Recently, Luo et al. proposed two new codebooks based on the operations of some given sets, which are asymptotically optimal. In the paper, we present new construction of codebooks. We determine maximal cross-correlation amplitude of the constructed codebooks. The constructed codebooks are near optimal to the Welch bound. This new codebooks in the paper generalize Luo et al.′s constructions. The parameters

This paper is a study on main properties and characterizations of the DMP inverse. Also, corresponding representations and computational procedures are derived. Particularly, an upgrade of the bordering method to the case of the DMP inverse is considered as well as applications of the DMP inverse in solving singular linear systems. Also, the DMP inverse of an upper block triangular matrix and its sign

The construction of the generalized Bézier model with shape parameters is one of the research hotspots in geometric modeling and CAGD. In this paper, a novel shape-adjustable generalized Bézier (or SG-Bézier, for short) surface of order (m, n) is introduced for the purpose to construct local and global shape controllable free-form complex surfaces. Meanwhile, some properties of SG-Bézier surfaces and

The transfer matrix method is an analytical method for investigating the vibrations in many structures such as beams, sheets, and shells. In this method, the inverse of “zero matrices” should be calculated to determine the transfer matrix. The calculation of the inverse matrix increases the computational cost in computer programming. In this paper, a method is presented to reduce the order of the inverse

We study global dynamics of phase transition evaporation interfaces in horizontally extended domains of porous layers where a water located over a vapor. The derivation of the model equation describing the secondary structures, which bifurcate from the ground state in a small neighborhood of the instability threshold in the case of a quasi-stationary approach to the description of the diffusion process

In this paper, we investigate the effect of water temperature on phytoplankton–zooplankton dynamics with Holling type III functional response. Remarkably, growth rate, capture rate, handling time, death rate and Holling parameter are considered to be temperature dependent, which makes the model different from those in the existing related literatures. First, the relationships between model parameters

In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions considered so far. Some properties of the new parameterized solution, compared to the parameterized solution considered so far, and a new application direction are presented

The monodomain model is a common description for explaining the electrical activity of the heart. The model is nonlinear and consists of an ODE system that describes electrochemical reactions in the cardiac cells and a parabolic PDE that express the diffusion of the electrical signal. FEM approaches for the numerical solution of the monodomain equations can be classified into those that simultaneously

As the concept of sustainable development and environmental awareness has aroused huge attention from the public, environmental and social factors have gradually been critical to the development of upstream and downstream enterprises in the supply chain. An uncertain sustainable supply chain involving the factors of cost, environmental impact and social benefits is considered. Some factors (e.g., demand

In this paper, we investigate the multi-scale orthogonal basis method for fractional integral boundary value problems. We apply the Newton iteration method to linearize the nonlinear problems and employees the idea of collocation method to determine the coefficients of multi-scale orthogonal basis, then the approximation solution is obtained. The error estimation and stable analysis are presented in

In this present article, we establish two new kinds of nonlinear contraction mappings to obtain fixed point results in the structure of ordered b - metric space via wt-distance. In fact, our presented results are extensions of recent theorems due to Lakzian-Rhoades [2019. Appl. Math. Comput.] and other existing classical results of fixed point theory. Furthermore, we provide examples to show the validity

This paper examines the dynamical analysis of the Lengyel-Epstein system with a discrete delay in detail. Under the assumption that the unique positive equilibrium of the model is locally asymptotically stable in the absence of the delay, the effect of the increase of delay on the stability of the unique positive equilibrium is analyzed in detail. It is found that under suitable conditions on the other

In this work, a three-level implicit compact difference scheme for the generalised form of fourth order parabolic partial differential equation is developed. The discretization is derived by approximating the lower order derivative terms using the governing differential equation with the imbedding technique and is fourth order accurate in space and second order accurate in time. The current approach

We give new criteria for nonuniform dichotomy of nonautonomous systems on the whole line in terms of admissibility relative to an integral equation. In our approach the input space I(R,X) is an intersection of spaces that can be successively minimized and the output space C(R,X) can be one of some well-known spaces of continuous functions. Using computational arguments, we show that the admissibility

