In this article, numerical solutions of the seven different forms of the single soliton and double soliton solutions of the Korteweg‐de Vries equation are investigated. Since numerical solution of the six test problems for small‐times do not exist in the literature, the present numerical results firstly are reported with exact solutions. Besides small‐time solutions, long‐time solutions of all test

In this manuscript, we present a novel and highly accurate wavelet‐based approximation technique to explore the sensitivities and value of American options diagnosed by linear complementarity problems. For a detailed analysis of such financially relevant problems, we transform the actual final value problem into a dimensionless initial value problem. To avoid the unacceptable large truncation error

In this study, the analysis of the new finance chaotic model was expanded to Atangana–Baleanu–Caputo fractional derivative. The existence solution was investigated using the fixed model theorem of the new model. Then, the uniqueness solution of model was examined by using the Sumudu transformation.

Considering the both effect of boundary approximation and numerical quadrature, a second‐order isoparametric element method is given to solve the homogeneous isotropic plane linear elasticity problem in domain Ω with curved boundary. By using technically analysis, the optimal error estimate with is obtained, where the function is an extension of the true solution to . It yields better accuracy than

A linearized orthogonal spline collocation (OSC) method with C1 splines of degree ≥3 on a suitable graded mesh is formulated and analyzed for approximate solution of an initial‐boundary‐value problem of semilinear subdiffusion equations with nonsmooth solutions in time. The sharp error estimate in the L2 norm is established without any restriction on the relative temporal and spatial mesh sizes. Such

The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I − Q(QTQ)−1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I − QTQT, with correction matrix T. When T = (QTQ)−1

Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) ℳ ‐tensors. In this article, we introduce H‐splitting and H‐compatible splitting and investigate the relationship between these different splittings and their convergence. Meanwhile, we also consider a preconditioned AOR iterative method for solving

In the case of homogeneous linear difference equations with constant coefficients, only a relatively small part of the equations is practically solvable. This is connected to impossibility to solve all polynomial equations of degree bigger than four. In the case of nonlinear difference equations and systems the situation is even worse. So it is of interest to find new classes of practically solvable

In the paper, we consider the local‐in‐time and the global‐in‐time convergence of infinity‐ion‐mass limit for bipolar Euler–Maxwell systems by setting the mass of an electron m e = 1 and letting the mass of an ion mi → +∞. We use the method of asymptotic expansions to handle the local‐in‐time convergence problem and find that the limiting process from bipolar models to unipolar models is actually decoupling

In this paper, we investigate some properties of the domains c0(Cn), c(Cn), and ℓp(Cn) with 0 < p < 1 of the Cesàro matrix of order n in the classical spaces c0, c, and ℓp of null, convergent, and absolutely p‐summable sequences, respectively, and compute the α‐, β‐, and γ‐duals of these spaces. We characterize the classes of infinite matrices from the space ℓp(Cn) to the spaces ℓ∞, c, and c0 and from

This paper is concerned with an initial and boundary value problem of the Navier‐Stokes equations for compressible viscous barotropic flow subject to large external potential forces in a half space ℝ + 3 with Navier's boundary conditions. The global well‐posedness of strong solutions with large oscillations and vacuum is established, provided that the initial energy is suitably small and that the unique

Infectious diseases affect prey populations, and predators choosing susceptible prey may lead to the extinction of the prey population. We propose a mathematical model of prey–predator interaction with the prey population divided into two classes: susceptible and infected. The susceptible prey subpopulation becomes infected by direct contact with the infected prey subpopulation, and the predator consumes

This paper is an introduction to countable and separable elementary soft topological spaces, which includes concepts such as dense soft set, first countability, second countability, separability and Lindelöf properties and some basic properties of them in the elementary soft topological spaces.

