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Abstract: In this paper, we present some sixth-order class of modified Ostrowski’s methods for solving nonlinear equations. Per iteration each class member requires three function and one first derivative evaluations, and is shown to be at least sixth-order convergent. Several numerical examples are given to illustrate the performance of some of the presented methods. [Copyright &y& Elsevier]

A nonoscillation criterion for a second-order linear difference equation is established correcting a result in [1]. [Copyright &y& Elsevier]

Abstract In this paper, we consider the following nonlinear waveequation with variable exponents: u t t − div (| ∇ u | r (⋅) − 2 ∇ u) + | u t | m (⋅) − 2 u t = 0. By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m , r and the initial data. We also give two numerical applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

A ring R is said to be left uniquely generated if R a = R b in R implies that a = u b for some unit u in R . These rings have been of interest since Kaplansky introduced them in 1949 in his classic study of elementary divisors. Writing l ( b ) = { r ∈ R | r b = 0 } , a theorem of Canfell asserts that R is left uniquely generated if and only if, whenever R a + l ( b ) = R where a , b ∈ R , then a − u ∈ l ( b ) for some unit u in R . By analogy with the stable range 1 condition we call a ring with this property left annihilator-stable. In this paper we exploit this perspective on the left UG rings to construct new examples and derive new results. For example, writing J for the Jacobson radical, we show that a semiregular ring R is left annihilator-stable if and only if R / J is unit-regular, an analogue of Bass' theorem that semilocal rings have stable range 1. [ABSTRACT FROM AUTHOR]

Two words u and v are k -abelian equivalent if for each word x of length at most k , x occurs equally many times as a factor in both u and v . The notion of k -abelian equivalence is an intermediate notion between the abelian equivalence and the equality of words. In this paper, we study the equivalence classes induced by the k -abelian equivalence, mainly focusing on the cardinalities of the classes. In particular, we are interested in the number of singleton k -abelian classes, i.e., classes containing only one element. We find a connection between the singleton classes and cycle decompositions of the de Bruijn graph. We show that the number of classes of words of length n containing one single element is of order O ( n N m ( k − 1 ) − 1 ) , where N m ( l ) = 1 l ∑ d | l φ ( d ) m l / d is the number of necklaces of length l over an m -ary alphabet. We conjecture that the upper bound is sharp. We also remark that, for k even and m = 2 , the lower bound Ω ( n N m ( k − 1 ) − 1 ) follows from an old conjecture on the existence of Gray codes for necklaces of odd length. We verify this conjecture for necklaces of length up to 15. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we establish the formulas of the maximal and minimal ranks of the quaternion matrix expression where X is a variant quaternion matrix subject to quaternion matrix equations . As applications, we give a new necessary and sufficient condition for the existence of solutions to the system of matrix equations , which was investigated by Wang [Q.W. Wang, A system of four matrix equations over von Neumann regular rings and its applications, Acta Math. Sin., 21(2) (2005) 323–334], by rank equalities. In addition, extremal ranks of the generalized Schur complement with respect to an inner inverse A − of A, which is a common solution to quaternion matrix equations , are also considered. Some previous known results can be viewed as special cases of the results of this paper. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of singular positive radial solutions of second order quasilinear elliptic equations. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]

Abstract: A stochastic response surface method (SRSM) which has been previously proposed for problems dealing only with random variables is extended in this paper for problems in which physical properties exhibit spatial random variation and may be modeled as random fields. The formalism of the extended SRSM is similar to the spectral stochastic finite element method (SSFEM) in the sense that both of them utilize Karhunen–Loeve (K–L) expansion to represent the input, and polynomial chaos expansion to represent the output. However, the coefficients in the polynomial chaos expansion are calculated using a probabilistic collocation approach in SRSM. This strategy helps us to decouple the finite element and stochastic computations, and the finite element code can be treated as a black box, as in the case of a commercial code. The collocation-based SRSM approach is compared in this paper with an existing analytical SSFEM approach, which uses a Galerkin-based weighted residual formulation, and with a black-box SSFEM approach, which uses Latin Hypercube sampling for the design of experiments. Numerical examples are used to illustrate the features of the extended SRSM and to compare its efficiency and accuracy with the existing analytical and black-box versions of SSFEM. [Copyright &y& Elsevier]

