super p restricted edge connectivity of line graphs super restricted connectivity and super restricted edge connectivity are more refined network reliability indices than connectivity and edge connectivity in this paper we first introduce the concepts of super restricted connectivity and super restricted edge connectivity and then give a property of graphs with equal p restricted edge connectivity and 1 p restricted connectivity applying this property we show a sufficient condition for a line graph to be super p restricted edge connected and a relationship between super 1 p restricted connected graphs and super p restricted edge connected graphs

matching preclusion for n dimensional torus networks abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings wang et al 13 proved that a class of n dimensional tours networks with even order are super matched later cheng et al 8 further showed that all n dimensional tours networks with even order are super matched in this paper we prove that all n dimensional torus networks with odd order are super matched if n 3 two dimensional torus networks with odd order is maximally matched except for c 3 c 3 our results are complementary to those of wang et al 13 and cheng et al 8

small deformations superposed on large deformations of an elastic plastic material abstract in the context of a purely mechanical rate type theory of plasticity and utilizing a strain space formulation an infinitesimal theory is developed for motions superposed on any given motion of an elastic plastic material the given motion may involve all forms of elastic plastic deformation including both loading and unloading and in addition the loading conditions are allowed to change due to the superposed motion the infinitesimal theory is properly invariant under arbitrary finite superposed rigid motions

recursive circulants and their embeddings among hypercubes we propose an interconnection structure for multicomputer networks called recursive circulant recursive circulant g n d is defined to be a circulant graph with n nodes and jumps of powers of d g n d is node symmetric and has some strong hamiltonian properties g n d has a recursive structure when n cdm 1 c d we develop a shortest path routing algorithm in g cdm d and analyze various network metrics of g cdm d such as connectivity diameter mean internode distance and visit ratio g 2m 4 whose degree is m compares favorably to the hypercube qm g 2m 4 has the maximum possible connectivity and its diameter is 3m 1 4 recursive circulants have interesting relationship with hypercubes in terms of embedding we present expansion one embeddings among recursive circulants and hypercubes and analyze the costs associated with each embedding the earlier version of this paper appeared in park and chwa proc internat symp parallel architectures algorithms and networks ispan 94 kanazawa japan december 1994 pp 73 80

on the dynamical axisymmetric stress field in a finite pre stretched bilayered slab resting on a rigid foundation the dynamic axisymmetric stress field in an initially finite pre stretched bilayered slab resting on a rigid foundation is studied within the framework of the piecewise homogeneous body model the three dimensional linearized theory of elastic waves in initially stressed bodies is used it is assumed that a time harmonic point located normal force acts on the free face plane of the slab the considered problem is solved by employing the hankel integral transformation the materials of the layers are assumed to be incompressible and the elastic relations are given through the treloar potential the formulation and solution to the problem coincide with the corresponding ones of classical linear theory of elasticity for an incompressible body in the case where there is no initial stretching in the layers numerical results are presented and these results involve stresses acting on the interface planes in particular it is established that stresses on the interface planes decrease as the pre stretching is increased

matching preclusion number in product graphs abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings or almost perfect matchings for many interconnection networks the matching preclusion number is equal to the minimum degree of a vertex in the network and the sets of edges attaining the minimum are precisely those incident to a single vertex of minimum degree we say such networks are super matched in this paper we derive upper and lower bounds for the matching preclusion number for networks constructed using a variety of binary graph operations and give sufficient conditions for such networks to be super matched

strong matching preclusion for n dimensional torus networks the strong matching preclusion number of a graph is the minimum number of edges and or vertices whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings in 14 wang et al proved that c k c k is super strongly matched where k 3 is odd in this paper we show that c k 1 c k 2 c k n is super strongly matched where n 3 is an integer and k i 3 is an odd integer for each i 1 n our studies generalize the results of wang et al 14

calculating functions of fuzzy numbers abstract this paper discusses the calculation of functions of fuzzy numbers our general approach follows that of the fuzzy weighted algorithm fwa of wong and dong however by developing a classification scheme for functions and their arguments we show that there are many cases for which the fwa and all other published methods will give wrong results we suggest an alternative approach which will work in all cases for certain restricted classes of functions we develop methods which require less computation than the fwa these algorithms have been implemented in a constraint based logic programming language examples are given to illustrate the method and its relation to other discrete methods and the exact nonlinear programming approach

strong matching preclusion of n k star graphs the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings this is an extension of the matching preclusion problem that was introduced by park and ihm the generalized n k star graph was introduced to address scaling issues of the star graph and it has many desirable properties in this paper the goal is to find the strong matching preclusion number of n k star graphs and to categorize all optimal strong matching preclusion sets of these graphs since bipartite graphs generally have low strong matching preclusion numbers we assume that k n 2

