the g good neighbor conditional diagnosability of star graphs under the pmc and mm model diagnosability plays an important role in measuring the fault tolerance and reliability of interconnection networks the g good neighbor conditional faulty set is a special faulty set that every fault free vertex should have at least g fault free neighbors the g good neighbor conditional diagnosability is a metric that can give the maximum cardinality of g good neighbor conditional faulty set that the system is guaranteed to identify this paper shows that the g good neighbor conditional diagnosabilities of star graph sn under the pmc and mm model are ng g 1 1 for n4 and 0gn2 our study shows the g good neighbor conditional diagnosability of star graph is several times larger than the classical diagnosability of star graph

an 0 n 2 5 fault identification algorithm for diagnosable systems consider a system composed of n independent processors each of which tests a subset of the others it is assumed that at most tp of these processors are permanently faulty and that the outcome of a test is reliable if and only if the processor which performed the test is fault free such a system is said to be tp diagnosable if given any complete collection of test results the set of faulty processors can be uniquely identified in this paper it is shown that tp diagnosable systems due to their robust interconnection structure possess heretofore unknown graph theoretic properties relative to vertex cover sets and maximum matchings an 0 n2 5 algorithm is given which exploits these properties to identify the set of faulty processors in a tp diagnosable system the algorithm is shown to be correct complete not based on any conjecture and superior to any other known fault identification algorithm for the general class of tp diagnosable systems

diagnosability for two families of composition networks abstract diagnosability is an important parameter to assess the reliability of multiprocessor systems a multiprocessor system is called t diagnosable if all faulty processors can be identified without replacement as long as the number of faulty processors does not exceed t the diagnosability is the maximum value of t such that multiprocessors system is t diagnosable matching composition networks mcns and cycle composition networks ccns are two typical network structures to construct multiprocessor systems let g be a mcn which is obtained by adding a perfect matching between two graph g 0 and g 1 and let h be a ccn obtained by adding a perfect matching between g i and g i 1 mod m for each i 0 1 m 1 with m 3 in this paper we show that the diagnosability of g under the pmc g 2 model and mm model g 5 is n 1 if g 0 g 1 k n otherwise g furthermore we show that the diagnosability of h under the pmc model h 4 and mm model h 5 is h

finite dimensional behaviour for the derivative ginzburg landau equation in two spatial dimensions abstract in this paper we study the long time behaviour of the solutions for the generalized derivative ginzburg landau equation in two spatial dimensions we show the existence of the global attractor for this equation and establish the estimates of the upper bounds of hausdorff and fractal dimensions for the global attractor

conditional diagnosability of alternating group graphs let an be the alternating group of degree n with n 3 set s 1 2 i 1 i 2 3 i n the alternating group graph denoted by agn is defined as the cayley graph on an with respect to s jwo et al networks 23 1993 315 326 introduced alternating group graph agn as an interconnection network topology for computing systems conditional diagnosability a new measure of diagnosability introduced by lai et al ieee transactions on computers 54 2 2005 165 175 can better measure the diagnosability of regular interconnection networks this paper determines that under pmc model the conditional diagnosability of agn is 4 for n 4 and 6n 18 for each n 5

convergence of the pseudospectral method for the ginzburg landau equation abstract the convergence of the pseudospectral fourier method for the ginzburg landau equation in nonlinear wave theory is proved the rate of convergence depends on the smoothness of the initial data

the g good neighbor conditional diagnosability of twisted hypercubes under the pmc and mm model abstract connectivity and diagnosability are important parameters in measuring the fault tolerance and reliability of interconnection networks the g good neighbor conditional faulty set is a special faulty set that every fault free vertex should have at least g fault free neighbors the rg vertex connectivity of a connected graph g is the minimum cardinality of a g good neighbor conditional faulty set x v g such that g x is disconnected the g good neighbor conditional diagnosability is a metric that can give the maximum cardinality of g good neighbor conditional faulty set that the system is guaranteed to identify the twisted hypercube is a new variant of hypercubes with asymptotically optimal diameter introduced by x d zhu in this paper we first determine the rg vertex connectivity of twisted hypercubes then establish the g good neighbor conditional diagnosability of twisted hypercubes under the pmc model and mm model respectively