In this paper, we present a Newton-type method for a class of mathematical programs with complementarity constraints. Under the MPEC-LICQ, we use the definition of B-stationary point to construct a constrained equations model, and apply the Newton method to solve the problem. At the end of this paper, numerical results are reported to show our method's validity. [Copyright &y& Elsevier]

Abstract: A Cramer rule for solving a kind of restricted matrix equationsis presented in [G. Wang, Jie Sun, A Cramer rule for solution of the general restricted matrix equation, Appl. Math. Comput. 154 (2004) 415–422]. This paper gives a more condensed Cramer rule for the solution of the matrix equations. The results in [G. Wang, Z.L. Xu, Solving a kind of restricted matrix equations and Cramer rule, Appl. Math. Comput. 162 (2005) 329–338, Chao Gu, G.R. Wang, Z.L. Xu, PCR Algorithm for the Parallel Computation of the Solution of a class of Singular linear Systems, Appl. Math. Comput. 176 (2006) 237–244] are partially the special cases in our paper. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to build sequences of suitably smooth approximate solutions to the Saint-Venant model that preserve the mathematical structure discovered in [D. Bresch, B. Desjardins, Comm. Math. Phys. 238 (1–2) (2003) 211–223]. The stability arguments in this paper then apply to such sequences of approximate solutions, which leads to the global existence of weak solutions for this model. Extension of this mollifying procedure to the case of compressible Navier–Stokes equations is also provided. Using the recent paper written by the authors, this provides global existence results of weak solutions for the barotropic Navier–Stokes equations and for compressible Navier–Stokes equations with heat conduction using a particular cold pressure term close to vacuum. [Copyright &y& Elsevier]

Abstract: In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equations under new conditions. The main results of the present paper are new and extend the previously known results. [Copyright &y& Elsevier]

Abstract: The present paper describes an efficient algorithm to integrate the equations of motion implicitly in the frequency domain. The standard FEM displacement model (Galerkin formulation) is employed to perform space discretization, and the time-marching process is carried out through an algorithm based on the Green’s function of the mechanical system in nodal coordinates. In the present formulation, mechanical system Green’s functions are implicitly calculated in the frequency domain. Once the Green’s functions related matrices are computed, a time integration procedure, which demands low computational effort when applied to non-linear mechanical systems, becomes available. At the end of the paper numerical examples are presented in order to illustrate the accuracy of the present approach. [Copyright &y& Elsevier]

This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models. [Copyright &y& Elsevier]

The problem of solving min-implication fuzzy relation equations based on S-implications is studied in this paper. Decomposition of min-implication fuzzy relation equations is given in a finite case. The solution existence problem of min-implication fuzzy relation equations is discussed, and for NS-implications, a new solvability criterion based upon “solution matrices” introduced in this paper is studied. It is shown that for each solution r of a min-implication fuzzy relation equation, there exists a maximal solution r* of this equation, such that r* is greater than or equal to r, whenever the solution set of this equation is nonempty. The complete solution set of min-implication fuzzy relation equation can be determined by the maximal solution set of this equation, which is finite. An effective method to solve min-implication fuzzy relation equations based on S-implication is proposed. [Copyright &y& Elsevier]

In many applications, it is useful to know how the solution to a set of simultaneous linear equations depends on parameters entering into the coefficients. To this end, this paper addresses the classical equation with matrix and vector depending on an -tuple of parameters with components entering in a rank-one manner. Given such a system, the following problems are considered: For solution component and parameter , determine if the first and second order partial derivatives of with respect to are of one sign for all in a prescribed hypercube of radius ; i.e., we determine which components enter the solution either monotonically, convexly or concavely. In this paper, we provide extreme point results for these problems. Namely, we need only check the sign of three specially constructed multilinear functions at the extreme points (vertices) of in order to ascertain whether the desired one-sign condition is satisfied over the entire hypercube. Central to the proof of extremality is a special “multilinear factorization” of the partial derivatives of . This leads to a simple method to compute the so-called radii of convexity, concavity and monotonicity. [Copyright &y& Elsevier]

In this paper, we consider the convergence criteria for iterative algorithms of Uzawa type for solving linear saddle point problems. Theoretically weaker convergence criteria than before are established for the general case and these are used to deduce conditions for convergence of two special cases: the exact Uzawa algorithm and the linear one-step method. The conclusions given here hold for both symmetric and nonsymmetric saddle point problems. These new sufficient conditions are compared with some known results and illustrated by two examples. Numerical experiments to verify the conclusions in this paper for the preconditioned exact Uzawa algorithm are provided. [Copyright &y& Elsevier]

