soils in meadows and open forests, from sea level in the north of the range, up to 1,600 m in the southeast and 2,500 m in the southwest.

Medicine
The plant is highly toxic, causing nausea and vomiting. If the poison is not evacuated, cold sweat and vertigo appears. Respiration slows, cardiac rhythm and blood pressure falls, eventually leading to death. It is used externally by several Native American nations for external treatment. Although is rarely ever used modern herbalism due to its concentration of various alkaloids, it has been used in the past against high blood pressure and rapid heartbeat. The root contains even higher concentrations than the aerial parts.

The plant was used by some tribes to elect a new leader. All the candidates would eat the root, and the last to start vomiting would become the new leader.

title: Horticulture/Veratrum viride


text:
Physics Exercises/Kinematics in 2-3 Dimensions/Solutions

Without Calculus

 * 1) The most important thing to notice in this problem is that there is no force in the horizontal direction: so there is no horizontal acceleration, and therefore the horizontal velocity is constant.
 * 2) From trigonometry (draw a figure and find the right triangle with) $$v_x = v_0 cos(\theta)$$.
 * 3) Same as above, $$v_y = v_0 sin(\theta)$$.
 * 4) Because $$a_x = 0$$, $$v_x = v_0 cos(\theta)$$.
 * 5) Note that at the top, the cannon ball is neither moving higher or lower (by definition), so the vertical velocity must be: $$v_y = 0$$.
 * 6) Again, because $$a_x = 0$$, $$v_x = v_0 cos(\theta)$$.
 * 7) One easy way to find this is by symmetry. In general (esp. if the final height is not the same as the initial height), we can use conservation of energy (but you most likely haven't learned this yet). $$v_y = -v_0 sin(\theta)$$. The negative sign denotes the downward direction.
 * 8) This problem uses what is called Galilean relativity. Arithmatics used here are approximately correct only at speeds much less than speed of light, c, which is correct for every day objects.
 * 9) 5 km/h. Keep in mind that velocity is a vector, and add two velocities vectorially. By the Pythagorean theorem, her speed relative to shore is given by: $$v = \sqrt{v_{\mathrm{boat}}^2 + v_{\mathrm{walk}}^2}$$ .  Plugging in the given numbers yields the answer above.
 * 10) 53.1 deg. The easiest way to see this is by drawing two vectors tails together (so that you can see the triangle). The angle, which is the angle between the sum of two vectors and the direction north, can be found in terms of inverse tangent of ratio of the legs: $$\theta = \arctan(4/3)$$, which has the approximate value given above.

With Calculus

 * 1) This problem is more or less a calculus exercise (which is why we told you to ignore units for this problem—it's not very physical).
 * 2) Remember speed is the scalar quantity equal to the magnitude of the velocity vector. Use the Pythagorean theorem to calculate the magnitude: $$v(t) = \sqrt{(sin(t))^2 + e^{2t}}$$.
 * 3) For this, remember that in general, $$x(t) = \int_0^t v(t) dt'$$. Performing the integral separately for each perpendicular direction gives: $$\vec{x}(t) = -cos(t)~\hat{x} + e^t~\hat{y}$$. Here, the integration constant is zero because we start out at origin.
 * 4) Remember that acceleration is also a vector quantity. This is same as above, except this time, you perform a derivative, since $$\vec{a} = \frac{d\vec{v}}{dt}$$. After the differentiation, we get: $$\vec{a}(t) = cos(t)~\hat{x} + e^t~\hat{y}$$.


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User:Dureo

I am Dureo on En.wiki also.

Interests

 * Computers
 * electrical technology
 * Gaming
 * Everquest retired, Level 75 Monk, 75 Shaman, 75 Ranger, 3 accounts, triple boxer(Tarew Marr -> Drinal)
 * World of Warcraft retired, Level 70 Hunter, 70 Rogue, 70 Pally, all on same account, no need to multibox(Icecrown)
 * Stints on Dark Age of Camelot and Star Wars Galaxies. I didn't pay past the first free month though.
 * Reading
 * anything I can get my hands on, really big on Richard Dawkins work at the moment. I also collect books, more books than I know what to do with. I have a beautiful copy of this 1875 US History book... though it isn't all that current :P, and I have this older geometry text, in fairly good condition. I also have every textbook I used during high school I graduated in 2001(with the schools permission, as they threw them out over time I was offered copies.) I also have numerous older California Vehicle Code and Penal Code books from various years including 1947 and 1959.

 * I have a large fascination with Snakes and have 6 of them at the moment, they are listed here:
 * 2.1.0 Ball Python (Python regius)
 * Herbie(adult), Jada(adult), and unnamed male(juvenile) no strikes.
 * 0.1.0 Green Anaconda(Eunectes murinus)
 * Steve (juvenile) 1 bite, numerous strikes.
 * 0.0.1 Kenyan Sand Boa (Gongylophis colubrinus)
 * Erasmus (adult) 1 bite(did not break skin), 1 strike.
 * 0.1.0 Red-tailed Boa (Boa constrictor constrictor)
 * Algernon (adult) 1 bite, 3 strikes.

