odd cycles embedding on folded hypercubes with conditional faulty edges let ff e be the set of ff e 4 and n is even under this assumption we show that every fault free edge of fq n lies on a fault free cycle of every odd length from n 1 to 2 n 1 in terms of the number of tolerant faulty edges and embedding odd cycles in fq n our result improves not only the result in xu and ma 2006 where ff e 0 but also the previous best result gotten by xu et al 2006 where ff e

fault tolerant edge bipancyclicity of faulty hypercubes under the conditional fault model it is well known that the n dimensional hypercube qn is one of the most versatile and efficient interconnection network architecture yet discovered for building massively parallel or distributed systems let f be the faulty set of qn and let fv fe be the numbers of faulty vertices and faulty edges in f respectively an edge e x y is said to be free if e x y are not in f and a cycle is said to be fault free if there is no faulty vertex or faulty edge on the cycle in this paper we prove that each free edge x y in qn for n 3 lies on a fault free cycle of any even length from 6 to 2 n 2 f v if f v f e 2 n 5 f e n 2 and both x and y are incident to at least two free edges this result confirms a conjecture reported in the literature

navier stokes equations for almost incompressible flow the isentropic navier stokes equations at low mach numbers describe almost incompressible flow by a variable transformation the equations take a symmetric form suitable for computation estimates of the solution and its derivatives are obtained for the linearized equations on domains with open boundaries this is a necessary basis for the application of any numerical method whenever some part of the computational boundary is not a solid wall a semi implicit difference approximation is applied to the nonlinear equations for computation of flow over a backward facing step

application of time iterative schemes to incompressible flow the computation of steady incompressible flows by an euler implicit algorithm is studied using both the incompressible equations and the low mach number compressible equations the incompressible equations are handled by adding an artificial time derivative to the continuity equation this allows both the pressure and velocity to be obtained implicitly in one dimensional problems both systems converge rapidly even at low mach numbers where the eigenvalues are very stiff in two dimensions where approximate factorization is required the presence of stiff eigenvalues is highly detrimental stiffness can be avoided in the incompressible equations by selecting an appropriate pseudo mach number this insures reliable convergence and results in an efficient incompressible flow algorithm in the case of compressible equations the mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed a matrix preconditioning factor that accomplishes this is developed and demonstrated with this modification the convergence rate is the same as in the incompressible case and is independent of mach number rapid convergence is observed at mach numbers as low as 6 05

third order iterative methods with applications to hammerstein equations a unified approach the geometrical interpretation of a family of higher order iterative methods for solving nonlinear scalar equations was presented in s amat s busquier j m gutierrez geometric constructions of iterative functions to solve nonlinear equations j comput appl math 157 1 2003 197 205 this family includes as particular cases some of the most famous third order iterative methods chebyshev methods halley methods super halley methods c methods and newton type two step methods the aim of the present paper is to analyze the convergence of this family for equations defined between two banach spaces by using a technique developed in j a ezquerro m a hernandez halley s method for operators with unbounded second derivative appl numer math 57 3 2007 354 360 this technique allows us to obtain a general semilocal convergence result for these methods where the usual conditions on the second derivative are relaxed on the other hand the main practical difficulty related to the classical third order iterative methods is the evaluation of bilinear operators typically second order frechet derivatives however in some cases the second derivative is easy to evaluate a clear example is provided by the approximation of hammerstein equations where it is diagonal by blocks we finish the paper by applying our methods to some nonlinear integral equations of this type

