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... interest in the Fibonacci and related numbers, especially with respect to new results, research proposals, and challenging problems. The Quarterly seeks articles that are intelligible yet stimulating to its readers, most of whom are university teachers and students. These articles should be lively a ...
... interest in the Fibonacci and related numbers, especially with respect to new results, research proposals, and challenging problems. The Quarterly seeks articles that are intelligible yet stimulating to its readers, most of whom are university teachers and students. These articles should be lively a ...
A Risk Minimization Framework for Information Retrieval
... Mathematically big-O is more subtle. L8 ...
... Mathematically big-O is more subtle. L8 ...
Notes
... Another method: we make each subset correspond to a sequence of 0s and 1s as follows. The ith digit in the sequence is 1 if xi ∈ S and is 0 if xi 6∈ S. (For example, if n = 5 and S = {x1 , x4 , x5 }, then the corresponding sequence is 10011.) Now it is easy to see that each subset gives a sequence, ...
... Another method: we make each subset correspond to a sequence of 0s and 1s as follows. The ith digit in the sequence is 1 if xi ∈ S and is 0 if xi 6∈ S. (For example, if n = 5 and S = {x1 , x4 , x5 }, then the corresponding sequence is 10011.) Now it is easy to see that each subset gives a sequence, ...
39(2)
... has an integral solution (u, v, w) e N3. One can derive more equations in the system (1) but this is not necessary for our proof. The system (1) yields u3 + v3 = 2w3 with (u, v, w) GN3. ...
... has an integral solution (u, v, w) e N3. One can derive more equations in the system (1) but this is not necessary for our proof. The system (1) yields u3 + v3 = 2w3 with (u, v, w) GN3. ...
Sequence entropy pairs and complexity pairs for a measure
... Ergodic theory and topological dynamics exhibit a remarkable parallelism. Classical examples are the concepts of ergodicity, weak mixing and mixing in ergodic theory which can be considered as the analogues of transitivity, topological weak mixing and topological mixing in topological dynamics; or t ...
... Ergodic theory and topological dynamics exhibit a remarkable parallelism. Classical examples are the concepts of ergodicity, weak mixing and mixing in ergodic theory which can be considered as the analogues of transitivity, topological weak mixing and topological mixing in topological dynamics; or t ...
Preferences and Utility - UCLA Economics Homepage
... Theorem 1 assumes that the consumer chooses from a finite number of goods. While this is realistic, it is more mathematically convenient to allow consumers to choose from a continuum of goods. For example, if the agent has $10 and a hamburger costs $2, it is easier to allow the consumer to any numbe ...
... Theorem 1 assumes that the consumer chooses from a finite number of goods. While this is realistic, it is more mathematically convenient to allow consumers to choose from a continuum of goods. For example, if the agent has $10 and a hamburger costs $2, it is easier to allow the consumer to any numbe ...
An Introduction to Prime Numbers
... Later we will meet some very sophisticated methods for telling if a number is a prime or not, but for now it’s about time we got to the first serious theorem about primes: ...
... Later we will meet some very sophisticated methods for telling if a number is a prime or not, but for now it’s about time we got to the first serious theorem about primes: ...
The 3n + 1 conjecture
... And as we can see, these sequences all eventually ’converge’ to 1, after which the sequences repeat the cycle (1, 4, 2). One might now expect that the cycles never get too wild; all of the above sequences end in the (1, 4, 2) cycle after less than 20 iterations, and the highest value encountered in ...
... And as we can see, these sequences all eventually ’converge’ to 1, after which the sequences repeat the cycle (1, 4, 2). One might now expect that the cycles never get too wild; all of the above sequences end in the (1, 4, 2) cycle after less than 20 iterations, and the highest value encountered in ...
New Perspectives of Quantum Analogues - UKnowledge
... given to all outside sources. I understand that I am solely responsible for obtaining any needed copyright permissions. I have obtained needed written permission statement(s) from the owner(s) of each thirdparty copyrighted matter to be included in my work, allowing electronic distribution (if such ...
... given to all outside sources. I understand that I am solely responsible for obtaining any needed copyright permissions. I have obtained needed written permission statement(s) from the owner(s) of each thirdparty copyrighted matter to be included in my work, allowing electronic distribution (if such ...
K-THEORETIC CHARACTERIZATION OF C*
... C*-algebras with approximately inner flip. Understanding that “classifiable” means “classifiable by K-theory and traces,” then the classification results to date (including Kirchberg-Phillips’ classification of purely infinite C*-algebras [17, 24] and the Gong-Lin-Niu classification of C*-algebras o ...
