Results 11 to 20 of about 308,452 (217)
THE GROTHENDIECK CONSTANT IS STRICTLY SMALLER THAN KRIVINE’S BOUND
Forum of Mathematics, Pi, 2013 The (real) Grothendieck constant ${K}_{G} $ is the infimum over those $K\in (0, \infty )$ such that for every $m, n\in \mathbb{N} $ and every $m\times n$ real matrix $({a}_{ij} )$ we have $$\begin{eqnarray*}\displaystyle \max _{\{ x_{i}\} _{i= 1}^{m} , \{
MARK BRAVERMAN +3 more
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The Nicolas and Robin inequalities with sums of two squares [PDF]
, 2007 In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $\sigma(n)5040$, where $\sigma(n)$ is the sum of divisors function, and $\gamma$ is the Euler-Mascheroni constant.
Banks, William D. +3 more
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The sum of squared logarithms inequality in arbitrary dimensions [PDF]
, 2015 We prove the sum of squared logarithms inequality (SSLI) which states that for nonnegative vectors x, y ∈ ℝn whose elementary symmetric polynomials satisfy ek(x) ≤ ek(y) (for 1 ≤ k < n) and en(x) = en(y) , the inequality ∑i(log xi)2 ≤ ∑i(log yi)2 holds ...
L. Borisov, P. Neff, S. Sra, C. Thiel
semanticscholar +1 more source
Resource Allocation for Millimeter Wave Self-Backhaul Network Using Markov Approximation
IEEE Access, 2019 Millimeter wave (mmW) self-backhaul has been regarded as a high-capacity and low-cost solution to deploy dense small cell networks but its performance depends on a resource allocation strategy, which can effectively reduce interference (including co-tier
Wenjuan Pu +3 more
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On the sum of digits of the factorial [PDF]
, 2014 Let b > 1 be an integer and denote by s_b(m) the sum of the digits of the positive integer m when is written in base b. We prove that s_b(n!) > C_b log n log log log n for each integer n > e, where C_b is a positive constant depending only on b.
Sanna, Carlo
core +4 more sources
A generalization of primitive sets and a conjecture of Erdős
Discrete Analysis, 2020 A generalization of primitive sets and a conjecture of Erdős, Discrete Analysis 2020:16, 13 pp. Call a set $A$ of integers greater than 1 _primitive_ if no element of $A$ divides any other. How dense can a primitive set be?
Tsz Ho Chan +2 more
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Optimal primitive sets with restricted primes [PDF]
, 2013 A set of natural numbers is primitive if no element of the set divides another. Erd\H{o}s conjectured that if S is any primitive set, then \sum_{n\in S} 1/(n log n) \le \sum_{n\in \P} 1/(p log p), where \P denotes the set of primes.
Banks, William D., Martin, Greg
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On the sum of squared logarithms inequality and related inequalities [PDF]
, 2014 We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors $a,b\in\mathbb{R}_+^n$ so that $\sum_{i=1}^n(\log a_i)^2\ \
F. Dannan, P. Neff, C. Thiel
semanticscholar +1 more source
FAILURE OF THE $L^{1}$ POINTWISE AND MAXIMAL ERGODIC THEOREMS FOR THE FREE GROUP
Forum of Mathematics, Sigma, 2015 Let $F_{2}$ denote the free group on two generators $a$ and $b$. For any measure-preserving system $(X,{\mathcal{X}},{\it\mu},(T_{g})_{g\in F_{2}})$ on a finite measure space $X=(X,{\mathcal{X}},{\it\mu})$, any $f\in L^{1}(X)$, and any $n\geqslant 1 ...
TERENCE TAO
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On the generalised sum of squared logarithms inequality [PDF]
, 2014 Assume n≥2$n\geq2$. Consider the elementary symmetric polynomials ek(y1,y2,…,yn)$e_{k}(y_{1},y_{2},\ldots, y_{n})$ and denote by E0,E1,…,En−1$E_{0},E_{1},\ldots,E_{n-1}$ the elementary symmetric polynomials in reverse order Ek(y1,y2,…,yn):=en−k(y1,y2 ...
W. Pompe, P. Neff
semanticscholar +1 more source