- published: 02 Dec 2012
- views: 3437
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Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+16i and 10+11i. Then we solve for the coefficients in Bezout's identity in this case.
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems.
- published: 02 Mar 2015
- views: 489
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].
- published: 08 Dec 2012
- views: 3038
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof.M.Majumdar
- published: 19 May 2016
- views: 11
Maiya Loucks, Samantha Meek, and Levi Overcast
Abstract: Bertrand’s postulate states that for all n greater than 1 there exists a prime, p, such that n-1 less than p less than 2n. We explore an extension of Bertrand’s postulate to the Gaussian integers. The Gaussian integers are the complex numbers where the real and imaginary parts are integers. We define notions of doubling and betweenness for the Gaussian integers and conjecture that there exists a Gaussian prime between any Gaussian integer and its double.
- published: 20 Aug 2015
- views: 78
http://demonstrations.wolfram.com/FactoringGaussianIntegers
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Every nonzero Gaussian integer a+b i, where a and b are ordinary integers and i=SqrtBox[RowBox[{-, 1}]], can be expressed uniquely as the product of a unit and powers of special Gaussian primes. Units are 1, i, -1, -i. Special Gaussian primes are 1+i an...
Contributed by: Izidor Hafner
- published: 21 Apr 2010
- views: 507
http://demonstrations.wolfram.com/PatternsForFunctionsOnTheGaussianIntegers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A complex-valued function is applied to the Gaussian integers in a square centered at the origin, showing nested patterns and motifs.
Contributed by: Daniel de Souza Carvalho
Additional work by: Jeff Bryant
- published: 11 Jul 2009
- views: 186
Hunter Lehmann and Andrew Park
Abstract: A graph of n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that several families of trees as well as all trees of order at most 54 admit a prime labeling with the Gaussian integers.
- published: 20 Aug 2015
- views: 48
Gaussian integer
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. This integral domain is a particular case of a commutative ring of quadratic integers. It does not have a total ordering that respects arithmetic.
Formal definition
Formally, the Gaussian integers are the set
Note that when they are considered within the complex plane the Gaussian integers may be seen to constitute the 2-dimensional integer lattice.
Norm of a Gaussian integer
The (arithmetic or field) norm of a Gaussian integer is the square of its absolute value (Euclidean norm) as a complex number. It is the natural number defined as
where ⋅ (an overline) is complex conjugation.
The norm is multiplicative, since the absolute value of complex numbers is multiplicative, i.e., one has
The latter can also be verified by a straightforward check. The units of Z[i] are precisely those elements with norm 1, i.e. the set {±1, ±i}.
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http://wn.com/Gaussian_integer
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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6:39RNT2.3.1. Euclidean Algorithm for Gaussian Integers
RNT2.3.1. Euclidean Algorithm for Gaussian IntegersRNT2.3.1. Euclidean Algorithm for Gaussian Integers
Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+16i and 10+11i. Then we solve for the coefficients in Bezout's identity in this case. -
14:35Complex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's Formula
Complex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's FormulaComplex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's Formula
Trostle -
51:16Number Theory: Lecture 11, Gaussian Integers Applied
Number Theory: Lecture 11, Gaussian Integers AppliedNumber Theory: Lecture 11, Gaussian Integers Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems. -
22:31RNT2.4. Gaussian Primes
RNT2.4. Gaussian PrimesRNT2.4. Gaussian Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i]. -
36:49The Gaussian Integers (MATH)
The Gaussian Integers (MATH)The Gaussian Integers (MATH)
Subject :- Mathematics Paper:-Number Theory and Graph Theory Principal Investigator:- Prof.M.Majumdar -
20:56Bertrand’s Postulate for the Gaussian Integers
Bertrand’s Postulate for the Gaussian IntegersBertrand’s Postulate for the Gaussian Integers
Maiya Loucks, Samantha Meek, and Levi Overcast Abstract: Bertrand’s postulate states that for all n greater than 1 there exists a prime, p, such that n-1 less than p less than 2n. We explore an extension of Bertrand’s postulate to the Gaussian integers. The Gaussian integers are the complex numbers where the real and imaginary parts are integers. We define notions of doubling and betweenness for the Gaussian integers and conjecture that there exists a Gaussian prime between any Gaussian integer and its double. -
