three dimensional exact solution for the vibration of functionally graded rectangular plates abstract a three dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations which are then solved by employing the power series method the exact solution is valid for thick and thin plates and for arbitrary variation of material properties in the thickness direction results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistent schemes exact natural frequencies displacements and stresses are used to assess the accuracy of the classical plate theory the first order shear deformation theory and a third order shear deformation theory for functionally graded plates parametric studies are performed for varying ceramic volume fractions volume fraction profiles and length to thickness ratios results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the mori tanaka and the self consistent methods forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized

a state space finite element for laminated composite plates this paper presents a semi analytical finite element solution for the stress analysis of cross ply laminated composite plates the method is based on a mixed variational principle that includes the variations of both displacements and stresses finite element approximation is introduced only for the in plane variations of displacements and stresses while the through thickness distributions of them are obtained by using the method of state equation numerical tests show that the results obtained approach the analytical three dimensional solutions moreover the use of the recursive formulation of the state equation leads to the solution of an algebra equation system whose order does not depend on the number of material layers of the laminate compared with the traditional finite element method the new solution always provides continuous distributions of both displacements and transverse stresses across material interfaces

the t k diagnosability of star graph networks the t k diagnosis is a diagnostic strategy at system level that can significantly enhance the system s self diagnosing capability it can detect up to t faulty processors or nodes units which might include at most k misdiagnosed processors where k is typically a small number somani and peleg 1996 claimed that an n dimensional star graph denoted s n a well studied interconnection model for multiprocessor systems is k 1 n 3k 2 k diagnosable recently chen and liu 2012 found counterexamples for the diagnosability obtained in without further pursuing the cause of the flawed result in this paper we provide a new complete proof that an mbi n dimensional star graph is actually k 1 n 3k 1 k diagnosable where 1 leq k leq 3 and investigate the reason that caused the flawed result in based on our newly obtained fault tolerance properties we will also outline an o n log n diagnostic algorithm n n is the number of nodes in s n to locate all up to k 1 n 3k 1 faulty processors among which at most k 1 leq k leq 3 fault free processors might be wrongly diagnosed as faulty

the pessimistic diagnosabilities of some general regular graphs the pessimistic diagnosis strategy is a classic strategy based on the pmc model a system is t t diagnosable if provided the number of faulty processors is bounded by t all faulty processors can be isolated within a set of size at most t with at most one fault free node mistaken as a faulty one the pessimistic diagnosability of a system g denoted by t p g is the maximal number of faulty processors so that the system g is t t diagnosable in this paper we study the pessimistic diagnosabilities of some general k regular k connected graphs g n the main result t p g n 2 k 2 g under some conditions is obtained where g is the maximum number of common neighbors between any two adjacent vertices in g n as applications of the main result every pessimistic diagnosability of many famous networks including some known results such as the alternating group networks an n the k ary n cubes q n k the star graphs s n the matching composition networks g g 1 g 2 m and the alternating group graphs ag n are obtained we study the pessimistic diagnosabilities of some general regular graphs under the pmc model the exact value of t p g n is obtained as applications the pessimistic diagnosability of an n q n k s n some mcn and ag n etc are obtained

nonlinear vibration of functionally graded circular cylindrical shells based on improved donnell equations abstract in the present work the study of the nonlinear vibration of a functionally graded cylindrical shell subjected to axial and transverse mechanical loads is presented material properties are graded in the thickness direction of the shell according to a simple power law distribution in terms of volume fractions of the material constituents governing equations are derived using improved donnell shell theory ignoring the shallowness of cylindrical shells and kinematic nonlinearity is taken into consideration one term approximate solution is assumed to satisfy simply supported boundary conditions the galerkin method the volmir s assumption and fourth order runge kutta method are used for dynamical analysis of shells to give explicit expressions of natural frequencies nonlinear frequency amplitude relation and nonlinear dynamic responses numerical results show the effects of characteristics of functionally graded materials pre loaded axial compression and dimensional ratios on the dynamical behavior of shells the proposed results are validated by comparing with those in the literature

panpositionable hamiltonicity and panconnectivity of the arrangement graphs abstract the arrangement graph an k is a generalization of the star graph it is more flexible in its size than the star graph there are some results concerning hamiltonicity and pancyclicity of the arrangement graphs in this paper we propose a new concept called panpositionable hamiltonicity a hamiltonian graph g is panpositionable if for any two different vertices x and y of g and for any integer l satisfying d x y l v g d x y there exists a hamiltonian cycle c of g such that the relative distance between x and y on c is l a graph g is panconnected if there exists a path of length l joining any two different vertices x and y with d x y l v g 1 we show that an k is panpositionable hamiltonian and panconnected if k 1 and n k 2

