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An introduction to the Smarandache Square
An introduction to the Smarandache Square

... Case 1. According to the theorem 7 Ssc(n)=n and Ssc(n+1)=n+1 that implies that Ssc(n)<>Ssc(n+1) Case 2. Without loss of generality let's suppose that: n = pa ⋅ q b n + 1 = p a ⋅ qb + 1 = sc ⋅ t d where p,q,s and t are distinct primes. According to the theorem 4: Ssc( n) = Ssc ( p a ⋅ q b ) = p odd ( ...
Pi and the Fibonacci Numbers
Pi and the Fibonacci Numbers

... Since 60° is a sixth of a full turn (360°) then 60° = 2 Pi/ 6 = Pi/3 radians = (Pi/3)r and so 30° = Pi/6 radians = (Pi/6)r. ...
Problem Set 1 Solutions
Problem Set 1 Solutions

... Induction step: Assume P (n) is true, so by definition Q(k) is true for all k ∈ N with 1 ≤ k ≤ n. Thus our assumption guarantees Q(n + 1) is true. We see that both P (n) and Q(n + 1) are both true, and since the statement ‘P (n) and Q(n + 1) are both true’ is equivalent to P (n + 1), we conclude P ( ...
TRAPEZOIDAL APPROXIMATION OF FUZZY NUMBERS
TRAPEZOIDAL APPROXIMATION OF FUZZY NUMBERS

Distribution of Prime Numbers
Distribution of Prime Numbers

Discrete Mathematics Lecture Notes Incomplete Preliminary Version
Discrete Mathematics Lecture Notes Incomplete Preliminary Version

... authors’ contempt for their readers’ intelligence; the result is a multitude of unnecessary case distinctions, destroying a fundamental element of mathematical aesthetics. (To these authors, for instance, x | x does not hold for all x; there is an exception: x = 0. And then, to them, x − y does not ...
University of Chicago “A Textbook for Advanced Calculus”
University of Chicago “A Textbook for Advanced Calculus”

Lectures on Sieve Methods - School of Mathematics, TIFR
Lectures on Sieve Methods - School of Mathematics, TIFR

13(4)
13(4)

... The California Mathematics Council All subscription correspondence should be addressed to Professor Leonard Klosinski, Mathematics Department, University of Santa Clara, Santa Clara, California 95053. All checks ($12.00 per year) should be made out t o the Fibonacci Association or the Fibonacci Quar ...
Introduction to analytic number theory
Introduction to analytic number theory

... tables have been found, dating back to 2000 BC. When ancient civilizations reached a level which provided leisure time to ponder about things, some people began to speculate about the nature and properties of numbers. This curiosity developed into a sort of numbermysticism or numerology, and even to ...
34(5)
34(5)

... Lagrange interpolation must be considered as describing the properties of a linear operator sending a function of one variable to a symmetric function. It can be written as a summation on a set or as a product of divided differences; it is this latter version that we shall use here. In fact, in Sect ...
numbers and uniform ergodic theorems
numbers and uniform ergodic theorems

Weighted trapezoidal approximation
Weighted trapezoidal approximation

Here
Here

Lecture Notes
Lecture Notes

... MAPPINGS AND FUNCTIONS ...
Chapter 12 Applications of Series
Chapter 12 Applications of Series

APSC 174J Lecture Notes
APSC 174J Lecture Notes

... MAPPINGS AND FUNCTIONS ...
Applied Science 174: Linear Algebra Lecture Notes
Applied Science 174: Linear Algebra Lecture Notes

local copy  - Harvard Mathematics Department
local copy - Harvard Mathematics Department

... [24]. Also distance 2 is sometimes included as a twin. Their appearance on Im(z) = 1 was studied by [48] who gave the corresponding Hardy-Littlewood constant. While one does not know whether infinitely many Gaussian prime twins exist, one can estimate that there are asymptotically Ct r/ log2 (r) of ...
Theory of L-functions - Institut für Mathematik
Theory of L-functions - Institut für Mathematik

15(1)
15(1)

Full text
Full text

1 Halton Sequences for Mixed Logit By Kenneth Train Department of
1 Halton Sequences for Mixed Logit By Kenneth Train Department of

(pdf)
(pdf)

Exponential Sums and Diophantine Problems
Exponential Sums and Diophantine Problems

1 2 3 4 5 ... 44 >

Karhunen–Loève theorem

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