R. Mutalip, B.A. Duisengaliyeva, A.S. Naurazbekova
We prove the elementary reducibility of any nonaffine automorphism of a free nonassociative algebra of rank two over an arbitrary field. Using this result establish a property of automorphisms of this algebra that will be needed in later. We then derive a necessary and sufficient condition for the isomorphism of two free braided nonassociative algebras of rank two over a field with diagonal braidings. We describe the automorphism groups of two generated free braided nonassociative algebras with involutive diagonal braidings over an arbitrary field of characteristic not equal to two. Depending on the form of the diagonal involutive braiding, five different automorphism groups of a two-generated free nonassociative algebra arise in this case: 1) the group of all automorphisms, 2) the group of all odd automorphisms, 3) the subgroup of the group of triangular automorphisms, 4) the toric automorphism group, 5) the semidirect product of the toric automorphism group with the subgroup generated by an automorphism that permutes two variables.
Marine propellers are studied in design and off-design modes of operation like crashback, where the propeller rotates in reverse while the vehicle is in forward motion. Past experiments (Jessup et al., Proceedings of the 25th Symposium on Naval Hydrodynamics, St John's, Canada, 2004; Proceedings of the 26th Symposium on Naval Hydrodynamics, Rome, Italy, 2006) studied the marine propeller David Taylor Model Basin 4381 in the open-jet test section of the 36-inch variable pressure water tunnel (VPWT). In crashback, a significant discrepancy with unclear sources exists between the mean propeller loads from the VPWT and open-water towing tank (OW) experiments (Ebert et al., 2007 ONR Propulsor S & T Program Review, October, 2007). We perform large-eddy simulation at $Re=561\,000$ and advance ratios $J=-0.50$ and $-0.82$ with the VPWT geometry included, contrasting to the unconfined (OW) case at those same $J$ and $Re=480\,000$. We identify and delineate the water tunnel interference effects responsible, and demonstrate that these effects resemble those of a symmetric solid model or bluff body. Solid blockage due to jet expansion and nozzle blockage due to proximity to the tunnel nozzle are identified as the primary interference effects. Their impact varies with the advance ratio $J$ and strengthens for higher magnitudes of $J$. The effective length scale to assess the severity of interference effects is found to be larger than the vortex ring diameter.
The work is related to the study of the model-theoretic properties of Jonsson theories, which, generally speaking, are not complete. In the article, on the Boolean of Jonsson subsets of the semantic model of some fixed Jonsson theory, the concept of the Jonsson closure operator Jcl was introduced, defining the J-pregeometry on these subsets, and some results were obtained describing this closure operator.
The paper concerns a nonlinear second-order parabolic evolution equation, one of the well-known objects of mathematical physics, which describes the processes of high-temperature thermal conductivity, nonlinear diffusion, filtration of liquid in a porous medium and some other processes in continuum mechanics. A particular case of it is the well-known porous medium equation. Unlike previous studies, we consider the case of several spatial variables. We construct and study solutions that describe disturbances propagating over a zero background with a finite speed, usually called ‘diffusion-wave-type solutions’. Such effects are atypical for parabolic equations and appear since the equation degenerates on manifolds where the desired function vanishes. The paper pays special attention to exact solutions of the required type, which can be expressed as either explicit or implicit formulas, as well as a reduction of the partial differential equation to an ordinary differential equation that cannot be integrated in quadratures. In this connection, Cauchy problems for second-order ordinary differential equations arise, inheriting the singularities of the original formulation. We prove the existence of continuously differentiable solutions for them. A new example, an analog of the classic example by S.V. Kovalevskaya for the considered case, is constructed. We also proved a new existence and uniqueness theorem of heat-wave-type solutions in the class of piece-wise analytic functions, generalizing previous ones. During the proof, we transit to the hodograph plane, which allows us to overcome the analytical difficulties.
This paper is devoted to a new type of boundary-value problems for Sturm-Liouville equations defined on three disjoint intervals (−π,−π+d),(−π+d,π−d) and (π−d,π) together with eigenparameter dependent boundary conditions and with additional transmission conditions specified at the common end points −π+d and π−d, where 0<d<π. The considered problem cannot be treated by known techniques within the usual framework of classical Sturm-Liouville theory. To establish some important spectral characteristics we introduced the polynomial-operator formulation of the problem. Moreover, we develop a new modification of the Rayleigh method to obtain lower bound of eigenvalues.
The present paper simplifies the naturally formed dunes (riverbeds) as large-scale three-dimensional staggered wavy walls to investigate the features of the accompanying secondary flows and streamwise vortices via large-eddy simulation. A comparison between the swirling strength and the mean velocities suggests where a secondary flow induces upwash or downwash motions. Moreover, we propose a pseudo-convex wall mechanism to interpret the directionality of the secondary flow. The centrifugal instability criterion is then used to reveal the generation of the streamwise vortices. Based on these analytical results, we found that the streamwise vortices are generated in the separation and reattachment points on both characteristic longitudinal–vertical and horizontal cross-sections, which is related to the curvature effect of the turbulent shear layer. Furthermore, the maximum Görtler number characterized by the ratio of centrifugal to viscous effects suggests that, for fixed ratio of spanwise- to streamwise-wavelength cases, the strongest centrifugal instability occurring on the longitudinal–vertical cross-section gradually dominates with the increases in amplitude. A similar trend for the cases with varied spanwise wavelength can also be found. It is also found that the streamwise vortices are generated more readily via transverse flow around the crest near the separation and reattachment points when the ratio of spanwise- to streamwise-wavelength equals 1.
