An example of Bautin-type bifurcation in a delay differential equation

In a previous paper we gave sufficient conditions for a system of delay differential equations to present Bautin-type bifurcation. In the present work we present an example of delay equation that satisfies these conditions.     

Construction of Lyapunov functionals for delay differential equations in virology and epidemiology

In the present paper, we present a method for constructing a Lyapunov functional for some delay differential equations in virology and epidemiology. Here some delays are incorporated to the original ordinary differential equations, for which a Lyapunov function is already obtained. We present simple and clear explanation of our method using some models whose Lyapunov functionals are already obtained. Moreover, we present several new results for constructing Lyapunov functionals using our method.     

A bounce back-immersed boundary-lattice Boltzmann model for curved boundary

In this paper, a bounce back-immersed boundary-lattice Boltzmann model(BB-IB-LBM) is proposed for curved boundary.In the present model, a modified density distribution function is proposed for curved boundary including stationary and moving curved boundaries. A special treatment is also developed to satisfy no-slip boundary condition for the curved boundary with large curvature. On Lagrangian boundary points, the modified distribution functions are implemented to replace the artificial correction force in conventional immersed boundary-lattice Boltzmann methods(IB-LBMs). Numerical experiments are given to illustrate the accuracy and efficiency of present BB-IB-LBM. The drag coefficient of the test cases predicted by the present model is in better agreement with the results of experimental results than that of the previous IB-LBMs. It is also concluded that the average drag coefficient of present model are consistent with the experimental results. Comparing with conventional IB-LBMs, the present model eliminates the non-physical vortex at the tail of an airfoil. Simulation of flow over a sphere also proves the extensibility of present method in three-dimensional simulation.     

A Lagrangian relaxation approach to solve the second phase of the exam scheduling problem

The problem of scheduling final exams at a large university can be viewed as a three phase process. The first phase consists of grouping the exams into sets called exam blocks. The second phase deals with the assignment of exam blocks to exam days and the third phase consists of arranging the exam days and also arranging the blocks within days.In this paper, we present new integer programming formulations for the second phase of the scheduling problem. We present an integer program with a single objective of minimizing the number of students with two or more exams per day. We then present a Lagrangian relaxation based solution procedure to solve this problem. Further, we present a bicriterion integer programming formulation to minimize the number of students with two exams per day and the number of students with three exams per day. Finally, we present some computational experience using randomly generated problems as well as real world data obtained from the State University of New York at Buffalo.     

Finitarily deterministic generators for zero entropy systems

Zero entropy processes are known to be deterministic—the past determines the present. We show that each is isomorphic, as a system, to a finitarily deterministic one, i.e., one in which to determine the present from the past it suffices to scan a finite (of random length) portion of the past. In fact we show more: the finitary scanning can be done even if the scanner is noisy and passes only a small fraction of the readings, provided the noise is independent of our system. The main application we present here is that any zero entropy system can be extended to a random Markov process (namely one in which the conditional distribution of the present given the past is a mixture of finite state Markov chains). This allows one to study zero entropy transformations using a procedure completely different from the usual cutting and stacking.     

Multinomial convolution polynomials

In [9] Knuth shows how to derive the convolution formulas of Hagen, Rothe and Abel from Vandermonde's convolution and the binomial theorem for integer exponents. In the present paper, we shall first present a short and elementary proof of the multi-extension of the above convolution formulas, due to Raney and Mohanty. In the second part we shall present a multi-version of Knuth's approach to convolution polynomials and derive another short proof of the above formulas.     

Vibration and stability analysis of a simply-supported Rayleigh beam with spinning and axial motions

The vibration and stability of a simply supported beam are analyzed when the beam has an axially moving motion as well as a spinning motion. When a beam has spinning and axial motions, rotary inertia plays an important role on the lateral vibration. Compared to previous studies, the present study adopts the Rayleigh beam theory and derives more exact kinetic energy and equations of motion. The rotary inertia terms derived by the present study are compared to those of the previous studies. We investigate the natural frequencies between the present and previous studies. In addition, the critical speed and stability boundary for the spinning and moving speeds are also analyzed. It can be observed from the computed natural frequencies and dynamic responses that the present equations of motion are more reliable than the previous equations because the present equations fully consider the rotary inertia terms.     