 * I am an Eagle Scout in the Boy Scouts of America, this was my project(a water fountain at the local YMCA walking track) [[Image:Eagle Scout project completed at the local YMCA in Corcoran, California.jpg]]

title: User:Dureo


text:
User:Kartiksura/monobook.js

document.write(' ');

title: User:Kartiksura/monobook.js


text:
Horticulture/Viburnum prunifolium

Viburnum prunifolium (Blackhaw, also spelled Black haw, Blackhaw Viburnum, or Stag Bush), is a species of small trees or large shrubs native to southeastern North America, from Connecticut west to eastern Kansas, and south to Alabama and Texas.

Description
It is a deciduous shrub or small tree growing to 2–9 m tall with a short crooked trunk and stout spreading branches; in the northern parts of its range, it is a shrub, becoming a small tree in the southern parts of its range. The bark is reddish-brown, very rough on old stems. The branchlets are red at first, then green, finally dark brown tinged with red. The winter buds are coated with rusty tomentum. The flower buds ovate, 1 cm long, much larger than the axillary buds. The leaves are simple, up to 9 cm long and 6 cm broad, oval, ovate or orbicular, wedge-shaped or rounded at base, serrate, acute, with serrated edges with a grooved and slightly winged red petiole 1.5 cm long; they turn red in fall. The leaves are superficially similar to some species of ../Prunus/ (thus "prunifolium"); they come out of the bud involute, shining, green, tinged with red, sometimes smooth, or clothed with rusty tomentum; when full grown dark green and smooth above, pale, smooth or tomentose beneath.

The flowers are creamy white, 9 mm diameter; the calyx is urn-shaped, five-toothed, persistent; the corolla is five-lobed, with rounded lobes, imbricate in bud; the five stamens alternate with the corolla lobes, the filaments slender, the anthers pale yellow, oblong, two-celled, the cells opening longitudinally; the ovary is inferior, one-celled, with a thick, pale green style and a flat stigma and a single ovule. The flowers are borne in flat-topped cymes 10 cm in diameter in mid to late spring. The fruit is a drupe 1 cm long, dark blue-black with glaucous bloom, hangs until winter, becomes edible after being frosted, then eaten by birds; the stone is flat and even, broadly oval. Wherever it lives, black haw prefers sunny woodland with well-drained soil and adequate water.

Uses
It has both value in the pleasure garden, providing good fall color and early winter provender for birds, and medicinal properties.

It has hybridized with ../Viburnum lentago/ in cultivation, to give the garden hybrid ../Viburnum × jackii/.

The wood is brown tinged with red; heavy, hard, close-grained with a density of 0.8332.

Medicinal uses
For centuries, black haw has been used for medical purposes, mainly for gynecological conditions. The bark is the part of the plant used in treatments.

The active components include scopoletin, aesculetin, salicin, 1-methyl-2,3 clibutyl hemimellitate, and viburnin. Tannin is another chemical component of black haw.

Native Americans used a decoction of black haw to treat gynecological conditions, including menstrual cramps, aiding recovery after childbirth, and in treating the effects of menopause. As a folk remedy, black haw has been used to treat menstrual pain, and morning sickness. Due to its antispasmodic properties, the plant may also be of use in treating cramps of the digestive tract or the bile ducts.

Black haw's primary use was to prevent miscarriages. American slaveholders also used the plant to prevent abortions. Slaves were a valuable asset, and their owner also owned their offspring, so ensuring that female slaves gave birth was of paramount importance. In defiance, some slave women would attempt to use cotton seeds to cause a miscarriage. The slaveowners would therefore force pregnant slaves to drink an infusion of black haw to prevent that.

The primary use of black haw today is to prevent menstrual cramps. The salicin in black haw may also be of use in pain relief.

Safety issues
As black haw contains salicin, a chemical relative of aspirin, people who are allergic to that substance should not use black haw. In addition, due to the connection between aspirin and Reye's syndrome, young people or people afflicted with a viral disease should not use black haw.

The chemicals in black haw do relax the uterus and therefore probably prevent miscarriage; however, the salicin may be teratogenic. Consequently, pregnant women should not use black haw. Furthermore, anyone using herbs for medical reasons should only use them under the supervision of a qualified medical professional.

Black haw is not on the FDA's "generally recognized as safe list".

title: Horticulture/Viburnum prunifolium


text:
Horticulture/Phlox paniculata

Phlox paniculata is an herbaceous perennial widely grown for its showy panicles of large, sweet-scented flowers borne from early summer through autumn.

Description
The plants are clump-forming and erect, with terminal panicles of trumpet-shaped flowers. Flower colors vary from white through pink, red, purple, and nearly blue.

Growing Conditions
Performs best in full sun with humus-rich, well-drained soils.

Varieties
Numerous varieties are available in the trade. Modern cultivars have been selected for resistance to powdery mildews.

Uses
Grown for the showy flowers, which are also attractive to both hummingbirds and butterflies. Flowers hold up well in the vase as well.

Maintenance
Deadheading encourages rebloom.

Propagation
Self-sows readily. Cultivars are generally reproduced by cuttings or tissue culture.

