Generalizations Of The Sidon-telyakovskii Theorem

The well-known Sidon-Telyakovskii integrability condition is considerably lightened as follows. © 1987 American Mathematical Society

Using Tuangou to reduce IP transit costs

A majority of ISPs (Internet Service Providers) support connectivity to the entire Internet by transiting their traffic via other providers. Although the transit prices per Mbps decline steadily, the overall transit costs of these ISPs remain high or even increase, due to the traffic growth. The discontent of the ISPs with the high transit costs has yielded notable innovations such as peering, content distribution networks, multicast, and peer-to-peer localization. While the above solutions tackle the problem by reducing the transit traffic, this paper explores a novel approach that reduces the transit costs without altering the traffic. In the proposed CIPT (Cooperative IP Transit), multiple ISPs cooperate to jointly purchase IP (Internet Protocol) transit in bulk. The aggregate transit costs decrease due to the economies-of-scale effect of typical subadditive pricing as well as burstable billing: not all ISPs transit their peak traffic during the same period. To distribute the aggregate savings among the CIPT partners, we propose Shapley-value sharing of the CIPT transit costs. Using public data about IP traffic of 264 ISPs and transit prices, we quantitatively evaluate CIPT and show that significant savings can be achieved, both in relative and absolute terms. We also discuss the organizational embodiment, relationship with transit providers, traffic confidentiality, and other aspects of CIPT

Tauberian Conditions For V-convergence Of Fourier Series

It is proved that Fourier series with asymptotically even coefficients and satisfying (formula present here), for some 1 \u3c p \u3c 2, con­verge in L1-norm if and only if (formula present here), where En(t) =Σk=0neiktRecent results of Stanojevic [1], Bojanic and Stanojevic [2], and Goldberg and Stanojevic [3] are special cases of some corollaries to the main theorem. © 1982 American Mathematical Society

A Class Of Functional Equations And Mielnik Probability Spaces

Let S be the unit sphere of a normed real linear space N and let (S, p) be a Mielnik space of dimension two. For p(x, y) = f(‖x+y‖), x, yєS, where /is a continuous, strictly increasing function from [0, 2] onto [0, 1], it has been shown that (S, p) being two dimensional is equivalent to N being an inner product space. In some polarization problems modeled on the unit sphere of an inner product space, the transition probability p(x, y) may not be as well behaved as p(x, y) = f(‖x + y‖). In order to provide a more suitable setting, we have constructed wide classes of two-dimensional transitional probability spaces (S, p), all having the same set of bases ℬ with p=⌽ ° f where ⌽ is a solution of a certain functional equation. In particular, for p(x, y) = ‖x+y‖24, we answer a question due to B. Mielnik. © American Mathematical Society 1976

The Lebesgue Integral As The Almost Sure Limit Of Random Riemann Sums

A method is given for generating random intermediate points for a sequence of partitions. For the corresponding random Riemann sums it is shown that they converge almost surely to the Lebesgue integral. © 1982 American Mathematical Society

Review of eating disorders and oxytocin receptor polymorphisms.

BACKGROUND AND AIMS: Oxytocin, a nine amino acid peptide synthesised in the hypothalamus, has been widely recognised for its role in anxiolysis, bonding, sociality, and appetite. It binds to the oxytocin receptor (OXTR)-a G-protein coupled receptor-that is stimulated by the actions of oestrogen both peripherally and centrally. Studies have implicated OXTR genotypes in conferring either a risk or protective effect in autism, schizophrenia, and eating disorders (ED). There are numerous DNA variations of this receptor, with the most common DNA variation being in the form of the single nucleotide polymorphisms (SNPs). Two OXTR SNPs have been most studied in relation to ED: rs53576 and rs2254298. Each SNP has the same allelic variant that produces genotypes AA, AG, and GG. In this critical review we will evaluate the putative role of rs53576 and rs2254298 SNPs in ED. Additionally, this narrative review will consider the role of gene-environment interactions in the development of ED pathology. FINDINGS: The OXTR SNPs rs53576 and rs2254298 show independent associations between the A allele and restrictive eating behaviours. Conversely, the G allele of the OXTR rs53576 SNP is associated with binging behaviours, findings that were also evident in neuroanatomy. One study found the A allele of both OXTR SNPs to confer risk for more severe ED symptomatology while the G allele conferred some protective effect. An interaction between poor maternal care and rs2254298 AG/AA genotype conferred increased risk for binge eating and purging in women. CONCLUSIONS: Individual OXTR SNP are unlikely in themselves to explain complex eating disorders but may affect the expression of and/or effectiveness of the OXTR. A growing body of G x E work is indicating that rs53576G homozygosity becomes disadvantageous for later mental health under early adverse conditions but further research to extend these findings to eating pathology is needed. The GWAS approach would benefit this area of knowledge

Rydberg trimers and excited dimers bound by internal quantum reflection

Quantum reflection is a pure wave phenomena that predicts reflection of a particle at a changing potential for cases where complete transmission occurs classically. For a chemical bond, we find that this effect can lead to non-classical vibrational turning points and bound states at extremely large interatomic distances. Only recently has the existence of such ultralong-range Rydberg molecules been demonstrated experimentally. Here, we identify a broad range of molecular lines, most of which are shown to originate from two different novel sources: a single-photon associated triatomic molecule formed by a Rydberg atom and two ground state atoms and a series of excited dimer states that are bound by a so far unexplored mechanism based on internal quantum reflection at a steep potential drop. The properties of the Rydberg molecules identified in this work qualify them as prototypes for a new type of chemistry at ultracold temperatures.Comment: 6 pages, 3 figures, 1 tabl

γʹ and γ″ co-precipitation phenomena in directly aged Alloy 718 with high δ-phase fractions

Co-precipitation of γ′ and γ′′ is the main strengthening mechanism that provides superior high-temperature strength in directly aged Alloy 718 aerospace parts. Control of their morphology, fraction, and configuration might allow exposure to more demanding operation environments in next-generation aircraft engines. The density of geometrically necessary dislocations introduced during hot deformation has been shown to significantly affect the co-precipitate morphology of γ′ and γ′′ in materials free of the δ-phase. However, the combined effects of geometrically necessary dislocation density and lower Nb content due to higher δ-phase fractions on co-precipitation behaviour and strengthening remain unknown. We verify these effects by hardness testing as a proxy for high-temperature strength in materials with 4.1 % δ-phase fraction. Deformation at 950 °C yields a remarkable increase of 12 % in hardness after direct ageing, explained by the prevalence of complex co-precipitate configurations. Deformation at 1000 °C decreases the δ-phase fraction and geometrically necessary dislocation density but achieves up to 19 % volume fractions of γ″, leading to a predominance of monoliths and duplet co-precipitates and a better direct ageing response. Atom probe microscopy reveals the flux of elements during co-precipitation. We recommend a δ-annealing treatment before the final forging step for manufacturing stronger Alloy 718 aerospace parts

Reduction of Surface Roughness Induced Spin Relaxation in SOI MOSFETs

Abstract-Silicon is the main element of modern chargebased electronics. Understanding the details of the spin propagation in silicon structures is elementary for novel spin-based device applications. We investigate valley splitting, surface roughness scattering, and spin relaxation matrix elements in thin silicon films by using a perturbative k ⋅ p approach. We demonstrated that applying uniaxial stress along the [110] direction considerably suppresses the intersubband spin relaxation elements