diagnosability of star graphs with missing edges in this paper we study the system diagnosis on an n dimensional star under the comparison model following the concept of local diagnosability 3 the strong local diagnosability property 7 is discussed this property describes the equivalence of the local diagnosability of a node and its degree we prove that an n dimensional star has this property and it keeps this strong property even if there exist n 3 missing edges in it

hyper hamiltonian laceability on edge fault star graph the star graph possess many nice topological properties edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes in this paper we show that the n dimensional star graph is n 3 edge fault tolerant hamiltonian laceable n 3 edge fault tolerant strongly hamiltonian laceable and n 4 edge fault tolerant hyper hamiltonian laceable all these results are optimal in a sense described in this paper

routing properties of supercubes abstract usually each vertex of the s 1 dimensional hypercube is labeled with a unique integer k with 0 k 2 s 1 1 the supercube s n of n nodes with 2 s n 2 s 1 is constructed by merging nodes u and u 2 s with n u 2 s 1 1 in the s 1 dimensional hypercube into a single node labeled as u 2 s and leaving other nodes in the s 1 dimensional hypercube unchanged in this paper we give the exact distance between any two nodes of supercube and present a new shortest path routing algorithm on s n then we show how to construct s n disjoint paths between any two nodes of the supercube where s n is the connectivity of s n finally we compute the wide diameter and the fault diameter of s n we show that both the wide diameter and the fault diameter are equal to s 2 if n 2 s 1 2 i 1 0 i s 1 and s 1 otherwise

diagnosability of cayley graphs generated by transposition trees with missing edges recently strong local diagnosability properties for star graphs were proved even with missing edges we extend these results to cayley graphs generated by transposition trees

approximate elasticity solution for laminated anisotropic finite cylinders this paper deals with the static response of the axisymmetric problem of arbitrarily laminated anisotropic cylindrical shells of finite length using three dimensional elasticity equations the closed cylinder is simply supported at both ends the highly coupled partial differential equations pdes are reduced to ordinary differential equations odes with variable coefficients by choosing the solution composed of trigonometric functions along the axial direction through dividing each layer into thin laminas the variable coefficients in odes become constants and the resulting equations can be solved exactly numerical examples are presented for 45 0 deg and 45 457 45 deg laminations under sinusoidal normal loading on the outer surface and uniform internal pressure from the present study it is found that although the general behavior is similar to that of isotropic shells the coupling is obvious in general and the shear effect is very important in the edge region moreover the initial curvature effect plays an essential role especially in stress distributions tatic and dynamic responses of composite laminated closed cylindrical shells and curved panels have received wide attention in recent years because of the anisotropy in composites and the presence of curvature in shell structures obtaining exact three dimensional elasticity solutions for lami nated closed cylinders and open panels subjected to general loading and arbitrary boundary conditions becomes a chal lenging task the mathematical complexity in analyzing three dimensional elasticity equations usually makes exact solutions difficult to obtain however certain problems in which a three dimensional approach can be used still exist most of these problems can be solved by assuming the solution to be composed of trigonometric functions in the axial and circumferential directions the main reason is that the partial differential equations pdes governing three di mensional problems can be reduced to one dimension al ordi nary differential equations odes with variable coefficients the solution for the resulting odes can be obtained by intro ducing the displacement potential function usually this method is used with isotropic and transversely isotropic mate rials whereas the frobenius method is used with orthotropic materials when the three dimensional elasticity solutions are available they are very useful in evaluating the accuracy of approximate results e g in the case of two dimensional shell theories for the static problem flugge and kelkar1 and yao2 ob tained an exact solution for closed isotropic long cylinders under general two dimensional surface traction using the frobenius method srinivas3 developed an exact three dimen sional solution for orthotropic finite cylinders with simply supported conditions however the numerical results are given for free vibration only varadan and bhaskar4 also performed the static stress analysis using the procedures pro posed by srinivas pagano5 obtained the stress field for a homogeneous anisotropic closed cylinder under two dimen sional surface loads in which the problems are independent of the axial coordinate however numerical results are reported only for a single orthotropic layer recently ren6 7 presented an exact solution for simply supported laminated cross ply circular cylindrical panels of infinite and finite length in the

properties of a hierarchical network based on the star graph this paper introduces a new class of interconnection networks named star pyramid an n level star pyramid is formed by piling up star graphs of dimensions 1 to n in a hierarchy connecting any node in each i dimensional star 1

dynamic stability of cylindrical panels with transverse shear effects abstract the dynamic stability of simply supported isotropic cylindrical panels under combined static and periodic axial forces are investigated an extension of donnells shell theory to a first order shear deformation theory is used and a system of mathieu hill equations are obtained via a normal mode expansion and the parametric resonance response was analyzed using bolotins method results are compared with those obtained using the classical shell theory the effects of the thickness to radius ratio on the instability regions are examined in detail