Pests and Diseases
Powdery mildew is a serious issue for this species. See ..Phlox/ for a list of pests and diseases affecting the genus.

title: Horticulture/Phlox paniculata


text:
Talk:Study Skills

=Ideas=

=Techniques=

=Suggestions=

=Comments=

I'm planning to pull some of the wiki content that we use for study skills in other sources onto this page. If I can find the time to do it, this should lead to some significant changes over the next 6 months. If anyone's involved in managing this page and wants to touch base with me, could you please comment on this blog post - http://massageonline.wordpress.com/2008/10/07/study-skills/ ? Cheers --202.49.0.2 (talk) 22:06, 7 October 2008 (UTC)

Hey this place looks pretty good already. It's definately not "struggling" anymore. Are there any other people who take regular care of this Wikibook? GoodStuff 13:34, 26 Oct 2004 (UTC)

I have seen a good 'Dutch' book on this subject. It's going to take a while to summarise it (translating into English won't be that tough though). Carry On --83.116.2.193 13:15, 21 Nov 2004 (UTC)

 * Looked good until: "If you come to an essay question that you are not prepared for, you can try stating that you weren't prepared for it, and then substitute in its place an equally difficult question for which you WERE prepared and answer that instead. The idea is to demonstrate the strong points in your absorption of the material, rather than allow yourself to be penalized by what you don't know". THIS IS THE ONE THING YOU MUST NEVER DO! Never try to answer a question that is not asked. The result will only be that the examiner ignores all your hard work, as it was a question that was not set! If no one has any objections within a week, I propose to delete this rubbish. Any standardised, decent exam will have a syllabus and the questions will stick to that syllabus --Mark Lewis 18:00, 12 Jan 2005 (UTC)

honey-tongue
Someone needs to explain the "honey-tongue" technique. I added a link to wikipedia a while back, hoping someone would explain it, but not so far. --160.36.156.243 22:38, 3 Feb 2005 (UTC)

 * This book currently says
 * "honey-tongue" Cicero used this technique thousands of years ago to memorize his...

 * At first I, like the anonymous writer above, thought this was introducing the next technique, meaning "Cicero used the "honey-tongue" technique ...".
 * But now I'm starting to think it's a continuation of the previously-mentioned technique, and the original author meant something more like "This technique was also used by the smooth-talking Cicero ...", where "honey-tongue" is merely an adjective describing Cicero, and "this technique" refers to the previously-mentioned method of loci.
 * That interpretation seems consistent with the mention of Cicero at art of memory.
 * There's no such thing as a "honey-tongue" memorization technique, right? --DavidCary (talk) 22:29, 10 December 2009 (UTC)

I think It's Enough
Hello! Sorry that i'm not logged in but although you can click on the link for my Wikibook user page Mastermind 007. The thing I wanted to say was that you can remove the link of Study Skills from "Requested Wikibooks" because it looks fine and it's enough to teach one how to guide himself for studies especially. I'll add your Wikibook as an external link in "How To Become A Good Student" & you can make it a little formal (language). Have a good day!

Clean up
Can this be divided up into subpages for easier reading? Pufferfish101 03:14, 28 February 2006 (UTC)
 * Necroing this a over 15 years later, but done! --Mbrickn (discuss • contribs) 06:19, 31 October 2021 (UTC)

title: Talk:Study Skills


text:
Talk:Circuit Idea/Why Creative Persons are Unhappy

I would like to start the discussion about relations between creative and ordinary thinking people by citing a short text that I have moved from the Wikipedia Virtual ground discussion page. Circuit-fantasist (talk) 17:58, 25 December 2007 (UTC)

(moved by Circuit-fantasist from Wikipedia Virtual ground discussion page)

...People (especially those that have managed to advance in life and to hold a high position) do not like someone (especially staying below them) to express own ideas even if they are more than obvious. This upsets their mental equilibrium and they react to this "intervention" trying to redress the balance exactly as an op-amp reacts to any intervention to virtual ground:) Contrary, people adopt willingly, use and benefit from nobody's ideas. I have known this truth from my experience since I have been bearing the reactions of people around me through my life... Circuit-fantasist 08:07, 19 December 2007 (UTC)

The text below is copied from Wikipedia Voltage-to-current converter talk page. Circuit-fantasist (talk) 18:15, 22 May 2010 (UTC)

... You and your likes have cognitive, emotional and moral problems predestining your behavior here, in Wikipedia. Your great problem is that you do not see the concepts behind circuits; you do not see the forest behind the trees. You know perfectly the specific circuit implementations but you can't generalize them into a functional block-diagram and a universal operational algorithm. Simply, you know circuits but you do not understand them; as a result, you can't explain them to readers so that they to understand them. The main reason for this behavior is your unwillingness to see the existing connection between apparently different phenomena (both electrical and non-electrical) in this world, to establish associations between them, to use analogies...

Besides this cognitive problem you have emotional problems as well. Actually, you do not like circuits; circuitry is more job than favorite pursuit for you. Contrary to you, I like circuits and great ideas behind them; I love them; I adore them. Circuitry is my vocation, my pet pursuit. I created this page three years ago with plenty of love placing all the best of my abilities here. To show the truth behind these legendary circuits, I show their evolution from passive to active version: first, I have introduced passive versions looking at Ohm's law from two points; then, I have considered their imperfections and finally, I have found a remedy converting the passive versions into active ones. Later, I realized that, in this form, the article did not match the specific encyclopedic Wikipedia style and it had to be rewritten. Then I gave this opportunity to wikipedians and began creating a series of Circuit idea stories about them (1, 2, 3, 4 and 5). I agree with you the form has to be changed but the main points of the content have to be kept. As all you can (already) see, both the V-to-I and I-to-V op-amp inverting configurations are based on the same powerful Miller's idea - modifying (zeroing) the impedance by adding a proportional voltage. I have discerned this common great idea in these specific circuits and I would like to share this simple truth with people. Will you keep it in your "about 3 paragraphs"? No, you will remove it; you will remove the truth about these circuits and will leave only banal, specific and formal "explanations" that do not explain anything; you will hide the forest behind the trees.