link wise artificial compressibility method the artificial compressibility method acm for the incompressible navier stokes equations is link wise reformulated referred to as lw acm by a finite set of discrete directions links on a regular cartesian mesh in analogy with the lattice boltzmann method lbm the main advantage is the possibility of exploiting well established technologies originally developed for lbm and classical computational fluid dynamics with special emphasis on finite differences at least in the present paper at the cost of minor changes for instance wall boundaries not aligned with the background cartesian mesh can be taken into account by tracing the intersections of each link with the wall analogously to lbm technology lw acm requires no high order moments beyond hydrodynamics often referred to as ghost moments and no kinetic expansion like finite difference schemes only standard taylor expansion is needed for analyzing consistency preliminary efforts towards optimal implementations have shown that lw acm is capable of similar computational speed as optimized bgk lbm in addition the memory demand is significantly smaller than bgk lbm importantly with an efficient implementation this algorithm may be among the few which are compute bound and not memory bound two and three dimensional benchmarks are investigated and an extensive comparative study between the present approach and state of the art methods from the literature is carried out numerical evidences suggest that lw acm represents an excellent alternative in terms of simplicity stability and accuracy

majorizing sequences for newton s method from initial value problems the most restrictive condition used by kantorovich for proving the semilocal convergence of newton s method in banach spaces is relaxed in this paper providing we can guarantee the semilocal convergence in situations that kantorovich cannot to achieve this we use kantorovich s technique based on majorizing sequences but our majorizing sequences are obtained differently by solving initial value problems

embedding long cycles in faulty k ary 2 cubes abstract the class of k ary n cubes represents the most commonly used interconnection topology for distributed memory parallel systems given an even k 4 let v 1 v 2 be the bipartition of the k ary 2 cube f v 1 f v 2 be the numbers of faulty vertices in v 1 and v 2 respectively and f e be the number of faulty edges in this paper we prove that there exists a cycle of length k 2 2max f v 1 f v 2 in the k ary 2 cube with 0 f v 1 f v 2 f e 2 this result is optimal with respect to the number of faults tolerated

comparison of the lattice boltzmann method and the artificial compressibility method for navier stokes equations this paper compares in detail the lattice boltzmann method and an isothermal navier stokes method it is found that these two methods are closely related to each other both methods satisfy similar macroscopic governing equations in their continuous forms but they differ from each other in their discrete forms besides the obvious differences in stencils for spatial discretization these two methods also differ from each other in temporal discretization numerical tests show that these differences have little impact on the simulation of velocity fields but do generate noticeable differences in the pressure fields both methods are capable of simulating transient flows and exhibit oscillatory behavior due to the propagation of pressure waves the lattice boltzmann method may be more accurate for capturing the pressure waves

a family of halley chebyshev iterative schemes for non frechet differentiable operators a modification of some classical third order methods is studied the main advantage of these methods is that they do not need evaluate any frechet derivative a convergence theorem in banach spaces just assuming that the second divided difference is bounded by a nondecreasing function and a punctual condition is presented frechet differentiability is not required finally a particular example is analyzed where our conditions are fulfilled and the classical ones fail

a new semilocal convergence theorem for newton s method abstract a new semilocal convergence theorem for newton s method is established for solving a nonlinear equation f x 0 defined in banach spaces it is assumed that the operator f is twice frechet differentiable and f satisfies a lipschitz type condition results on uniqueness of solution and error estimates are also given finally these results are compared with those that use kantorovich conditions

the 2 path bipanconnectivity of hypercubes in this paper we introduce the concept of the k path bi panconnectivity of bipartite graphs it is a generalization of the bi panconnectivity and of the paired many to many k disjoint path cover the 2 path bipanconnectivity with only one exception of the n cube q n n 4 is proved precisely the following result is obtained in an n cube with n 4 given any four vertices u 1 v 1 u 2 v 2 such that two of them are in one partite set and the another two are in the another partite set let s t 5 if c u 1u 2v 1v 2 is a cycle of length 4 and s d u 1 v 1 1 and t d u 2 v 2 1 otherwise where d u v denotes the distance between two vertices u and v and let i and j be any two integers such that both i s 0 and j t 0 are even with i j 2 n then there exist two vertex disjoint u 1 v 1 path p and u 2 v 2 path r with v p i and v r j as consequences many properties of hypercubes such as bipanconnectivity bipanpositionable bipanconnectivity 18 bipancycle connectivity 12 two internally disjoint paths with two given lengths and the 2 disjoint path cover with a path of a given length 21 follow from our result