1:39Using Gaussian integers to generate Pythagorean triples
Using Gaussian integers to generate Pythagorean triplesUsing Gaussian integers to generate Pythagorean triples
Recorded December 2012 -
0:13Factoring Gaussian Integers
Factoring Gaussian IntegersFactoring Gaussian Integers
http://demonstrations.wolfram.com/FactoringGaussianIntegers The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Every nonzero Gaussian integer a+b i, where a and b are ordinary integers and i=SqrtBox[RowBox[{-, 1}]], can be expressed uniquely as the product of a unit and powers of special Gaussian primes. Units are 1, i, -1, -i. Special Gaussian primes are 1+i an... Contributed by: Izidor Hafner -
0:17Patterns for Functions on the Gaussian Integers
Patterns for Functions on the Gaussian IntegersPatterns for Functions on the Gaussian Integers
http://demonstrations.wolfram.com/PatternsForFunctionsOnTheGaussianIntegers/ The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. A complex-valued function is applied to the Gaussian integers in a square centered at the origin, showing nested patterns and motifs. Contributed by: Daniel de Souza Carvalho Additional work by: Jeff Bryant -
43:08Prime Labeling of Trees with Gaussian Integers
Prime Labeling of Trees with Gaussian IntegersPrime Labeling of Trees with Gaussian Integers
Hunter Lehmann and Andrew Park Abstract: A graph of n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that several families of trees as well as all trees of order at most 54 admit a prime labeling with the Gaussian integers.
-
RNT2.3.1. Euclidean Algorithm for Gaussian Integers
Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+16i and 10+11i. Then we solve for the coefficients in Bezout's identity in this case. -
Complex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's Formula
Trostle -
Number Theory: Lecture 11, Gaussian Integers Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems. -
RNT2.4. Gaussian Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i]. -
The Gaussian Integers (MATH)
Subject :- Mathematics Paper:-Number Theory and Graph Theory Principal Investigator:- Prof.M.Majumdar -
Bertrand’s Postulate for the Gaussian Integers
Maiya Loucks, Samantha Meek, and Levi Overcast Abstract: Bertrand’s postulate states that for all n greater than 1 there exists a prime, p, such that n-1 less than p less than 2n. We explore an extension of Bertrand’s postulate to the Gaussian integers. The Gaussian integers are the complex numbers where the real and imaginary parts are integers. We define notions of doubling and betweenness for the Gaussian integers and conjecture that there exists a Gaussian prime between any Gaussian integer and its double. -
Using Gaussian integers to generate Pythagorean triples
Recorded December 2012 -
Factoring Gaussian Integers
http://demonstrations.wolfram.com/FactoringGaussianIntegers The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Every nonzero Gaussian integer a+b i, where a and b are ordinary integers and i=SqrtBox[RowBox[{-, 1}]], can be expressed uniquely as the product of a unit and powers of special Gaussian primes. Units are 1, i, -1, -i. Special Gaussian primes are 1+i an... Contributed by: Izidor Hafner -
Patterns for Functions on the Gaussian Integers
http://demonstrations.wolfram.com/PatternsForFunctionsOnTheGaussianIntegers/ The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. A complex-valued function is applied to the Gaussian integers in a square centered at the origin, showing nested patterns and motifs. Contributed by: Daniel de Souza Carvalho Additional work by: Jeff Bryant -
Prime Labeling of Trees with Gaussian Integers
Hunter Lehmann and Andrew Park Abstract: A graph of n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that several families of trees as well as all trees of order at most 54 admit a prime labeling with the Gaussian integers.
RNT2.3.1. Euclidean Algorithm for Gaussian Integers
- Order: Reorder
- Duration: 6:39
- Updated: 02 Dec 2012
- views: 3437
Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+16i and 10+11i. Then we solve for the coefficients in Bezout's identit...
Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+16i and 10+11i. Then we solve for the coefficients in Bezout's identity in this case.
wn.com/Rnt2.3.1. Euclidean Algorithm For Gaussian Integers
Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+16i and 10+11i. Then we solve for the coefficients in Bezout's identity in this case.
- published: 02 Dec 2012
- views: 3437
Complex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's Formula
- Order: Reorder
- Duration: 14:35
- Updated: 23 May 2014
- views: 445
Trostle
Trostle
wn.com/Complex Numbers, Gaussian Integers, Gaussian Rationals, And Euler's Formula
Trostle
- published: 23 May 2014
- views: 445
Number Theory: Lecture 11, Gaussian Integers Applied
- Order: Reorder
- Duration: 51:16
- Updated: 02 Mar 2015
- views: 489
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Still...