comparison of several methods for calculating vibration mode shape derivatives four methods for the calculation of derivatives of vibration mode shapes eigenvectors with respect to design parameters are described these are finite difference method modal method a modified modal method and nelson s method the methods are implemented in a general purpose commercial finite element program and applied to the following test problems a cantilever beam and a stiffened cylinder with a cutout design variables are a beam tip mass a beam root height and specific dimensions of the cylinder model the methods are compared on the basis of central processor cp seconds required to obtain the derivatives and two of the methods are also evaluated for the rapidity of convergence data is presented showing the amount of cp time used to compute the first four eigenvector derivatives for each example problem a scalar measure of the error in the mode shape derivative is defined and numerical results illustrating the rapidity of convergence of the approximate derivative to the exact derivative are presented results indicate an advantage in using nelson s method because this method is exact and requires less cp time especially when derivatives with respect to several design variables are computed

on conditional diagnosability of the folded hypercubes the n dimensional folded hypercube fq n a variation of the hypercube proposed by ahmed et al a el amawy s latifi properties and performance of folded hypercubes ieee transactions on parallel and distributed systems 2 3 1991 31 42 is an n 1 regular n 1 connected graph conditional diagnosability a new measure of diagnosability introduced by lai et al pao lien lai jimmy j m tan chien ping chuang lih hsing hsu conditional diagnosability measures for large multiprocessor systems ieee transactions on computers 54 2 2005 165 175 can better measure the diagnosability of regular interconnection networks this paper determines that under pmc model the conditional diagnosability of fq n t c fq n is 4n 3 when n 5 or n 8 t c fq 3 3 t c fq 4 7

passive vibration suppression of flexible space structures via optimal geometric redesign acomputationalframework is presented for the design of large flexible space structures with nonperiodicgeometries to achieve passive vibration suppression the present system combines an approximationmodel management framework ammf developed for evolutionary optimization algorithms eas with reduced basis approximate dynamic reanalysis techniques a coevolutionary genetic search strategy is employed to ensure that design changes during the optimization iterations lead to low rank perturbations of the structural system matrices for which thereduced basis methods give high quality approximations the k means algorithm is employed for cluster analysis of the population of designs to determine design points at which exact analysis should be carried out the fitness of the designs in an ea generation is then approximated using reduced basis models constructed around the points where exact analysis is carried out results are presented for the optimal design of a two dimensional cantilevered space structure to achieve passive vibration suppression it is shown that significant vibration isolation of the order of 50 db over a 100 hz bandwidth can be achieved further it is demonstrated that the ammf can potentially arrive at a better design compared to conventional approaches when a constraint is imposed on the computational budget available for optimization

structure connectivity and substructure connectivity of twisted hypercubes abstract let g be a graph and t a certain connected subgraph of g the t structure connectivity g t or resp t substructure connectivity s g t of g is the minimum number of a set of subgraphs f t 1 t 2 t m or resp f t 1 t 2 t m such that t i is isomorphic to t or resp t i is a connected subgraph of t for every 1 i m and f s removal will disconnect g the twisted hypercube h n is a new variant of hypercubes with asymptotically optimal diameter introduced by zhu in this paper we will determine both h n t and s h n t for t k 1 r p k respectively where 3 r 4 and 1 k n

higher order eigenpair perturbations a matrix method is presented for the exact calculation of large eigenpair perturbations arising from design variable changes this method of forward analysis is presented that takes into account all order of the perturbation expansion

the 2 good neighbor diagnosability of cayley graphs generated by transposition trees under the pmc model and mm model diagnosability is an important metric for measuring the reliability of multiprocessor systems in 2012 peng et al proposed a new measure for fault diagnosis of the system which is called g good neighbor diagnosability that restrains every fault free node containing at least g fault free neighbors as a favorable topology structure of interconnection networks the cayley graph c n generated by the transposition tree n has many good properties in this paper we give that the 2 good neighbor diagnosability of c n under the pmc model and mm model is g n 2 1 where n 4 and g is the girth of c n