vertex method for computing functions of fuzzy variables abstract this paper is to introduce a new approach the vertex method for computing functions of fuzzy variables the method is based on the cut concept and interval analysis the vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi occurrence of variables in the functional expression by conventional interval analysis methods the algorithm is very easy to implement and can be applied to many practical problems some examples are given to illustrate the applications

strong matching preclusion number of graphs 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 the strong matching preclusion number or simply smp number s m p g of a graph g is the minimum number of vertices and or edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings this is an extension of the matching preclusion problem and has been introduced by park and ihm in this paper we first study the smp number of some special graph classes and give some sharp upper and lower bounds of smp number next graphs with large and small smp number are characterized respectively in the end we investigate the nordhaus gaddum type relations on smp number

strong matching preclusion for k composition networks abstract let g 1 v 1 e 1 g 2 v 2 e 2 g k v k e k be k graphs and let f 1 v 1 v 2 f 2 v 2 v 3 f k 1 v k 1 v k f k v k v 1 be k bijections the k composition networks g induced by g 1 g 2 g k is the graph with v g t 1 k v g t and e g t 1 k e g t a t f t a t a t v g t and 1 t k many interconnection networks such as n dimensional torus networks recursive circulant graphs and cayley graphs on abelian groups generated by minimal generating sets are special k composition networks the strong matching preclusion number of a graph is the minimum number of edges and or vertices whose deletion results in the remaining graph has neither perfect matchings nor almost perfect matchings in this paper we study the strong matching preclusion number and strong matching preclusion sets for k composition networks with odd order our results generalize the main conclusion in 12

fuzzy weighted averages and implementation of the extension principle abstract this paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and in particular to weighted average operations in risk and decision analysis a computational algorithm based on the cut representation of fuzzy sets and interval analysis is described the method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non linear programming the algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers

many to many disjoint path covers in the presence of faulty elements a many to many k disjoint path cover k dpc of a graph g is a set of k disjoint paths joining k sources and k sinks in which each vertex of g is covered by a path it is called a paired many to many disjoint path cover when each source should be joined to a specific sink and it is called an unpaired many to many disjoint path cover when each source can be joined to an arbitrary sink in this paper we discuss about paired and unpaired many to many disjoint path covers including their relationships application to strong hamiltonicity and necessary conditions and then we give a construction scheme for paired many to many disjoint path covers in the graph h0 oplus h1 obtained from connecting two graphs h0 and h1 with v h0 v h1 by v h1 pairwise nonadjacent edges joining vertices in h0 and vertices in h1 where h0 g0 oplus g1 and h1 g2 oplus g3 for some graphs gj using the construction we show that every m dimensional restricted hl graph and recursive circulant g 2m 4 with f or less faulty elements have a paired k dpc for any f and k ges 2 with f 2k les m

conditional edge fault tolerant edge bipancyclicity of hypercubes the hypercube has been one of the most popular interconnection networks for parallel computer communication systems in this paper we assume that each node is incident with at least two fault free links under this assumption we show that every fault free edge lies on a fault free cycle of every even length from 6 to 2 n inclusive even if it has up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated

calculating functions of interval type 2 fuzzy numbers for fault current analysis in this work functions of type 2 fuzzy numbers are analyzed for the special case of interval type 2 fuzzy numbers the type 2 membership function of the output variable is calculated using the lower and upper membership functions of the input variables and the vertex method this procedure is used in an application where the type 2 fuzzy fault currents of an electric distribution system are calculated the results are shown and the advantages of the approach are discussed

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

strong matching preclusion for augmented cubes the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings the concept was introduced by park and son in this paper we study the strong matching preclusion problem for the augmented cube graphs as a result we find smp aqn and classify all optimal solutions

strong matching preclusion for non bipartite torus networks the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings the torus network is one of the most popular interconnection network topologies for massively parallel computing systems because of its desirable properties it is known that bipartite torus networks have low strong matching preclusion numbers hu et al 13 proved that non bipartite torus networks with an odd number of vertices have good strong matching preclusion properties to complete the study of strong matching preclusion problem for non bipartite torus networks in this paper we establish the strong matching preclusion number and classify all optimal strong matching preclusion sets for the n dimensional non bipartite torus network with an even number of vertices where n 3