the globally bi 3 connected property of the honeycomb rectangular torus the honeycomb rectangular torus is an attractive alternative to existing networks such as mesh connected networks in parallel and distributed applications because of its low network cost and well structured connectivity assume that m and n are positive even integers with n 4 it is known that every honeycomb rectangular torus hret m n is a 3 regular bipartite graph we prove that in any hret m n there exist three internally disjoint spanning paths joining x and y whenever x and y belong to different partite sets moreover for any pair of vertices x and y in the same partite set there exists a vertex z in the partite set not containing x and y such that there exist three internally disjoint spanning paths of g z joining x and y furthermore for any three vertices x y and z of the same partite set there exist three internally disjoint spanning paths of g z joining x and y if and only if n 6 or m 2

linearly many faults in cayley graphs generated by transposition trees abstract we prove that when linearly many vertices are deleted in a cayley graph generated by a transposition tree the resulting graph has a large connected component containing almost all remaining vertices

semi invariants of quivers and saturation for littlewood richardson coefficients q is defined in the space of all weights by one homogeneous linear equation and by a finite set of homogeneous linear inequalities in particular the set q is saturated i e if n q then also q these results when applied to a special quiver q tn n n and to a special dimension vector show that the gln module v appears in v v if and only if the partitions and satisfy an explicit set of inequalities this gives new proofs of the results of klyachko 7 3 and knutson and tao 8 the proof is based on another general result about semi invariants of quivers theorem 1 in the paper 10 schofield defined a semi invariant cw for each indecomposable representation w of q we show that the semi invariants of this type span each weight space in si q this seems to be a fundamental fact connecting semi invariants and modules in a direct way given this fact the results on sets of weights follow at once from the results in another paper of schofield 11

a comparison of some shell theories used for the dynamic analysis of cross ply laminated circular cylindrical panels abstract the free vibration problem of thin elastic cross ply laminated circular cylindrical panels is considered for this problem a theoretical unification as well as a numerical comparison of the thin shell theories most commonly used in engineering applications is presented in more detail the problem is formulated in such a way that by using some tracers which have the form of kronecker s deltas the stress strain relations constitutive equations and equations of motion obtained produce as special cases the corresponding relations and equations of donnell s love s sanders and flugge s theories by using a closed form solution obtained for simply supported panels a comparison of corresponding numerical results obtained on the basis of all of the aforementioned shell theories is attempted

fault diagnosability of arrangement graphs the growing size of the multiprocessor system increases its vulnerability to component failures it is crucial to locate and to replace the faulty processors to maintain a system s high reliability the fault diagnosis is the process of identifying faulty processors in a system through testing in this paper we show that the largest connected component of the survival graph contains almost all of the remaining vertices in the n k arrangement graph a n k when the number of moved faulty vertices is up to twice or three times the traditional connectivity using this fault resiliency we establish the conditional diagnosability of a n k under the comparison model and prove that the conditional diagnosability of a n k is 3k 2 n k 3 for k 4 n k 2 and the conditional diagnosability of a n n 1 is 3n 7 for n 5

strong sampling surfaces formulation for layered shells abstract the strong sas formulation for the three dimensional 3d stress analysis of layered shells is based on a new concept of sas located at chebyshev polynomial nodes throughout the layers and integration of the equilibrium equations of elasticity the idea of the sas method consists in choosing the arbitrary number of sas parallel to the middle surface in order to introduce the displacements of these surfaces as basic shell unknowns such choice of unknowns with the use of the lagrange polynomials in assumed approximations of displacements and strains through the layer thicknesses leads to a compact form of the layered shell formulation the feature of the proposed approach is that all sas are located inside the layers at chebyshev polynomial nodes the use of interfaces is avoided that makes possible to minimize uniformly the error due to the lagrange interpolation therefore the strong sas formulation can be applied efficiently to the 3d analysis of layered composite shells

super rk vertex connectedness abstract for a graph g v e a subset f v g is called an rk vertex cut of g if g f is disconnected and each vertex u v g f has at least k neighbours in g f the rk vertex connectivity of g denoted by k g is the cardinality of a minimum rk vertex cut of g in this paper we further study the rk vertex connectivity by introducing the concept called super rk vertex connectedness the graph g is called super rk vertex connectedness if for every minimum rk vertex cut s g s contains a component which is isomorphic to a certain graph h where h is related to the graph g and integer k for the cayley graphs generated by wheel graphs h is isomorphic to k2 when k 1 and h is isomorphic to c4 when k 2 in this paper we show that the cayley graphs generated by wheel graphs are super r1 vertex connectedness and super r2 vertex connectedness our studies generalize the main result in 8

