On power series statistical convergence and new uniform integrability of double sequences

In the present paper,we mostly focus on P_(p)^(2)-statistical convergence.We will look into the uniform integrability via the power series method and its characterizations for double sequences.Also,the notions of P_(p)^(2)-statistically Cauchy sequence,P_(p)^(2)-statistical boundedness and core for double sequences will be described in addition to these findings.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.

ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 2:Musculotendon Dynamics and Related Stress Effects

In this paper we develop an elasto-dynamic model of the human arm that includes effects of neuro-muscular control upon elastic deformation in the limb.The elasto-dynamic model of the arm is based on hybrid parameter multiple body system variational projection principles presented in the companion paper.Though the technique is suitable for detailed bone and joint modeling,we present simulations for simplified geometry of the bones,discretized as Rayleigh beams with elongation,while allowing for large deflections.Motion of the upper extremity is simulated by incorporating muscle forces derived from a Hill-type model of musculotendon dynamics.The effects of muscle force are modeled in two ways.In one approach,an effective joint torque is calculated by multiplying the muscle force by a joint moment ann.A second approach models the muscle as acting along a straight line between the origin and insertion sites of the tendon.Simple arm motion is simulated by utilizing neural feedback and feedforward control.Simulations illustrate the combined effects of neural control strategies, models of muscle force inclusion,and elastic assumptions on joint trajectories and stress and strain development in the bone and tendon.

Singular solitons and other solutions to a couple of nonlinear wave equations

This paper addresses the extended （G′/G）-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method.

Quasi-Periodic Structures Based on Symmetrical Lucas Function of (2+1)-Dimensional Modified Dispersive Water-Wave System

By introducing the Lucas-Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a （2＋1）-dimensional modified dispersive water-wave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riecati equation that the symmetrical Lucas functions satisfy. From the variable separation sohition and by selecting appropriate functions, some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons are investigated.

A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 1:Model Development

In this paper we develop an elasto-dynamic model of the human arm for use in neuro-muscular control and dynamic interaction studies.The motivation for this work is to present a case for developing and using non-quasistatic models of human musculo-skeletal biomechanics.The model is based on hybrid parameter multiple body system(HPMBS)variational projection principles.In this paper,we present an overview of the HPMBS variational principle applied to the full elasto-dynamic model of the arm.The generality of the model allows one to incorporate muscle effects as either loads transmitted through the tendon at points of origin and insertion or as an effective torque at a joint.Though the technique is suitable for detailed bone and joint modeling,we present in this initial effort only simple geometry with the bones discretized as Rayleigh beams with elongation, while allowing for large deflections.Simulations demonstrate the viability of the mcthod for use in the companion paper and in future studies.

RATIONAL COMBINATION OF{x^(λ_n)}ARE ALWAYS DENSE IN C_([0,1])

The present paper shows that for any sequence of real numbers with infinite distinct elements{λ_n},the rational combination of{x~λ}are always dense in C_[0,1].

Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor

A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring tra- jectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1>0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate λ1 has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.

A Note on the Statistical Approximation Properties of the Modified Discrete Operators

In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.

Confidence Intervals for Relative Intensity of Collaboration(RIC)Indicators

Purpose:We aim to extend our investigations related to the Relative Intensity of Collaboration(RIC)indicator,by constructing a confidence interval for the obtained values.Design/methodology/approach:We use Mantel-Haenszel statistics as applied recently by Smolinsky,Klingenberg,and Marx.Findings:We obtain confidence intervals for the RIC indicatorResearch limitations:It is not obvious that data obtained from the Web of Science(or any other database)can be considered a random sample.Practical implications:We explain how to calculate confidence intervals.Bibliometric indicators are more often than not presented as precise values instead of an approximation depending on the database and the time of measurement.Our approach presents a suggestion to solve this problem.Originality/value:Our approach combines the statistics of binary categorical data and bibliometric studies of collaboration.

Distribution Functions of Copulas

A general method was proposed to evaluate the distribution function of （C1｜C2 ） . Some examples were presented to validate the application of the method. Then the sufficient and necessary condition for that the distribution function of （ C1 ｜ C2 ） is uniform was proved.

Upper Bound of Scalars in the Integer Sub-decomposition Method： The Theoretical Aspects

The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） with max {｜k11｜, ｜k12｜} 〈 Ca√n and max{｜k21｜, ｜k22｜}≤C√, where C=I that uses efficiently computable endomorphisms ψj for j=1,2 to compute any multiple kP of a point P of order n lying on an elliptic curve E. The upper bounds of sub-scalars in ISD method are presented and utilized to enhance the rate of successful computation of scalar multiplication kP. Important theorems that establish the upper bounds of the kernel vectors of the ISD reduction map are generalized and proved in this work. The values of C in the upper bounds, that are greater than 1, have been proven in two cases of characteristic polynomials （with degree 1 or 2） of the endomorphisms. The upper bound of ISD method with the case of the endomorphism rings over an integer ring Z results in a higher rate of successful computations kP. Compared to the case of endomorphism rings, which is embedded over an imaginary quadratic field Q = [4-D]. The determination of the upper bounds is considered as a key point in developing the ISD elliptic scalar multiplication technique.