Stationary splitting iterative methods for solving AXB=C are considered in this paper. The main tool to derive our new method is the induced splitting of a given nonsingular matrix A=M−N by a matrix H such that (I−H)−1 exists. Convergence properties of the proposed method are discussed and numerical experiments are presented to illustrate its computational efficiency and the effectiveness of some preconditioned

A graph G is t*-connected if there exist t internally disjoint (u, v)-paths, between any two vertices u and v, whose union spans G. In this sense, t*-connectedness is a natural extension of hamiltonicity. In this paper, we provide a sufficient condition for graphs to be t*-connected by generalizing a classic result given by Chavátal [7]. Furthermore, as byproducts, we extend some known results concerning

In this work, we deal with the quasilinearization technique for a class of nonlinear Riemann-Liouville fractional-order two-point boundary value problems. Using quasilinearization technique, we construct a monotone sequence of approximate solutions which has quadratic convergence to the unique solution of the original problem, and establish the corresponding convergence estimates. Moreover, the performance

The Taylor series method for initial value problems associated with dynamic equations of first order on time scales with delta differentiable graininess function is introduced. The trapezoidal rule for the same types of problems is derived and applied to specific examples. Numerical results are presented and discussed.

In this paper, we use quadratic forms diagonalization methods applied to the function thermodynamic energy to analyze the stability of physical systems. Taylor’s expansion was useful to write a quadratic expression for the energy function. We consider the same methodology to expanding the thermodynamic entropy and investigate the signs of the second-order derivatives of the entropy as well as previously

In this paper, the multiple disturbances reference mode tracking control problem is investigated for uncertain turbofan systems with unmeasurable states. The concerned disturbances are existing in the dynamics of turbofan systems, output measurement and control output. The control objective is described via a reference mode system, and a tracking controller is built for turbofan systems by using the

The evolution of network cooperation has become a hot topic in recent years. When players participate in a network game, they gain payoffs by playing games with their neighbors according to their different choices. Besides the network game itself, we focus on two interesting human behaviors: transcendental behavior and disturbance behavior. The former means some players choose a different strategy

In this paper, we focused on the issue of fault detection subject to a class of conic-type nonlinear systems in the finite frequency domain (FFD). Applying Takagi Sugeno (T-S) fuzzy models, the conic-type dynamic error system is established. To prove that the residual vector is robust to external disturbances and sensitive to faults, we provide some conditions to realize H− fault sensitivity performance

The loyalty program (LP) is a marketing campaign designed to encourage customer loyalty by rewarding them. Motivated by extensively applied LP in real society, we propose a public loyalty program (PLP) in the public goods game (PGG). In the PLP, players are rewarded differentially depending on whether their cumulative contribution exceeds the reward threshold. The progressive accumulation rate scheme

This paper introduces a novel replicator equations to cover evolutionary games. This replicator is applied on a finite set of agent communities organized on arbitrary graphs. The communities located at the nodes of the graph compete with their neighbours according to the weights of the links that connect them. The communities replicate by imitation probabilities those neighbourhood’s strategies with

In this paper, we establish a Lie type invariance condition for second order delay partial differential equations. The determining equations are obtained using Taylor’s theorem for a function of several variables. The symmetries of the wave equation with delay, its kernel and extensions of the kernel have been found. We make a complete group classification of the wave equation containing an arbitrary

This paper addresses the distributed bipartite finite-time event-triggered output consensus issue for heterogeneous linear multi-agent systems under directed signed communication topology. Both cooperative interaction and antagonistic interaction between neighbor agents are considered. A novel distributed bipartite compensator with intermittent communication mechanism is first proposed to estimate

A modulus-based nonmonotone line search method is proposed for nonlinear complementarity problem. The considered problem is first reformulated to a nonsmooth nonlinear system based on the modulus-based decomposition. Then a nonmonotone line search method using simulated annealing rule is generalized to solve the resulting system. The global convergence of the proposed method is established under some

In the analysis of the economic growth factors, people often use the CES (constant elasticity of substitution) production function model to calculate the contribution rate of influencing factors to economic growth. However, the traditional CES production function model does not consider the period characteristic of technological progress on economic growth, so this paper puts forward a modified CES