three dimensional free vibration analysis of thick cylindrical shells resting on two parameter elastic supports three dimensional free vibration of a circular cylindrical shell in contact with an elastic medium will be studied the response of the elastic medium is formulated by the winkler pasternak model the layerwise theory in conjunction with a three dimensional form of hamilton s principle is used to obtain the transversely discretized equations of motion and the related boundary conditions the differential quadrature method is employed to discretize the resulting equations in the axial direction and for the solution procedure to validate the formulation the results are compared with the available exact solutions and also with ansys finite elements solutions by examining the results for thick circular shells under various boundary conditions and on different elastic foundations the influence of such parameters and in particular those due to elastic foundations are studied

the free vibrations of inhomogeneous elastic cylinders and spheres abstract the variational statement governing equations and corresponding ritz approximations are derived in cartesian cylindrical and spherical coordinates for the evaluation of the natural frequencies of free vibrations of elastic cylinders and spheres the formulation can account for orthotropic material symmetry and can be applied to either solid or hollow geometries the approximating functions selected for the displacement components depend on the geometry and coordinate system used to describe the problem and are a combination of power series fourier series and spherical harmonics representative examples are given in the various coordinate systems for both the cylinder and the sphere in general excellent agreement is found with results obtained by other methods

skew group algebras in the representation theory of artin algebras then the corresponding crossed product algebra i g or i x g for short has an elements cgieg gi a li i addition is componentwise and multiplication is given by g a g and g g2 y g g2 m in this paper we assume that the values of y lie in the center z a of i hence the action of g on i is given by a group homomorphism g p aut i and 3 can be left out in the special case that y is the trivial map we write 1g instead of i g and the elements as c c li gi ag is then called a skew group ring there is a lot of literature on skew group algebras and crossed product algebras and on the relationship with the ring ac whose elements are those elements of a left fixed by g much work has been done on which properties of li are inherited by n g or ac some of the work on the relationship between these rings has its roots in trying to develop a galois theory for noncommutative rings we refer to 3 7 13 15 19 21 23 25 27 281 and their references in this paper we study these constructions when i is an artin algebra and g a finite group of order n such that n is invertible in 1 under these assumptions the construction preserves central properties of interest in the

edge fault tolerant pancyclicity of arrangement graphs the arrangement graph a n k is a well known interconnection network day and tripathi proved that a n k is pancyclic for n k 2 in this paper we improve this result and we demonstrate that a n k is also pancyclic even if it has no more than k n k 2 faulty edges for n k 2 our result is optimal concerning the edge fault tolerance

on reliability of the folded hypercubes in terms of the extra edge connectivity for a graph g and a non negative integer g the g extra edge connectivity of g is the minimum cardinality of a set of edges in g if it exists whose deletion disconnects g and each remaining component will have at least g vertices the extra edge connectivity is an important parameters for the reliability evaluation of interconnection networks in this paper we explore g extra edge connectivity g fq n of the folded hypercube fq n for g n denote g by i 0 s 2 t i where t 0 log 2 g and t i log 2 g r 0 i 1 2 t r we show that g fq n g n 1 i 0 s t i 2 t i i 0 s 2 i 2 t i for n 6 this result generalizes the previous results by zhu et al 2007 for 3 fq n and by hsieh and tsai in press for 4 fq n and so on

orienting cayley graphs generated by transposition trees day and tripathi k day a tripathi unidirectional star graphs inform process lett 45 1993 123 129 proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs cheng and lipman e cheng m j lipman on the day tripathi orientation of the star graphs connectivity inform process lett 73 2000 5 10 e cheng m j lipman connectivity properties of unidirectional star graphs congr numer 150 2001 33 42 studied the connectivity properties of these unidirectional star graphs the class of star graphs is a special case of cayley graphs generated by transposition trees in this paper we give directions on these graphs and study the connectivity properties of the resulting unidirectional graphs

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

restricted connectivity for three families of interconnection networks vertex connectivity and edge connectivity are two important parameters in interconnection networks even though they reflect the fault tolerance correctly they undervalue the resilience of large networks by the concept of conditional connectivity and super connectivity the concept of restricted vertex connectivity and restricted edge connectivity of graphs was proposed by esfahanian a h esfahanian generalized measures of fault tolerance with application to n cube networks ieee transactions on computers 38 1989 1586 1591 such measures take the resilience of large networks into consideration in this paper we propose three families of interconnection networks and discuss their restricted vertex connectivity and restricted edge connectivity in particular the hypercubes twisted cubes crossed cubes mobius cubes star graphs pancake graphs recursive circulant graphs and k ary n cubes are special cases of these families

hyper hamilton laceable and caterpillar spannable product graphs abstract we define a hamilton laceable graph g to be hyper hamilton laceable hyper hl if either 1 a g is equitable and if v is any node of g then g v is hl or 2 b g is nearly equitable and if v is any node in its larger color set then g v is hl in particular the hypercube q n is hyper hl a graph g is caterpillar spannable cs if it has a spanning tree which is a caterpillar we present several theorems concerning products of cs graphs it is shown that the product of two cs graphs such that at least one of them has maximum degree 3 is cs