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems.
wn.com/Number Theory Lecture 11, Gaussian Integers Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to prove Fermat's two square theorem. Most of this is directly from Stillwell, but I tried to add a bit here and there about why Z[i] still supports Division Algorthim, Euclidean Algorithm, Prime Divisor Property and Unique Factorization. To be careful, I would have to write much, much more. But, the point here is not to be super rigorous, the point is to be reasonably rigorous and see how abstraction solves problems.
- published: 02 Mar 2015
- views: 489
RNT2.4. Gaussian Primes
- Order: Reorder
- Duration: 22:31
- Updated: 08 Dec 2012
- views: 3038
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answe...
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].
wn.com/Rnt2.4. Gaussian Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in the Euclidean domain of Gaussian integers Z[i]. Not only is the answer somewhat elegant, but it contains a beautiful theorem on prime integers due to Fermat. We finish with examples of factorizations in Z[i].
- published: 08 Dec 2012
- views: 3038
The Gaussian Integers (MATH)
- Order: Reorder
- Duration: 36:49
- Updated: 19 May 2016
- views: 11
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof.M.Majumdar
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof.M.Majumdar
wn.com/The Gaussian Integers (Math)
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof.M.Majumdar
- published: 19 May 2016
- views: 11
Bertrand’s Postulate for the Gaussian Integers
- Order: Reorder
- Duration: 20:56
- Updated: 20 Aug 2015
- views: 78
Maiya Loucks, Samantha Meek, and Levi Overcast
Abstract: Bertrand’s postulate states that for all n greater than 1 there exists a prime, p, such that n-1 less ...
Maiya Loucks, Samantha Meek, and Levi Overcast
Abstract: Bertrand’s postulate states that for all n greater than 1 there exists a prime, p, such that n-1 less than p less than 2n. We explore an extension of Bertrand’s postulate to the Gaussian integers. The Gaussian integers are the complex numbers where the real and imaginary parts are integers. We define notions of doubling and betweenness for the Gaussian integers and conjecture that there exists a Gaussian prime between any Gaussian integer and its double.
wn.com/Bertrand’S Postulate For The Gaussian Integers
Maiya Loucks, Samantha Meek, and Levi Overcast
Abstract: Bertrand’s postulate states that for all n greater than 1 there exists a prime, p, such that n-1 less than p less than 2n. We explore an extension of Bertrand’s postulate to the Gaussian integers. The Gaussian integers are the complex numbers where the real and imaginary parts are integers. We define notions of doubling and betweenness for the Gaussian integers and conjecture that there exists a Gaussian prime between any Gaussian integer and its double.
- published: 20 Aug 2015
- views: 78
Using Gaussian integers to generate Pythagorean triples
- Order: Reorder
- Duration: 1:39
- Updated: 12 Apr 2014
- views: 189
Recorded December 2012
Recorded December 2012
wn.com/Using Gaussian Integers To Generate Pythagorean Triples
Factoring Gaussian Integers
- Order: Reorder
- Duration: 0:13
- Updated: 21 Apr 2010
- views: 507
http://demonstrations.wolfram.com/FactoringGaussianIntegers
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new ...
http://demonstrations.wolfram.com/FactoringGaussianIntegers
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Every nonzero Gaussian integer a+b i, where a and b are ordinary integers and i=SqrtBox[RowBox[{-, 1}]], can be expressed uniquely as the product of a unit and powers of special Gaussian primes. Units are 1, i, -1, -i. Special Gaussian primes are 1+i an...
Contributed by: Izidor Hafner
wn.com/Factoring Gaussian Integers
http://demonstrations.wolfram.com/FactoringGaussianIntegers
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Every nonzero Gaussian integer a+b i, where a and b are ordinary integers and i=SqrtBox[RowBox[{-, 1}]], can be expressed uniquely as the product of a unit and powers of special Gaussian primes. Units are 1, i, -1, -i. Special Gaussian primes are 1+i an...
Contributed by: Izidor Hafner
- published: 21 Apr 2010
- views: 507
Patterns for Functions on the Gaussian Integers
- Order: Reorder
- Duration: 0:17
- Updated: 11 Jul 2009
- views: 186
http://demonstrations.wolfram.com/PatternsForFunctionsOnTheGaussianIntegers/
The Wolfram Demonstrations Project contains thousands of free interactive visualiz...
http://demonstrations.wolfram.com/PatternsForFunctionsOnTheGaussianIntegers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A complex-valued function is applied to the Gaussian integers in a square centered at the origin, showing nested patterns and motifs.