The paper discusses the numerical investigation involving forced convective heat transfer (HT) in the laminar flow regime is carried out for nanofluid (NF) and hybrid NF (HNF) in a microtube and wavy microchannel. Water‐based Al2O3 NF and water‐based Al2O3‐Ag HNF is studied for this purpose. Reynolds number (Re), temperature, volume fraction, and nanoparticle (NP) size are varied for the analysis at

In this article, the Bielecki metric on the space 𝒞 ( [ a , b ] ) is used to analyze the different types of stability results of nonlinear fractional integral equation with delay in its corresponding fractional boundary value problems. Sufficient conditions are obtained to prove stability results for fractional nonlinear Volterra and Fredholm integral equations with delay, given by Ulam, Hyer, and

Let χ ′ ⊂ ( G ) be the least number of colours necessary to properly colour the edges of a graph G with minimum degree δ ≥ 2 so that the set of colours incident with any vertex is not contained in a set of colours incident to any of its neighbours. We provide an infinite family of examples of graphs G with χ ′ ⊂ ( G ) ≥ ( 1 + 1 δ − 1 ) Δ , where Δ is the maximum degree of G , and we conjecture that

Let G be a planar graph with a list assignment L . Suppose a preferred color is given for some of the vertices. We prove that if G is triangle‐free and all lists have size at least four, then there exists an L ‐coloring respecting at least a constant fraction of the preferences.

The purpose of this paper is to study radially symmetric solutions of a parabolic–elliptic chemotaxis system (0.1)ut=Δu−∇⋅(f(u)∇v)inBR×(0,+∞),0=Δv−μ(t)+g(u)inBR×(0,+∞)subject to homogeneous Neumann boundary conditions, where BR=BR(0)⊂Rn with n⩾1, R>0 and μ(t)=1|BR|∫BRg(u(x,t))dx denotes the time-dependent spatial mean of g(u). The chemosensitivity f and nonlinear signal production g are suitably regular

We establish Freidlin–Wentzell results for a nonlinear ordinary differential equation starting close to the stable state 0, say, subject to a perturbation by a stochastic integral which is driven by an 𝜀-small and (1/𝜀)-accelerated Lévy process with exponentially light jumps. For this purpose, we derive a large deviations principle for the stochastically perturbed system using the weak convergence

We discuss the problem of recovering geometric objects from the spectrum of a quantum integrable system. In the case of one degree of freedom, precise results exist. In the general case, we report on the recent notion of good labelings of asymptotic lattices.

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn–Hilliard–Navier–Stokes phase- field model, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently

Let T be a complete, model complete o-minimal theory extending the theory RCF of real closed ordered fields in some appropriate language L. We study derivations δ on models ℳ⊧T. We introduce the notion of a T-derivation: a derivation which is compatible with the L(∅)-definable 𝒞1-functions on ℳ. We show that the theory of T-models with a T-derivation has a model completion TGδ. The derivation in models

We continue our investigation [S. Beier, M. Holzer: Properties of right one-way jumping finite automata. In Proc. 20th DCFS, LNCS, 2018] on (right) one-way jumping finite automata (ROWJFAs), a variant of jumping automata, which is an automaton model for discontinuous information processing. Here we focus on decision problems for ROWJFAs. It turns out that most problems such as, e.g., emptiness, finiteness

A closed string contains a proper factor occurring as both a prefix and a suffix but not elsewhere in the string. Closed strings were introduced by Fici (WORDS 2011) as objects of combinatorial interest. This paper addresses a new problem by extending the closed string problem to the k-closed string problem, for which a level of approximation is permitted up to a number of Hamming distance errors,

In this paper, certain delayed virus dynamical models with cell-to-cell infection and density-dependent diffusion are investigated. For the viral model with a single strain, we have proved the well-posedness and studied the global stabilities of equilibria by defining the basic reproductive number R0 and structuring proper Lyapunov functional. Moreover, we found that the infection-free equilibrium

How to understand the dynamical collective performances is of particular significance in both theories and applications. In this paper, we are interested in investigating the combined influences of local interaction and processing delay on the asymptotic behavior in a particle model with local communication weights. With new observations, we show that the desired particle system undergoes both periodic

In the recent developments of regularization theory for inverse and ill‐posed problems, a variational quasi‐reversibility (QR) method has been designed to solve a class of time‐reversed quasi‐linear parabolic problems. Known as a PDE‐based approach, this method relies on adding a suitable perturbing operator to the original problem and consequently, on gaining the corresponding fine stabilized operator

This paper aims at studying the vibrational behavior and dynamical stability of small‐scale axially moving beams resting on the viscoelastic‐Pasternak foundation in a hygro‐thermal environment, according to a nonlocal strain gradient Rayleigh beam model. The Galerkin procedure is applied to determine the eigenvalues of the dynamic system of equations together with the stability regions of the system

