一种基于校正无线电传播时间的室内三维定位模型

对室内终端进行基于无线通信基站的三维定位时,由于无线电在传播过程中,存在建筑物或树木遮挡、反射、折射等物理现象,导致基站到终端传播时间的测量值与精确值之间存在误差.为了减少上述误差对定位精度的影响,运用无线定位原理建立了一种基于校正无线电传播时间的改进的室内三维定位模型.通过对2016年全国研究生数学建模问题C题所提供的不同场景的数据分析,发现基站与终端无线电传播时间的测量值与其精确值之间存在线性关系,而且同一场景下近似有相同的线性关系,场景不同线性关系一般不同.基于这一现象,对基本的定位模型进行了合理的修正形成了改进的定位模型,数值实验表明改进的定位模型有很好的定位精度和鲁棒性.     

The graph structure of a deterministic automaton chosen at random

An n‐state deterministic finite automaton over a k‐letter alphabet can be seen as a digraph with n vertices which all have k labeled out‐arcs. Grusho (Publ Math Inst Hungarian Acad Sci 5 (1960), 17–61). proved that whp in a random k‐out digraph there is a strongly connected component of linear size, i.e., a giant, and derived a central limit theorem. We show that whp the part outside the giant contains at most a few short cycles and mostly consists of tree‐like structures, and present a new proof of Grusho's theorem. Among other things, we pinpoint the phase transition for strong connectivity. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 428–458, 2017     

A nonstandard finite difference method for solving a mathematical model of HIV-TB co-infection

We design and analyze an unconditionally convergent nonstandard finite-difference method to study transmission dynamics of a mathematical model of HIV-TB co-infection. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves positivity of the solution which is one of the essential requirements when modelling epidemic diseases. Furthermore, we show that the numerical method is unconditionally stable. Competitive numerical results confirming theoretical investigations are provided. Comparisons are also made with other conventional approaches that are routinely used to solve these types of problems.     

Constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3

The main results of this paper are in two directions. First, the family of finite local Frobenius non-chain rings of length 4 (hence of nilpotency index 3) is determined. As a by-product all finite local Frobenius non-chain rings with $p^4$ elements, (p a prime) are given. Second, the number and structure of γ-constacyclic codes over finite local Frobenius non-chain rings with nilpotency index 3, of length relatively prime to the characteristic of the residue field of the ring, are determined.     

Rees–Shishikura’s theorem for geometrically finite rational maps

In this paper, we generalize Rees–Shishikura’s theorem to the class of geometrically finite rational maps.     

关于半clean群环

环$R$称为是半clean的, 是指环中的每个元素都是一个单位与一个周期元的和. clean环是半clean的. 刻画半clean群环的一般情形是不容易的. 我们的目的是考虑如下问题：若$G$ 是局部有限群或者是阶是3的循环群, 群环$RG$何时是semiclean的. clean群环上的一些已有结果被推广.     

Structural Properties of Hachimoji Nucleic Acids and Their Building Blocks: Comparison of Genetic Systems with Four,Six and Eight Alphabets

Expansion of the genetic alphabet is an ambitious goal. A recent breakthrough has led to the eight-base (hachimoji) genetics having canonical and unnatural bases. However, very little is known on the molecular-level features that facilitate the candidature of unnatural bases as genetic alphabets. Here we amalgamated DFT calculations and MD simulations to analyse the properties of the constituents of hachimoji DNA and RNA. DFT reveals the dominant syn conformation for isolated unnatural deoxyribonucleosides and at the 5′-end of oligonucleotides, although an anti/syn mixture is predicted at the nonterminal and 3′-terminal positions. However, isolated ribonucleotides prefer an anti/syn mixture, but mostly prefer anti conformation at the nonterminal positions. Further, the canonical base pairing combinations reveals significant strength, which may facilitate replication of hachimoji DNA. We also identify noncanonical base pairs that can better tolerate the substitution of unnatural pairs in RNA. Stacking strengths of 51 dimers reveals higher average stacking stabilization of dimers of hachimoji bases than canonical bases, which provides clues for choosing energetically stable sequences. A total of 14.4 μs MD simulations reveal the influence of solvent on the properties of hachimoji oligonucleotides and point to the likely fidelity of replication of hachimoji DNA. Our results pinpoint the features that explain the experimentally observed stability of hachimoji DNA.     

Synthesis,computational, experimental antimicrobial activities and theoretical molecular docking studies of (E)-4-((4-hydroxy-3-methoxy-5-nitrobenzylidene) amino)-N-(thiazole-2-yl) benzenesulfonamide

The compound (E)-4-((4-hydroxy-3-methoxy-5-nitrobenzylidene) amino)-N-(thiazole-2-yl) benzene sulfonamide (5NVTH) was synthesized and characterized by the Infrared, UV-Visible, and NMR analysis. The compound theoretical study was done by using DFT. The compound molecular structure and geometry were defined using DFT. Topological studies, like ELF, LOL, ALIE, and RDG studies, were done with the Multiwfn-3.8 to find the main binding areas and weak interactions in the molecule. Using the IEFPCM solvation model was used to study the calculated UV-Visible spectrum. The HOMO-LUMO, MEP, and NBO properties were carried out in the gas phase. The NBO calculations are used to study how charges move between and within the molecule and the stability of this molecule. A pharmacological analysis is done using an online tool like Swiss-ADME, to see if the molecule could be a potential drug candidate; this evaluation looks at the drug-likeness, ADME, and eco-friendly toxicity properties of the 5NVTH molecule. Auto-dock suite is used for molecular docking study and discovery studio is used for analyzing the docking results. Antimicrobial activity studies indicate the compound Klebsiella pneumonia and Candida albicans have good antibacterial and antifungal activity compared to positive control and other microorganisms.     

Explicit finite difference simulations for accelerating cross diffusion flow over a perpendicular shield with parabolic motion

The heat transfer phenomenon subject to thermos-diffusion effects convey important applications in the heating processes, extrusion systems, chemical processes and various engineering systems. The objective of current work is to observe the contribution of Soret and Dufour effects in oscillating shield for cross diffusion flow. The perpendicular shield with oscillating motion induced the flow. The magnitude of oscillations is assumed to be small so that laminar flow due to oscillating shield has been resulted. The motivations for addressing the thermos-diffusion phenomenon due to oscillating of shield are due to applications in oscillatory pumps, moving surface, metal detectors, power systems etc. The dimensionless problem is obtained via introducing the appropriate set of variables. The numerical outcomes are suggested by using the most interesting explicit finite difference scheme. The physical illustration for flow parameters is presented. Moreover, the aspect of physical quantities involving the flow are graphically reported.