a fast geometric method for defuzzification of type 2 fuzzy sets generalized type 2 fuzzy logic systems cannot currently be used for practical problems because the amount of computation required to defuzzify a generalized type 2 fuzzy set is too large this paper presents a new method for defuzzifing a type 2 fuzzy set the new much faster technique is based on geometric representations and operations the results of a real world example contained in this paper show this new approach to be over 200 000 times faster than type reduction we present a new method for assessing the accuracy of the membership function of a type 2 fuzzy set this method is used to show that the new representation used by the defuzzifier is not detrimental to the accuracy of the set we also discuss the differences between the new approach and type reduction identifying the origin of this massive improvement in execution speed

small strain accompanied by moderate rotation this paper is mainly concerned with the construction of a theory of material behavior with infinitesimal strain accompanied by moderate rotation after introducing a definition for moderate rotation and establishing a number of theorems pertaining to its properties precise estimates are obtained for the local moderate rotation and related kinematical results in terms of infinitesimal strain for motions which result in small strain accompanied by moderate rotation the invariance of constitutive equations under arbitrary superposed rigid body motions is discussed with particular reference to an elastic material

axisymmetric bifurcations of thick spherical shells under inflation and compression incremental equilibrium equations and corresponding boundary conditions for an isotropic hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure a thick walled spherical shell during inflation is analyzed using four different material models specifically one and two terms in the ogden energy formulation the gent model and an i1 formulation recently proposed by lopez pamies we investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness these results are then used to investigate axisymmetric bifurcations of the inflated shell the analysis is extended to determine the behavior of a thick walled spherical shell subject to an external pressure we find that the results of the two terms ogden formulation the gent and the lopez pamies models are very similar for the one term ogden material we identify additional critical stretches which have not been reported in the literature before

on reliability of the folded hypercubes in this paper we explore the 2 extra connectivity and 2 extra edge connectivity of the folded hypercube fq n we show that k 2 fq n 3n 2 for n 8 and l 2 fq n 3n 1 for n 5 that is for n 8 resp n 5 at least 3n 2 vertices resp 3n 1 edges of fq n are removed to get a disconnected graph that contains no isolated vertices resp edges when the folded hypercube is used to model the topological structure of a large scale parallel processing system these results can provide more accurate measurements for reliability and fault tolerance of the system

conditional matching preclusion for the arrangement graphs 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 recently the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings in this paper we find this number and classify all optimal sets for the arrangement graphs one of the most popular interconnection networks

approximate kinematical relations in plasticity abstract within the framework of finite plasticity it is shown how a number of kinematical approximations can be systematically derived from the multiplicative decomposition of the deformation gradient particular attention is devoted to two types of approximate theories a those in which elastic deformations are of a different order of magnitude than plastic deformations and b those in which rotations are of a different order of magnitude than strains

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

application of fuzzy sets of type 2 to the solution of fuzzy equation systems abstract the present paper continues the authors investigation on fuzzy equation systems with tolerances we consider the situation that the outputs of an object are modelled by fuzzy sets of type 2 for special membership functions this problem can be attributed to a problem with tolerances moreover this concept enables us to define solutions for fuzzy outputs of type 1 when classical solution concepts may fail

strong matching preclusion for torus networks the torus network is one of the most popular interconnection network topologies for massively parallel computing systems strong matching preclusion that additionally permits more destructive vertex faults in a graph is a more extensive form of the original matching preclusion that assumes only edge faults in this paper we establish the strong matching preclusion number and all minimum strong matching preclusion sets for bipartite torus networks and 2 dimensional nonbipartite torus networks

general theory of small elastic deformations superposed on finite elastic deformations using tensor notations a general theory is developed for small elastic deformations of either a compressible or incompressible isotropic elastic body superposed on a known finite deformation without assuming special forms for the strain energy function the theory is specialized to the case when the finite deformation is pure homogeneous when two of the principal extension ratios are equal the changes in displacement and stress due to the small superposed deformation are expressed in terms of two potential functions in a manner which is analogous to that used in the infinitesimal deformation of hexagonally aeolotropic materials the potential functions are used to solve the problem of the infinitesimally small indentation by a spherical punch of the plane surface of a semi infinite body of incompressible isotropic elastic material which is first subjected to a finite pure homogeneous deformation symmetrical about the normal to the force free plane surface

physically nonlinear and related approximate theories of elasticity and their invariance properties the existing developments of physically nonlinear elasticity have several shortcomings with the aim of remedying these deficiencies a number of approximate theories of elasticity are discussed in the present paper and in particular a theory of physically nonlinear elasticity is systematically developed more specifically stress strain relations for anisotropic physically nonlinear materials are derived the method of casey naghdi 1 is then applied to obtain properly invariant results this method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle called a pivot the auxiliary motions represent the original motions in the approximate theory the connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated

an invariant infinitesimal theory of motions superposed on a given motion abstract the development is applicable to any material but special attention is given to elastic solids included as a special case is an infinitesimal theory of elasticity with the following properties 1 it is properly invariant under arbitrary not necessarily infinitesimal superposed rigid body motions 2 it reduces by specialization to the theory of rigid bodies undergoing finite motion and 3 it can be brought into correspondence with the classical linear elasticity through a suitable reinterpretation of the symbols in the constitutive equation of the latter author

conditional matching preclusion for hypercube like interconnection networks the conditional matching preclusion number of a graph with n vertices is the minimum number of edges whose deletion results in a graph without an isolated vertex that does not have a perfect matching if n is even or an almost perfect matching if n is odd we develop some general properties on conditional matching preclusion and then analyze the conditional matching preclusion numbers for some hl graphs hypercube like interconnection networks

reliability analysis of twisted cubes connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model let g v e g v e be a connected graph a connected graph g is called supper resp super if every minimum vertex cut edge cut of g is the set of neighbors of some vertex in g let f v f v be a vertex set f is called extra cut if g f g f is not connected and each component of g f g f has more than k vertices the extraconnectivity k g k g is the cardinality of the minimum extra cuts a r component cut of g is a set s of vertices g s g s has at least r components r component connectivity c r g c r g of g is the size of the smallest r component cut the r component edge connectivity c r g c r g can be defined similarly in this paper we determine the r component edge connectivity of twisted cubes tn n t n n for small r and we also prove other properties of tn n t n n

operations on type 2 fuzzy sets in this paper we discuss set operations on type 2 fuzzy sets including join and meet under minimum product t norm algebraic operations properties of membership grades of type 2 sets and type 2 relations and their compositions all this is needed to implement a type 2 fuzzy logic system fls

the diagnosability of the matching composition network under the comparison diagnosis model the classical problem of diagnosability is discussed widely and the diagnosability of many well known networks has been explored we consider the diagnosability of a family of networks called the matching composition network mcn a perfect matching connects two components the diagnosability of mcn under the comparison model is shown to be one larger than that of the component provided some connectivity constraints are satisfied applying our result the diagnosability of the hypercube qn the crossed cube cq sub n the twisted cube tq sub n and the mobius cube mq sub n can all proven to be n for n spl ges 4 in particular we show that the diagnosability of the four dimensional hypercube q sub 4 is 4 which is not previously known

matching preclusion for balanced hypercubes matching preclusion is a measure of robustness in the event of edge failure in interconnection networks the matching preclusion number of a graph g is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching and the conditional matching preclusion number of g is the minimum number of edges whose deletion leaves the resulting graph with no isolated vertices and without a perfect matching or an almost perfect matching in this paper we consider balanced hypercubes we obtain that an n dimension balanced hypercube bh n has the matching preclusion number 2n and mainly prove that for the balanced hypercube bh n each matching preclusion set of cardinality 2n is trivial and the conditional matching preclusion number of balanced hypercube is 4n 2 whenever n 2

on computing normalized interval type 2 fuzzy sets this paper explains how to compute normalized interval type 2 fuzzy sets in closed form and explains how the results reduce to well known results for type 1 fuzzy sets and interval sets such normalized interval type 2 fuzzy sets may be needed in linguistic probability computa tions or multiple criteria decision analysis under uncertainty index terms fuzzy weighted average fwa interval type 2 fuzzy sets it2 fss interval weighted average iwa linguistic probability linguistic weighted average lwa normalized interval type 2 fuzzy sets

centroid of a type 2 fuzzy set abstract in this paper we introduce the centroid and generalized centroid of a type 2 fuzzy set both of which are essential for implementing a type 2 fuzzy logic system and explain how to compute them for practical use we show how to compute the centroid of interval and gaussian type 2 fuzzy sets an exact computation procedure is provided for an interval type 2 set whereas an approximation is provided for both interval and gaussian type 2 sets examples are given that compare the exact computational results with the approximate results

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

on steady motions of an elastic rod with application to contact problems based on the directed theory of an elastic rod developed by green naghdi and several of their co workers this paper presents a formulation which is convenient to use when considering steady motions of elastic rods a properly invariant linear theory of this formulation is also developed and used to analyze several systems these systems involve surface constraints and find application in various technologies where elastic rod like bodies are present

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

matching preclusion number of graphs abstract the matching preclusion number of a graph g denoted by mp g is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings in this paper we first give some sharp upper and lower bounds of matching preclusion number next graphs with large and small matching preclusion number are characterized respectively in the end we investigate some extremal problems and the nordhaus gaddum type relations on matching preclusion number

