Mathematical Problems in Engineering

https://www.hindawi.com/journals/mpe/

List of Papers (Total 6,716)

A hybrid domain analysis for systems with delays in state and control

The solution of time-delay systems is obtained by using a hybrid function. The properties of the hybrid functions consisting of block-pulse functions and Chebyshev polynomials are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. The operational matrix of delay is introduced. The operational matrices of...

Absolute stability of nonlinear systems with time delays and applications to neural networks

In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications...

Modified guidance laws to escape microbursts with turbulence

This paper introduces Modified Altitude- and Dive-Guidance laws for escaping a microburst with turbulence. The goal is to develop a procedure to estimate the highest altitude at which an aircraft can fly through a microburst without running into stall. First, a new metric is constructed that quantifies the aircraft upward force capability in a microburst encounter. In the absence...

Determination of an unknown parameter in a semi-linear parabolic equation

Some finite difference approximations are developed for an inverse problem of determining an unknown parameter p(t) which is a coefficient of the solution u in a semi-linear parabolic partial differential equation subject to a boundary integral overspecification. The accuracy and efficiency of the procedures are discussed. Some computational results using the newly proposed...

On potential energies and constraints in the dynamics of rigid bodies and particles

A new treatment of kinematical constraints and potential energies arising in the dynamics of systems of rigid bodies and particles is presented which is suited to Newtonian and Lagrangian formulations. Its novel feature is the imposing of invariance requirements on the constraint functions and potential energy functions. These requirements are extensively used in continuum...

A new formulation of the equivalent thermal in optimization of hydrothermal systems

In this paper, we revise the classical formulation of the problem depriving it of the concepts that are superfluous from the mathematical point of view. We observe that a number of power stations can be substituted by a single one that behaves equivalently to the entire set. Proceeding in this way, we obtain a variational formulation in its purest sense (without restrictions...

Sliding mode control on electro-mechanical systems

The first sliding mode control application may be found in the papers back in the 1930s in Russia. With its versatile yet simple design procedure the methodology is proven to be one of the most powerful solutions for many practical control designs. For the sake of demonstration this paper is oriented towards application aspects of sliding mode control methodology. First the...

Analytical investigations of the Sumudu transform and applications to integral production equations

The Sumudu transform, whose fundamental properties are presented in this paper, is little known and not widely used. However, being the theoretical dual to the Laplace transform, the Sumudu transform rivals it in problem solving. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. Here, we...

Volterra equations with fractional stochastic integrals

Some fractional stochastic systems of integral equations are studied. The fractional stochastic Skorohod integrals are also studied. The existence and uniquness of the considered stochastic fractional systems are established. An application of the fractional Black-Scholes is considered.

Solution of nonlinear Fredholm-Hammerstein integral equations by using semiorthogonal spline wavelets

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally...

On the reliability of a renewable multiple cold standby system

We present a general reliability analysis of a renewable multiple cold standby system attended by a single repairman. Our analysis is based on a refined methodology of queuing theory. The particular case of deterministic failures provides an explicit exact result for the survival function of the duplex system.

On modelling the drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer

Luikov's theory of heat and mass transfer provides a framework to model drying porous materials. Coupled partial differential equations governing the moisture and heat transfer can be solved using numerical techniques, and in this paper we solve them analytically in a setting suitable for industrial drying situations. We discuss the nature of the solutions using the physical...

Characterization of the speed of a two-phase interface in a porous medium

A typical situation of oil reservoir simulation is considered in a porous medium where the resident oil is displaced by water injection. An explicit expression of the speed of the oil-water interface is given in a pseudo-2D case via the resolution of an auxiliary Riemann problem. The explicit 2D solution is then corroborated with numerical simulations by solving the transport...

Heronian Mean Operator of Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Methods

Many aggregation operators in multiattribute decisions assume that attributes are independent of each other; this leads to an unreasonable situation in information aggregation and decision-making. Heronian mean is the aggregation operator that can embody the interaction between attributes. In this paper, we merge the linguistic neutrosophic cubic number (LNCN) and the Heronian...

