Topology optimization is widely applied to various design problems in both structure and fluid dynamics engineering. Specifically, the development of energy dissipation devices with vibration control remains a key consideration. The aim of this study is to improve devices that maximize the absorption or dissipation of the vibration of an oscillating object and propose an approach in which the level

Within the framework of three-dimensional (3D) nonlocal elasticity theory, the authors develop an asymptotic theory to investigate the free vibration characteristics of simply supported, single-walled carbon nanotubes (SWCNTs) non-embedded or embedded in an elastic medium using the multiple time scale method. Eringen’s nonlocal constitutive relations are adopted to account for the small length scale

T-IFISS is a finite element software package for studying finite element solution algorithms for deterministic and parametric elliptic partial differential equations. The emphasis is on self-adaptive algorithms with rigorous error control using a variety of a posteriori error estimation techniques. The open-source MATLAB framework provides a computational laboratory for experimentation and exploration

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

In this paper, we study the multiplicity of solutions for a class of p-Laplacian type fractional differential equations with both instantaneous and non-instantaneous impulses. By using the critical points theorem of B. Ricceri, a theorem is developed for the existence of at least three solutions for the impulsive problem depending on two parameters.

Let p be a prime number, in this paper, we investigate the structures of all constacyclic codes of length ps over the ring Ru2,v2,pm=Fpm[u,v]∕〈u2,v2,uv−vu〉. The units of the ring Ru2,v2,pm can be divided into following five forms: α, λ1=α+δ1uv, λ2=α+γv+δuv, λ3=α+βu+δuv, λ4=α+βu+γv+δuv, where α,β,γ,δ1∈Fpm∗ and δ∈Fpm. We obtain the algebraic structures of all constacyclic codes of length ps over Ru2

An odd [1,b]-factor of a graph G is a spanning subgraph H such that for each vertex v∈V(G), dH(v) is odd and 1≤dH(v)≤b. Let λ3(G) be the third largest eigenvalue of the adjacency matrix of G. For positive integers r≥3 and even n, Lu et al. (2010) proved a lower bound for λ3(G) in an n-vertex r-regular graph G to guarantee the existence of an odd [1,b]-factor in G. In this paper, we improve the bound;

In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR. First, we find a natural obstruction that prevents a finite group from admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive

We show there is a bijection between the binary necklaces with n black beads and k white beads and certain (n,k)-codes when n is prime. The main idea is to come up with a new map on necklaces called slime migration.

In this paper, we give necessary and sufficient conditions on the compatibility of a kth-order homogeneous linear elliptic differential operator A and differential constraint C for solutions toAu=fsubject toCf=0 in Rn to satisfy the estimates‖Dk−ju‖Lnn−j(Rn)⩽c‖f‖L1(Rn) for j∈{1,…,min⁡{k,n−1}} and‖Dk−nu‖L∞(Rn)⩽c‖f‖L1(Rn) when k≥n.

We establish the continuity of a surface as a function of its first two fundamental forms for several Fréchet topologies, which include in particular those of the space Wloc1,p for the first fundamental form and of the space Llocp for the second fundamental form, for any p>2.

In [31] we defined a regularized analytic torsion for quotients of the symmetric space $\operatorname{SL}(n,\mathbb{R})/\operatorname{SO}(n)$ by arithmetic lattices. In this paper we study the limiting behavior of the analytic torsion as the lattices run through sequences of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for principal congruence subgroups and strongly

We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for $\mathit{GSp}_{4}/\mathbb{Q}$ in various aspects. A main tool is Arthur’s invariant trace formula. While Shin [Automorphic Plancherel density theorem, Israel J. Math.192(1) (2012), 83–120] and Shin–Templier [Sato–Tate theorem for families and low-lying zeros of automorphic $L$ -functions, Invent. Math.203(1) (2016)

We extend T. Y. Thomas’s approach to projective structures, over the complex analytic category, by involving the $\unicode[STIX]{x1D70C}$ -connections. This way, a better control of projective flatness is obtained and, consequently, we have, for example, the following application: if the twistor space of a quaternionic manifold $P$ is endowed with a complex projective structure then $P$ can be locally

We show for sequences $\left(a_{n}\right)_{n \in \mathbb N}$ of distinct positive integers with maximal order of additive energy, that the sequence $\left(\left\{a_{n} \alpha\right\}\right)_{n \in \mathbb N}$ does not have Poissonian pair correlations for any α. This result essentially sharpens a result obtained by J. Bourgain on this topic.