This paper deals with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equation by employing the fixed-point theorem in cones. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results. [Copyright &y& Elsevier]

We prove that the equation x2 − kxy + y2 + x = 0 with k ∊ N+ has an infinite number of positive integer solutions x and y if and only if k = 3. For k = 3 the quotient SHAPE="SOL" ALIGN="C" STYLE="S">xy is asymptotically equal to (3 + √5)/2 or (3 − √5)/2. Results of the paper are based on data obtained via Computer Algebra System (derive 5). Some derive procedures presented in the paper made it possible to discover interesting regularities concerning simple continued fractions of certain numbers. [Copyright &y& Elsevier]

In this paper conditions are derived for the existence of a common solution X to the matrix equations AiXBj=Cij,(i,j)∈Γ, where the matrices Ai,Bj,Cij and X have suitable dimensions and the (i,j)’s are index pairs in some set Γ. The purpose of this paper is to present, for certain specific sets of index pairs Γ, verifiable necessary and sufficient solvability conditions that are stated directly in terms of the matrices and that do not use Kronecker products. [Copyright &y& Elsevier]

This paper deals with magnetic equations of the type dH=J where the current J is a δ-function on a brane worldvolume and H a p-form field strength. In many situations in M-theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac-branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern-kernels, and provide relevant applications, among which the anomaly-free effective action for open M2-branes ending on M5-branes. The unobservability of the Dirac-brane requires a Dirac quantization condition; we show that the requirement of “unobservability” of the Chern-kernel leads in M-theory to classical gravitational anomalies which cancel precisely their quantum counterparts. [Copyright &y& Elsevier]

The development of a novel second-order accurate both in time and space kinetic scheme, called the Kinetic Wave/Particle Split (KWPS) scheme is reported in this paper. It is demonstrated that the first-order KWPS algorithm, while computationally efficient and robust, is very diffusive on a reasonable mesh. The KWPS scheme is derived by employing the following steps: the molecular velocity in the Boltzmann equation is split as a sum of fluid velocity and thermal (peculiar) velocity, thus the flux vector in the Boltzmann equation is divided into a convective part and an acoustic part. The Boltzmann equation is then discretized using an upwind differencing. Moments of the discretized Boltzmann equation with the collision invariant vector and Maxwellian distribution function then yield the KWPS scheme for the Euler equations. The second-order formulation is obtained through the application of a Taylor series expansion of the Maxwellian distribution function to include the first-order derivatives. Numerical test cases, both in 1-D and 2-D, are computed to demonstrate the improved accuracy of the second-order KWPS scheme, while maintaining both the efficiency and robustness of the first-order scheme. It should be noted that the new second-order KWPS formulation cannot be obtained using the standard numerical approach employed in the literature for second-order extension. The methodology employed in this paper can be easily extended to formulate a KWPS scheme to any order of accuracy. [Copyright &y& Elsevier]

In a recent paper [1] a number of numerical schemes for the shallow water equations based on a conservative linearization are analyzed. In particular, it is established that the schemes are related through the use of a source term. In this paper this technique is applied to the Euler equations, and further analysis suggests a new formulation of an existing scheme having the same key properties. [Copyright &y& Elsevier]

This paper deals with the solvability of interval matrix equations in max-plus algebra. Max-plus algebra is the algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a ⊕ b = max ⁡ { a , b } and a ⊗ b = a + b . The notation A ⊗ X ⊗ C = B represents an interval max-plus matrix equation, where A , B , and C are given interval matrices. We define four types of solvability of interval max-plus matrix equations, i.e., the tolerance, weak tolerance, left-weak tolerance, and right-weak tolerance solvability. We derive the necessary and sufficient conditions for checking each of them, whereby all can be verified in polynomial time. [ABSTRACT FROM AUTHOR]