You have boasted of your famous tutors at university. Well, it is wonderful that they were teaching perfectly circuit analysis to their alumni. But it would be also very well if they were showing concepts behind circuits and finally, if they were bringing up some elementary human ethics to them. Because, if you had such morals, when encountering a mind that excels (in some respect) yours, you would not consider his/her success as your unsuccess; you would not destroy else's creations or (worse) instigate stupidity and mediocrity to do this and then enjoy seeing the results... You would try to rise to his/her level instead to pull down him/her to your level; you would admire his/her achievements; you would join and improve them (what is the great Wikipedia idea); you would be wikipedian, not the opposite. If you respect the elementary Wikipedia ethics, you would restore the link to the most popular op-amp Miller integrator or current integrator in the Miller effect page that you have removed absolutely intentionally. Circuit dreamer...


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Talk:Circuit Idea/How Do We Swap Circuit Inputs and Outputs?

In order to provoke discussion about the unique feature of negative feedback to reverse the causality in circuits, I have extracted here a part of correspondence between me and Gordon Deboo (the inventor of Deboo integrator). Circuit-fantasist (talk) 19:54, 25 December 2007 (UTC)

From: Gordon Deboo To: "Cyril"  Sent: Tuesday, October 09, 2007 3:34 PM Subject: Re: Deboo Integrator

... Looking at a problem in a different way can sometimes lead to new ideas. Just to give a simple example (Fig. 1), consider the attenuator (Figure a) and the well-known non-inverting amplifier (Figures b and c) shown in the pdf attachment.

The equation (4-1) for the attenuator shows that the input voltage V1 is attenuated to V2 depending on the values of the two resistors. Equation 4-1 can be solved for V1 as in Equation 4-2, where V1 is great than V2, so that amplification has occurred. Of course this can’t happen with two resistors because it would involve the creation of energy. However, if the required energy is supplied from an external source, such as an operational amplifier (resulting in a  conventional non-inverting amplifier as in Figure b, more usually  drawn as in Figure c) the equation can be satisfied.

I often manipulated circuits in this way, drawing a “box” with the input and output I required and then figuring out what I needed to do to get the desired result. This may seem obvious, but the idea was think about supplying energy to an attenuator to make it an amplifier after rearranging the equation told me what was needed. This type of thinking can enable one to create...

Gordon Deboo California

From: Cyril Mechkov To: Gordon Deboo Sent: Saturday, October 13, 2007 8:32 PM Subject: How to reverse circuit ports by applying negative feedback (Re: Re: Deboo integrator)

Dear Gordon,

Reading your last email, I was deeply struk by your idea of how to transmute a voltage divider into a non-inverting amplifier. Will you believe me that for the first time I consider a valuable circuit idea with someone? Today's people do not like to think about fundamental ideas and principles. Every time when I tried to discuss some basic circuit idea I run upon the rocks...

Surprise. Imagine my amazement when I was reading your excellent explanations (I suppose that the scanned page is from your book) because the same great idea conceived in my mind in the early 1990s! Then I was writing down (regrettably, in Bulgarian) all the ideas arising in my mind on squared sheets of A5 paper. I have scanned especially for you the yellowed record that I made on May 14, 1992 at my home (I was writing the circumstances surrounding the recorded idea on the top of the sheet; now, I continue doing the same).

"Reversed" voltage divider. This is the title of the record, which is eloquent; the drawing too. As you can see, I have drawn (likewise you on Fig. b) the circuit with an unusual shape to show the basic idea in the best way; also, I have colored the added op-amp in a different blue color. The idea is the same: to make the passive voltage divider work conversely we supply it by an additional (properly supplied) op-amp that observes the difference between the divider's output voltage and the actual input voltage. As a result, the op-amp adjusts its output voltage Vout so that an R2/(R1 + R2) part of it to be equal to the input voltage Vin. Thus, the old output voltage VR2 is always equal to the new input voltage Vin; the old divider's input voltage serves as a new output voltage Vout = (R1 + R2)/R2.

Mechanical analogy. On another sheet, I have described a lever analogy of a non-inverting amplifier that exploits the same powerful idea. A man is looking continuously at point A (the output of the "lever divider") and is comparing its height Hin' with the input height Hin. If there is a difference between them, the man moves the end of the lever (the point B) to make Hin' = Hin. As a result, Hout/Hin = (l1 + l2)/l1. By the way, this second-class lever analogy is more truthful than the third-class lever analogy of non-inverting amplifier presented by Tony Kuphald in his Lessons in Electric Circuits.