Let (R, 𝔪) be a commutative noetherian local ring. In this paper, we prove that if 𝔪 is decomposable, then for any finitely generated R-module M of infinite projective dimension 𝔪 is a direct summand of (a direct sum of) syzygies of M. Applying this result to the case where 𝔪 is quasi-decomposable, we obtain several classifications of subcategories, including a complete classification of the thick

This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic differential inclusion for the damage function. A solution existence and uniqueness result is commented. A fully discrete scheme is introduced with the time derivative

In this paper, a super extension of Sawada–Kotera hierarchy is proposed. This hierarchy is derived by considering a third order Lax operator with a quasi-local term. Bi-Hamiltonian structure is constructed for the super Sawada–Kotera hierarchy.

For given graphs H1,…,Ht, we say that G is Ramsey for H1,…,Ht and we write G⟶(H1,…,Ht), if no matter how one colors the edges of G with t colors, say 1,…,t, there exists a monochromatic copy of Hi in the ith color for some 1≤i≤t. The multicolor Ramsey number r(H1,…,Ht) is the smallest integer n such that the complete graph Kn is Ramsey for (H1,…,Ht). The multicolor size Ramsey number rˆ(H1,…,Ht) is

In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic structure in the sense of Crawley-Boevey-Etingof-Ginzburg [15], on the cobar construction of its co-unitalized Koszul dual coalgebra, and hence its DG representation schemes, in the sense of Berest-Khachatryan-Ramadoss [3], have a shifted symplectic structure in the sense of Pantev-Toën-Vaquié-Vezzosi [28]

The backward problems for the elliptic equation (BPEE) are widely used for modelling problems in many fields such as physics, geometry or engineering. This paper is the first investigation of BPEE in unbounded multiple-dimensional domain associated with locally Lipschitz source as follows ∂2u∂x12+∂2u∂x22+...∂2u∂xn2+∂2u∂y2=S(x1,x2,…,xn,y,u(x1,x2,…,xn,y)),in which (x1,x2,…,xn,y)∈Rn×0,L, where L>0. Based

We consider the following problem with the critical exponent p−1=r ut=d1Δu−a1u+upvq+δ1(x,t),x∈Ω,t>0,vt=d2Δv−a2v+urvs+δ2(x,t),x∈Ω,t>0,∂u∂η=∂v∂η=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω.Here q,r,d1,d2,a1 and a2 are positive constants, p>1, s>−1, δ1, δ2, u0 and v0 are nonnegative smooth functions, Ω⊂Rd(d≥1) is a bounded smooth domain. Whether d1≠d2 or d1=d2, we establish the results on the finite-time

We find minimal and maximal length of intersections of lines at a fixed distance to the origin with the cross-polytope. We also find maximal volume non-central sections of the cross-polytope by hyperplanes which are at a fixed large distance to the origin and minimal volume sections by symmetric slabs of a large fixed width. This parallels recent results about non-central sections of the cube due to

We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of examples and prove that every non-discrete locally compact group with an open abelian subgroup has a subset that fails reduced spectral synthesis. We introduce compact operator synthesis as an operator algebraic counterpart

The first published version of this article included formatting and coding errors on pages 2, 3, 9 and 10. These were unintentional errors that were introduced during the typesetting process. The article has now been amended to correctly depict the author’s work as it was originally accepted.

For ${\mathcal{C}}$ a factorisable and pivotal finite tensor category over an algebraically closed field of characteristic zero we show: (1) ${\mathcal{C}}$ always contains a simple projective object; (2) if ${\mathcal{C}}$ is in addition ribbon, the internal characters of projective modules span a submodule for the projective $\text{SL}(2,\mathbb{Z})$ -action; (3) the action of the Grothendieck ring

Abstract This paper concerns the cohomological aspects of Donaldson–Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the integrality conjecture and the wall crossing formula, and furthermore realise the isomorphism in both of these theorems as Poincaré–Birkhoff–Witt isomorphisms

According to the well-known age replacement policy, the system is replaced preventively at time t or correctively at system failure, whichever occurs first. For a coherent system consisting of components having common failure time distribution which has increasing failure rate, we present necessary conditions for the existence of the unique optimal value which minimizes the mean cost rate. The conditions

In the present research article, we investigated the slip flow of an unsteady incompressible Oldroyd-B fluid model. The electroosmosis and the pressure gradient have been seized for the stimulation of flow. The progress of the fluid is treated to be as passage composed by two micro-parallel plates. The potential difference alive between hard surface and the fluid is taken to be non symmetric. The governing