relationship between conditional diagnosability and 2 extra connectivity of symmetric graphs the conditional diagnosability and the 2 extra connectivity are two important parameters to measure ability of diagnosing faulty processors and fault tolerance in a multiprocessor system the conditional diagnosability t c g of g is the maximum number t for which g is conditionally t diagnosable under the comparison model while the 2 extra connectivity 2 g of a graph g is the minimum number k for which there is a vertex cut f with f k such that every component of g f has at least 3 vertices a quite natural problem is what is the relationship between the maximum and the minimum problem this paper partially answers this problem by proving t c g 2 g for a regular graph g with some acceptable conditions as applications the conditional diagnosability and the 2 extra connectivity are determined for some well known classes of vertex transitive graphs including star graphs n k star graphs alternating group networks n k arrangement graphs alternating group graphs cayley graphs obtained from transposition generating trees bubble sort graphs k ary n cube networks dual cubes pancake graphs and hierarchical hypercubes as well furthermore many known results about these networks are obtained directly we reveal the relationship between conditional diagnosability and 2 extra connectivity of graphs the conditional diagnosability under the comparison model is equal to the 2 extra connectivity as applications these parameters are determined for some well known classes of graphs

global spatially periodic solutions to the ginzburg landau equation on etudie l existence globale et la non existence de solutions spatialement periodiques pour le probleme aux valeurs initiales de l equation de ginzburg landau

the g good neighbor conditional diagnosability of hypercube under pmc model abstract processor fault diagnosis plays an important role in multiprocessor systems for reliable computing and the diagnosability of many well known networks has been explored for example hypercubes crossed cubes mobius cubes and twisted cubes of dimension n all have diagnosability n the conditional diagnosability of n dimensional hypercube q n is proved to be 4 n 2 1 under the pmc model in this paper we study the g good neighbor conditional diagnosability of q n under the pmc model and show that it is 2 g n g 2 g 1 for 0 g n 3 the g good neighbor conditional diagnosability of q n is several times larger than the classical diagnosability

on the conditional diagnosability of matching composition networks the conditional diagnosability of interconnection networks has been studied by using a number of ad hoc methods recently gathering various ad hoc methods developed in the last decade a unified approach was developed and this approach was used to find the conditional diagnosability of many interconnection networks in this paper we study the conditional diagnosability of matching composition networks including those that are not triangle free

hybrid perturbation polynomial chaos approaches to the random algebraic eigenvalue problem the analysis of structures is affected by uncertainty in the structure s material properties geometric parameters boundary conditions and applied loads these uncertainties can be modelled by random variables and random fields amongst the various problems affected by uncertainty the random eigenvalue problem is specially important when analyzing the dynamic behavior or the buckling of a structure the methods that stand out in dealing with the random eigenvalue problem are the perturbation method and methods based on monte carlo simulation in the past few years methods based on polynomial chaos pc have been developed for this problem where each eigenvalue and eigenvector are represented by a pc expansion in this paper four variants of a method hybridizing perturbation and pc expansion approaches are proposed and compared the methods use rayleigh quotient the power method the inverse power method and the eigenvalue equation pc expansions of eigenvalues and eigenvectors are obtained with the proposed methods the new methods are applied to the problem of an euler bernoulli beam and a thin plate with stochastic properties