Human analogies. Thinking about the essence of this phenomenon, I began discerning similar manifestations in many everyday situations (some of them -quite funny:) Secretary > boss. Imagine a male chief that has a beautiful female secretary (or v.v.:); so, he indulges the pretty woman satisfying all her wishes. As a result, the boss thinks that he manages the secretary but, actually, the secretary leads the chief by the nose:) Wife > husband. Similarly, husbands that indulge their wives think that they manage their wives; actually, wives manage their husbands:) Generally speaking, women lead men by the nose in this world:)

Cat > owner. I am also a victim of this phenomenon. I think that I manage my (female) cat Futie; but giving a portion of food to "her" every time when "she" says "miaou" actually, the cat leads me by the nose:(

Generalization. Finally, I made a general conclusion that systems with negative feedback have the unique property to reverse the cause and effect relations between the input and output quantities of the objects. In this way, they can "reverse" the objects. Imagine a block diagram where a converter implementing a function y = f(x) is connected in the feedback loop; as a result, the whole nfb system will implement the reverse function Y = F(X), where Y = x, X = y and F = 1/f.

Applications. For our purposes in electronics, we can use this technique to swap the converter's ports (especially of the one-way devices) by connecting them into the feedback loop. From this viewpoint, an active voltage-to-current converter is actually a reversed passive current-to-voltage converter, an op-amp non-inverting amplifier is a reversed voltage divider (your idea), an op-amp integrator is a reversed differentiator and v.v., an op-amp logarithmic converter is a reversed antilogarithmic converter and v.v., an analog-to-digital converter is a reversed digital-to-analog converter, etc. Another very interesting example is a transdiode that is actually a transistor connected in the op-amp feedback loop; in this odd and never explained circuit configuration, the collector current is the input quantity (?!?) while the base-emitter voltage is the output quantity (?!?) Maybe, the same trick is used in the input part of a current mirror - the active diode, which is actually a transistor with parallel negative feedback (again, although it seems strange, the collector current serves as an input quantity while the base-emitter voltage serves as an output quantity)...

Popularization. Gordon, I am sure you will say "Oh" when you see the picture below (Fig. 5):) Here is the story about it.

In the end of 1990s, I prepared a series of 22 short 1-page articles under the title How to invent circuits. I designed them for Popular electronics (later Poptronics) magazine. Only, Poptronics ceased and I refused all the print undertaking and moved to the web. A few years later I put all the ready stories into a pdf file. As you can see, the story on the page 14 (with a title Compensating by injecting a current) is dedicated to your great integrator. The last story (Let's reverse causality!), which is not completed, is dedicated to the present idea. See the picture on the right - it is exactly as your picture! Is it not amazing that the same idea and the same picture can conceive in different minds? Below the left figure is written in red "a normal divider"; above the right figure is written "a reversed divider".

In the beginning of 2000s I began creating circuit-fantasia.com. Then I included this basic idea in a hierarchical circuit idea classification (time was when I was thinking that this collection was my supreme achievement but others were not thinking as me; so, I did not obtain the recognition that I had expected). Later, I used this technique (likewise you) as a possible way to "invent" the non-inverting amplifier. By the way, another possible way of "inventing" is to "disturb" an op-amp voltage follower by putting an attenuation R2/(R1 + R2) into the feedback loop. As a result, it "reacts" to this intervention by (R1 + R2)/R2 amplification (see Class Exercise 8: Op-amp Amplifiers with Negative Feedback). I have named this great principle "attenuation causes amplification". Actually, it represents the main property of negative feedback systems to compensate disturbances).

Circuit idea. I have reserved a special place for this "reversing causality" phenomenon in the contents of Circuit idea (see the section about negative feedback). I imagine that this part has to contain an introductory "philosophical" story and a series of specific stories dedicated to various circuits based on this idea. I would like to include in some way your materials in these stories. There are a lot of possibilities to do that.

For example, you can develop a story about "inventing" a non-inverting amplifier based on your idea exposed on the scanned text. It may consist of a text based on the image or a few paragraphs and the very scanned image included. If you do not want to do that, I might cite your text and include the original image into the story. Or, I can share with readers in the discussion page how I thought that... but ...

Gordon, believe me, your way of thinking in this material is even more valuable than the same idea. Thinking in this way, young people can invent new circuits. But yet, have you reveal this great idea? Have you written this text (I mean the scan)? Is this published and where? Can I place a link pointing to the source where it is published? It is extremely useful for Circuit idea, if you send me more clever circuit ideas...

Circuit-fantasist (talk) 18:39, 25 December 2007 (UTC)

See also: A 2007 e-mail exchange with Asst. Professor Cyril Mechkov, Technical University of Sofia, Bulgaria (created by the very Gordon Deboo)


text:
Talk:More C++ Idioms/Move Constructor

I think that the wording "temporaries are const objects by default" is incorrect. If this was true, then it wouldn't be possible to do "this->resource_ = 0" in operator proxy, because code that modifies a constant object has undefined behavior.

The real reason for auto_ptr-style workaround is that function calls (temporary objects holding return values) are rvalues (C++98 standard, 5.2.2#10: "A function call is an lvalue if and only if the result type is a reference"), and rvalues can only be bound to const references (8.5.3#5).