一类随机利率下的确定年金

我们考虑在一定的约束条件下利率是随机变量的某些确定年金的现值的计算问题,目的在于研究给付现值的期望和方差.本文给出两种方法计算在某些年内一类延付年金的现值之和的期望和方差,获得了给付现值的方差的递推关系,并且解决了这些关系,这在计算简单方面明显地更好.     

Artificial boundary conditions to compute correctors in linear elasticity

We present the derivation of a transparent boundary condition of order two to solve the equations of linear elasticity in a half plane. The resolution of the boundary value problem leads to a noncoercive variational formulation. We also present some numerical examples.     

Hybrid Conjugate Gradient Method for a Convex Optimization Problem over the Fixed-Point Set of a Nonexpansive Mapping

The main aim of the paper is to accelerate the existing method for a convex optimization problem over the fixed-point set of a nonexpansive mapping. To achieve this goal, we present an algorithm (Algorithm 3.1) by using the conjugate gradient direction. We present also a convergence analysis (Theorem 3.1) under some assumptions. Finally, to demonstrate the effectiveness and performance of the proposed method, we present numerical comparisons of the existing method with the proposed method.     

A Numerical Method to Solve Higher-Order Fractional Differential Equations

Mediterranean Journal of Mathematics - In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present...     

Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations

The purpose of this paper is to present some fixed point theorems in a complete metric space endowed with a partial order by using altering distance functions. We also present some applications to first and second order ordinary differential equations.     

Optimizing the simultaneous management of blood pressure and cholesterol for type 2 diabetes patients

We present a Markov decision process (MDP) model to determine the optimal timing of blood pressure and cholesterol medications. We study the use of our model for a high-risk population of patients with type 2 diabetes; however, the model and methods we present are applicable to the general population. We compare the optimal policies based on our MDP to published guidelines for initiation of blood pressure and cholesterol medications over the course of a patient’s lifetime. We also present a bicriteria analysis that illustrates the trade off between quality-adjusted life years and costs of treatment.     

Canonical transformations,umbral calculus,and orthogonal theory

We present a theory of representations of canonical transformations which links together the theories of evolution semigroups, Hamiltonian flows, umbral operators, and cross-sequences. We also present a different approach to the orthogonal theory of moment systems.     

An improved iteration regularization method and application to reconstruction of dynamic loads on a plate

We present an improved iteration regularization method for solving linear inverse problems. The algorithm considered here is detailedly given and proved that the computational costs for the proposed method are nearly the same as the Landweber iteration method, yet the number of iteration steps by the present method is even less. Meanwhile, we obtain the optimum asymptotic convergence order of the regularized solution by choosing a posterior regularization parameter based on Morozov’s discrepancy principle, and the present method is applied to the identification of the multi-source dynamic loads on a surface of the plate. Numerical simulations of two examples demonstrate the effectiveness and robustness of the present method.     

多状态概率转移模型在医院住院管理系统的应用

在医院现代化管理的进程中，医院管理者需要经常了解医院病人的流动情况，尤其是住院病人。根据部门反馈的信息，综合分析，对病人的收容和病床的使用安排作出科学的管理决策。本文试用随机过程理论分析医院住院管理系统，建立了医院住院管理系统的多状态概率转移模型（简称ＨＱＭ模型），并分析了住院管理系统的几个优化指标。     

Monte Carlo simulation via a numerical algorithm for solving a nonlinear inverse problem

This paper is intended to provide a numerical algorithm involving the combined use of the finite differences scheme and Monte Carlo method for estimating the diffusion coefficient in a one-dimensional nonlinear parabolic inverse problem. In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. To modify the values of estimated coefficients of this polynomial form, we introduce a random search algorithm in Monte Carlo method for global optimization. A numerical test is performed in order to show the efficiency and accuracy of the present work.     

运用多重分形和小波变换预测油气储量及确定勘探井位

本文尝试将多重分形和小波变换紧密结合用于预测油 田储量及勘探蝇位，相应地提出了一种新型实用算法，这种算法计算简便，精度高。本文在运用多重分形进行分析时，引入了反映多重分形谱图凸性的新指标，并提出了在运用多重分形指标的同时进行综合分析的方法。