Change in Energy of Non-Spinning Black Holes w.r.t. the Change in Mass

The present work discusses the derivation of the formula for the change in energy of non-spinning black holes with respect to the change in mass (dE/dM), which gives a constant quantity equal to 8.9998 x 1016 Joule/kg in both categories of X-ray binaries (XRBs) and Active Galactic Nuclei (AGN). This formula can be used to justify the life time of black hole given by Γ = 2.098(M/Mο)3 x 1067 years as proposed by Stephen Hawking, where M and Mο are the mass of the black hole and the sun respectively. The authors also calculate the change in energy and mass of non-spinning black holes with respect to the change in the radius of event horizon as well as (dE/dM) for different test non-spinning black holes in X-ray binaries (XRBs) and Active Galactic Nuclei (AGN).

Effects of Nonparabolicity on Electron Thermopower of Size-Quantized Semiconductor Films

Effects of nonparabolicity of energy band on thermopower, in-plane effective mass and Fermi energy are inves- tigated in size-quantized semiconductor films in a strong while non-quantized magnetic field. We obtain the expressions of these quantities as functions of thickness, concentration and nonparabolicity parameter. The influence of nonparabolicity is studied for degenerate and non-degenerate electron gases, and it is shown that nonparabolicity changes the character of thickness and the concentration dependence of thermopower, in-plane effective mass and Fermi energy. Moreover, the magnitudes of these quantities significantly increase with respect to the nonparabolicity parameter in the case of strong nonparabolicity in nano-films. The concentration depen- dence is also studied, and it is shown that thermopower increases when the concentration decreases. These results are in agreement with the experimental data.

REDUCED MINIMAL NUMERICAL RANGES OF OPERATORS ON A HILBERT SPACE

In this note,the reduced minimal numerical ranges of a bounded linear oper- ators on a Hilbert space are defined and some of its properties are established.

细胞内吞纳米颗粒药物的数值模拟研究

受体介导的内吞是细胞与外界物质交换的常见方式.采用配体修饰表面的纳米脂质体颗粒,将药物有针对性地投放到肿瘤细胞以提高药物传输的效率,是药物传输系统设计中的核心问题之一.本文假设内吞是准静态过程,采用三维数学模型来模拟球状纳米颗粒的内吞,建立了包含绑定键的系统变形能方程,通过求解能量方程的最小值,得到药物在每个内吞包裹阶段的变形以及药物的被动内吞所需最小能量,分析不同药物半径对内吞所需最小能量的影响.研究表明,细胞膜变形能与绑定键变形能占总能量的绝大部分,各组分随着包裹区域增加均有变化;在给定细胞膜和药物颗粒的硬度、绑定键强度等物理特性下存在最优药物尺寸,使得内吞过程中总能耗最小;在药物内吞进行的后期,包裹区域边缘的绑定键因伸长过大发生断裂,影响内吞的顺利完成.本研究为受体介导的高效药物设计提供了理论支撑.

A New Random Forest Applied to Heavy Metal Risk Assessment

As soil heavy metal pollution is increasing year by year,the risk assess-ment of soil heavy metal pollution is gradually gaining attention.Soil heavy metal datasets are usually imbalanced datasets in which most of the samples are safe samples that are not contaminated with heavy metals.Random Forest(RF)has strong generalization ability and is not easy to overfit.In this paper,we improve the Bagging algorithm and simple voting method of RF.AW-RF algorithm based on adaptive Bagging and weighted voting is proposed to improve the classifica-tion performance of RF on imbalanced datasets.Adaptive Bagging enables trees in RF to learn information from the positive samples,and weighted voting method enables trees with superior performance to have higher voting weights.Experi-ments were conducted using G-mean,recall and F1-score to set weights,and the results obtained were better than RF.Risk assessment experiments were conducted using W-RF on the heavy metal dataset from agricultural fields around Wuhan.The experimental results show that the RW-RF algorithm,which use recall to calculate the classifier weights,has the best classification performance.At the end of this paper,we optimized the hyperparameters of the RW-RF algorithm by a Bayesian optimization algorithm.We use G-mean as the objective function to obtain the opti-mal hyperparameter combination within the number of iterations.

Analytical Approach to Fractional Zakharov-Kuznetsov Equations by He's Homotopy Perturbation Method

The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.

LOOMIS-WHITNEY'S INEQUALITY ABOUT MIXED BODY

In this article, the authors establish two theorems for mixed body, which are the generalizations of the well-known Loomis-Whitney＇s inequality.