vibration of thick cylindrical shells on the basis of three dimensional theory of elasticity abstract in this paper an approximate analysis using a layerwise approach is presented to study the vibration of thick circular cylindrical shells on the basis of three dimensional theory of elasticity the boundary conditions studied are simply supported simply supported and clamped clamped boundary conditions in this approach the thick cylindrical shell is discretized into an arbitrary number of thin cylindrical layers in the thickness direction and each layer assumes a three dimensional stress state the approach is similar in concept to the finite strip method the displacements for each layer are approximated by trigonometric functions in the axial and circumferential directions and by some linear shape functions in the thickness direction the governing equation is obtained using an energy minimization principle extensive frequency parameters never seen in the literature before have been presented for a wide range of thickness to radius ratios and thickness to length ratios in addition the frequency characteristics of thin and thick cylindrical shells are also studied and the displacement fields in the thickness direction for various thickness to radius ratios are also presented the analysis has been verified by comparing results with those in the literature and excellent agreement is obtained

exact electroelastic analysis of functionally graded piezoelectric shells abstract a paper focuses on implementation of the sampling surfaces sas method for the three dimensional 3d exact solutions for functionally graded fg piezoelectric laminated shells according to this method we introduce inside the nth layer in not equally spaced sas parallel to the middle surface of the shell and choose displacements and electric potentials of these surfaces as basic shell variables such choice of unknowns yields first a very compact form of governing equations of the fg piezoelectric shell formulation and second allows the use of strain displacement equations which exactly represent rigid body motions of the shell in any convected curvilinear coordinate system it is worth noting that the sas are located inside each layer at chebyshev polynomial nodes that leads to a uniform convergence of the sas method as a result the sas method can be applied efficiently to 3d exact solutions of electroelasticity for fg piezoelectric cross ply and angle ply shells with a specified accuracy by using a sufficient number of sas

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

application of a three dimensional shell theory to the free vibration of shells arbitrarily deep in one direction abstract a three dimensional shell theory is presented which is applicable to doubly curved thick open shells which are arbitrarily deep have a large side length to radius of curvature ratio in one principal direction but are shallow in the other direction the strain displacement equations for the proposed deep shallow shell theory are expressed in cartesian co ordinates and the limits of applicability of these equations are discussed these equations are then used in a ritz variational formulation with algebraic polynomials as trial functions to solve for the natural frequencies of a number of doubly curved shell problems a novel approach is also proposed in which penalty functions are introduced to enforce continuity of displacements at two opposite ends of a shell of rectangular platform increasing the range of problems which can be treated to include closed shells such as cylinders barrels cooling tower type structures toroids rings etc a sub class of shells of revolution

linearly many faults in cayley graphs generated by transposition triangle free unicyclic graphs abstract we consider a kind of cayley graphs including the modified bubble sort graphs m b n the cayley graphs generated by lollipop graphs h n n 1 and the other cayley graphs generated by unicyclic triangle free graphs we get that if we delete linearly many vertices in cayley graphs generated by transposition unicyclic triangle free graphs then the resulting graphs has a large connected component that comprises of nearly all residual vertices

near embeddings of hypercubes into cayley graphs on the symmetric group simulations of hypercube networks by certain cayley graphs on the symmetric group are investigated let q k be the familiar k dimensional hypercube and let s n be the star network of dimension n defined as follows the vertices of s n are the elements of the symmetric group of degree n two vertices x and y being adjacent if xo 1 i y for some i that is xy is an edge if x and y are related by a transposition involving some fixed symbol which we take to be spl i bold 1 this network has nice symmetry properties and its degree and diameter are sublogarithmic as functions of the number of vertices making it compare favorably with the hypercube network these advantages of s n motivate the study of how well it can simulate other parallel computation networks in particular the hypercube the first step in such a simulation is the construction of a one to one map f q k spl rarr s n of dilation d for d small that is one wants a map f such that images of adjacent points are at most distance d apart in s n an alternative approach best applicable when one to one maps are difficult or impossible to find is the construction of a one to many map g of dilation d defined as follows for each point x spl isin q k there is an associated subset g x spl sube v s n such that for each edge xy in q k every x spl isin g x is at most distance d in s n from some y spl isin g y such one to many maps allow one to achieve the low interprocessor communication time desired in the usual one to one embedding underlying a simulation this is done by capturing the local structure of q k inside of s n via the one to many embedding when the global structure cannot be so captured our results are the following 1 there exist the following one to many embeddings a f q k spl rarr s 3k 1 with dilation f 1 b f q 11k 2 spl rarr s 13k 2 with dilation f 2 2 there exists a one to one embedding f q n2 sup n spl minus 1 spl rarr s 2 sup n with dilation f 3