We present some classes of homogeneous linear difference equations with constant coefficients such that their associated characteristic polynomials have multiple zeros, and all solutions to the equations are convergent. The cases of the equations of third and fourth order are considered in detail, whereas in the case of equations of arbitrary order bigger than four, we present a subclass of such equations

The paper reports the new forms of the fundamental solutions for 3D magnetoelectroelasticity equations. The state-of-art presented in the paper shows that the fundamental solutions for magnetoelectroelasticity equations take complex forms, especially considering their applications in the boundary element method. In the paper, the magnetoelectroelastic continuum serves as a homogenized model of the

The Brachistochrone problems with various penalties for fuel expense for a mass moving in a vertical plane in a uniform field of gravity are considered. The resistance of the medium is considered viscous. The lift force or normal component of the reaction force of the curve and thrust are considered as control variables. The optimal control problems are reduced to a boundary value problems for a system

In this paper, a resolved CFD-DEM method based on the immersed boundary method is proposed to simulate the proppant transport process, which is a multi-phase problem with strong fluid-particle coupling mechanisms in the oil and gas industry. A multi-sphere model is integrated into this method to describe complex particle shapes, in which Lagrangian points uniformly distributed on the particle surface

This work presents a method dedicated to the simultaneous identification of the thermal diffusivities of coatings or thin film materials. To ensure non-destructive thermal characterization of the coating, the present method also implies the identification of the substrate thermal properties, which may be orthotropic. The estimation of thermal diffusivities is based on the resolution of an inverse problem

The interface failure (micro-annulus and de-bonding) at the first interface between cement sheath and formation, or at the second interface between cement sheath and casing can be easily caused by alternating change of internal pressure and temperature in the casing during large-scale multistage hydraulic fracturing in shale-gas well. It is likely to have a great impact on casing stress and pose a

The different loading conditions often occur in polymer matrix composites during their service life. In order to use effectively the materials in high-performance applications, analyzing the effect of hygrothermal effects on a ballistic impact event is necessary. This paper considers a heat sink and humidity sink for the hygrothermal diffusion in the composites and solves the Luikov equations by means

Dynamic-based methods for detecting the location of damage in structures are generally based on changes caused by damage in the dynamic properties of structures such as modal frequencies and mode shapes. Mode shape curvature damage detection method is one of these techniques in which the difference in mode shape curvatures between undamaged and damaged structures is used to identify the location of

ABSTRACT Firstly, original poly(vinyl alcohol-co-ethylene) (PVA-co-PE)/cellulose composite membranes were prepared and characterized. Then these composite membranes were applied for wastewater treatment. For this purpose, separation of Iron (III) and Copper (II) ions from the aqueous solutions with stirred ultrafiltration cell was investigated. These metal ions were complexed by using alginic acid

ABSTRACT Astragalus spinous is a native perennial shrubs from Leguminosae family that widely distributed in severely degraded lands at northern Kuwait. A restoration program was applied via levelling and refilling the quarries and rehabilitation of the natural vegetation and wildlife to their original outward appearance before degradation. The existence of Astragalus shrubs indicated that soil after

The 2019 coronavirus disease (COVID‐19), caused by severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2), has become a global pandemic. Until 13 September 2020, SARS‐CoV‐2 caused more than twenty eight million infections and nine hundred thousand deaths worldwide. SARS‐CoV‐2 uses angiotensin‐converting enzyme 2 (ACE2) for cell entry into various lung cells including endothelial cells and alveolar

Upon entry into the lungs, SARS‐CoV‐2 uses the angiotensin‐converting enzyme 2 (ACE2) receptor to facilitate viral entry into the epithelial cells that cover the airways and the alveolar gas‐exchanging space, leading to extensive epithelial injury, which contributes to local inflammatory storm and a series of respiratory syndromes.1 A number of drugs, based on their modes of action, have been suggested

Immunodeficient mice injected with human cancer cell lines have been used for human oncology studies and anti‐cancer drug trials for several decades. However, rodents are not ideal species for modelling human cancer because rodents are physiologically dissimilar to humans. Therefore, anti‐tumour drugs tested effective in rodents have a failure rate of 90% or higher in phase III clinical trials. Pigs

The authors would like to draw the reader's attention to an error in Figure 7d. The “mtDNA+DNaseI” column was inadvertently duplicated for the “Oxi‐mtDNA+DNaseI” images. The correct Figure 7 appears below. FIGURE 7 Open in figure viewerPowerPoint