Tensor computation is intensive and difficult. Invariably, a vital component is the truncation of tensors, so as to control the memory and associated computational requirements. Various tensor toolboxes have been designed for such a purpose, in addition to transforming tensors between different formats. In this paper, we propose a simple Q-less QR truncation technique for tensors { x ( i ) } with x ( i ) ∈ R n 1 × ⋯ × n d in the simple and natural Kronecker product form. It generalizes the QR decomposition with column pivoting, adapting the well-known Gram–Schmidt orthogonalization process. The main difficulty lies in the fact that linear combinations of tensors cannot be computed or stored explicitly. All computations have to be performed on the coefficients α i in an arbitrary tensor v = ∑ i α i x ( i ) . The orthonormal Q factor in the QR decomposition X ≡ [ x ( 1 ) , ⋯ , x ( p ) ] = Q R cannot be computed but expressed as X R − 1 when required. The resulting algorithm has an O ( p 2 d n ) computational complexity, with n = max ⁡ n i . Some illustrative examples in the numerical solution of tensor linear equations are presented. [ABSTRACT FROM AUTHOR]

In the very recent work Wang and Wang (2014) proved that the initial value problem for the three dimension incompressible MHD equations has a global solutions ( u , B ) ∈ C ( [ 0 , ∞ ) ; χ − 1 ) , provided that the norms of the initial data are bounded exactly by the minimal value of the viscosity coefficients. In this paper, we prove that global solutions u , B that was obtained in Wang and Wang (2014) is asymptotic to zero in sense of the norm of the space χ − 1 as time goes to infinity. Moreover, stability of global solutions is also discussed. [ABSTRACT FROM AUTHOR]

A higher order Kirchhoff type equation ∫ R 2 m ( ∣ ∇ m u ∣ 2 + ∑ γ = 0 m − 1 a γ ( x ) ∣ ∇ γ u ∣ 2 ) d x ( ( − Δ ) m u + ∑ γ = 0 m − 1 ( − 1 ) γ ∇ γ ⋅ ( a γ ( x ) ∇ γ u ) ) = f ( x , u ) ∣ x ∣ β + ϵ h ( x ) in R 2 m is considered in this paper. We assume that the nonlinearity of the equation has exponential critical growth and prove that, for a positive ϵ which is small enough, there are two distinct nontrivial solutions to the equation. When ϵ = 0 , we also prove that the equation has a nontrivial mountain-pass type solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider the asymptotic behavior of solutions for nonlocal dispersal equation with non-homogeneous boundary conditions. We find that the long-time behavior is determined by the boundary value. [ABSTRACT FROM AUTHOR]

The Frequency Difference of Arrival (FDOA) equations derived in this paper are intended to increase the standard accuracy of the Low Earth Orbit (LEO) satellites dedicated to locate non-cooperative emitters placed on the Earth surface or in orbit about the Earth. The equations contain terms that are of the order of the corrections already taken into account in Navigation by GPS. In particular, two of them should not be neglected to this end, since they can be of the order of 10 − 10 . [ABSTRACT FROM AUTHOR]

Finding the solution of the absolute value equation (AVE) A x − | x | = b has attracted much attention in recent years. In this paper, we propose a relaxed nonlinear PHSS-like iterative method, which is more efficient than the Picard-HSS iterative method for the AVE, and is a generalization of the nonlinear HSS-like iteration method for the AVE. By using the theory of nonsmooth analysis, we prove the convergence of the relaxed nonlinear PHSS-like iterative method for the AVE. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the relaxed nonlinear HSS-like method. [ABSTRACT FROM AUTHOR]

In this paper, we remove the bounded total variation condition on the initial data and the restriction of the concentration of a fixed background charge being a constant in the paper "Relaxation of the Isothermal Euler–Poisson System to the Drift-Diffusion Equations," (Quart. Appl. Math., 58 (2000), 511–521), and obtain the zero relaxation time limits to isothermal hydrodynamic model for semiconductor by using the varying viscosity method. [ABSTRACT FROM AUTHOR]

In this note, we correct the statement of Theorem 12 from the paper in the title above (McLean et al., 2020) and fill some gaps in the proof. [ABSTRACT FROM AUTHOR]

Abstract: This paper reports results from a written assessment given to 290 third-, fourth-, and fifth-grade students prior to any instructional intervention. We share and discuss students’ responses to items addressing their understanding of equation structure and the meaning of the equal sign. We found that many students held an operational conception of the equal sign and had difficulty recognizing underlying structure in arithmetic equations. Some students, however, were able to recognize underlying structure on particular tasks. Our findings can inform early algebra efforts by highlighting the prevalence of the operational view and by identifying tasks that have the potential to help students begin to think about equations in a structural way at the very beginning of their early algebra experiences. [Copyright &y& Elsevier]