a kind of conditional connectivity of cayley graphs generated by unicyclic graphs abstract for a graph g v e a subset f v g is called an r k vertex cut of g if g f is disconnected and each vertex u v g f has at least k neighbors in g f the r k vertex connectivity of g denoted by k g is the cardinality of the minimum r k vertex cut of g which is a refined measure for the fault tolerance of network g in this paper we study 2 for cayley graphs generated by unicyclic graphs let sym n be the symmetric group on 1 2 n and t be a set of transpositions of sym n let g t be the graph on vertex set 1 2 n and edge set ij ij t if g t is a unicyclic graph then simply denote the cayley graph cay sym n t by ug n in particular if g t is a cycle then ug n is the well known modified bubble sort graph mb n we prove in this paper that if m is the length of the unique cycle in g t then 2 ug n 4 n 10 if 3 m n 4 n 8 if 4 m n

skew group algebras of path algebras and preprojective algebras abstract we compute explicitly up to morita equivalence the skew group algebra of a finite group acting on the path algebra of a quiver and the skew group algebra of a finite group acting on a preprojective algebra these results generalize previous results of reiten and riedtmann 1985 rr for a cyclic group acting on the path algebra of a quiver and of reiten and van den bergh 1989 rv proposition 2 13 for a finite subgroup of sl c x c y acting on c x y

a kind of conditional vertex connectivity of cayley graphs generated by 2 trees let g be a graph then t v g is called an r k vertex cut if g t is disconnected and each vertex in v g t has at least k neighbors in g t the size of a smallest r k vertex cut is the r k vertex connectivity of g and is denoted by k k g in this paper we determine the numbers k 1 and k 2 for cayley graphs generated by 2 trees including the popular alternating group graphs

a kind of conditional connectivity of cayley graphs generated by wheel graphs for a connected graph g v e a subset fv is called an rk vertex cut of g if gf is disconnected and each vertex in vf has at least k neighbors in gf the cardinality of the minimum rk vertex cut is the rk vertex connectivity of g and is denoted by k g the conditional connectivity is a measure to explore the structure of networks beyond the vertex connectivity let sym n be the symmetric group on 1 2 n and t be a set of transpositions of sym n denote by g t the graph with vertex set 1 2 n and edge set ij ij t if g t is a wheel graph then simply denote the cayley graph cay sym n t by wgn in this paper we determine the values of 1 and 2 for cayley graphs generated by wheel graphs and prove that 1 wgn 4n6 and 2 wgn 8n18

embedding an arbitrary binary tree into the star graph binary tree structures have been very useful in solving divide and conquer type of problems embedding binary trees into another network the host network helps in designing solutions for the host network using the known solutions on binary trees embedding arbitrary binary trees into networks in particular into the hypercube has been addressed in the literature the latter was achieved with load 1 and constant dilation the n star graph is a recently introduced interconnection network for massively parallel systems it enjoys symmetry and fault tolerance properties that make it a viable alternative to the hypercube in this paper we address the problem of embedding arbitrary binary trees into the n star graph this work is the first to present such an embedding the tree has e n 1 1 or fewer vertices the embedding leads to load 1 and constant dilation for all values of n it therefore enables the star graph to efficiently simulate an arbitrary binary tree with only a constant factor of communication delay

the conditional fault diagnosability of n k star graphs abstract the growing size of the multiprocessor system increases its vulnerability to component failures it is crucial to locate and replace the faulty processors to maintain a system s high reliability the fault diagnosis is the process of identifying faulty processors in a system through testing this paper shows that the largest connected component of the survival graph contains almost all the remaining vertices when a lot of faulty vertices occur in the n k star graph s n k n 5 k 3 n k 2 based on this fault resiliency it establishes the conditional fault diagnosability of s n k under the comparison model

linearly many faults in dual cube like networks the dual cubes were introduced as a better interconnection network than the hypercubes for large scale distributed memory multiprocessors in this paper we introduce a generalization of these networks called dual cube like networks which preserve the basic structure of dual cubes and retain many of its topological properties we investigate structural properties of these networks beyond simple measures such as connectivity we prove that if up to kn k k 1 2 vertices are deleted from a dual cube like n regular network then the resulting graph will either be connected or will have a large component and small components having at most k 1 vertices in total and this result is sharp for k n as an application we derive additional results such as the cyclic vertex connectivity and the restricted vertex connectivity of these networks

dynamic analysis of a hollow cylinder subject to a dual traveling force imposed on its inner surface abstract the dynamic behavior of a hollow cylinder under a dual traveling force applied to the inner surface is investigated in this study the cylinder is constrained at both the top and bottom surfaces not to move in the length direction but free in other directions and a dual force travels at a constant velocity along the length direction on the inner surface of the hollow cylinder the resulting governing field equations and the associated boundary conditions are ruled by the general hooke s law due to the nature of the field equations proper adjoint system of equations and biorthogonality conditions were derived in a precise and detailed manner to solve these field equations in this study the method of separation of variable is used and the method of fr o benius is employed for the differential equations in the radial direction using the field equations the eigenanalyses on both the original and its adjoint system were performed with great care which results in the eigenfunction sets of both systems the biorthogonality conditions were applied to the field equations to obtain the discretized equation for each mode using the solutions of the discretized equations that account for the boundary forcing terms the critical speed for a dual traveling force for each mode could be computed

three dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels abstract the free vibration problem of a homogeneous isotropic thick cylindrical shell or panel subjected to a certain type of simply supported edge boundary conditions is considered for this problem the governing equations of three dimensional linear elasticity are employed and solved by using a new iterative approach which in practice leads to the prediction of the exact frequencies of vibration in the particular case of a flat plate or a complete shell excellent agreement is achieved between results based on the present approach and corresponding results based on other exact analyses available in the literature for certain cylindrical panel geometries comparisons are also made between corresponding numerical results based on the present analysis and certain two dimensional shell theories

on embedding rings into a star related network abstract it is shown that in the star graph it is always possible to form a hamiltonian path between two nodes as long as the distance between them is odd this result leads to the proof of hamiltonicity for the clustered star graph the results can readily be used in optimal embedding of a linear array of processors or a ring in the star graph the embedding problem is also solved when one or more processors are faulty in the network the length of the linear array and the ring in this case is shown to be n m where m is the dimension of the smallest star graph which contains all the faulty processors

adaptive system level diagnosis for hypercube multiprocessors using a comparison model fault detection and localization are important in multiprocessor computing systems several methods of system self diagnosis have been developed including the model proposed by preparata metze and chien known as the pmc model and a comparison model proposed by maeng and malek the mm model adaptive diagnosis is a practical system level diagnostic scheme whose main design objectives are to reduce the number of test rounds and the total number of tests a number of interesting research results have been presented for adaptive diagnosis using the classical pmc model however adaptive diagnosis using the mm model has been discussed only in relation to completely connected systems and torus systems in this paper we consider the problem of adaptive fault diagnosis in an n dimensional hypercube using the mm model the hypercube is an important interconnection network and an n dimensional hypercube has been shown to be n diagnosable using the mm model the goal is to correctly identify the status of all processors assuming that the number of faulty vertices does not exceed the hypercube dimension for a cycle of n vertices we show that at least four test rounds are necessary for complete diagnosis if n is not a multiple of three we propose a scheme that completely diagnoses a 4 dimensional hypercube in at most seven test rounds and an n dimensional hypercube for n 5 in at most six test rounds and at most n 2n 3 8n 2 tests where n 2 n

forced vibrations of solid elastic cylinders abstract a method is presented to determine the vibration response of a solid elastic isotropic cylinder with arbitrary length to radius ratio when subject to arbitrary distribution of axisymmetric excitation on its surfaces in this method the axial and radial components of displacement are expressed as a sum of two infinite series each term in both the series is an exact solution to the governing equations of motion and has a coefficient that is used to satisfy boundary conditions one series contains bessel functions that form a complete set in the radial direction and the other contains trigonometric functions that form a complete set in the axial direction the components of stress are also expressed in terms of complete sets of functions by using the expression for displacement the coefficients in the series are determined by using the orthogonal properties of the functions to satisfy the boundary conditions in a mean square error sense numerical results are presented to illustrate the broadband responses of cylinders to uniform and concentrated loads on the flat and curved surfaces they are in good agreement with results obtained using atila a commercial finite element software

a note on generalized matching preclusion in bipartite graphs abstract for a graph with an even number of vertices the matching preclusion number is the minimum number of edges whose deletion results in a graph with no perfect matchings the conditional matching preclusion number introduced as an extension of the matching preclusion number has the additional requirement that the resulting graph have no isolated vertices in bipartite graphs the edge sets that achieve these minimum numbers can be construed in terms of obstruction sets of vertices from this perspective the generalized matching preclusion problem was developed the matching preclusion number of order a is the minimum number of edges whose deletion results in a graph with no perfect matchings and no obstruction sets with fewer than a vertices in this paper we extend known sufficient conditions regarding the matching preclusion and conditional matching preclusion numbers orders 1 and 2 respectively to give sufficient conditions for the matching preclusion problem of order a for any positive integer a

conditional connectivity of star graph networks under embedding restriction the n dimensional star graph s n is one of the most attractive interconnection networks of large scale multiprocessor systems the k embedding restricted edge connectivity h k s n z k s n of s n is defined to be the cardinality of a minimum subset of edges nodes if any whose deletion disconnects s n and each node of the remaining components lies in an undamaged k dimensional substar s k in this paper we investigate the k embedding restricted edge connectivity of s n and determine the values of h k s n and z k s n for some k s

constructing coherently g invariant modules abstract let g be a reductive group acting on a path algebra kq as automorphisms we assume that g admits a graded polynomial representation theory and the action is polynomial we describe the quiver q g of the smash product algebra k q k m g where m g is the associated algebraic monoid of g we use q g representations to construct coherently g invariant modules of q as an application we construct algebraic semi invariants on the quiver representation spaces from those g invariant modules

