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In this article, the non-singular variable-order fractional derivative in the Heydari-Hosseininia concept is used to formulate the variable-order fractional form of the coupled nonlinear Ginzburg-Landau equations. To solve this system, a numerical scheme is constructed based upon the shifted Vieta-Lucas polynomials. In this method, with the help of classical and fractional derivative matrices of the shifted Vieta-Lucas polynomials (which are extracted in this study), solving the studied problem is transformed into solving a system of nonlinear algebraic equations. The convergence analysis and the truncation error of the shifted Vieta-Lucas polynomials in two dimensions are investigated. Numerical problems are demonstrated to confirm the convergence rate of the presented algorithm.

In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grunwald difference (tempered-WSGD) operators for the tempered fractional diffusion equation. We also show stability and convergence analysis for the fully discrete scheme based a Crank–Nicolson scheme in time. A third-order scheme for the tempered Black–Scholes equation is also proposed and tested numerically. Some numerical experiments are carried out to confirm accuracy and effectiveness of these proposed methods.

In this paper, two efficient two-grid algorithms with L 1 scheme are presented for solving two-dimensional nonlinear time fractional diffusion equations. The classical L 1 scheme is considered in the time direction, and the two-grid FE method is used to approximate spatial direction. To linearize the discrete equations, the Newton iteration approach and correction technique are applied. The two-grid algorithms reduce the solution of the nonlinear fractional problem on a fine grid to one linear equation on the same fine grid and an original nonlinear problem on a much coarser grid. As a result, our algorithms save total computational cost. Theoretical analysis shows that the two-grid algorithms maintain asymptotically optimal accuracy. Moreover, the numerical experiment presented further confirms the theoretical results.

Recently, an innovative hypercube-variant network called bicube, denoted as B Q n , has been proposed to possess both short diameter and symmetry advantages. Unlike other existing hypercube-variant networks, they lose their symmetry in pursuit of short diameters. For solving the problems of fault-tolerant transmission and secure message distribution in a reliable network, one solution suggested a dual-CIST (two completely independent spanning trees) to design a multi-path routing (e.g., a recently proposed secure-protection routing). We can make the construction using the standard arrangement guideline (SAG) like the hypercubes to obtain a dual-CIST with a diameter of 2 n − 1 on B Q n . This paper proposes a newly generic adjustment scheme (GAS) for reducing the diameter of the dual-CIST under this construction. As a result, the diameter of T i for i = 1 , 2 we constructed for B Q n are as follows: diam ( T i ) = { 7 if n = 4 ; 2 n − 2 if n ⩾ 5 and n is odd ; 2 n − 3 if n ⩾ 6 and n is even .

The method of numerical and algebraic formalization and solution of the problem of synthesizing systems with the structure of one of the four varieties of combinatorial block designs has been substantiated. Analytical representations of the blocks and duality blocks of such systems are obtained when representing elements and numbering blocks and duality blocks by initial non-negative integers. In this case, algebraic block identifiers are used, which allows building blocks in a distributed manner, i.e. independently of one another. According to the substantiated method of formalizing the meaningful representations of systems, the same combinatorial block design can be a model of various synthesized systems. This thesis is illustrated by an example of the synthesis of a computer network and a key distribution scheme in a wireless sensor network.

Within the framework of mathematical models based on the concept of a local M-derivative with respect to time variable, statements are made and closed-form solutions to some two-dimensional boundary-value problems of convective and convective-diffusion mass transfer and mass exchange of soluble substances during geofiltration are obtained. In particular, an inverse retrospective problem of convective diffusion is posed according to the scheme of two-dimensional geofiltration from an infinite reservoir to drainage, its regularized solution is obtained, and some estimates of convergence are given.

An implicit Crank–Nicolson procedure can be replaced with an explicit iteration process. An explicit finite‐difference time‐domain method based on the iterated Crank–Nicolson scheme that has been widely used for solving Einstein's equations is newly developed. The formulation is presented with two iterations and its stability condition is also derived. Numerical results are found to agree well with those obtained from the traditional explicit finite‐difference time‐domain method, showing the validity of the present iterated Crank–Nicolson–finite‐difference time‐domain method.

In this paper fourth order of accuracy difference scheme for approximate solution of a multi-point elliptic overdetermined problem in a Hilbert space is proposed. The existence and uniqueness of the solution of the difference scheme are obtained by using the functional operator approach. Stability, almost coercive stability, and coercive stability estimates for the solution of difference scheme are established. These theoretical results can be applied to construct a stable highly accurate difference scheme for approximate solution of multi-point overdetermined boundary value problem for multidimensional elliptic partial differential equations.

In this paper, the convergence of a three-step iterative process i.e., K-iteration scheme is established in complex valued Banach spaces under the setting of generalized F- contractions. Also, the convergence of Picard Ishikawa hybrid process is established with same conditions. This work hence extends the convergence of three step iterative schemes in complex valued Banach spaces and further enhances the scope of research and analysis of the work in this area.