Contributed by: Daniel de Souza Carvalho
Additional work by: Jeff Bryant
wn.com/Patterns For Functions On The Gaussian Integers
http://demonstrations.wolfram.com/PatternsForFunctionsOnTheGaussianIntegers/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A complex-valued function is applied to the Gaussian integers in a square centered at the origin, showing nested patterns and motifs.
Contributed by: Daniel de Souza Carvalho
Additional work by: Jeff Bryant
- published: 11 Jul 2009
- views: 186
Prime Labeling of Trees with Gaussian Integers
- Order: Reorder
- Duration: 43:08
- Updated: 20 Aug 2015
- views: 48
Hunter Lehmann and Andrew Park
Abstract: A graph of n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers ...
Hunter Lehmann and Andrew Park
Abstract: A graph of n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that several families of trees as well as all trees of order at most 54 admit a prime labeling with the Gaussian integers.
wn.com/Prime Labeling Of Trees With Gaussian Integers
Hunter Lehmann and Andrew Park
Abstract: A graph of n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that several families of trees as well as all trees of order at most 54 admit a prime labeling with the Gaussian integers.
- published: 20 Aug 2015
- views: 48
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6:39
RNT2.3.1. Euclidean Algorithm for Gaussian Integers
Ring Theory: We use the Euclidean algorithm to find the GCD of the Gaussian integers 11+1...
published: 02 Dec 2012
RNT2.3.1. Euclidean Algorithm for Gaussian Integers
RNT2.3.1. Euclidean Algorithm for Gaussian Integers
- Report rights infringement
- published: 02 Dec 2012
- views: 3437
14:35
Complex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's Formula
Trostle
published: 23 May 2014
Complex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's Formula
Complex Numbers, Gaussian Integers, Gaussian Rationals, and Euler's Formula
- Report rights infringement
- published: 23 May 2014
- views: 445
51:16
Number Theory: Lecture 11, Gaussian Integers Applied
Here I wrap up our thoughts on Chapter 6. We see how Z[i] provides a natural framework to ...
published: 02 Mar 2015
Number Theory: Lecture 11, Gaussian Integers Applied
Number Theory: Lecture 11, Gaussian Integers Applied
- Report rights infringement
- published: 02 Mar 2015
- views: 489
22:31
RNT2.4. Gaussian Primes
Ring Theory: As an application of all previous ideas on rings, we determine the primes in...
published: 08 Dec 2012
RNT2.4. Gaussian Primes
RNT2.4. Gaussian Primes
- Report rights infringement
- published: 08 Dec 2012
- views: 3038
36:49
The Gaussian Integers (MATH)
Subject :- Mathematics
Paper:-Number Theory and Graph Theory
Principal Investigator:- Prof...
published: 19 May 2016
The Gaussian Integers (MATH)
The Gaussian Integers (MATH)
- Report rights infringement
- published: 19 May 2016
- views: 11
20:56
Bertrand’s Postulate for the Gaussian Integers
Maiya Loucks, Samantha Meek, and Levi Overcast
Abstract: Bertrand’s postulate states that...
published: 20 Aug 2015
Bertrand’s Postulate for the Gaussian Integers
Bertrand’s Postulate for the Gaussian Integers
- Report rights infringement
- published: 20 Aug 2015
- views: 78
1:39
Using Gaussian integers to generate Pythagorean triples
Recorded December 2012
published: 12 Apr 2014
Using Gaussian integers to generate Pythagorean triples
Using Gaussian integers to generate Pythagorean triples
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- published: 12 Apr 2014
- views: 189
0:13
Factoring Gaussian Integers
http://demonstrations.wolfram.com/FactoringGaussianIntegers
The Wolfram Demonstrations Pr...
published: 21 Apr 2010
Factoring Gaussian Integers
Factoring Gaussian Integers
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- published: 21 Apr 2010
- views: 507
0:17
Patterns for Functions on the Gaussian Integers
http://demonstrations.wolfram.com/PatternsForFunctionsOnTheGaussianIntegers/
The Wolfram ...
published: 11 Jul 2009
Patterns for Functions on the Gaussian Integers
Patterns for Functions on the Gaussian Integers
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- published: 11 Jul 2009
- views: 186
43:08
Prime Labeling of Trees with Gaussian Integers
Hunter Lehmann and Andrew Park
Abstract: A graph of n vertices is said to admit a prime l...
published: 20 Aug 2015
Prime Labeling of Trees with Gaussian Integers
Prime Labeling of Trees with Gaussian Integers
- Report rights infringement
- published: 20 Aug 2015
- views: 48
RNT2.3.1. Euclidean Algorithm for Gaussian Intege...