conservative high order finite difference schemes for low mach number flows three finite difference algorithms are proposed to solve a low mach number approximation for the navier stokes equations these algorithms exhibit fourth order spatial and second order temporal accuracy they are dissipation free and thus well suited for dns and les of turbulent flows the key ingredient common to each of the methods presented is a poisson equation with variable coefficient that is solved for the hydrodynamic pressure this feature ensures that the velocity field is constrained correctly it is shown that this approach is needed to avoid violation of the conservation of kinetic energy in the inviscid limit which would otherwise arise through the pressure term in the momentum equation an existing set of finite difference formulae for incompressible flow is generalized to handle arbitrary large density fluctuations with no violation of conservation through the non linear convective terms an algorithm which conserves mass momentum and kinetic energy fully is obtained when an approximate equation of state is used instead of the exact one results from a model problem are used to show both spatial and temporal convergence rates and several test cases are presented to illustrate the performance of the algorithms

long paths and cycles in hypercubes with faulty vertices a fault free path in the n dimensional hypercube q n with f faulty vertices is said to be long if it has length at least 2 n 2f 2 similarly a fault free cycle in q n is long if it has length at least 2 n 2f if all faulty vertices are from the same bipartite class of q n such length is the best possible we show that for every set of at most 2n 4 faulty vertices in q n and every two fault free vertices u and v satisfying a simple necessary condition on neighbors of u and v there exists a long fault free path between u and v this number of faulty vertices is tight and improves the previously known results furthermore we show for every set of at most n 2 10 n 2 1 faulty vertices in q n where n 15 that q n has a long fault free cycle this is a first quadratic bound which is known to be asymptotically optimal

analysis of artificial pressure equations in numerical simulations of a turbulent channel flow abstract recently several methods have been proposed to simulate incompressible fluid flows using an artificial pressure evolution equation avoiding the resolution of a poisson equation these methods can be seen as various levels of approximation of the compressible navier stokes equation in the low mach number limit we study the simulation of incompressible wall bounded flows using several artificial pressure equations in order to determine the most relevant approximations the simulations are stable using a finite difference method in a staggered grid system even without diffusive term and converge to the incompressible solution both in direct numerical simulations and for coarser meshes to be used in large eddy simulations a pressure equation with a convective and a diffusive term produces a more accurate solution than a compressible solver or methods involving more approximations this suggests that it is near to an optimal level of approximation the presence of a convective term in the pressure evolution equation is in particular crucial for the accuracy of the method the rate of convergence of the solution in terms of artificial mach number is studied numerically and validates the theoretical quadratic convergence rate we demonstrate that this property can be used to accelerate the rate of convergence using an extrapolation in terms of artificial mach number since the approach is based on an explicit and local system of equations the numerical procedure is massively parallelisable and has low memory requirements

conditional fault tolerant edge bipancyclicity of hypercubes with faulty vertices and edges let f be a faulty set in an n dimensional hypercube q n such that in q n f each vertex is incident to at least two edges and let f v f e be the numbers of faulty vertices and faulty edges in f respectively in this paper we consider the fault tolerant edge bipancyclicity of hypercubes it is shown that each edge in q n f for n 3 lies on a fault free cycle of any even length from 6 to 2 n 2 f v if f v f e 2 n 5 this gives an answer for a problem proposed by yang et al 2016 33 consider hypercubes with mixed faulty edges and faulty vertices under conditional fault model improve the previous results about the fault tolerant edge bipancyclicity of hypercubes give an affirmative answer for a problem proposed by yang et al 2016