The result is that one can implement move semantics by tricking this artificial limitation without using debatable techniques such as const_cast. The new C++09 standard will introduce rvalue references, which will make the workaround unnecessary.

title: Talk:More C++ Idioms/Move Constructor


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User:Citizencontact

Daniel Bennett Working on using XML Query language to explain and develop prototype sites for the legislative branch/U.S. Congress.

title: User:Citizencontact


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User:TakuyaMurata/SandBox

Lemma 1:

Lemma 2: Suppose P is elliptic. If Pu \in D^(s) (\Omega) and Pu = 0 in \Omega, then u satisfies the condition (i).

title: User:TakuyaMurata/SandBox


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Ancient History/Greece/Minoan Civilization

The Minoans were a Bronze Age civilization that flourished on the Greek Aegean island of Crete from around 3000 to 1450 BCE. From around 1450 BCE the Minoan palace culture began to collapse and the vacuum was filled by the Greek mainland Mycenaean culture whose ascendancy is mythologized in the story of King Agamemnon who led the Greek expedition to Troy. The name Minoan was coined by the British archaeologist Sir Arthur Evans, who from 1900 to 1906 excavated the palace at Knossos, which he believed to be the capital of the empire of the mythical King Minos.

History
Greek archeologist Nikolaos Platon devised a chronology of the civilization based on excavations of Minoan palaces. He divides the civilization into the following eras:

Prepalatial period (3000-1900)
Archaeological evidence shows that Crete may have been inhabited as early as the seventh millennium BCE. New settlers skilled in metallurgy arrived by the end of the fourth millennium BCE, and replaced the earlier Neolithic peoples.

Protopalatial period (1900-1700)
The first large palaces, most notably at Knossos and Phaistos, were built during the Protopalatial period, leading to more urbanized life and centralized political authority. Around 1700 BCE the major palaces were all destroyed perhaps due to natural causes, such as an earthquake, or perhaps an invasion from Anatolia.

Neopalatial period (1700-1450)
After their destruction, the palaces soon were rebuilt, giving rise to the Neopalatial period. This period represents the apex of Minoan civilization. Population increased, new settlements were built, and impressive art, architecture, and technologies (such as plumbing) were developed. Despite these many advances, the Minoans suffered some sort of catastrophe around 1450.

Final Palace period (1450-1380 BCE)
Many theories have been put forth to the cause of this sudden and rapid decline. Theories include a massive volcanic eruption of Mt. Thera on the nearby island of Santorini, internal strife, or an invasion of the Mycenaeans from mainland Greece. A combination of these factors may be reason for the Minoan collapse. Minoan power and influence in the region had effectively ended by 1420 BCE supplanted by the Mycenaeans. Excavations reveal that pottery and writings from Crete after 1450 resemble those of mainland Greece more so than those of pre-1450 Crete. Knossos then served as the administrative center of Mycenaean Crete, until it was destroyed by fire in 1380.

Post Palatial period (1380-1100 BCE)
After the destruction of Knossos, economic and political influence shifted to the town of Khaniá. Despite this, Cretan civilization began to further decline, and many Minoan sites were abandoned. Hondros is one of few new sites to be settled during this period. The last Minoan site to fall was the isolated mountain town of Karfi, which was able to resist assimilation into the Mycenaean culture until the early Iron Age. The widespread use of iron tools (brought by the Mycenaeans) rather than bronze ones (used by Minoans) is one of the main indications archaeologists used to determine the date of the final Minoan collapse.

Culture
The Minoan culture featured a very distinctive religion, art style, and language. The Minoans were also pioneers in naval exploration, establishing several colonies on the Greek mainland and other Aegean islands, such as Akrotiri on Thera. The Minoan cultural influence spread throughout the region, including over the Mycenaean culture.

Religion
Many conclude there to be evidence of animal and human sacrifice in Minoan Crete during the palatial period. Recent Minoan scholars have disputed the ideas and the focus’ of past Scholars. However, these sources are blurred and we should not come to any conclusions as yet, to whether sacrificial rituals did exist in Minoan Crete.

Although the Minoan religious system had come under much consideration and debate, it had never been fully explored or written about in much depth. That is until 1921 when Sir Arthur Evans wrote his works on Minoan religion. Evans portrayed Crete as having an interconnection and an oneness. This was sustained by the idea of them all worshiping one god and this “culture as a whole…shows an essential unity,” (Arthur Evans PM 1:13) portraying the culture as a whole was more important than sacrificial rituals. Evans is known as the advocator of this idea of unity and worship of a sole God. However, Minoan Crete was the perfect example for one to take and write about as it was secluded from other cultures as a lone island. However, though you could infer this there is evidence of them having a key trading port as in the ‘flotilla fresco,’ it clearly shows many boats leaving from Crete.

You could infer there to be evidence of them only worshiping one God, as there is what looks like a Neolithic figurine of a goddess. This source is provided to us by the Spartan Museum. It portrays a woman holding two snakes suggesting her divineness, as it is believed to be a goddess. The significance of the snakes around the arms is widely unknown however, they have survived for decades and in great numbers which shows the significance of it. The importance of sacrificial rituals is colossally important to link with them only worshiping one god. This is due to polytheistic cultures utilizing sacrifice, for example, Rome in order to gain favor with the gods. However, there is insufficient evidence to draw conclusions. This is due to her coming across as if she is in an altered state, holding in both hands snakes which highlights the unreliability of this theory. In the temple, there were also many objects and another woman in the surrounding picture. One object shows a bowl/vase suggesting libation either from or to one or the other woman. However, in this image, we see no evidence of any type of animal sacrifice.