Within the philosophy of science, the realism debate has been revitalised by the development of forms of structural realism. These urge a shift in focus from the object oriented ontologies that come and go through the history of science to the structures that remain through theory change. Such views have typically been elaborated in the context of theories of physics and are motivated by, first of all, the presence within such theories of mathematical equations that allow straightforward representation of the relevant structures; and secondly, the implications of such theories for the individuality and identity of putative objects. My aim in this paper is to explore the possibility of extending such views to biological theories. An obvious concern is that within the context of the latter it is typically insisted that we cannot find the kinds of highly mathematised structures that structural realism can point to in physics. I shall indicate how the model-theoretic approach to theories might help allay such concerns. Furthermore, issues of identity and individuality also arise within biology. Thus Dupré has recently noted that there exists a ‘General Problem of Biological Individuality’ which relates to the issue of how one divides ‘massively integrated and interconnected’ systems into discrete components. In response Dupré advocates a form of ‘Promiscuous Realism’ that holds, for example, that there is no unique way of dividing the phylogenetic tree into kinds. Instead I shall urge serious consideration of those aspects of the work of Dupré and others that lean towards a structuralist interpretation. By doing so I hope to suggest possible ways in which a structuralist stance might be extended to biology. [Copyright &y& Elsevier]

Abstract: In this paper we extend the migrative property of triangular norms by allowing an arbitrary fixed t-norm in the defining equation instead of the originally used product. Equivalent forms of this extended migrativity are also provided and proved. Two particular cases when is either the minimum or the Łukasiewicz t-norm are studied. In these cases all continuous extended migrative t-norms are characterized and represented. The proofs are constructive, which helps the reader to build up various families of extended migrative t-norms. [Copyright &y& Elsevier]

Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the controllability of a parabolic system with nonlinear memory. Based on the localized estimate of the solution, we prove that the system with a superlinear growth memory is not controllable. Furthermore, two controllability results for some initial data and targets are given as well. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the static response of an infinite beam supported on a unilateral (tensionless) two-parameter Pasternak foundation and subjected to complex transverse loads, including self weight. The transfer displacement function method (TDFM) is employed to determine the initially unknown lengths that remain in contact. In contrast to a Winkler Foundation System (WFS), the lift-off points in a PFS (Pasternak Foundation System) are not necessarily at zero displacement but may be determined sequentially through considering the compatibility conditions at the junctions of contact and non-contact segments. After the response of the whole system including the beam and foundation is expressed through the displacement constants of the initial segment, the contact problem is reduced to two nonlinear algebraic equations with two unknowns. The foundation reactions and the internal actions of the beam may also be determined from the displacement response of the system. Two simple cases are solved to illustrate the influence of the foundation stiffness factors and finally, a third example of a beam with several contact segments is presented to demonstrate the application of the TDFM. [Copyright &y& Elsevier]

Abstract: Pipe bend or elbow is one of the important components in any piping system. Accurate integrity assessment of these pipe bends is very important for reliable operation of all types of plants including nuclear plants. While considerable research has been done in the last few decades to develop accurate integrity assessment procedures of straight pipe with or without cracks, similar efforts were missing for pipe bend or elbow. Reactor Safety Division, Bhabha Atomic Research Centre in collaboration with MPA, University of Stuttgart had embarked upon a comprehensive component integrity test program (CITP) in around 1998 to develop improved integrity assessment methods of piping components in general and elbow in particular. As a part of this program, detailed analytical, numerical and experimental investigations for so many years have generated large number of new equations for improved integrity assessment of elbows. Mainly three aspects of the integrity assessment procedure are focused – development of improved plastic collapse moment equations, proposing new elastic–plastic J-integral and crack opening displacement (COD) estimation schemes to simplify leak-before-break (LBB) analysis and presenting new eta and gamma expressions to evaluate J–R curve from test data. All these newly proposed equations have been validated with the findings of the test data, generated as a part of the CITP. A reasonably good to excellent matching between predictions of the newly proposed equations and test results have been observed in all the cases. The present paper enumerates these research findings in a consolidated yet brief manner. [Copyright &y& Elsevier]

Abstract: For most parallel manipulators, the inverse kinematics is straightforward, while the direct kinematics is challenging. The latter requires the solution of a system of nonlinear equations. In this paper we use the homotopy continuation method to solve the forward and inverse kinematic problems of an offset 3-UPU translational parallel manipulator. The homotopy continuation method is a novel method which alleviates drawbacks of the traditional numerical techniques, namely; the acquirement of good initial guess values, the problem of convergence and computing time. The direct kinematics problem of the manipulator leads to 16 real solutions. [Copyright &y& Elsevier]

