Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

A note on Herglotz’s theorem for time series on function spaces

In this article, we prove Herglotz’s theorem for Hilbert-valued time series. This requires the notion of an operator-valued measure, which we shall make precise for our setting. Herglotz’s theorem for functional time series allows to generalize existing results that are central to frequency domain analysis on the function space. In particular, we use this result to prove the existence of a functional Cramér representation of a large class of processes, including those with jumps in the spectral distribution and long-memory processes. We furthermore obtain an optimal finite dimensional reduction of the time series under weaker assumptions than available in the literature. The results of this paper therefore enable Fourier analysis for processes of which the spectral density operator does not necessarily exist.     

Effective intervals and regular Dirichlet subspaces

It is shown in Li and Ying (2019) that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces. The first result is a complete characterization for a Dirichlet form to be a regular subspace of such a Dirichlet form in terms of effective intervals. Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals in the representation above. Finally applying previous results, we shall prove that every regular and local Dirichlet form has a special standard core generated by a continuous and strictly increasing function.     

Synthesis and characterization of new homologue multinary selenides,M2Sb5Bi5Se17 (M = Sn,Pb)

New quaternary selenides M₂Sb₅Bi₅Se₁₇ (M = Sn, Pb) were synthesized using solid-state sintering reactions that crystallize in the monoclinic system with C2/m (No. 12) space group with lattice parameters a = 27.914(7) Å, b = 4.0804(11) Å, c = 15.512(4) Å, and β = 114.881(9)° for M = Sn, and a = 27.987(3) Å, b = 4.1062(5) Å, c = 15.6372(19) Å, and β = 115.318(3)° for M = Pb, respectively. The crystal structure is related to a homologous series [A⁺²_2x−4B⁺³₄ Se⁻²_2x−2][B⁺³_2y−2Se⁻²_3y−3] with (x, y) = (3, 4) that contains building units of two-dimensional slabs of NaCl¹¹¹-type [Sb₂Bi₄Se₁₁] separated by 1D ribbons NaCl¹⁰⁰-type [Pb₂Sb₃BiSe₆]. The NaCl¹¹¹ unit contains edge-shared octahedra filled with Sb³⁺ and Bi³⁺ cations, which are parallel and overlapped to form a step-layer 2D network stacking alone [001]. The NaCl¹⁰⁰ type ribbons containing Pb²⁺ and Sb³⁺ in square or trigonal pyramidal environments with the general formula [M₆Se₆] filled in the space between 2D layers of NaCl¹¹¹ units. The conductivity measurement revealed semiconducting property with band gaps of ~0.1 eV. Pb₂Sb₅Bi₅Se₁₇ exhibits low thermal conductivity 3,000 μW cm⁻¹ K⁻¹ in a temperature range of 300–480 K.     

In silico study of novel niclosamide derivatives,SARS-CoV-2 nonstructural proteins catalytic residue-targeting small molecules drug candidates

The severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2)-mediated coronavirus disease 2019 (COVID-19) infection remains a global pandemic and health emergency with overwhelming social and economic impacts throughout the world. Therapeutics for COVID-19 are limited to only remdesivir; therefore, there is a need for combined, multidisciplinary efforts to develop new therapeutic molecules and explore the effectiveness of existing drugs against SARS-CoV-2. In the present study, we reported eight (SCOV-L-02, SCOV-L-09, SCOV-L-10, SCOV-L-11, SCOV-L-15, SCOV-L-18, SCOV-L-22, and SCOV-L-23) novel structurally related small-molecule derivatives of niclosamide (SCOV-L series) for their targeting potential against angiotensin-converting enzyme-2 (ACE2), type II transmembrane serine protease (TMPRSS2), and SARS-COV-2 nonstructural proteins (NSPs) including NSP5 (3CLpro), NSP3 (PLpro), and RdRp. Our correlation analysis suggested that ACE2 and TMPRSS2 modulate host immune response via regulation of immune-infiltrating cells at the site of tissue/organs entries. In addition, we identified some TMPRSS2 and ACE2 microRNAs target regulatory networks in SARS-CoV-2 infection and thus open up a new window for microRNAs-based therapy for the treatment of SARS-CoV-2 infection. Our in vitro study revealed that with the exception of SCOV-L-11 and SCOV-L-23 which were non-active, the SCOV-L series exhibited strict antiproliferative activities and non-cytotoxic effects against ACE2- and TMPRSS2-expressing cells. Our molecular docking for the analysis of receptor-ligand interactions revealed that SCOV-L series demonstrated high ligand binding efficacies (at higher levels than clinical drugs) against the ACE2, TMPRSS2, and SARS-COV-2 NSPs. SCOV-L-18, SCOV-L-15, and SCOV-L-09 were particularly found to exhibit strong binding affinities with three key SARS-CoV-2’s proteins: 3CLpro, PLpro, and RdRp. These compounds bind to the several catalytic residues of the proteins, and satisfied the criteria of drug-like candidates, having good adsorption, distribution, metabolism, excretion, and toxicity (ADMET) pharmacokinetic profile. Altogether, the present study suggests the therapeutic potential of SCOV-L series for preventing and managing SARs-COV-2 infection and are currently under detailed investigation in our lab.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

A statistical approach to characterize the viscoelastic creep compliances of a vinyl ester polymer

The objective of this study was to develop a model to predict the viscoelastic material functions of a vinyl ester (VE) polymer with variations in its experimentally obtained material properties under combined isothermal and mechanical loading. Short-term tensile creep experiments were conducted at three temperatures below the glass transition temperature of the VE polymer, with 10 replicates for each test configuration. The measured creep strain versus time responses were used to determine the creep compliances using the generalized viscoelastic constitutive equation with a Prony series representation. The variation in the creep compliances of a VE polymer was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the creep compliances using a two-parameter Weibull distribution. Both Weibull scale and shape parameters of the creep compliance distributions were shown to be time and temperature dependent. Two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and, subsequently, the CDFs of the creep compliances for the complete design temperature range during steady state creep. At each test temperature, creep compliance curves were obtained for constant CDF values and compared with the experimental data. The predicted creep compliances of the selected VE polymer in the design space are in good agreement with the experimental data for all three test temperatures.     

一类弱奇性Volterra积分微分方程的级数展开数值解法

本文考察了一类弱奇性积分微分方程的级数展开数值解法,并给出了相应的收敛性分析.理论分析结果表明,若用已知函数的谱配置多项式逼近已知函数,那么方程的数值解以谱精度逼近方程的真解.数值实验数据也验证了这一理论分析结果.     

The lower order and linear order of multiple dirichlet series

The article investigates the growth of multiple Dirichlet series.The lower order and the linear order of n-tuple Dirichlet series in C~n are defined and some relations between them and the coefficients and exponents of n-tuple Dirichlet series are obtained.