In the Toreador Fresco currently placed in the Palace of Knossos, there is what looks like an image of three men and a bull. We should assume that “every depiction of a bull on a seal or fresco is to be associated with a supposed sacrificial ritual,” (Cromarty, 2008,). However, it could also be a depiction of a sequence in changing a young boy into a man. This is due to the end figure being more pronounced than the others suggesting adulthood.

Another example of sacrifice is labeled a sacrifice by the Agia Triada sarcophagus. This pictorial image shows a slaughtered bull in the middle with two terrified animals under it. We should take into account the double axe which is normally associated with bull sacrifice. Another interesting aspect is the appearance of a woman in this image as well. This has become a reoccurring theme throughout Minion Crete. We see her hovering her hands over what appears to be an animal of the bovine variety which suggests prayer and worship. It also presents her as a priestess rather than a goddess which proves controversy towards the Neolithic figurine of a goddess we believed we previously saw.

Of late it is to be believed that Archaeologists have found evidence of a sacrificial ritual, which included the sacrifice of animals, whose broken bones were found under a deposit of rubble. This was along with a woman’s bones being found which links back to the priestess’s conduction of the religious ceremonies and rituals. However, I quote from Maria Andreadaki Vlazaki “We have yet to reach a final conclusion since the bones need to be studied further, especially as the latest finds, which include the woman’s skull, were found only recently.” This causes problems due to the unknown fact of what time these people lived in and as to whether it was around the time period being studied.

Though sacrificial rituals were an important part of the religious system there were many other important parts to it as well. Many outdoor shrines have been discovered some in caves, others on hill tops. There are depictions of women dancing around the trees, shaking the branches suggesting a sort of religious ceremony, further highlighting the role woman played. Household shrines and shrines at tombs have also been discovered and this presents a real religious background to Minoan Crete. Artifacts indicate that religious practice involved dance, procession, sacrifice, and offerings, which were all key factors of the religious system. To further the theory of processions occurring or ceremonial events we gain and insight in the Saffron Gatherers fresco. This pictorial image shows two clear women dancing around a monkey (cannot be confirmed) type figure. This further amplifies their role as they have appeared numerous times in sources.

Art
Excavations have revealed frescoes, statues, and pottery. Pottery was the dominant art form of the Minoans from their arrival on Crete up until the Neopalatial period, when pottery-making technology allowed for a standardization of design. Fresco-painting soon rose in prominence, and focused heavily on religious and naturalistic themes. Bulls and snakes, both religious symbols, featured prominently in many works of art, as do other non-religious animals. Perhaps the most famous of the Minoan frescoes is one depicting the religious ritual of bull-leaping, which was found in the palace of Minos. Interestingly, no frescoes depict any of the many gods.

Architecture
Minoans also pioneered many architectural methods. Cities featured roads paved with stone, sewers, and plumbing. The most-recognized type of Minoan architecture is the palace. The construction of the first palaces (the famous palace at Knossos was one of the first) ended the Prepalatial period. Palaces were centers of government, allowing the dozens of individual communities to come under centralized political authority. Palaces also were used to store crop surpluses, and were house shrines to goddesses.

Economy
The Minoan economy was very diverse. Several crops were cultivated, such as wheat, barley, grapes, olives, and figs. They raised several animals, including cattle, goats, and pigs. Bees were kept for honey production, as were donkeys and oxen for plowing purposes. The Minoans also had an established shipping industry, as evidenced by the many colonies they established throughout the eastern Mediterranean. They were involved in the tin trade. As bronze tools and weapons made from tin and copper were replaced by superior iron ones the Minoan economy in trading tin declined. Their trade network extended from Mesopotamia and Egypt all the way to Spain.

Language
Minoan civilization featured several written languages. During the Prepalatial period, a primitive hieroglyphic script was used, but fell out of use by 1700. A writing system called Linear A developed during the Protopalatial period, and continued to be used through the Neopalatial period. Linear A featured many symbols, each of which represented a syllable, word, or number. Linear A was used for record-keeping, and some religious functions. Linear B was the script used for government records. After the Mycenean conquest, Linear A was replaced by Linear B, which would eventually evolve into what is now the modern Greek language. Linear B was deciphered in the 1950s, but Linear A and the hieroglyphic texts have yet to have been completely translated.


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Talk:Circuit Idea/Parallel Connected Negative Resistor

Starting the discusiion
I would like to start the discussion about this exotic negative resistance application by inserting my comment to the EDN's article Negative-Resistance Load Canceller Helps Drive Heavy Loads. In this story I have revealed the secret behind negative resistance phenomenon and its most popular implementation - negative impedance converter (NIC). Circuit-fantasist (talk) 08:16, 26 December 2007 (UTC)

A reader's comment to a relative EDN's article
(reader's comment to the EDN's article Negative-Resistance Load Canceller Helps Drive Heavy Loads)

This exotic circuit solution seems to be original; actually, it is very, very old. For the first time, I saw it in the book "L’amplificateur opérationnel et ses applications Masson, Paris, 1971" by J. C. Marchais; then I was a student and was trying without success to grasp the idea behind the odd circuit). In spite of that, I have not yet seen any reasonable human friendly explanation of this clever circuit arrangement (including the book mentioned).

