There are several statements equivalent to the famous Riemann hypothesis. In 2011, Solé and Planat stated that hypothesis is true if only inequality \(\zeta(2) \cdot \prod_{q\leq q_{n}} (1+\frac{1}{q}) > e^{\gamma} \log \theta(q_{n})\) holds for all prime numbers \(q_{n}> 3\), where \(\theta(x)\) Chebyshev function, \(\gamma \approx 0.57721\) Euler-Mascheroni constant, \(\zeta(x)\) zeta f...

Given a supercritical branching random walk $$\{Z_n\}_{n\ge 0}$$ on $${\mathbb {R}}$$ , let $$Z_n(A)$$ be the number of particles located in set $$A\subset {\mathbb at generation n. It is known from Biggins (J Appl Probab 14:630–636, 1977) that under some mild conditions, for $$\theta \in [0,1)$$ $$n^{-1}\log Z_n([\theta x^* n,\infty ))$$ converges almost surely to $$\log \left( {E}}[Z_1({\math...

We study the stability and electronic structure of magic-angle twisted bilayer graphene on hexagonal boron nitride (TBG/BN). Full relaxation has been performed for commensurate supercells heterostructures with different twist angles ($\theta'$) stackings between TBG BN. find that slightly misaligned configuration $\theta' = 0.54^\circ$ AA/AA stacking globally lowest total energy due to construc...

Online working of a government or providing its services online to its citizens at their door step is known as E-Governance. E-Governance is E-Commerce technology means online availability of government services. The technology and the methods used in E-Governance project provide a roadmap for efficient delivery of services at the door step. In today's time the development of any country d...

‎The problem of shrinkage testimation (test-estimation) for the Rayleigh scale‎ ‎parameter θ based on censored samples under the reflected‎ ‎gamma loss function is considered‎. We obtain the minimum risk‎ ‎estimator among a subclass and compute its risk‎. ‎A shrinkage‎ ‎testimator based on acceptance or rejection of a null hypothesis&lr...

Low-dimensional excitonic materials have inspired much interest owing to their novel physical and technological prospects. In particular, those with strong in-plane anisotropy are among the most intriguing but short of general analyses. We establish universal functional form anisotropic dispersion in small $k$ limit for 2D dipolar systems. While energy is linearly dispersed direction parallel d...

Phylogenetic fears involve stimuli representing a real or potential threat to the species’ evolutionary ancestors. We tested whether individuals with a phylogenetic fear (spider phobics, n = 17) differed in EEG general activity (delta band power) of the oldest brain system and in complexity from individuals with a non-phylogenetic fear (flight phobics, n = 15) during eyes open and eyes closed r...

The public sector needs to change over to communicating digitally. This development makes great demands both on work processes in the public sector and on the Information Technology systems, on which e-government is based. From the economic perspective, the change-over poses great challenges, as huge investments will have to be made in Information Technology in the public sector. It is therefor...

Some recent work of Gross and Prasad [14] suggests that the root numbers attached to certain symplectic representations of the Weil-Deligne group of a local field F control certain branching rules for representations of orthogonal groups over F . On a global level, this local phenomenon should have implications for the structure of the value at the center of symmetry for certain L-functions of ...