Oscillation of Systems of Parabolic Differential Equations with Deviating Arguments

To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.

On a Class of Second Order Differential Inequality with Continuous Distributed Deviating Arguments

Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.

Periodic Solutions of Mixed Type p-Laplacian Equations with Deviating Arguments

Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.

Novel high torque bearingless two-sided rotary ultrasonic motor

Applications are limited at present because the currently available ultrasonic motors (USMs) do not provide suffi-ciently high torque and power. The conventional travelling-wave USM needs the bearing to support, which required lubricant. To solve the above problem, a bearingless travelling-wave USM is designed. First, a novel structure of the two-sided USM consisting of a two-sided teeth stator and two disk-type rotors is designed. And the excitation principle of the two-sided travelling-wave USM is analyzed. Then, using ANSYS software, we set up the model of the stator to predict the excitation frequency and modal response of the stator. The shape of the vibration mode was obtained. Last, the load characteristics of the USM are measured using ex-perimental method. The maximum stall torque and the no-load speed were obtained. The results showed that the characteristics of the two-sided USM are better than those of the conventional one-sided USM.

Nonlinear vibration analysis of a circular micro-plate in two-sided NEMS/MEMS capacitive system by using harmonic balance method

In this study, forced nonlinear vibration of a circular micro-plate under two-sided electrostatic, two-sided Casimir and external harmonic forces is investigated analytically. For this purpose, at first, von Karman plate theory including geometrical nonlinearity is used to obtain the deflection of the micro-plate. Galerkin decomposition method is then employed, and nonlinear ordinary differential equations (ODEs) of motion are determined. A harmonic balance method (HBM) is applied to equations and analytical relation for nonlineaT frequency response (F-R) curves are derived for two categories (including and neglecting Casimir force) separately. The analytical results for three cases:(1) semi-linear vibration;(2) weakly nonlinear vibration;(3) highly non linear vibration, are validated by comparing with the numerical solutio ns. After validation, the effects of the voltage and Casimir force on the natural frequency of two-sided capacitor system are investigated. It is shown that by assuming Casimir force in small gap distances, reduction of the natural frequency is considerable. The influences of the applied voltage, damping, micro-plate thickness and Casimir force on the frequency response curves have been presented too. The results of this study can be useful for modeling circular parallel-plates in nano /microelectromechanical transducers such as microphones and pressure sensors.

Effective Hybrid Teaching-learning-based Optimization Algorithm for Balancing Two-sided Assembly Lines with Multiple Constraints

Due to the NP-hardness of the two-sided assembly line balancing （TALB） problem, multiple constraints existing in real applications are less studied, especially when one task is involved with several constraints. In this paper, an effective hybrid algorithm is proposed to address the TALB problem with multiple constraints （TALB-MC）. Considering the discrete attribute of TALB-MC and the continuous attribute of the standard teaching-learning-based optimization （TLBO） algorithm, the random-keys method is hired in task permutation representation, for the purpose of bridging the gap between them. Subsequently, a special mechanism for handling multiple constraints is developed. In the mechanism, the directions constraint of each task is ensured by the direction check and adjustment. The zoning constraints and the synchronism constraints are satisfied by teasing out the hidden correlations among constraints. The positional constraint is allowed to be violated to some extent in decoding and punished in cost fimction. Finally, with the TLBO seeking for the global optimum, the variable neighborhood search （VNS） is further hybridized to extend the local search space. The experimental results show that the proposed hybrid algorithm outperforms the late acceptance hill-climbing algorithm （LAHC） for TALB-MC in most cases, especially for large-size problems with multiple constraints, and demonstrates well balance between the exploration and the exploitation. This research proposes an effective and efficient algorithm for solving TALB-MC problem by hybridizing the TLBO and VNS.

FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY

In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given.

ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS

In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type （DEPCAG）. This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.

A Heuristic Method for Two-sided Assembly Line Balancing Problem

A two-sided assembly line is typically found in plants producing large-sized products. Its advantages over a one-sided line and the difficulties faced in two-sided line balancing problems were discussed. A mathematical model for two-ALB problem was suggested. A modification of the “ranked positional weight” method, namely two-ALB RPW for two-ALB problems was developed. Experiments were carried out to verify the performance of the proposed method and the results show that it is effective in solving two-sided assembly line balancing problems.