... C*-algebras with approximately inner flip. Understanding that “classifiable” means “classifiable by K-theory and traces,” then the classification results to date (including Kirchberg-Phillips’ classification of purely infinite C*-algebras [17, 24] and the Gong-Lin-Niu classification of C*-algebras o ...
Seed and Sieve of Odd Composite Numbers with
... out. First, Theorem 1, 2 and 3 provide a kind of direct search approach such that finding an x to satisfy (6 x 1) | (n x) or (6 x 1) | (n x) for big odd number N 6n 1 , or finding an x to satisfy (6 x 1) | (n x) or (6 x 1) | (n x) for big odd number N 6n 1 . Either Theorem 2 ...
... out. First, Theorem 1, 2 and 3 provide a kind of direct search approach such that finding an x to satisfy (6 x 1) | (n x) or (6 x 1) | (n x) for big odd number N 6n 1 , or finding an x to satisfy (6 x 1) | (n x) or (6 x 1) | (n x) for big odd number N 6n 1 . Either Theorem 2 ...
a classification of gaussian primes
... introduced because a Greek merchant wished to know the solution to 3x + 4 = 6, but from a mathematician’s point of view most real world questions could be boiled down to such a problem. So with the rationals fell equations such as those above, negative numbers toppled those such as x + 1 = 0 which d ...
... introduced because a Greek merchant wished to know the solution to 3x + 4 = 6, but from a mathematician’s point of view most real world questions could be boiled down to such a problem. So with the rationals fell equations such as those above, negative numbers toppled those such as x + 1 = 0 which d ...
Document
... problems can be easily solved. Even when Maple cannot determine the solution, problem-solving hints can be identified and inferred from the approximate values calculated and solutions to similar problems, as determined by Maple. For this reason, Maple can provide insights into scientific research. I ...
... problems can be easily solved. Even when Maple cannot determine the solution, problem-solving hints can be identified and inferred from the approximate values calculated and solutions to similar problems, as determined by Maple. For this reason, Maple can provide insights into scientific research. I ...
Interpolated Schur multiple zeta values
... (k1 , . . . , kr ) by a Young tableau k = (λ, (ki,j )). Here λ is a partition of a natural number, i.e. a non-decreasing sequence (λ1 , . . . , λh ) of non-negative integers and the ki,j are arbitrary integers for indices (i, j) with 1 ≤ i ≤ h and 1 ≤ j ≤ λi . We will make this more precise in the n ...
... (k1 , . . . , kr ) by a Young tableau k = (λ, (ki,j )). Here λ is a partition of a natural number, i.e. a non-decreasing sequence (λ1 , . . . , λh ) of non-negative integers and the ki,j are arbitrary integers for indices (i, j) with 1 ≤ i ≤ h and 1 ≤ j ≤ λi . We will make this more precise in the n ...
PLANE ISOMETRIES AND THE COMPLEX NUMBERS 1. Introduction p in R
... So unless α = 1 and β = 0, which means h is the identity, h(z) has at most 1 fixed point. Case 2: h(z) = αz + β. The condition h(z) = z is the same as αz + β = z. We will show the set of solutions to this equation, if it is not empty, lie along a line. Thus h doesn’t have three fixed points not lyin ...
... So unless α = 1 and β = 0, which means h is the identity, h(z) has at most 1 fixed point. Case 2: h(z) = αz + β. The condition h(z) = z is the same as αz + β = z. We will show the set of solutions to this equation, if it is not empty, lie along a line. Thus h doesn’t have three fixed points not lyin ...
Full text
... Theorem 1: Let r - max,^-^-. The number of entries in the rfi1 row of the Fibonacci triangle not divisible hyp is 2*13*24*3... rSr~l, where % is the number of I'S in the base p expansion of n. Proof: First, we note that the maximum exists. It is well known that rx
... Theorem 1: Let r - max,^-^-. The number of entries in the rfi1 row of the Fibonacci triangle not divisible hyp is 2*13*24*3... rSr~l, where % is the number of I'S in the base p expansion of n. Proof: First, we note that the maximum exists. It is well known that rx
Selected Chapters from Number Theory and Algebra
... 10 Problem 1.9. As a warm-up, find the three smallest primes larger than 41 which are not in the list of 40 primes just mentioned. Answer. These are the first three primes not in the range: 59, 67, 73 6= n2 − n + 41 for any natural number n. We now address the question which other primes besides 41 ...
... 10 Problem 1.9. As a warm-up, find the three smallest primes larger than 41 which are not in the list of 40 primes just mentioned. Answer. These are the first three primes not in the range: 59, 67, 73 6= n2 − n + 41 for any natural number n. We now address the question which other primes besides 41 ...