Results 41 to 50 of about 106,566 (267)
Gauss’ Second Theorem for
MathematicsTwo summation theorems concerning the F12(1/2)-series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and binomial/multinomial coefficients will be evaluated in ...
Chunli Li, Wenchang Chu
doaj +1 more source
Microbiome‐blood–brain barrier interactions in aging — mechanisms and therapeutic potential
FEBS Letters, EarlyView.Aging reshapes the gut microbiome (↓SCFA‐producing commensals; ↑pro‐inflammatory outputs), shifting circulating metabolites (↓SCFAs; ↑LPS, ↑TMAO, ↑PAA) that act at the BBB to increase nonspecific transcytosis, alter transport, and promote astrocyte reactivity, heightening brain vulnerability.
Daniel Cuervo‐Zanatta +3 more
wiley +1 more source
Cubic harmonics and Bernoulli numbers
Journal of Combinatorial Theory, Series A, 2012 18 pages, 3 ...
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Infinitary harmonic numbers [PDF]
Bulletin of the Australian Mathematical Society, 1990 The infinitary divisors of a natural number n are the products of its divisors of the , where py is an exact prime-power divisor of n and (where yα = 0 or 1) is the binary representation of y. Infinitary harmonic numbers are those for which the infinitary divisors have integer harmonic mean.
Hagis, Peter jun., Cohen, Graeme L.
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Series of convergence ratios “±427 $\frac{{\pm}4}{27}$ ” containing harmonic numbers
Demonstratio MathematicaThree accelerating transformation formulae for hypergeometric series are systematically analyzed by the “coefficient extraction method”. Numerous harmonic series of convergence ratios “±427 $\frac{{\pm}4}{27}$ ” are evaluated in closed form, which fills ...
Li Chunli, Chu Wenchang
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Parametric Integrals for Binomial Series with Harmonic Polynomials
AxiomsBinomial series involving harmonic polynomials are expressed in terms of parametric integrals. By evaluating these parametric integrals, we establish several remarkable closed formulae for the infinite series containing both central binomial coefficients
Chunli Li, Wenchang Chu
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Utility harmonic impedance estimation based on mutual information and data optimization
电力工程技术, 2023 Accurate calculation of harmonic impedance is the premise of harmonic control and reasonable division of harmonic responsibility. The existing harmonic impedance estimation methods should meet the conditions that the background harmonic fluctuations are ...
XU Fangwei +5 more
doaj +1 more source
Loss of IGF‐1R impairs DNA‐PKcs recruitment to chromatin leading to defective end‐joining
Molecular Oncology, EarlyView.IGF‐1R promotes radioresistance by facilitating DNA‐PKcs recruitment to chromatin, enabling non‐homologous end‐joining (NHEJ) repair of double‐strand breaks. Inhibition or loss of IGF‐1R disrupts this recruitment to damage sites, driving compensatory reliance on microhomology‐mediated end‐joining (MMEJ) repair.
Matthew O. Ellis +3 more
wiley +1 more source
Harmonic sets and the harmonic prime number theorem
Bulletin of the Australian Mathematical Society, 2005 We restrict primes and prime powers to sets . Let . Then the error in θH(x) has, unconditionally, the expected order of magnitude . However, if then ψH (x) = x log 2 + O (log x). Some reasons for and consequences of these sharp results are explored. A proof is given of the “harmonic prime number theorem”, πH (x)/π (x) → log 2.
Broughan, Kevin A., Casey, Rory J.
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