This work aims to study some qualitative features of piecewise smooth systems applied to the dynamics of the Human Immunodeficiency Virus (HIV). The application of sliding mode control and strategies of structured treatment interruptions in HIV is a new and challenging research area, which deserves attention and improvement. We investigate the dynamic behavior of the discontinuous mathematical model

In this article, the global existence of a unique strong solution to the 2D Sobolev equation with Burgers’ type nonlinearity is established using weak or weak* compactness type arguments. When the forcing function (f ≠ 0) is in L∞(L2), new a priori bounds are derived, which are valid uniformly in time as t↦∞ and with respect to the dispersion coefficient μ as μ↦0. It is further shown that the solution

We focus here on using a Newtonian velocity field to evaluate numerical schemes for two different formulations of viscoelastic flow. The two distinct formulations we consider, correspond to either using a fixed basis for the elastic stress or one that uses the flow directions or streamlines. The former is the traditional Cartesian stress formulation, whilst the later may be referred to as the natural

In this paper, we presented an ε-accurate approach to conduct a continuous optimization on the pollution routing problem (PRP). First, we developed an ε-accurate inner polyhedral approximation method for the nonlinear relation between the travel time and travel speed. The approximation error was controlled within the limit of a given parameter ε, which could be as low as 0.01% in our experiments. Second

In the numerical solution of elliptic equations, multiscale methods typically involve two steps: the solution of families of local solutions or multiscale basis functions (an embarrassingly parallel task) associated with subdomains of a domain decomposition of the original domain, followed by the solution of a global problem. In the solution of multiphase flow problems approximated by an operator splitting

In monitoring subsurface aquifer contamination, we want to predict quantities—fractional flow curves of pollutant concentration—using subsurface fluid flow models with expertise and limited data. A Bayesian approach is considered here and the complexity associated with the simulation study presents an ongoing practical challenge. We use a Karhunen–Loève expansion for the permeability field in conjunction

We describe three distinct stress boundary layer structures that can arise in the high Weissenberg number limit for the upper convected Maxwell (UCM) model. One is a single layer structure previously noted by M. Renardy, High Weissenberg number boundary layers for the upper convected Maxwell fluid J. Non-Newtonian Fluid Mech. 68 (1997), 125–132. The other two are double layer structures. These latter

Subspace properties are presented for the trust-region subproblem that appears in the Augmented Lagrangian-Trust-Region method recently proposed by Wang and Yuan (2015). Specifically, when the approximate Lagrangian Hessians are updated by suitable quasi-Newton formulas, we show that any solution of the corresponding kth subproblem belongs to the subspace spanned by all gradient vectors of the objective

This note studies global fixed-time stabilization for switched stochastic nonlinear systems under rational switching powers. With the aid of stochastic fixed-time stability theorem, a new control approach is presented to ensure that the system state globally reaches zero almost surely in fixed time independent of initial conditions. The developed scheme is used to controller design of the liquid-level

In this paper, we propose a penalized gradient projection algorithm for solving the continuous convex separable knapsack problem, which is simpler than existing methods and competitive in practice. The algorithm only performs function and gradient evaluations, sums, and updates of parameters. The relatively complex task of the algorithm, which consists in minimizing a function in a compact set, is

The long-term operation of hydro-thermal power generation systems is modeled by a large-scale stochastic optimization problem that includes nonlinear constraints due to the head computation in hydroelectric plants. We do a detailed development of the problem model and state it by a non-anticipative scenario analysis, leading to a large-scale nonlinear programming problem. This is solved by a filter

Optimization applied to radiotherapy planning is a complex scientific issue seeking to deliver both possible highest dose into tumor tissue and lowest one into adjacent tissues. It is composed of one or more of the following main problems: beam choice, dose intensity and blades opening. In this paper, a mixed integer nonlinear optimization model is developed for radiation treatment planned by intensity

The application of sliding mode control and piecewise smooth vector fields in cancer is an incipient research area. Here we propose a piecewise dynamics to explore chemoimmunotherapeutic strategies. We investigate the dynamic behavior of the discontinuous mathematical model and we observe the occurrence of typical singularities. The on-off treatment strategies are defined in terms of a time-dependent