Believe me, it is not sufficient to say that "a negative resistance -R connected in parallel with a positive resistance R gives an infinite resistance". In order to really understand the circuit, readers (as human beings) need to know what problem the op-amp solves, why it is connected there, what it actually does in the circuit, how it does this magic, etc.

The idea is extremely simple; we may see it in the daily round when someone (something) helps someone (something) else to such extent that the latter needn't do anything. Examples of this "exact helping": parents help children to such extent that they needn't do anything, a husband supports his wife to such extent that she needn't do anything:), compensating the load by an anti-load (anti-weight) used in the lift systems and cranes, etc.

In the circuit discussed, the op-amp (or, more precisely, the whole NIC converter acting as a negative resistor) does exactly the same - it "helps exactly" the input reference voltage source by injecting the whole current needed through the load. In this way, it serves as an "exact helping" source, which has actually replaced the input source. As a result, the load does not consume any energy from the input source since it is supplied completely by the "helping" source. There is no current flowing between the output of the reference source and the load since the whole rest part of the circuit (the load + the NIC) behaves as a dynamic load with infinite internal resistance. Actually, this is the famous "bootstrapping" technique; it is put in practice for the first time by Baron Munchhausen who was using his own boot straps to pull himself out of the sea:)

In this circuit, the parallel connected negative resistor -R "neutralizes" the positive one R giving the whole load current. Then, in another implementation of this powerful idea - the famous Howland current source (and Deboo integrator as well) - the negative resistance absorbs a part of the positive one (the positive resistance dominates); it adds only a "correcting" supplementary current, in order to keep a constant current through the load. Finally, if the negative resistance dominates (it has completely absorbed the positive one and some negative resistance is left) the circuit will act as a negative resistance amplifier (in this case, the input voltage source has to have an output resistance).

Cyril Mechkov (cyril@circuit-fantasia.com) Circuit-fantasist (talk) 08:48, 26 December 2007 (UTC)

An extract from a related Wikipedia article
(after Wikipedia's Negative resistance)

...Compensating the load resistance. In nature, real sources (for example, human beings) have a limited power. Therefore, if they are loaded (for example, by a weight), they droop. A similar problem exists in electronics (electricity) when imperfect voltage sources are loaded. For example, the simplest varying voltage source (Fig. 7) consists of a steady voltage source VIN and a potentiometer P (a voltage divider r1-r2). If there is no load connected, this real voltage source works well - VOUT = r2/(r1 + r2). However, when a load RL is connected, it "sucks" a current IL and the output voltage VL drops. The classic solution is to connect an op-amp voltage follower (a unity-gain amplifier acting as a buffer amplifier) before the load, in order to decrease the current IL (to increase the load resistance RL). Unfortunately, this remedy introduces some errors inherent for this circuit. In mechanics, there is another powerful idea that is referred to as anti-weight or anti-load (Fig. 7). It is widely used in the lift systems, cranes etc. In electronics, this exotic solution is implemented by a voltage-driven negative resistor (a negative load); it is connected in parallel to the "positive" load (Fig. 7), in order to "help" the imperfect voltage source ,.

The compensating voltage source BH (a non-inverting amplifier with K = 2) produces two times higher "helping" voltage VH= 2VL. It makes a current IH = (VH - VL)/R = (2VL - VL)/RL = VL/RL = IL flow through the load. In this way, the whole load current IL is provided by the "helping" current source IH (the negative resistor -RL) instead by the real voltage source. The load does not consume any energy from the input source since it is supplied completely by the "helping" source. In order to put this circuit into practice, they use usually a negative impedance converter acting as a voltage-driven negative resistor,. There is a striking resemblance between the mechanical and electrical versions, which helps understanding the phenomenon. According to this intuitive viewpoint, the load "pulls" the point A down toward the ground while the resistor R "pulls" the point A up toward the voltage VH. As a result of this "stretching", the point A "experiences" weightlessness (as it pulls itself up) and it follows easily the point B. There is no current flowing between the point B and point A since the whole right part of the circuit (RL, R and VH) behaves as a load with infinite internal resistance. This phenomenon is referred to as bootstrapping and it is put in practice for the first time by Baron Munchhausen (the legend says that he was using his own boot straps to pull himself out of the sea)... Circuit-fantasist (talk) 09:02, 26 December 2007 (UTC)

Resources
Negative resistance A heuristic approach to teaching negative resistance phenomenon Understanding negative impedance converter (NIC) - reveals in three consecutive steps the basic idea behind NIC. How to Compensate Resistive Losses by a Parallel Connected Negative Resistor Negative-Resistance Load Canceller Helps Drive Heavy Loads - an interesting material from Electronic Design Negative Resistor Cancels Op Amp Load (AN 1868) - a similar material from MAXIM


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User talk:Santee72

Hello friends

As a gift please visit my blog to read about 'kc'. What is KC. TO KNOW MORE HERE IS THE LINK ......

www.santee-santee.blogspot.com

santee72

title: User talk:Santee72


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Talk:Programming:Common Lisp/Advanced topics/Packages

IMHO The packages are not explained here very well. --uk:Користувач:VictorAnyakin