conditional diagnosability and strong diagnosability of split star networks under the pmc model an interconnection network s diagnosability is an important measure of its self diagnostic capability the classical problems of fault diagnosis are explored widely the conditional diagnosability is proposed by lai et al as a new measure of diagnosability which can better measure the diagnosability of regular interconnection networks the conditional diagnosability is an important indicator of the robustness of a multiprocessor system in presence of failed processors furthermore a multiprocessor system is strongly t diagnos able if it is t diagnosable and can achieve diagnosability t 1 except for the case where a node s neighbors are all faulty the conditional diagnosability and strong diagnosability were proposed later to better reflect the networks self diagnostic capability under more realistic assumptions in this paper we determine the conditional diagnosability of an n dimensional split star network denoted as s n 2 a well known interconnection network model for multiprocessor systems under the pmc preparata metze and chien model we show that the conditional diagnosability of s n 2 n 4 is 8 n 23 which is about four times of its traditional diagnosability as a byproduct the strong diagnosability of s n 2 is also obtained we investigate the combinatorial properties and fault tolerant properties of the split star network we show that as long as a fault set f has 6 n 17 or fewer nodes s n 2 f excluding a subset of at most two nodes contains one large connected component we show that as long as a fault set f has 8 n 25 or fewer nodes s n 2 f excluding a subset of at most three nodes contains one large connected component we show that the classic diagnosability of s n 2 n 2 under the pmc model is 2 n 3 we also establish that the conditional diagnosability and the strong diagnosability of s n 2 are 8 n 23 and 2 n 3 under the pmc model

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

conditional diagnosability of matching composition networks under the mm model diagnosability is a critical metric for determining the reliability of a multiprocessor system in 2005 lai et al proposed a new measure for the fault diagnosis of a system i e conditional diagnosability in which it is assumed that at least one of the neighbors of an arbitrary node in the system is not faulty in this paper we obtain a sufficient condition for a class of networks called matching composition networks mcns which are conditionally t diagnosable under the mm model then we apply the sufficient condition to show the conditional diagnosability of bijective connection bc networks finally we show that the sufficient condition can be applied to networks other than bc networks

periodic solutions of the ginzburg landau equation abstract spatially periodic solutions to the ginzburg landau equation are considered in particular we obtain criteria for primary and secondary bifurcation limit cycle solutions nonlinear dispersion relations relating spatial and temporal frequencies only relatively simple tools appear in the treatment and as a result a wide range of parameter cases are considered finally we briefly treat the case of spatial bifurcations

improvement of normalization methods for eigenvector derivatives the subject algorithms are all forward analysis i e the eigenvector changes are being driven by design parameter perturbations the new method emphasizes proper mass normalization and is most needed when iteratively computing eigenvector perturbations within a reduced dimension space

improved first order approximation of eigenvalues and eigenvectors a method based on reduced basis approximation concepts is presented for improved first order approximation of eigenvalues and eigenvectors of modified structural dynamic systems the terms of a local approximation based on taylor or matrix power series are used as basis vectors for approximating the perturbed eigenparameters for each eigenmode a reduced eigensystem is generated by using the baseline eigenvector and the first order approximation term as ritz vectors the solution of the reduced eigensystem leads to two possible estimates of each perturbed eigenvalue and eigenvector criteria for selection of the best approximation are presented the zero and first order rayleigh quotient approximation can be directly recovered as special cases of the present method results are presented for approximate dynamic reanalysis of a 25 bar planar truss structure it is shown that high quality approximation of the perturbed eigenparameters can be obtained for moderate perturbations in the stiffness and mass matrices for very large local perturbations of the structure including deletion of some structural members it is shown that the present method yields reasonable quality approximations

g good neighbor conditional diagnosability measures for 3 ary n cube networks the diagnosability of a parallel system is defined as the maximum number of faulty processors or nodes that the system can guarantee to identify in this study we investigate the g good neighbor conditional diagnosability which indicates that every fault free node in a system contains at least g fault free neighbors compared with the conventional diagnosability g good neighbor conditional diagnosability improves accuracy in measuring the reliability of interconnection networks in heterogeneous environments we apply the pmc and mm models to study the g good neighbor conditional diagnosability of 3 ary n cube networks which represent a family of popular parallel systems such as ibm s blue gene and cray t3d the findings made in this study facilitate accurate reliability measurements in modern parallel systems powered by 3 ary n cube networks specifically our results show that the g good neighbor conditional diagnosability of 3 ary n cube is g 2 2 n g 1 1 and g 1 2 4 n 2 g 1 1 when the g value is even and odd respectively the r g connectivity of 3 ary n cube networks was determined for n 3 and 0 g n 1 applying the pmc model and the mm model we investigated and measured the g good neighbor conditional diagnosability of 3 ary n cube networks for n 4 and 0 g n 1