artificial compressibility method revisited asymptotic numerical method for incompressible navier stokes equations the artificial compressibility method for the incompressible navier stokes equations is revived as a high order accurate numerical method fourth order in space and second order in time similar to the lattice boltzmann method the mesh spacing is linked to the mach number an accuracy higher than that of the lattice boltzmann method is achieved by exploiting the asymptotic behavior of the solution of the artificial compressibility equations for small mach numbers and the simple lattice structure an easy method for accelerating the decay of acoustic waves which deteriorate the quality of the numerical solution and a simple cure for the checkerboard instability are proposed the high performance of the scheme is demonstrated not only for the periodic boundary condition but also for the dirichlet type boundary condition

low mach number limit of the full navier stokes equations the low mach number limit for classical solutions of the full navier stokes equations is here studied the combined effects of large temperature variations and thermal conduction are taken into account in particular we consider general initial data the equations lead to a singular problem depending on a small scaling parameter whose linearized system is not uniformly well posed yet it is proved that solutions exist and they are uniformly bounded for a time interval which is independent of the mach number ma 0 1 the reynolds number re 1 and the peclet number pe 1 based on uniform estimates in sobolev spaces and using a theorem of g metivier s schochet 30 we next prove that the penalized terms converge strongly to zero this allows us to rigorously justify at least in the whole space case the well known computations given in the introduction of p l lions book 26

fully conservative higher order finite difference schemes for incompressible flow conservation properties of the mass momentum and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out in particular it is found that none of the existing higher order schemes for a staggered mesh system simultaneously conserve mass momentum and kinetic energy this deficiency is corrected through the derivation of a general family of fully conservative higher order accurate finite difference schemes for staggered grid systems finite difference schemes in a collocated grid system are also analyzed and a violation of kinetic energy conservation is revealed the predicted conservation properties are demonstrated numerically in simulations of inviscid white noise performed in a two dimensional periodic domain the proposed fourth order schemes in a staggered grid system are generalized for the case of a non uniform mesh and the resulting scheme is used to perform large eddy simulations of turbulent channel flow

on the bipanpositionable bipanconnectedness of hypercubes a bipartite graph g is bipanconnected if for any two distinct vertices x and y of g it contains an x y path of length l for each integer l satisfying dg x y v g 1 and 2 l dg x y where dg x y denotes the distance between vertices x and y in g and v g denotes the vertex set of g we say a bipartite graph g is bipanpositionably bipanconnected if for any two distinct vertices x and y of g and for any vertex z v g x y it contains a path pl k of length l such that x is the beginning vertex of pl k z is the k 1 th vertex of pl k and y is the ending vertex of pl k for each integer l satisfying dg x z dg y z v g 1 and 2 l dg x z dg y z and for each integer k satisfying dg x z k l dg y z and 2 k dg x z in this paper we prove that an n cube is bipanpositionably bipanconnected if n 4 as a consequence many properties of hypercubes such as bipancyclicity bipanconnectedness bipanpositionable hamiltonicity etc follow directly from our result

edge fault tolerant bipanconnectivity of hypercubes this paper shows that for any two distinct vertices u and v with distance d in the hypercube q n n 3 with at most 2n 5 faulty edges and each vertex incident with least two fault free edges there exist fault free uv paths of length in q n for every with d 4 2 n 1 and d 0 mod2 this result improves some known results on edge fault bipanconnectivity of hypercubes the proof is based on the recursive structure of q n

a three dimensional incompressible navier stokes flow solver using primitive variables an implicit finite difference computer code has been developed to solve the incompressible navier stokes equations in a three dimensional curvilinear coordinate system the pressure field solution is based on the pseudocompressibility approach in which a time derivative pressure term is introduced into the mass conservation equation the solution procedure employs an implicit approximate factorization scheme the reynolds stresses which are uncoupled from the implicit scheme are lagged by one time step to facilitate implementing various levels of the turbulence model test problems for external and internal flows are computer and the results are compared with existing experimental data the application of this technique for general three dimensional problems is then demonstrated

