p matrices are just sufficient abstract the classes of sufficient matrices and of p matrices have recently arisen in connection with the linear complementarity problem it is known that p matrices are sufficient we show that conversely every sufficient matrix is a p matrix

sufficient matrices and the linear complementarity problem abstract we pose and answer two questions about solutions of the linear complementarity problem lcp the first question is concerned with the conditions on a matrix m which guarantee that for every vector q the solutions of the lcp q m are identical to the karush kuhn tucker points of the natural quadratic program associated with q m in answering this question we introduce the class of row sufficient matrices the transpose of such a matrix is what we call column sufficient the latter matrices turn out to furnish the answer to our second question which asks for the conditions on m under which the solution set of q m is convex for every q in addition to these two main results we discuss the connections of these twonew matrix classes with other well known matrix classes in linear complementarity theory

on the uniqueness of solutions to linear complementarity problems this paper characterizes the classu of all realn n matricesm for which the linear complementarity problem q m has a unique solution for all realn vectorsq interior to the conek m of vectors for which q m has any solution at all it is shown that restricting the uniqueness property to the interior ofk m is necessary because whenu the problem q m has infinitely many solutions ifq belongs to the boundary of intk m it is shown thatm must have nonnegative principal minors whenu andk m is convex finally it is shown that whenm has nonnegative principal minors only one of which is 0 andk m r n thenu andk m is a closed half space

criteria for copositive matrices abstract some finite criteria for copositive copositive plus and strictly copositive matrices are proposed and compared with existing determinantal tests the basic mathematical tool is principal pivoting

free vibration of an axially loaded prestressed planar frame abstract the influence of some parameters on the natural vibration frequency of a non linear two member frame is studied the perturbation method is used for solving the problem which is formulated on the basis of hamilton s principle numerical results concerning the influence of prestress and axial force on the natural frequency are compared with those from an experiment additional numerical results show the effect of the distribution of both the flexural and axial rigidities as well as the mass per unit length between frame s members on the natural frequency of the sytem the amplitude frequency relation for different loadings is demonstrated also

on the failure of static stability analyses of nonconservative systems in regions of divergence instability abstract the stability of perfect bifurcational discrete dissipative systems under follower loads in regions of existence non existence of adjacent equilibria is thoroughly re examined in the light of recent progress in nonlinear dynamics a general theory for such nongradient systems described by autonomous ordinary differential equations is developed conditions for the existence of adjacent equilibria the stability of precritical critical and postcritical states as well as for different types of local bifurcations are established focusing attention on the interaction of geometric nonlinearities and vanishing damping new findings contradicting widely accepted results of the classical linear analysis are discovered in a small region of adjacent equilibria near a compound branching point which is explicitly determined an interaction of two consecutive postbuckling modes occurs related to the following phenomena in case of vanishing damping loss of stability may occur via a hopf dynamic bifurcation prior to static divergence buckling moreover the critical states of divergence instability may be associated with a double zero jacobian eigenvalue satisfying also the conditions of a hopf local bifurcation besides local dynamic bifurcations global bifurcations are also found an example is used to illustrate the qualitative findings

criteria for sufficient matrices abstract column sufficient row sufficient and sufficient matrices have recently arisen in connection with the linear complementarity problem we review and supplement the basic theory of these matrix classes propose new criteria for identifying them and compare these criteria with the existing ones our main mathematical tool is principal pivoting

new characterizations of row sufficient matrices in dealing with a linear complementarity problem much depends on knowing that the matrix through which the particular lcp is defined belongs to a suitable matrix class two such classes are su the so called sufficient matrices and l which were introduced in r w cottle j s pang v venkateswaran sufficient matrices and the linear complementarity problem linear algebra appl 114 115 1989 231 249 b c eaves the linear complementarity problem manage sci 17 1971 612 634 respectively in an earlier article i adler r w cottle s verma sufficient matrices belong to l math prog 106 2006 391 401 the authors proved that su is a subclass of l by definition the class su is the intersection of two distinct classes rsu the row sufficient matrices and csu the column sufficient matrices in the present work we strengthen the aforementioned inclusion by showing that all row sufficient matrices belong to l using what we call structural properties of certain matrix classes we add to the existing characterizations of rsu in r w cottle s m guu two characterizations of sufficient matrices linear algebra appl 170 1992 65 74 s m guu r w cottle on a subclass of p0 linear algebra appl 223 224 1995 325 335 h valiaho criteria for sufficient matrices linear algebra appl 233 1996 109 129 this line of inquiry was inspired by asking what must be true of a row sufficient l matrix we establish three new characterizations of rsu in terms of the matrix classes l e0 and q0 and the structural properties of sign change invariance completeness and fullness the new characterizations of rsu provide new characterizations of su by adjoining a fourth structural property we call reflectiveness