New Criteria for Oscillation of Vector Parabolic Equations with Continuous Distribution Arguments

The oscillations of a class of vector parabolic partial differential equations with continuous distribution arguments are studied.By employing the concept of H-oscillation and the method of reducing dimension with inner product,the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional differential inequalities have not eventually positive solution.Some new sufficient conditions for the H-oscillation of all solutions of the equations are obtained under Dirichlet boundary condition,where H is a unit vector of RM.

Laboratory Research on Effective Test Area of Short-Crested Waves Generated by Two-Sided Segmented Wavemakers

The size and shape of the effective test area are crucial to consider when short-crested waves are created by segmented wavemakers. The range of the effective test area of short-crested waves simulated by two-sided segmented wavemakers is analyzed in this paper. The experimental investigation on the wave field distribution of short-crested waves generated by two-sided segmented wavemakers is conducted by using an array of wave gauges. Wave spectra and directional spreading function are analyzed and the results show that when the main direction is at a certain angle with the normal line of wave generators, the wave field of 3D short-crested waves generated by two-sided segmented wavemakers has good spatial uniformity within the model test area. The effective test area can provide good wave environments for seakeeping model tests of various ocean engineering structures in the deep ocean engineering basin.

Two-Sided First Exit Problem for Jump Diffusion Distribution Processes Having Jumps with a Mixture of Erlang

In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.

Generalized Central Factorial Numbers with Odd Arguments

In this paper, we consider r-generalization of the central factorial numbers with odd arguments of the first and second kind. Mainly, we obtain various identities and properties related to these numbers. Matrix representation and the relation between these numbers and Pascal matrix are given. Furthermore, the distributions of the signless r-central factorial numbers are derived. In addition, connections between these numbers and the Legendre-Stirling numbers are given.

Further Oscillation Results for a Class of Hyperbolic Equations with Continuous Distributed Deviating Arguments

A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify a number of existing results.

Oscillation of Differential Equations with Deviating Arguments

In this paper we establish new oscillation criteria for all solution of the first order differential equation with deviating argument. Our result can be applied to the case when coefficients and deviating arguments are oscillatory and essentially improve the known results in the literature.

New Results on Oscillation of even Order Neutral Differential Equations with Deviating Arguments

In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and improve many known oscillation criteria because the article just generalizes Meng and Xu’s results.

Analytical Approach to Differential Equations with Piecewise Continuous Arguments via Modified Piecewise Variational Iteration Method

In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization of the variables, linearization or small perturbations. The results seem to show that the method is very reliable and convenient for solving such equations.

Existence and Uniqueness of Solution to Two-Point Boundary Value for Two-Sided Fractional Differential Equations

In this paper, existence and uniqueness of solution to two-point boundary value for two-sided fractional differential equations involving Caputo fractional derivative is discussed, by means of the Min-Max Theorem.

Two-Sided Stable Matching Decision-Making Method Considering Matching Intention under a Hesitant Fuzzy Environment

In this paper,a stable two-sided matching(TSM)method considering the matching intention of agents under a hesitant fuzzy environment is proposed.The method uses a hesitant fuzzy element(HFE)as its basis.First,the HFE preference matrix is transformed into the normalized HFE preference matrix.On this basis,the distance and the projection of the normalized HFEs on positive and negative ideal solutions are calculated.Then,the normalized HFEs are transformed into agent satisfactions.Considering the stable matching constraints,a multiobjective programming model with the objective of maximizing the satisfactions of two-sided agents is constructed.Based on the agent satisfaction matrix,the matching intention matrix of two-sided agents is built.According to the agent satisfaction matrix and matching intention matrix,the comprehensive satisfaction matrix is set up.Furthermore,the multiobjective programming model based on satisfactions is transformed into a multiobjective programming model based on comprehensive satisfactions.Using the G-S algorithm,the multiobjective programming model based on comprehensive satisfactions is solved,and then the best TSM scheme is obtained.Finally,a terminal distribution example is used to verify the feasibility and effectiveness of the proposed method.

Logarithmic Sobolev Inequalities for Two-Sided Birth-Death Processes

In this paper, we study the logarithmic Sobolev inequalities for two-sided birth-death processes. An estimate of the logarithmic Sobolev constant α for a two-sided birth-death process is obtained by the Hardy-type inequality and a criteria for a is also presented.