on the newton kantorovich hypothesis for solving equations the famous newton kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of newton s method to a solution of an equation in connection with the lipschitz continuity of the frechet derivative of the operator involved here using lipschitz and center lipschitz conditions we show that the newton kantorovich hypothesis can be weakened the error bounds obtained under our semilocal convergence result are more precise than the corresponding ones given by the dominating newton kantorovich theorem

a numerical method for incompressible and compressible flow problems with smooth solutions abstract a semi implicit difference method of second order in space is introduced for the numerical solution of the euler equations if the mach number e is small the solutions are second order accurate also in time in particular the solutions converge to an approximate solution of the incompressible equations as e tends to zero numerical experiments are presented for channel flow and the theoretical results given for the linearized equations are shown to be valid also for the real nonlinear problem

edge pancyclicity and edge bipancyclicity of faulty folded hypercubes let f v and f e be sets of faulty vertices and faulty edges respectively in the folded hypercube fq n so that f v f e n 2 for n 2 choose any fault free edge e if n 3 then there is a fault free cycle of length l in fq n containing e for every even l ranging from 4 to 2 n 2 f v if n 2 is even then there is a fault free cycle of length l in fq n containing e for every odd l ranging from n 1 to 2 n 2 f v 1

a newton kantorvich theorem for equations involving m frechet differentiable operators and applications in radiative transfer abstract in this study we approximate a locally unique solution of a nonlinear operator equation in banach space using newton s method a complete error analysis showing the quadratic convergence of our method is also given our new theorem uses lipschitz or holder continuity assumptions on m frechet differentiable operators where m 2 is a positive integer a numerical example is given to show that our results provide a better information on the location of the solution as well as finer error bounds on the distances involved than earlier results a second numerical example shows how to solve a nonlinear integral equation appearing in radiative transfer

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

kinetically reduced local navier stokes equations for simulation of incompressible viscous flows recently another approach to study incompressible fluid flow was suggested s ansumali i karlin and h ottinger phys rev lett 94 080602 2005 the kinetically reduced local navier stokes krlns equations we consider a simplified two dimensional krlns system and compare it with chorin s artificial compressibility method a comparison of the two methods for steady state computation of the flow in a lid driven cavity at various reynolds numbers shows that the results from both methods are in good agreement with each other however in the transient flow it is demonstrated that the krlns equations correctly describe the time evolution of the velocity and of the pressure unlike the artificial compressibility method

efficient unicast in bijective connection networks with the restricted faulty node set the connectivity is an important criteria to measure the fault tolerant performance of a graph however the connectivity based on the condition of the set of arbitrary faulty nodes is generally lower in this paper in order to heighten this measure we introduce the restricted connectivity into bijective connection networks first we prove that the probability that all the neighbors of an arbitrary node becomes faulty in any n dimensional bijective connection network x n is very low when n becomes sufficient large then we give a constructive proof that under the condition that each node of an n dimensional bijective connection network x n has at least one fault free neighbor its restricted connectivity is 2n 2 about half of the connectivity of x n finally by our constructive proof we give an o n algorithm to get a reliable path of length at most n 3 log 2 f 1 between any two fault free nodes in an n dimensional bijective connection network in particular since the family of bc networks contains hypercubes crossed cubes mobius cubes etc our algorithm is appropriate for these cubes

many to many disjoint paths in faulty hypercubes this paper considers the problem of many to many disjoint paths in the hypercube q n with f v faulty vertices and f e faulty edges and obtains the following result for any integer k with 1 k n 1 any two sets s and t of k fault free vertices in different parts if f v f e n k 1 then there exist k disjoint fault free s t paths in q n which contains at least 2 n 2 f v vertices this result is optimal in the worst case