Abstract: This paper is concerned with iterative methods for solving a class of coupled matrix equations including the well-known coupled Markovian jump Lyapunov matrix equations as special cases. The proposed method is developed from an optimization point of view and contains the well-known Jacobi iteration, Gauss–Seidel iteration and some recently reported iterative algorithms by using the hierarchical identification principle, as special cases. We have provided analytically the necessary and sufficient condition for the convergence of the proposed iterative algorithm. Simultaneously, the optimal step size such that the convergence rate of the algorithm is maximized is also established in explicit form. The proposed approach requires less computation and is numerically reliable as only matrix manipulation is required. Some other existing results require either matrix inversion or special matrix products. Numerical examples show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, travelling wave solutions for a nonlinear variant of the PHI-four equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given. [Copyright &y& Elsevier]

Abstract: In this paper we consider constructing some higher-order modifications of Newton’s method for solving nonlinear equations which increase the order of convergence of existing iterative methods by one or two or three units. This construction can be applied to any iteration formula, and per iteration the resulting methods add only one additional function evaluation to increase the order. Some illustrative examples are provided and several numerical results are given to show the performance of the presented methods. [Copyright &y& Elsevier]

Abstract: In this paper, we study the long-time behavior of plate equation with nonlinear damping and critical nonlinearity. We prove the existence of a global attractor in the space . [Copyright &y& Elsevier]

Abstract: This paper presents a novel formulation and analytical solutions for adhesively bonded composite single lap joints by taking into account the transverse shear deformation and large deflection in adherends. On the basis of geometrically nonlinear analysis for infinitesimal elements of adherends and adhesive, the equilibrium equations of adherends are formulated. By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends. The obtained solutions are applied to single lap joints, whose adherends can be isotropic adherends or composite laminates with symmetrical lay-ups. A new formula for adhesive peel stress is obtained, and it can accurately predict peel stress in the bondline. The closed-form analytical solutions are then simplified for the purpose of practical applications, and a new simple expression for the edge moment factor is developed. The numerical results predicted by the present full and simplified solutions are compared with those calculated by geometrically nonlinear finite element analysis using MSC/NASTRAN. The agreement noted validates the present novel formulation and solutions for adhesively bonded composite joints. The simplified shear and peel stresses at the overlap ends are used to derive energy release rates. The present predictions for the failure load of single lap joints are compared with those available in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we study the positive and the negative modified Kadomtsev–Petviashvili (mKP) equations. The mKP equations are completely integrable equations that admit N-soliton solutions and an infinite number of conserved densities. Multiple-soliton solutions are obtained for the positive model, whereas multiple–singular soliton solutions are established for the negative model. The analysis depends mainly on the Hirota’s bilinear method. [Copyright &y& Elsevier]

Abstract: In this paper, a sixth order method is developed by extending a third order method of Weerakoon and Fernando [S. Weerakoon, T.G.I. Fernando, A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett. 13 (2000) 87–93] for finding the real roots of nonlinear equations in . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. In terms of computational cost, it requires evaluations of only two functions and two first derivatives per iteration. This implies that efficiency index of our method is 1.565. Our method is comparable with the methods of Neta [B. Neta, A sixth order family of methods for nonlinear equations, Intern. J. Computer Math. 7 (1979) 157–161] and that of Kou and Li [Jisheng Kou, Yitian Li, An improvement of Jarratt method, Appl. Math. Comput. 189 (2007) 1816–1821]. It does not require the evaluation of the second order derivative of the given function as required in the family of Chebyshev–Halley type methods [Jisheng Kou, Xiuhua Wang, Sixth-order variants of Chebyshev–Halley methods for solving non-linear equations, Appl. Math. Comput. 190 (2007) 1839–1843; Jisheng Kou, On Chebyshev–Halley methods with sixth-order convergence for solving non-linear equations, Appl. Math. Comput. 190 (2007) 126–131]. The efficacy of the method is tested on a number of numerical examples. It is observed that our method takes less number of iterations than Newton’s method and the method of Weerakoon and Fernando. On comparison with the other sixth order methods, it behaves either similarly or better for the examples considered. [Copyright &y& Elsevier]