The main goal of the study is the approximation of the solution to the Dirichlet boundary value problem (DBVP) of the heat equation on a rectangle by developing a new difference method on a grid system of hexagons. It is proved that the given special scheme is unconditionally stable and converges to the exact solution on the grids with fourth order accuracy in space variables and second order accuracy in time variable. Secondly, an incomplete block factorization is given for symmetric positive definite block tridiagonal (SPD-BT) matrices utilizing a conservative iterative method that approximates the inverse of the pivoting diagonal blocks by preserving the symmetric positive definite property. Subsequently, by using this factorization block hybrid preconditioning of the conjugate gradient (BHP-CG) method is applied to solve the obtained algebraic system of equations at each time level.
In this paper, we have solved several extremal problems of the best mean-square approximation of functions f on the semiaxis with a power-law weight. In the Hilbert space L 2 with a power-law weight t2α+1 we obtain Jackson-Stechkin type inequalities between the value of the Eσ(f)-best approximation of a function f(t) by partial Hankel integrals of an order not higher than σ over the Bessel functions of the first kind and the k-th order generalized modulus of smoothnes ωk(Brf,t), where B is a second-order differential operator.
This article is devoted to the solvability of degenerate nonlinear equations of pseudoparabolic type. Such problems appear naturally in physical and biological models. The article aims to study the solvability in the classes of regular solutions of (all derivatives generalized in the sense of S.L. Sobolev included in the equation) initial-boundary value problems for differential equations. For the problems under consideration, We have found conditions on parameters ensuring the existence of solutions and we have proved existence and uniqueness theorems. The main method for proving the solvability of boundary value problems is the regularization method.
Morphing structures, defined as body panels that are capable of a drastic autonomous shape transformation, have gained importance in the aerospace, automotive, and soft robotics industries since they address the need to switch between shapes for optimal performance over the range of operation. Laminated composites are attractive for morphing because multiple laminae, each serving a specific function, can be combined to address multiple functional requirements such as shape transformation, structural integrity, safety, aerodynamic performance, and minimal actuation energy. This paper presents a review of laminated composite designs for morphing structures. The trends in morphing composites research are outlined and the literature on laminated composites is categorized based on deformation modes and multifunctional approaches. Materials commonly used in morphing structures are classified based on their properties. Composite designs for various morphing modes such as stretching, flexure, and folding are summarized and their performance is compared. Based on the literature, the laminae in an n-layered composite are classified based on function into three types: constraining, adaptive, and prestressed. A general analytical modeling framework is presented for composites comprising the three types of functional laminae. Modeling developments for each morphing mode and for actuation using smart material-based active layers are discussed. Results, presented for each deformation mode, indicate that the analytical modeling can not only provide insight into the structure's mechanics but also serve as a guide for geometric design and material selection.
The oscillatory theory of fourth order differential equations has not yet been developed well enough. The results are known only for the case when the coefficients of differential equations are power functions. This fact can be explained by the absence of simple effective methods for studying such higher order equations. In this paper, the authors investigate the oscillatory properties of a class of fourth order differential equations by the variational method. The presented variational method allows to consider any arbitrary functions as coefficients, and our main results depend on their boundary behavior in neighborhoods of zero and infinity. Moreover, this variational method is based on the validity of a certain weighted differential inequality of Hardy type, which is of independent interest. The authors of the article also find two-sided estimates of the least constant for this inequality, which are especially important for their applications to the main results on the oscillatory properties of these differential equations.
In this paper for a new class of model and non-model partial integro-differential equations with singularity in the kernel, we obtained integral representation of family of solutions by aid of arbitrary functions. Such type of integro-differential equations are different from Cauchy-type singular integro-differential equations. Cauchy-type singular integro-differential equations are studied by the methods of the theory of analytic functions. In the process of our research the new types of singular integro-differential operators are introduced and main property of entered operators are learned. It is shown that the solution of studied equation is equivalent to the solution of system of two equations with respect to x and y, one of which is integral equation and the other is integro-differential equation. Further, non-model integro-differential equations are studied by regularization method. This regularization method for non-model equation is based on selecting and analysis of a model part of the equation and reduced to the solution of two second kind Volterra type integral equations with weak singularity in the kernel. It is shown that the presence of a non-model part in the equation does not affect to the general structure of the solutions. From here investigation of the model equations for given class of the integro-differential equations becomes important. In the cases, when the solution of given integro-differential equation depends on any arbitrary functions, a Cauchy type problems are investigated.
Maksat Ashyraliyev, Maral A. Ashyralyyeva, Allaberen Ashyralyev
In the present paper, a source identification problem for hyperbolic-parabolic equation with involution and Dirichlet condition is studied. The stability estimates for the solution of the source identification hyperbolicparabolic problem are established. The first order of accuracy stable difference scheme is constructed for the approximate solution of the problem under consideration. Numerical results are given for a simple test problem.
Abstract To understand the influence of the bending deformation on the stress evolution and crack propagation in nano flexible electrode during electrochemical cycling, an analytical model is developed based on core-shell structure in a cylindrical electrode. In the model, the analytical solution of stress specialized for the cylindrical electrode in the process of bending deformation and phase transformation is clarified. Further, the weight function is utilized to calculate the time-dependent stress intensity factor by combining the stress profiles as found in the analytical work. Thus, the behavior of the preexisting center and edge cracks in the electrode is discussed to investigate the effect of the initiation position on crack propagation. It is found that cracks tend to spread more easily in the early stages of discharging process due to the larger slope of the SIF curve within small edge cracks. Further, an analytical fracture mechanics study is presented and the formula of critical size for the flexible electrode is derived based on Griffith criterion, below which the crack does not spread under the superposition of the diffusion stress and the bending stress. In the light of the fracture mechanics study of the flexible electrode, the present work sheds some light on stress engineering and structural design of durable flexible lithium-ion batteries.