Prediction Model of Failure Zone in Roadway Sidewall considering the Lithologic Effect of Rock Formation

Coal seam damage area and its stress distribution law in roadway with medium thickness or extrathick coal seam are important issues for understanding the instability mechanism of roadway surrounding rock in weakly cemented soft rock strata in western China. Firstly, a variable parameter microelement analysis model is established based on the assumption of a plane stress...

A Family of Heuristic-Based Inequalities for Maximizing Overall Safety Margins in Aircraft Parking Stands Arrangement Problems

We consider the problem of arranging a set of aircraft in a maintenance hangar operated by an independent aircraft service provider. The overall safety margins of the parking layout need to be maximized within the limited available space, measured by the weighted sum of the individual discrete safety margins of each aircraft. A mixed-integer linear programming model is developed...

System Sizing with a Model-Based Approach: Application to the Optimization of a Power Transmission System

We test the relevance of a model-based approach for sizing and optimizing complex systems. Classically a model-based approach is characterized by a clear partition between the problem description and the solving process. In the case of a design problem, we show that the sizing task could be systematically characterized and therefore could lead to a declarative model combining...

Theoretical and Experimental Analysis of the Hydraulic Actuator Used in the Active Reflector System

In order to improve the control quality of the active reflector system which is used in the 500 m aperture spherical radio telescope (FAST) project, a study on hydraulic actuator is proposed. The dynamic performance of hydraulic actuator is due to the interaction of several physical phenomena. Modeling of such a system needs a unified approach to represent the nonlinear behavior...

A Simulated Annealing Algorithm to Construct Covering Perfect Hash Families

Covering perfect hash families (CPHFs) are combinatorial designs that represent certain covering arrays in a compact way. In previous works, CPHFs have been constructed using backtracking, tabu search, and greedy algorithms. Backtracking is convenient for small CPHFs, greedy algorithms are appropriate for large CPHFs, and metaheuristic algorithms provide a balance between...

Efficiency Bounds for Two-Stage Production Systems

Traditional data envelopment analysis (DEA) models find the most desirable weights for each decision-making unit (DMU) in order to estimate the highest efficiency score as possible. These efficiency scores are then used for ranking the DMUs. The main drawback is that the efficiency scores based on weights obtained from the standard DEA models ignore other feasible weights; this...

Study on the Rock Mass Caving and Surface Subsidence Mechanism Based on an In Situ Geological Investigation and Numerical Analysis

To deeply understand the mechanism of the rock mass caving and associated surface subsidence during sublevel caving mining, the Xiaowanggou iron mine was selected as an engineering project case study. The study area was analyzed by means of an in situ geological investigation and numerical simulation. First, a borehole television (BHTV) system and a GPS monitoring system were...

A Research on Fatigue Damage Constitutive Equation of Asphalt Mixture

The laboratory investigations of fatigue damage constitutive equation of asphalt mixture were carried out by three-point bending fatigue tests. The three-point bending fatigue tests were performed at three levels of stress-strength ratio (SSR), temperature, and loading rate. The coupled multifactor (stress-strength ratio, temperature, and loading rate) fatigue life equation was...

Self-Assisted First-Fix Method for A-BDS Receivers with Medium- and Long-Term Ephemeris Extension

As a sensor for standalone position and velocity determination, the BeiDou Navigation Satellite System (BDS) receiver is becoming an important part of the intelligent logistics systems under rapid development in China. The applications in the mass market urgently require the BDS receivers to improve the performance of such functions, that is, shorter Time to First Fix (TTFF) and...

A Triangle Algorithm of Padé-Type Approximant for Two-Dimensional Fredholm Integral Equations of the Second Kind

The function-valued Padé-type approximation (2DFPTA) is used to solve two-dimensional Fredholm integral equation of the second kind. In order to compute 2DFPTA, a triangle recursive algorithm based on Sylvester identity is proposed. The advantage of this algorithm is that, in the process of calculating 2DFPTA to avoid the calculation of the determinant, it can start from the...

Further Results on Diagonally Invariant Exponential Stability of Switching Linear Systems

The concept of diagonally invariant exponential stability (DIES) was originally introduced for single-model linear systems and subsequently expanded in the study of linear systems with interval-type uncertainties and linear systems with arbitrary switching. The results presented in this article refer to new approaches to DIES characterization for arbitrary switching systems...