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In this paper, minimizing makespan for singlemachine scheduling problem with human energy recovery function under nonlinear time-dependent deterioration is considered. Firstly, a human recovery function is proposed according to the length of a rate-modifying activity (RMA) (i.e. the length of the rest time). Meanwhile, it is the first paper to introduce the recovery function into a scheduling problem. And the problem is proved to be an NP-hard problem. Then, a special case of the problem is proved to be solved in polynomial time. [ABSTRACT FROM AUTHOR]

The model of interaction between PIP3, AKT, and FOXO3a in the PI3K/AKT signaling pathways in Acute Myeloid Leukemia (AML) is described and analyzed in this paper. We assume that the biochemical reaction in this pathway follows Hill's equation and consider the case that the mechanism of protein dephosphorylation does not work properly. Then, we analyze the model using the stability theory of differential equations to determine the parameters that play an important role in AML disease. Firstly, we discuss the existence of steady states and their stability. Furthermore, numerical simulations are given to support the analytical results of the model. Sensitivity index is also analyzed to identify parameters which have a significant influence on AML disease and should be targeted by intervention strategies. Our results show how targeted therapy can be performed on the PI3K/AKT pathway for the treatment of AML. [ABSTRACT FROM AUTHOR]

Multirate or multichannel sampling related theory and methods are some of the hottest research topics in modern signal processing community. Among them, the sampling associated with the signal and its derivatives is often encountered in various real applications. In this paper, we investigate the sampling theory related to the higher order derivatives of random signals with the fractional Fourier transform. We first obtain the uniform sampling theorem associated with the higher order derivatives of random signals, and then we generalize this results associated with the periodic nonuniform sampling model for random signals. The corresponding sampling rate will be reduced by a factor of n so that the workload will be greatly reduced. Finally, the simulations are performed to verify the proposed theorem. [ABSTRACT FROM AUTHOR]

In this paper, a Dirichlet-Neumann alternating method using elliptical arc artificial boundary is designed to solve exterior Poisson problem with a concave angle. It is shown that the method is equivalent to a preconditioned Richardson iteration. The convergence of this method and its discretization are studied. Finally, some numerical examples are given to show the effectiveness of this method [ABSTRACT FROM AUTHOR]

A new Taylor-series method which was originally developed for the solution of one-dimensional integral equations is extended to solve multivariate nonlinear integral equations. In this paper, a new method is constructed to approximate the solutions of a class of multivariate Hammerstein equations. One of the strength of the new method is that it lends itself to parallel computation. Hence it is a very highly efficient method. Another strength of the proposed method is that it also gives highly accurate approximations for all the derivatives of the solution up to the order of the Taylor-series approximation used in the method. Numerical examples are given to illustrate the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

The Dual Hesitant Fuzzy Sets (DHFSs) is a useful tool to deal with vagueness and ambiguity in the multiple attribute decision making (MADM) problems. The distance and similarity measures analysis are important research topics. In this paper, we propose some new distance measures for dual hesitant fuzzy sets, and study the properties of the measures. In the end, we develop an approach for multi-criteria decision making under dual hesitant fuzzy environment, and illustrate an example to show the behavior of the proposed distance measures. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a discrete-time neural network model with multiple delays. By analyzing the corresponding characteristic equation of the system, we discuss the stability and the existence of Neimark-Sacker bifurcation for the model. Applying the normal form method and the center manifold theory for discrete time system developed by Kuznetsov, we derive the explicit formula for determining the direction of Neimark-Sacker bifurcation and the stability of bifurcating periodic solution. Some numerical simulations which are in a good agreement with our theoretical analysis are carried out. Our results are new and complement previously known studies. [ABSTRACT FROM AUTHOR]

This paper is concerned with a Nicholson's blowflies model with time delays on time scales. Based on the theory of calculus on time scales, sufficient conditions for the existence and nonexistence of positive periodic solutions in shifts δ± are obtained by using Krasnoselskii's fixed point theorem and some mathematical methods. This is the first study to investigate the existence and nonexistence of positive periodic solutions for a Nicholson's blowflies model on time scales, especially for the nonexistence result. Finally, two examples are given to illustrate the feasibility and effectiveness of the results. [ABSTRACT FROM AUTHOR]

In present paper, the Sharma-Tasso-Olever (STO) equation is considered by the Lie symmetry analysis. All of the geometric vector fields to the STO equation are obtained, then the symmetry reductions and exact solutions of the STO equation are investigated. Our results witness that symmetry analysis was very efficient and powerful technique in finding the solutions of the proposed equation. [ABSTRACT FROM AUTHOR]

In this paper, we give a simple and straight forward definition for the neutrix limit of divergent series and use it to study the neutrix limits of the divergent series ralated to the Rieman-Zeta function ζ(α) and some series related to the polylogarith function Lin(z). Then, we apply the reults to some specific examles. Our reults on Riemann-Zeta function and its derivatives are consistent with the tranditional ones. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the nonlinear functional spaces based on pseudo-additions. Particularly, we obtain that the some properties of the upper-closures of the regular subspaces of the nonlinear functional space based on a continuous pseudo-addition. Furthermore, we prove that with respect to a strict pseudo-addition, a subset of the nonlinear functional space is an upper-complete normal subspace if and only if the family of all sets whose characteristic functionals are contained in the given subset of the nonlinear functional space is a σ-algebra. [ABSTRACT FROM AUTHOR]

Starting from the isospectral problem equipped with a loop algebra e Ã1, we first derive a new and more general KN-like hierarchy with two coefficient functions α(x) and β(t). We then establish a Hamiltonian structure of the KN-like hierarchy under the condition that β(t) is a nonzero constant by the use of Tu's scheme. Finally, we obtain some exact solutions of the first two equations of the KNlike hierarchy and give an open problem. This paper shows that the KN-like hierarchy is not only Lax integrable but also conditional Liouville integrable. [ABSTRACT FROM AUTHOR]

The paper introduces a smoothing method to the lower order penalty function for constrained optimization problems. It is shown that, under some mild conditions, an optimal solution of the smoothed penalty problem is an approximate optimal solution of the original problem. Based on the smoothed penalty function, an algorithm is presented and its convergence is proved under some mild assumptions. Numerical examples show that the presented algorithm is effective. [ABSTRACT FROM AUTHOR]

In this paper, we consider a stochastic Gilpin-Ayala model in polluted environments. Firstly, sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence of the species are established. The threshold between extinction and weak persistence is obtained. Then global attractivity of the model is studied. Finally, several numerical figures are introduced to validate the results. [ABSTRACT FROM AUTHOR]