path embedding in faulty hypercubes abstract there are some interesting results concerning longest paths or even cycles embedding in faulty hypercubes this paper considers the embeddings of paths of all possible lengths between any two fault free vertices in faulty hypercubes let fv respectively fe denote the number of faulty vertices respectively edges in an n dimensional hypercube qn we prove that there exists a fault free path of length l between any two distinct fault free vertices u and v in qn with f v f e n 2 for each l satisfying d q n u v 2 l 2 n 2 f v 1 and 2 l d q n u v the bounds on path length l and faulty set size f v f e for a successful embedding are tight that is the result does not hold if l d q n u v 2 or l 2 n 2 f v 1 or f v f e n 2 moreover our result improves some known results

extending the applicability of newton s method for k frechet differentiable operators in banach spaces we extend the applicability of newton s method for k frechet differentiable operators in a banach space setting by using a more flexible way of computing upper bounds on the inverses of the operators involved in particular we improve and extend the recent works by ezquerro et al 2012 2013 13 15 moreover we illustrate our study with some numerical examples involving hammerstein integral equations

an efficient fault tolerant routing algorithm in bijective connection networks with restricted faulty edges in this paper we study fault tolerant routing in bijective connection networks with restricted faulty edges first we prove that the probability that all the incident edges of an arbitrary node become faulty in an n dimensional bijective connection network denoted by x n is extremely low when n becomes sufficient large then we give an o n algorithm to find a fault free path of length at most email protected log 2 f 1 between any two different nodes in x n if each node of x n has at least one fault free incident edge and the number of faulty edges is not more than 2n 3 in fact we also for the first time provide an upper bound of the fault diameter of all the bijective connection networks with the restricted faulty edges since the family of bc networks contains hypercubes crossed cubes mobius cubes etc all the results are appropriate for these cubes

asymptotic single and multiple scale expansions in the low mach number limit an asymptotic analysis of the euler equations in the limit of vanishing mach number is presented which can be employed to extend the validity of numerical methods from the compressible to the low mach number regime r klein j comput phys 121 1995 pp 213 237 l hoffmann and a meister in proceedings of the fourth eccomas computational fluid dynamics conference vol 1 c hirsch et al eds athens 1998 pp 567 572 the work is based on the analysis recently proposed by klein whereby the paper is devoted to a rigorous mathematical justification of this asymptotic investigation in order to give reliable statements concerning the assumptions under which the results hold in contrast to klein a single scale as well as multiple scale expansion is used depending on the spatial domain under consideration

kinetically reduced local navier stokes equations an alternative approach to hydrodynamics an alternative approach the kinetically reduced local navier stokes krlns equations for the grand potential and the momentum is proposed for the simulation of low mach number flows the taylor green vortex flow is considered in the krlns framework and compared to the results of the direct numerical simulation of the incompressible navier stokes equations the excellent agreement between the krlns equations and the incompressible nonlocal navier stokes equations for this nontrivial time dependent flow indicates that the former is a viable alternative for computational fluid dynamics at low mach numbers

a unified approach to compressible and incompressible flows abstract we present a finite element formulation for solving the compressible navier stokes equations which accommodates the use of any set of variables if primitive variables p u t or entropy variables are used the incompressible limit is well behaved therefore one formulation can be used to solve both compressible and incompressible flows

cycle embedding in star graphs with edge faults the star graph is one of the famous interconnection networks edge fault tolerance is an important issue for networks and the cycle embedding problem is widely discussed in many researches in this paper we show that the cycles of even lengths from 6 to n can be embedded into the n dimensional star graph when the number of edge fault in the graph does not exceed n 3 since the graph is bipartite and n 1 regular our result is optimal

third order iterative methods under kantorovich conditions we study a class of third order iterative methods for nonlinear equations on banach spaces a characterization of the convergence under kantorovich type conditions and optimal estimates of the error are found though in general these methods are not very extended due to their computational costs we will show some examples in which they are competitive and even cheaper than other simpler methods we center our analysis in both analytic and computational aspects