We study the existence of forced traveling waves and gap formations for the lattice Lotka–Volterra competition system in a shifting habitat. By virtue of upper-lower solution method, we establish that the system admits a forced wave provided that the shifting speed of climate change falls in a certain interval. When the shifting speed is outside the range (except for the two endpoints), gap formations

Existence of global classical solutions with a certain periodic asymptotic behavior of a class of reaction diffusion systems with chemotactic terms is demonstrated. This class contains a system consisting of a parabolic equation with a logistic-like term describing the behavior of a biological species and an ordinary differential equation modeling the concentration of a chemical substance throughout

In this letter, a fractional-order prey-predator model with Holling III type functional response and discontinuous harvest is considered. The non-negative and boundedness of the model are proved. In addition, some conditions for the existence and stability of the positive equilibrium point are proposed. Finally, numerical simulations are given to confirm the correctness of theorem.

Unfortunately, the given names and the family name of the author Uchitha Jayawickrama are incorrectly published in the original article.

Abstract Granular computing is a widely used computational paradigm nowadays. Particularly, within the rough set theory, granular computing plays a key role. In this paper, we propose a generic approach of rough sets, the granular extended multigranular sets (GEMS) for dealing with both mixed and incomplete information systems. Not only our proposal does use the traditional optimistic and pessimistic

Abstract High-accuracy traffic flow forecasting is vital to the development of intelligent city transportation systems. Recently, traffic flow forecasting models based on the kernel method have been widely applied due to their great generalization capability. The aim of this article is twofold: A novel kernel learning method, relevance vector machine, is employed to short-term traffic flow forecasting

Abstract Many location-based services are supported by the moving k-nearest neighbour (k-NN) query, which continuously returns the k-nearest data objects for a query point. Most of existing approaches to this problem have focused on a centralized setting, which show poor scalability to work around massive-scale and distributed data sets. In this paper, we propose an efficient distributed solution for

Abstract In the evolutionary computing community, differential evolution (DE) is well appreciated as a simple yet versatile population-based, non-convex optimizer designed for continuous optimization problems. A simple two-phase DE algorithm is presented in this article, which aims to identify promising basins of attraction on a non-convex functional landscape in the first phase, and starting from

Abstract In this paper, a new optimization algorithm called the Hitchcock bird-inspired algorithm (HBIA) is proposed. It is inspired by the aggressive bird behavior portrayed by Alfred Hitchcock in the 1963 thriller “The Birds.” It is noteworthy to emphasize that the bird’s behavior as shown in the movie is itself inspired by a considered natural birds behavior when faced with extreme conditions. HBIA

Abstract With the rapid development of the Internet of Things, the massive amount of big data generated by the Internet of Things terminals and the real-time processing requirements have brought enormous challenges. A two-tier computing model consisting solely of two entities, cloud and user, will not be sufficient to support processing large numbers of concurrent data requests. Therefore, fog computing

Abstract Nowadays, big data plays a substantial part in information knowledge analysis, manipulation, and forecasting. Analyzing and extracting knowledge from such big datasets are a very challenging task due to the imbalance of data distribution, which could lead to a biased classification results and wrong decisions. The standard classifiers are not capable of handling such datasets. Hence, a new

Abstract Obtaining a useful and discriminative feature for facial expression recognition (FER) is a hot research topic in computer vision. In this paper, we propose a novel facial expression representation for FER. Firstly, we select the appropriate parameter of multi-scale block local binary pattern uniform histogram (MB-LBPUH) operator to filter the facial images for representing the holistic structural

Abstract Cloud computing has been one of the critical solutions to reduce heavy storage and computation burden of biometric identification. To protect the privacy of biometric data against untrusted cloud servers, outsourced biometric databases are usually encrypted by users. Performing biometric identification over encrypted data without revealing privacy to cloud servers attracts more and more attention

Abstract In this paper, we introduce a randomized version of the backward Euler method that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we consider Carathéodory-type functions satisfying a one-sided Lipschitz condition. After investigating the well-posedness and the stability properties of

In this paper, a general framework using tensor Krylov projection techniques is proposed for solving high order Sylvester tensor equations. After describing the tensor format of the generalized Hessenberg process, we combine the obtained different processes with a Galerkin orthogonality condition or with a minimal norm condition in order to derive the Hess−BTF and CMRH−BTF methods which are based on

We propose and analyze a linearly stabilized semi-implicit diffusive Crank–Nicolson scheme for the Cahn-Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic system with constant coefficients and provable discrete energy dissipation. Rigorous error analysis is carried out for the fully

In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction–diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional)

A linear Multistep Block Hybrid Method with four off-grid points is presented for the direct approximation of the solution of fourth order Boundary Value Problems. Multiple Finite Difference formulas are derived and grouped into a unique block to form a numerical integrator to solve directly the fourth order problem, without the need to reduce it previously to a first-order system. The convergence

In the article R. Ferro and J.A. Virtanen (2017), the authors conjecture that δToep,∗(A)=δ(A), where A is a block Toeplitz matrices whose blocks have no specific structure. In this work we answer the correctness of the conjecture.