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

fault tolerance of locally twisted cubes abstract let g v e be a connected graph and p be graph theoretic property a network is often modeled by a graph g v e one fundamental consideration in the design of networks is reliability the connectivity is an important parameter to measure the fault tolerance and reliability of network the conditional connectivity g p or g p is the minimum cardinality of a set of edges or vertices if it exists whose deletion disconnects g and each remaining component has property p let f be a vertex set or edge set of g and p be the property of with at least k components then we have the k component connectivity c k g and the k component edge connectivity c k g in this paper we determine the k component edge connectivity of locally twisted cubes ltqn for small k and we also prove other properties of ltqn

a justification of nonlinear properly invariant plate theories a single asymptotic derivation of three classical nonlinear plate theories is presented in a setting which preserves the frame invariance properties of three dimensional finite elasticity by a successive scaling of the external loading on the three dimensional body the nonlinear membrane theory the nonlinear inextensional theory and the von karman equations are derived as the leading order terms in the asymptotic expansion of finite elasticity the governing equations of the nonlinear inextensional theory are of particular interest where 1 plane strain kinematics and plane stress constitutive equations are derived simultaneously from the asymptotic analysis 2 the theory can be phrased as a minimization problem over the space of isometric deformations of a surface and 3 the local equilibrium equations are identical to those arising in the one director cosserat shell model furthermore it can be concluded that with a regular single scale asymptotic expansion it is not possible to obtain a system of plate equations in which finite membrane strain and finite bending strain occur simultaneously in the leading order term of an asymptotic analysis

matching preclusion and conditional matching preclusion problems for the folded petersen cube the matching preclusion number of an even graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex recently the conditional matching preclusion number of an even graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices and no perfect matchings in this paper we study this problem for the folded petersen cube fpq n k via some matching preclusion and conditional matching preclusion results of the cartesian products of graphs

fractional matching preclusion of product networks abstract the matching preclusion number of a graph introduced in 2 as a fault analysis is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings as a generalization liu and liu 14 recently introduced the concept of fractional matching preclusion number the fractional matching preclusion number of graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matching if the sets of edges of the graph attaining the minimum are precisely those incident to a single vertex of minimum degree we say such graph is fractional super matched in this paper the upper and lower bounds for the fractional matching preclusion number for cartesian product direct product strong product and lexicographic product are obtained and we give sufficient conditions for such graphs to be fractional super matched

a theory of shells with small strain accompanied by moderate rotation this paper is concerned with a constrained theory of shells in the presence of small strain accompanied by moderate rotation the constrained theory accounts for the effect of transverse normal strain and includes of course the special case corresponding to the kirchhoff love theory of shells in which the effect of transverse normal strain is absent after precise estimates for local moderate rotation and relative displacement gradients in terms of infinitesimal strain have been effected a complete theory is formulated with the use of linear constitutive equations the nature of the complete theory is further examined when initially the shell like body is a plate and it is shown that our kinematical formulae strain displacement relations as well as the relevant differential equations of the theory in the absence of the effect of transverse normal strain systematically reduce to those used in the von karman plate equations also in the light of the present results an assessment of kinematical aspects of previously developed theories of shells undergoing small strain and moderate rotation is indicated

edge fault tolerance of super edge connectivity for three families of interconnection networks let g v e be a connected graph g is said to be super edge connected or super l for short if every minimum edge cut of g isolates one of the vertex of g a graph g is called m super l if for any edge set s e g with s

the transformation method for the simulation and analysis of systems with uncertain parameters in this paper the transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters based on the concept of cuts the method represents a special implementation of fuzzy arithmetic that avoids the well known effect of overestimation which usually arises when fuzzy arithmetic is reduced to interval computation systems with uncertain model parameters can thus be simulated without any artificial widening of the simulation results as a by product of the implementation scheme the transformation method also provides a measure of influence to quantitatively analyze the uncertain system with respect to the effect of each uncertain model parameter on the overall uncertainty of the model output by this a special kind of sensitivity analysis can be defined on the basis of fuzzy arithmetic finally to show the efficiency of the transformation method the method is applied to the simulation and analysis of a model for the friction interface between the sliding surfaces of a bolted joint connection

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

strong matching preclusion the matching preclusion problem introduced by brigham et al r c brigham f harary e c violin and j yellen perfect matching preclusion congressus numerantium 174 2005 185 192 studies how to effectively make a graph have neither perfect matchings nor almost perfect matchings by deleting as small a number of edges as possible extending this concept we consider a more general matching preclusion problem called the strong matching preclusion in which deletion of vertices is additionally permitted we establish the strong matching preclusion number and all possible minimum strong matching preclusion sets for various classes of graphs