distributed fault tolerant ring embedding and reconfiguration in hypercubes to embed a ring in a hypercube is to find a hamiltonian cycle through every node of the hypercube it is obvious that no 2 sup n node hamiltonian cycle exists in an n dimensional faulty hypercube which has at least one faulty node however if a hypercube has faulty links only and the number of faulty links is at most n 2 at least one 2 sup n node hamiltonian cycle can be found in this paper we propose a distributed ring embedding algorithm that can find a hamiltonian cycle in a fault free or faulty n dimensional hypercube q and the complexity is o n parallel steps the algorithm is based on the recursion property of the hypercube and the free link dimension concept in some cases even when the number of faulty links is larger than n 2 hamiltonian cycles may still exist we show that the largest possible number of faulty links that can be tolerated is 2 sup n 1 1 the performance and the constraints of the fault tolerant algorithm is also analyzed in detail in this paper furthermore a dynamic reconfiguration algorithm for an embedded ring is proposed and discussed due to the distributed nature of the algorithms they are useful for the simulation of ring based multiprocessors on mimd hypercube multiprocessors

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

unified convergence domains of newton like methods for solving operator equations we present a unified semilocal convergence analysis in order to approximate a locally unique zero of an operator equation in a banach space setting using our new idea of restricted convergence domains we generate smaller lipschitz constants than in earlier studies leading to the following advantages weaker sufficient convergence criteria tighter error estimates on the distances involved and an at least as precise information on the location of the zero hence the applicability of these methods is extended these advantages are obtained under the same cost on the parameters involved numerical examples where the old sufficient convergence criteria cannot apply to solve equations but the new criteria can apply are also provided in this study

extending the applicability of the local and semilocal convergence of newton s method we present a local as well a semilocal convergence analysis for newton s method in a banach space setting using the same lipschitz constants as in earlier studies we extend the applicability of newton s method as follows local case a larger radius is given as well as more precise error estimates on the distances involved semilocal case the convergence domain is extended the error estimates are tighter and the information on the location of the solution is at least as precise as before numerical examples further justify the theoretical results

fault tolerant path embedding in folded hypercubes with both node and edge faults the folded hypercube fq n is a well known variation of the hypercube structure fq n is superior to q n in many measurements such as diameter fault diameter connectivity and so on let email protected fq n resp email protected fq n denote the set of faulty nodes resp faulty edges in fq n in the case that all nodes in fq n are fault free it has been shown that fq n contains a fault free path of length 2 n 1 resp 2 n 2 between any two nodes of odd resp even distance if email protected fq n n 1 where n 1 is odd and fq n contains a fault free path of length 2 n 1 between any two nodes if email protected fq n n 2 where n 2 is even in this paper we extend the above result to obtain two further properties which consider both node and edge faults as follows 1 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 resp 2 n 2 email protected fq n 2 between any two fault free nodes of odd resp even distance if email protected fq n email protected fq n n 1 where n 1 is odd 2 fq n contains a fault free path of length at least 2 n 2 email protected fq n 1 between any two fault free nodes if email protected fq n email protected fq n n 2 where n 2 is even

conditional matching preclusion sets abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex in this paper we look for obstruction sets beyond these sets we introduce the conditional matching preclusion number of a graph it is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings we find this number and classify all optimal sets for several basic classes of graphs

an inverse kinetic theory for the incompressible navier stokes equations abstract an inverse kinetic theory applying specifically to incompressible newtonian fluids which permits us to avoid the n 2 algorithmic complexity of the poisson equation for the fluid pressure is presented the theory is based on the construction of a suitable kinetic equation in phase space which permits us to determine exactly the fluid equations by means of the velocity moments of the kinetic distribution function it is found that the fluid pressure can also be determined as a moment of the distribution function without solving the poisson equation as is usually required in direct solution methods for the incompressible fluid equations finally the dynamical system underlying the incompressible navier stokes equations and advancing in time the fluid fields has been also identified and proven to produce an unique set of fluid equations