In this article we focus on option Greeks computation by means of Radial Basis Functions (RBF) with Partition of Unity methods. We start by presenting RBF applications to the financial world: we price single-underlying European and American barrier options and an American basket option on two correlated underlyings. Furthermore, we derive the expression for Greeks calculation via RBF and we compare

This paper primarily focuses on the distributions of the solutions for uncertain fractional difference equations by comparison theorems. First, comparison theorems are obtained for the fractional difference equations involving Riemann–Liouville type. Then the concepts of symmetrical uncertain variable and α-path to an uncertain fractional difference equation are introduced. Moreover, the relations

The main aim of this paper is to construct a new computational approach for the numerical solution of generalized Black–Scholes equation. In this approach, the temporal variable is discretized using Cranck-Nicolson scheme and spatial variable is discretized using sextic B-spline collocation method. Convergence analysis of the method is discussed. The proposed method is proved to be stable and have

We consider a Hartree equation for a random field, which describes the temporal evolution of infinitely many fermions. On the Euclidean space, this equation possesses equilibria which are not localized. We show their stability through a scattering result, with respect to localized perturbations in the not too focusing case in high dimensions d≥4. This provides an analogue of the results of Lewin and

The purpose of this paper is to study the sparse bound of the operator of the form f↦ψ(x)∫f(γt(x))K(t)dt, where γt(x) is a C∞ function defined on a neighborhood of the origin in (x,t)∈Rn×Rk, satisfying γ0(x)≡x, ψ is a C∞ cut-off function supported on a small neighborhood of 0∈Rn and K is a Calderón-Zygmund kernel supported on a small neighborhood of 0∈Rk. Christ, Nagel, Stein and Wainger gave conditions

In this paper, we construct and analyze a family of quadratic finite volume element schemes over triangular meshes for elliptic equations. This family of schemes cover some existing quadratic schemes. For these schemes, by element analysis, we find that each element matrix can be split as two parts : the first part is the element stiffness matrix of the standard quadratic finite element method, while

Assume that u(x) satisfies the problem Lu(x)≡−∂∂xi(aij∂u∂xj)=f(x),∀x∈Ω,u(x)=0,∀x∈∂Ω. In this article, using interpolation postprocessing technique, we will investigate the local ultraconvergence of the primal variable and the derivative of finite element approximation of u(x) using piecewise polynomials of degrees bi-k(k≥3) over a rectangular partition. Assume that k≥3 is odd and x0 is an interior

The aim of this paper is to propose and analyze a numerical method to solve transient eddy current problems formulated in terms of the magnetic field intensity. Space discretization is based on Nédélec edge elements, while a backward Euler scheme is used for time discretization; the curl-free constraint in the dielectric domain is imposed by means of a penalty strategy. Convergence of the penalized

Capillary pressure is a key parameter in reservoir numerical simulation. It is generally considered that the capillary force is an only function of water saturation in the current traditional reservoir numerical simulation methods. However, large amount of indoor experiments have shown that capillary force is not only dependent on the water saturation, but also the velocity of fluid flow. In this work

A block triple-relaxation-time (B-TriRT) lattice Boltzmann model for general nonlinear anisotropic convection–diffusion equations (NACDEs) is proposed, and the Chapman–Enskog analysis shows that the present B-TriRT model can recover the NACDEs correctly. There are some striking features of the present B-TriRT model: firstly, the relaxation matrix of B-TriRT model is partitioned into three relaxation

The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse matrices. The paper presents execution time analytical model for the time to solve the systems. The BiCGStab method and several modifications including the Reordered

In this paper, we have constructed a scheme combining generalized Polynomial Chaos (gPC) representation and B-spline wavelets. To begin with, semi-orthogonal compactly supported B-spline wavelets are constructed for the bounded interval [0,1] which are used for PC expansion of possible stochastic processes. To compute the deterministic coefficients of expansion, we have applied Galerkin projection