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

on the genus of star graphs the star graph has recently been suggested as an alternative to the hypercube the star graph has a rich structure and symmetry properties as well as desirable fault tolerant characteristics the star graph s maximum vertex degree and diameter viewed as functions of network size grow less rapidly than the corresponding measures in a hypercube we investigate the genus of the star graph and compare it with the genus of the hypercube

a characterization of finite ei categories with hereditary category algebras abstract in this paper we give an explicit algorithm to construct the ordinary quiver of a finite ei category for which the endomorphism groups of all objects have orders invertible in the field k we classify all finite ei categories with hereditary category algebras characterizing them as free ei categories in a sense which we define for which all endomorphism groups of objects have invertible orders some applications on the representation types of finite ei categories are derived

super connectivity and super edge connectivity for some interconnection networks let g v e be a k regular graph with connectivity k and edge connectivity l g is maximum connected if k k and g is maximum edge connected if l k moreover g is super connected if it is a complete graph or it is maximum connected and every minimum vertex cut is x v x e for some vertex email protected v and g is super edge connected if it is maximum edge connected and every minimum edge disconnecting set is v x v x e for some vertex email protected v in this paper we present three schemes for constructing graphs that are super connected and super edge connected applying these construction schemes we can easily discuss the super connected property and the super edge connected property of hypercubes twisted cubes crossed cubes mobius cubes split stars and recursive circulant graphs

dynamic response of thin walled structures by variable kinematic one dimensional models abstract this paper investigates the accuracy capabilities of using variable kinematic modeling in compact and thin walled beam like structures with dynamic loadings carrera unified formulation cuf is employed to introduce refined one dimensional 1d models with a variable order of expansion for the displacement unknowns over the beam cross section classical euler bernoulli and timoshenko beam theories are obtained as particular cases of these variable kinematic models while a higher order expansion permits the detection of in plane cross section deformation since it leads to shell like solutions finite element fe method is used to provide numerical results and the newmark method is implemented as a time integration scheme some assessments with closed form solutions are discussed and comparisons with shell type results obtained with commercial fe software are made further analyses address both compact and thin walled cross sections in particular the case of a deformable thin walled cylinder loaded by time dependent internal forces is discussed the results clearly show that finite elements which are formulated in the cuf framework do not introduce additional numerical problems with respect to classical beam theories comparisons with elasticity solutions prove that the present 1d cuf model offers an accuracy in analyzing thin walled structures which is typical of shell or three dimensional models with a remarkable reduction in the computational cost required

fault tolerance and diagnosability of burnt pancake networks under the comparison model processor fault diagnosis plays an important role in measuring the reliability of a multiprocessor system and the diagnosabilities of many well known multiprocessor systems have been investigated the conditional diagnosability has been widely accepted as a new measure of diagnosability by assuming an additional condition that any faulty set can t contain all the neighbors of any node in a multiprocessor system in this paper we explore algebraic and combinatorial properties of burnt pancake networks and investigate the structural vulnerability as well as super and extra connectivities furthermore we show that the classic diagnosability and the conditional diagnosability of n dimensional burnt pancake network bp n n 4 are n and 3 n 4 respectively algebraic and combinatorial properties of burnt pancake networks are established the structural vulnerability as well as super and extra connectivities are explored the classic and conditional diagnosabilities under the comparison model are derived

reliability evaluation of bc networks in terms of the extra vertex and edge connectivity reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems the extra connectivity and the extra edge connectivity are two important parameters for the reliability evaluation of interconnection networks the mbi n dimensional bijective connection network in brief bc network includes several well known network models such as hypercubes mobius cubes crossed cubes and twisted cubes in this paper we explore the extra connectivity and the extra edge connectivity of bc networks and discuss the structure of bc networks with many faults we obtain a sharp lower bound of g extra edge connectivity of an mbi n dimensional bc network for n geq 4 and 1 leq g leq 2 n over 2 we also obtain a sharp lower bound of g extra connectivity of an n dimensional bc network for n geq 4 and 1 leq g leq 2 n which improves the result in reliability evaluation of bc networks ieee trans computers doi 10 1109 tc 2012 106 for 1 leq g leq n 3 furthermore we give a remark about exploring the g extra edge connectivity of bc networks for the more general mbi g and we also characterize the structure of bc networks with many faulty nodes or links as an application we obtain several results on the mbi g extra edge connectivity and the structure of faulty networks on hypercubes mobius cubes crossed cubes and twisted cubes