In this paper, the determination of eccentric anomaly (E) for Kepler’s satellite orbit using Perturbation-Based Seeded Secant (PBSS) iteration algorithm is presented. The solution is meant for Kepler’s orbit with the value of eccentricity (e) in the range 0 ≤ e ≤ 1. Such orbits are either circular or elliptical. The demonstration of the applicability of the PBSS iteration is presented using sample numerical examples with different values of mean anomaly (M) and eccentricity (e). The summary of the results of E for M = 30° and e in the range 0.001 ≤ e ≤1 showed that the convergence cycle (n) increases as e increases. Particularly, n increased from 2 at e = 0.01 to n = 8 at e =1. The implication is that it takes more iterations to arrive at the value of E with the desired accuracy or error performance (which in this case is set to 10^(-12)). Another implication is that a good choice of the initial value of E is essential especially as the value of e increases. As such, effort should be made to develop a means of estimating the initial value of E which will reduce the convergence cycle for higher values of e.

The motive of this paper is to propose a new iterative algorithm for evaluating a solution of constrained minimization problem, variational inequality and split feasibility problem and common fixed point of two generalized $$\alpha $$ -nonexpansive mappings. We obtain few convergence results in the setting of uniformly convex Banach space. We also present some numerical examples for supporting our main results and to demonstrate the convergence behaviour of the obtained process.

We present a fast and accurate numerical scheme for approximating weakly singular oscillatory Volterra integral equations (VIEs) of the second kind. The main idea is the combination of the black-bo...

We prove that, given integers $m\geq 3$, $r\geq 1$ and $n\geq 0$, the moduli space of torsion free sheaves on $\mathbb P^m$ with Chern character $(r,0,\ldots,0,-n)$ that are trivial along a hyperplane $D \subset \mathbb P^m$ is isomorphic to the Quot scheme $\mathrm{Quot}_{\mathbb A^m}(\mathscr O^{\oplus r},n)$ of $0$-dimensional length $n$ quotients of the free sheaf $\mathscr O^{\oplus r}$ on $\mathbb A^m$., Minor improvements. Final version

In this paper, we develop a symmetric mixed covolume scheme for the nonlinear parabolic equations. The existence and uniqueness of the scheme are proved by using the lowest order Raviart–Thomas mixed element space on rectangular grids. We carry out a rigorous error estimates for the constructed scheme, establishing the first-order convergence for both velocity and pressure. Numerical examples are provided to verify that the numerical results are all in consistent with the theoretical analysis.

Recently, many authors studied the numerical solution of the classical Darboux problem in its integral form via a two-dimensional nonlinear Volterra-Fredholm integral equation. In the present article, a numerical technique based on the Chebyshev wavelet is proposed to solve the Darboux problem directly without converting into a nonlinear Volterra-Fredholm integral equation. The proposed technique is different from the techniques discussed in [1, 2, 4, 7, 11, 16, 17, 18, 19]. The proposed approach produces higher accuracy than its counterpart techniques. The proposed scheme illustrated with suitable examples to show the advantages in terms of its accuracy with lesser grid size.

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

In this paper, we propose and analyze a variant of the proximal point method for obtaining weakly efficient solutions of convex vector optimization problems in real Hilbert spaces, with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. The proposed method is a hybrid scheme that combines proximal point type iterations and projections onto some special halfspaces in order to achieve the strong convergence to a weakly efficient solution. To the best of our knowledge, this is the first time that proximal point type method with strong convergence has been considered in the literature for solving vector/multiobjective optimization problems in infinite dimensional Hilbert spaces.

In this paper, we investigate the approximate bound states solutions of Klein–Gordon equation with position-dependent mass for scalar and vector central Hulthen-type potentials by applying an approximation scheme to deal with the centrifugal potential for any l-states. The supersymmetric quantum mechanics (SUSYQM) and shape invariance approaches are used in the calculations. We obtain straightforwardly the relativistic energies and their corresponding normalized wavefunctions, expressed in terms of Jacobi polynomials. Special cases of interest of this problem are also deduced and it is found that our results are in good agreement with those obtained in the literature.

UDC 517.9 Phuengrattana and Suantai [J. Comput. and Appl. Math., 235, 3006 – 3014 (2011)] introduced an iteration scheme and they named this iteration as SP-iteration. In this paper, we study the convergence behaviour of SP-iteration scheme for the class of generalized nonexpansive mappings. One weak convergence theorem and two strong convergence theorems in uniformly convex Banach spaces are obtained. We also furnish a numerical example in support of our main result. In process, our results generalize and improve many existing results in the literature.

