A result on the sum of element orders of a finite group

Let G be a finite group and $$\psi (G)=\sum _{g\in {G}}{o(g)}$$. There are some results about the relation between $$\psi (G)$$ and the structure of G. For instance, it is proved that if G is a group of order n and $$\psi (G)>\dfrac{211}{1617}\psi (C_n)$$, then G is solvable. Herzog et al. in (J Algebra 511:215–226, 2018) put forward the following conjecture: Conjecture. If G is a non-solvable group of order n, then $$\begin{aligned} {\psi (G)}\,{\le }\,{{\dfrac{211}{1617}}{\psi (C_n)}}, \end{aligned}$$with equality if and only if $$G \cong A_5$$. In particular, this inequality holds for all non-Abelian simple groups. In this paper, we prove a modified version of Herzog’s Conjecture.     

Systemic Risk and Stochastic Games with Delay

We propose a model of inter-bank lending and borrowing which takes into account clearing debt obligations. The evolution of log-monetary reserves of banks is described by coupled diffusions driven by controls with delay in their drifts. Banks are minimizing their finite-horizon objective functions which take into account a quadratic cost for lending or borrowing and a linear incentive to borrow if the reserve is low or lend if the reserve is high relative to the average capitalization of the system. As such, our problem is a finite-player linear–quadratic stochastic differential game with delay. An open-loop Nash equilibrium is obtained using a system of fully coupled forward and advanced-backward stochastic differential equations. We then describe how the delay affects liquidity and systemic risk characterized by a large number of defaults. We also derive a closed-loop Nash equilibrium using a Hamilton–Jacobi–Bellman partial differential equation approach.     

Improving Thompson's Conjecture for Suzuki Groups

Let G be a finite group and cs(G) be the set of conjugacy class sizes of G. In 1987, J. G. Thompson conjectured that, if G is a finite group with Z(G) = 1 and M is a nonabelian simple group satisfying that cs(G) = cs(M), then G ? M. This conjecture has been proved for Suzuki groups in [5 Guiyun, C. (1996). On Thompson's conjecture. J. Algebra 185(1):184–193.[Crossref], [Web of Science ®] , [Google Scholar]]. In this article, we improve this result by proving that, if G is a finite group such that cs(G) = cs(Sz(q)), for q = 2^2m+1, then G ? Sz(q) × A, where A is abelian. We avoid using classification of finite simple groups in our proofs.     

Numerical simulation of a Gaussian beam profile passing through a Kerr medium

The circular Gaussian beam shape has been simulated by numerical evaluation on beam shape based on z-scan method through beam radius. This method is useful in many studies such as z-scan experiments. The validity of the relation between peak and valley separation in close aperture data and the diffraction length of the beam has been investigated by this method for some real cases. The results are in good agreement with the experimental studies.     

Orthogonal polynomials and continued fractions arising from contiguous relations and generalizations of Kummer and q-Kummer identities

The Ramanujan Journal - In this paper, we show formally how can we generate continued fractions starting from three-term contiguous relations. Then as examples, starting from certain contiguous...     

带鳍通道性能的遗传算法优化

与光滑通道相比,带鳍通道有更高的传热系数,附加的鳍,极大地增强了通道的传热.然而,传热的增强又与压降的升高相关联,这又导致泵动力需求的增加,因此应该寻求对该系统的优化设计.该文的主要目的是,通过如下方式来精确地确定鳍的位置和尺寸:利用遗传算法实现最小压降时达到最优传热.鳍的每种布局作为问题(遗传算法中的一个个体)的一个解.通常,首先随机地产生一个初始种群,然后该算法在所有这些解中搜索,利用布局函数迭代出新解,最后得到鳍的优化设计.     

Preparation and characterization of NiO nanoparticles from thermal decomposition of the [Ni(en)3](NO3)2 complex: A facile and low-temperature route

NiO nanoparticles with an average size of 15 nm were easily prepared via the thermal decomposition of the tris(ethylenediamine)Ni(II) nitrate complex [Ni(en)₃](NO₃)₂ as a new precursor at low temperature, and the nanoparticles were characterized by thermal analysis (TGA/DTA), X-ray diffraction (XRD), Fourier-transformed infrared spectroscopy (FT-IR), UV-Vis spectroscopy, BET specific surface area measurement, scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX), transmission electron microscopy (TEM) and magnetic measurements. The magnetic measurements confirm that the product shows a ferromagnetic behavior at room temperature, which may be ascribed to a size confinement effect. The NiO nanoparticles prepared by this method could be an appropriate photocatalytic material due to a strong absorption band at 325 nm. This method is simple, fast, safe, low-cost and also suitable for industrial production of high purity NiO nanoparticles for applied purposes.     

The Cost Reduction of Distributed Quantum Factorization Circuits

International Journal of Theoretical Physics - The number of qubits involved in a quantum system increases as the quantum computation is being progressed. Restrictions in monolithic quantum...     

Grafting of Anionic Decahydro-Closo-Decaborate Clusters on Keggin and Dawson-Type Polyoxometalates: Syntheses,Studies in Solution,DFT Calculations and Electrochemical Properties

Herein we report the synthesis of a new class of compounds associating Keggin and Dawson-type Polyoxometalates (POMs) with a derivative of the anionic decahydro-closo-decaborate cluster [B₁₀H₁₀]²⁻ through aminopropylsilyl ligand (APTES) acting as both a linker and a spacer between the two negatively charged species. Three new adducts were isolated and fully characterized by various NMR techniques and MALDI-TOF mass spectrometry, notably revealing the isolation of an unprecedented monofunctionalized SiW₁₀ derivative stabilized through intramolecular H-H dihydrogen contacts. DFT as well as electrochemical studies allowed studying the electronic effect of grafting the decaborate cluster on the POM moiety and its consequences on the hydrogen evolution reaction (HER) properties.