Complex Numbers, Gaussian Integers, Gaussian Ratio...
Number Theory: Lecture 11, Gaussian Integers Appli...
RNT2.4. Gaussian Primes...
The Gaussian Integers (MATH)...
Bertrand’s Postulate for the Gaussian Integers...
Using Gaussian integers to generate Pythagorean tr...
Factoring Gaussian Integers...
Patterns for Functions on the Gaussian Integers...
Prime Labeling of Trees with Gaussian Integers...
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World-record accuracy of gigahertz high-speed single-electron transfer —An important step toward a high-accuracy current standard— (NTT - Nippon Telegraph & Telephone Corporation)
Edit Public Technologies 06 Jul 2016
(Source ... (Press release material) ... 1 ) ... The quantum Hall resistance standard is a standard that uses the value of the quantized Hall resistance, which is the product of the von Klitzing constant (R=h/e) and the reciprocal of the integer number ... The Josephson voltage standard is a standard that uses the value of the quantized voltage, which is the integer multiple of the product of ƒ and the reciprocal of the Josephson constant (K=2e/h)....
Notice concerning Issuance of Stock Compensation-type Stock Options (Subscription Rights to Shares) (Sankyo Co Ltd)
Edit Public Technologies 05 Jul 2016
The total number of subscription rights to shares shall be the maximum integer whereby the total amount of fair value of the subscription rights to shares calculated using the Black-Scholes model on the date of allotment of subscription rights to shares is within the sum of the upper limit of each compensation....
'Maths is often way ahead of practical applications' (Universiteit Leiden)
Edit Public Technologies 04 Jul 2016
(Source. Universiteit Leiden). A secret code that we currently use to send e-mails securely is based on the maths of a century ago. The geometrical surfaces that Dino Festi studied during his PhD research will perhaps be used in future codes or new physics. PhD defence 5 July. Many mathematical formulae can be imagined as complex folded surfaces in space ... Festi ... A rational number is a fraction of whole integers a and b, in other words a/b....
InPost Express sold for PLN 110 mln
Edit Warsaw Business Journal 01 Jul 2016
Polish mail and parcel company Integer.pl has sold its unit InPost Express to Logistics Venture for PLN 110 million, the company informed in a statement. The consideration includes PLN 68 million for the 100 percent shareholding and PLN 42 million for the transfer of receivables. Payment will be made in three tranches. PLN 50 million by… This content is for Silver 6 months, Gold 1 Year and Bronze 2 weeks members only ... ....
Gujarat students got 90pc marks, but couldn’t tell a triangle from a circle
Edit Dawn 01 Jul 2016
NEW DELHI ... “They could not tell a triangle from a circle. One of them said a triangle has four sides and another student could not point out set two integers on a line bar, while many of them failed to solve two-digit multiplication and subtraction,” the Indian Express said about a test given to Class X students because they were believed to have cheated ... Also, all these students scored zero in the subjective section ... A ... ....
PhD defence by Adel Zahedi, Department of Electronic Systems (Aalborg Universitet)
Edit Public Technologies 30 Jun 2016
(Source. Aalborg Universitet). 01.07.2016 kl. 13.00 - 16.00. Title. Source Coding for Wireless Distributed Microphones in Reverberant Environments. Abstract ... In this thesis, we study both information-theoretic and audio coding aspects of this problem ... We solve the resulting rate-distortion problems using assumptions such as Gaussianity of the sources, and thereby establish mathematical bounds on the performance of the audio coding system....
In Gujarat, many in Class X don’t know shape of triangle, but got 90% in ...
Edit Indian Express 30 Jun 2016
Illustration by C R Sasikumar. They could not tell a triangle from a circle. One of them said a trikon (triangle) has four sides and another student could not point out set two integers on a line bar, while many of them failed to solve two-digit multiplication and subtraction. Some appeared honest and wrote avadtu nathi (do not know) on their answer sheets ... Also, all these students scored zero in the subjective section ... Related Article ... ....
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