This paper proposes and analyzes a globalized version of the Newton method for finding a singularity of the nonsmooth vector fields. Basically, the new method combines a version of nonsmooth Newton method with a nonmonotone line search strategy. The global convergence analysis of the proposed method as well as results on its rate are established under mild assumptions. Finally, numerical experiments illustrating the practical advantages of the proposed scheme are reported.

In a companion paper, we present the theoretical development of a new robust, relaxation-free iteration scheme for multiphysics k-eigenvalue problems. These types of problems are essential to the s...

In 1992, Frankel and Desmedt introduced a technique that enables one to reduce the secret space of an ideal homomorphic secret sharing scheme (IHSSS) into any of its characteristic subgroups. In this paper, we propose a similar technique to reduce the secret space of IHSSSs called the quotient technique. By using the quotient technique, we show that it is possible to yield an ideal linear scheme from an IHSSS for the same access structure, providing an alternative proof of a recent result by Jafari and Khazaei. Moreover, we introduce the concept of decomposition of secret sharing schemes. We give a decomposition for IHSSSs, and as an application, we present a necessary and sufficient condition for an IHSSS to be mixed-linear. Continuing this line of research, we explore the decomposability of some other scheme classes.

"In this paper xed point arguments and a critical point technique are combined leading to hybrid existence results for a system of three operator equations where only two of the equations have a variational structure. The components of the solution which are associated to the equations having a variational form represent a Nash-type equilibrium of the corresponding energy functionals. The result is achieved by an iterative scheme based on Ekeland's variational principle."

In the given work diagnostics of mathematical proof of the Beal Conjecture (Generalized Fermat’s Last Theorem) obtained in the earlier author’s works was conducted and truthfulness of the suggested proof was established. Realizing the process of the Bill Conjecture solution, the mathematical structure defining hypothetical equality of the Fermat theorem was determined. Such a structure turned to be one of Pythagorean theorem with whole numbers. With help of Euclid’s geometrical theorem and Fermat’s method of infinite descent one can manage to set that Pythagorean equation in whole numbers representing Fermat’s Last Theorem cannot exist and then the Fermat theorem is true, that is Fermat’s equality in natural numbers does not exist. Thus mental scheme of “demonstratio mirabile”, which Pierre de Fermat mentioned on the margins of Diophantus’s “Arithmetic”, was reconstructed.

This paper presents a new robust scheme for coupled physics nuclear reactor calculations. We focus specifically on high-fidelity whole-core transport calculations with coarse mesh finite difference...

A method to lower the MSE of a proposed estimator relative to the MSE of the linear regression estimator under two-phase sampling scheme is developed. Estimators are developed to estimate the mean of the variate under study with the help of auxiliary variate (which are unknown but it can be accessed conveniently and economically). The mean square errors equations are obtained for the proposed estimators. In addition, optimal sample sizes are obtained under the given cost function. The comparison study has been done to set up conditions for which developed estimators are more effective than other estimators with novelty. The empirical study is also performed to supplement the claim that the developed estimators are more efficient.

In this paper, we propose a new family of non-stationary subdivision scheme, based on mixed trigonometric hyperbolic B-spline basis functions with two tension and one shape parameters. We prove tha...

Predicate/pair encodings are simple frameworks for designing attribute-based encryption ( $$\textsf {ABE}$$ ) for complex predicates, with pair encodings being able to handle more complex predicates. Thus far, several generic constructions of prime-order $$\textsf {ABE}$$ schemes have been proposed with these encodings. Chen, Gay, and Wee ( $$\textsf {CGW}$$ ) (Eurocrypt’15) and Chen and Gong $$(\textsf {CG})$$ (Asiacrypt’17) proposed generic constructions with predicate encodings with a trade-off in efficiency. In particular, the former construction ( $$\textsf {CGW}$$ $$\textsf {ABE}$$ ) has the shorter secret keys, whereas the latter construction ( $$\textsf {CG}$$ $$\textsf {ABE}$$ ) has the shorter master public keys and ciphertexts. Moreover, $$\textsf {CG}$$ $$\textsf {ABE}$$ requires three pairing operations during decryption, while $$\textsf {CGW}$$ $$\textsf {ABE}$$ requires four. Agrawal and Chase ( $$\textsf {AC}$$ ) (TCC’16) proposed a generic construction with pair encodings that is an extension of $$\textsf {CGW}$$ $$\textsf {ABE}$$ and can handle more complex predicates. Specifically, if pair encoding schemes satisfy perfect security (resp. relaxed perfect security), then $$\textsf {AC}$$ $$\textsf {ABE}$$ satisfies full security (resp. semi-adaptive security) from the standard k-linear assumption. However, there is no extension of $$\textsf {CG}$$ $$\textsf {ABE}$$ with pair encodings. In this paper, we construct this extension. As with the trade-off between $$\textsf {CGW}$$ $$\textsf {ABE}$$ and $$\textsf {CG}$$ $$\textsf {ABE}$$ , our proposed $$\textsf {ABE}$$ has shorter master public keys and ciphertexts and larger secret keys, requires less pairing operations during decryption than $$\textsf {AC}$$ $$\textsf {ABE}$$ . Furthermore, as with $$\textsf {AC}$$ $$\textsf {ABE}$$ , our proposed $$\textsf {ABE}$$ satisfies full security (resp. semi-adaptive security) if pair encoding schemes satisfy perfect security (resp. relaxed perfect security) from the standard k-linear assumption. As an application, we propose a ciphertext-policy $$\textsf {ABE}$$ scheme for non-monotone span programs with compact ciphertexts satisfying semi-adaptive security.