In this paper, we analyze a second-order numerical algorithm for the non-stationary mixed Stokes/Darcy equations with Beavers–Joseph–Saffman’s interface condition. The scheme is based on a finite element method in space and the parareal method with spectral deferred correction in time. We present the unconditional stability and the optimal error estimate of the full-discrete scheme. Finally, some numerical

In this paper, we propose and develop a local and parallel Uzawa finite element method for the generalized Navier–Stokes equations. The Uzawa finite element method is no need to deal with the saddle point problem, and only solves one vector-valued elliptic equation and one simple scalar-valued equation. It has the geometric convergence with a crispation number γ what has nothing to do with the mesh

We present the successive linear Newton interpolation method for solving the large-scale nonlinear eigenvalue problems, establish locally linear convergence, and give the corresponding convergence factor of the method in terms of the left and right eigenvectors in this paper. To speed up the convergence rate, we develop the modified successive linear Newton interpolation method which updates the pole

In this paper, we consider the two-grid method for solving Cahn–Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential. This two-grid method consists of two steps. First step, solve the Cahn–Hilliard equation with full implicit mixed finite element method and Newton iteration method on a coarse grid. Second step, solve two linear equations on a

Based on exponential transformation, quadratic interpolation polynomial and Padé approximation, a new high order finite difference scheme is proposed for solving the two-dimensional (2D) time-fractional convection-dominated diffusion equation (of order α ∈ (0, 1)). The resulting scheme is of (3−α)-order accuracy in time and fourth-order accuracy in space. In order to reduce the amount of computation

In this paper, we consider the single machine scheduling problem with release times and a learning effect. The actual processing time of a job is a function that is the total processing time of the jobs already processed. The objective is to minimize the weighted sum of makespan, total completion time and maximum tardiness. This problem is NP-hard, some heuristic algorithms and branch-and-bound algorithm

In this paper, the space-time Jacobi spectral collocation method (JSC Method) is used to solve the time-fractional nonlinear Schro¨dinger equations subject to the appropriate initial and boundary conditions. At first, the considered problem is transformed into the associated system of nonlinear Volterra integro partial differential equations (PDEs) with weakly singular kernels by the definition and

A new integrable hierarchy related to a 4 × 4 matrix isospectral problem is proposed, in which the semi-discrete version of the coupled KdV system is the first member. Subsequently the N-fold Darboux transformation for the second member in the obtained hierarchy is constructed. As applications, the explicitly exact solutions to the equation in three cases of different seed solutions are discussed and

In this report, a pressure-correction projection scheme in rotational form for the unsteady incompressible magnetohydrodynamics(MHD) equations is given. This method uses the relations of the fluid velocity variable u, the magnetic field variable B and the electrical field variable E, the electrical field variable E were preserved. The theory analysis proves that the rotation form of the algorithm provides

The Bresse system is a recognized mathematical model for vibrations of a circular arched beam that contains the class of Timoshenko beams when the arch’s curvature is zero. It turns out that the majority of mathematical analysis to Bresse systems are concerned with the asymptotic stability of linear homogeneous problems. Under this scenario, we consider a nonlinear Bresse system modeling arched beams

Superconvergence of the second order cubic edge elements approximation is investigated on uniform and nonuniform mesh. Superconvergence of one order higher is established at the second order Gauss points for both the finite element solution and the curl of this solution. Numerical examples are presented to support our theoretical analysis.

In the present study, the polymer crystal growth under the flow field is numerically simulated by using a coupled phase field (PF) and lattice Boltzmann (LB) method. Firstly, the phase field method is presented to capture the growth interface of polymer crystals, including the common morphologies of spherulite and shish-kebab crystallites. Then the lattice Boltzmann method is introduced to solve the

The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately. One idea to overcome the difficulty associated with

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the

Geometrically continuous (Gk ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are Ck also for non-tensor-product layout. This paper describes and analyzes one such concrete C1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed

Let [Formula: see text] be the open unit disk, [Formula: see text] an analytic self-map of [Formula: see text] and [Formula: see text] an analytic function on [Formula: see text]. Let D be the differentiation operator and [Formula: see text] the weighted composition operator. The boundedness and compactness of the product-type operator [Formula: see text] from the weighted Bergman-Orlicz space to the

Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear

The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investigated