The rototranslation group ℛ T is the group comprising rotations and translations of the Euclidean plane which is a 3-dimensional Lie group. In this paper, we use the Riemannian approximation scheme to compute sub-Riemannian limits of the Gaussian curvature for a Euclidean C 2 -smooth surface in the rototranslation group away from characteristic points and signed geodesic curvature for Euclidean C 2 -smooth curves on surfaces. Based on these results, we obtain a Gauss–Bonnet theorem in the rototranslation group.

In this paper, we propose a new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems without pseudomonotonicity of the bifunction f in a real Hilbert space. When setting the solution of dual equilibrium problem is nonempty, we obtain a strong convergence theorem which is generated by the iterative scheme. Moreover, we also receive a new linesearch iterative scheme for finding a solution of the split equilibrium problem in suitable assumptions, and report some numerical results to illustrate the convergence of the proposed scheme.

In this paper, we study a three step iterative scheme to estimate fixed points of non-expansive mappings in the framework of Banach spaces. Further, some convergence results are proved for such mappings. A nontrivial numerical example is presented to verify our assertions and main results. Finally, we approximate the solution of a boundary value problem of second order differential equation.

In this study we consider an efficient sixth order scheme for solving Banach space-valued equations. The convergence criteria in earlier studies involve higher-order derivatives limiting the applicability of these methods. In this study, we use the first derivative only in our analysis to expand the usage of these schemes. The technique we use can be used on other schemes to obtain the same advantages. Numerical experiments compare favorably our results to earlier ones.

This paper is concerned with the topological structure, reachability, and stabilization for Boolean control networks (BCNs) with state constraints via event-triggered control (ETC) scheme. In the first part, the topological structure of BCNs with state constraints is studied. Under the framework of state constrain, the definitions of fixed point and cycle are first defined. A novel phenomenon is that there may exist two kinds constrained fixed points, which are, respectively, named as the livelock and deadlock ones. It is different with the traditional fixed point. Accordingly, a formula is presented to calculate the number of constrained fixed points and constrained cycles. In the second part, the constrained reachability and stabilization problem of the event-triggered controlled BCNs are investigated. Two necessary and sufficient criteria are, respectively, obtained. Furthermore, an algorithm is developed to design all feasible controllers. Finally, a reduced model of the lac operon in the Escherichia coli is shown to illustrate the efficiency of the obtained results.

This work presents a new approach to modelling of free surface non-Newtonian (viscoplastic or viscoelastic) fluid flows on dynamically adapted octree grids. The numerical model is based on the implicit formulation and the staggered location of governing variables. We verify our model by comparing simulations with experimental and numerical results known from the literature.

The invention "A four–plane cup-shaped trel-lis on metal arcs for vine growing with a square-nest planting scheme in the mecha-nized culture of vineyards is described. The characteristics of the analogs and prototype of the invention, the purpose of this invention, methods and objects of research are given. A general view of a vineyard with a four-plane cup-shaped trellis on metal arcs for growing vines with a quad-nest planting scheme is shown, the features of its design, installation and advantages over analogues and the proto-type are revealed. Examples of installing a four-plane cup-shaped trellis on metal arcs for vine growing with a quad-nesting planting scheme, for production vineyards and on pri-vate gardens are given.

We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions., The authors' version accepted for publication

A $$K{{P}_{1}}$$ scheme for accelerating the convergence of inner iterations is constructed for the transport equation in 2D $$r,z$$ geometry. This scheme is consistent with the nodal LD (Linear Discontinues) and LB (Linear Best) schemes of the third and fourth orders of accuracy with respect to the spatial variables. To solve the $${{P}_{1}}$$ system for acceleration corrections, an algorithm is proposed based on the splitting method combined with the tridiagonal matrix algorithm to solve auxiliary systems of two-point equations. A modification of the algorithm for 2D $$x,z$$ geometry is considered. Numerical examples of using the $$K{{P}_{1}}$$ scheme to solve radiation transport problems in 2D $$r,z$$ , $$x,z$$ , and $$r,\vartheta $$ geometries are given, including problems with a significant role of scattering anisotropy and highly heterogeneous problems with dominant scattering.