fully copositive matrices the class of fully copositive c 0 f matrices introduced in g s r murthy t parthasarathy siam journal on matrix analysis and applications 16 4 1995 1268 1286 is a subclass of fully semimonotone matrices and contains the class of positive semidefinite matrices it is shown that fully copositive matrices within the class ofq 0 matrices arep 0 matrices as a corollary of this main result we establish that a bisymmetricq 0 matrix is positive semidefinite if and only if it is fully copositive another important result of the paper is a constructive characterization ofq 0 matrices within the class ofc 0 f while establishing this characterization it will be shown that graves s principal pivoting method of solving linear complementarity problems lcps with positive semidefinite matrices is also applicable toc 0 f q 0 class as a byproduct of this characterization we observe that ac 0 f matrix is inq 0 if and only if it is completelyq 0 also from aganagic and cottle s m aganagic r w cottle mathematical programming 37 1987 223 231 result it is observed that lcps arising fromc 0 f q 0 class can be processed by lemke s algorithm 1998 the mathematical programming society inc published by elsevier science b v

non linear analysis of elastic plane frames with crooked bars in this investigation the postbuckling response of plane frames consisting of a large number of crooked bars is achieved by means of an efficient method based on non linear kinematic stability analysis the entire formulation of the non linear equilibrium equations presented in matrix form is implemented by the computer program nlsrf non linear stability of rod frames critical loads and critical displacements are obtained through a direct computation by using the additional stability condition resulting from the vanishing of the stability determinant the efficacy of the method proposed herein is demonstrated by a three storey single span frame

pseudomonotone and copositive star matrices abstract we study general and complementarity properties of matrices which are either pseudomonotone or copositive star on a closed convex cone in particular we show that if a matrix is pseudomonotone on the nonnegative orthant of r n then it belongs to p 0 q 0 we also show that if a matrix t is copositive star on a closed convex cone k then the linear complementarity problem lcp t k q is solvable for all q in r n iff zero is the only solution of the homogeneous problem lcp t k 0 we characterize pseudomonotonicity of a matrix t by the nonnegativity of the quadratic form tx x on a certain set

divergence of a rotating shaft with an intermediate support and conservative axial loads abstract the dynamic behavior of a rotating shaft with an intermediate support and conservative axial loads is analyzed using euler beam theory and the assumed mode method the equations of motion are then transformed to the standard form of eigenvalue problems for determining the critical dimensionless rotational speeds and the critical axial loads corresponding to the divergence type instability of the shaft results of numerical simulations are presented for various combinations of support locations axial loads and rotational speeds

almost copositive matrices abstract a real n n matrix is termed almost copositive if it is not copositive but all its principal submatrices of order n 1 are a real copositive n n matrix is called almost copositive plus almost strictly copositive if it is not copositive plus strictly copositive but all its principal submatrices of order n 1 are such matrices are of crucial importance in deriving criteria for copositivity the properties of these matrix classes are investigated the emphasis being on the less known class of almost copositive plus matrices the basic mathematical tools used are principal pivoting and quadratic programming

stability of a timoshenko beam resting on a winkler elastic foundation the influences of a winkler elastic foundation modulus slenderness ratio and elastically restrained boundary conditions on the critical load of a timoshenko beam subjected to an end follower force are investigated the characteristic equation for elastic stability is derived it is found that the critical flutter load for the cantilever timoshenko beam will first decrease as the elastic foundation modulus is increased and when the elastic foundation modulus is greater than the corresponding critical value which corresponds to the lowest critical load it will increase instead in particular if the elastic foundation modulus is large enough the critical flutter load for the cantilever timoshenko beam can be greater than that of the bernoulli euler beam for a clamped translational or clamped rotational elastic spring supported beam resting on an elastic foundation there exists a critical value of the spring constant for each beam at this critical point the critical load jumps and the type of instability mechanism changes the jump mechanisms for beams resting on elastic foundations of different modulus values are different

static and dynamic local and global bifurcations in nonlinear autonomous structural systems discrete damped or undamped gradient systems described by nonlinear autonomous ordinary differential equations ode of motion are examined in detail emphasis is given to the relationship between static with possibly existing dynamic bifurcations criteria for dynamic bifurcations and stability of precritical critical and postcritical states associated with the nature of jacobian eigenvalues are also presented cases of discrepancies between local and global dynamic analysis regarding the stability of equilibriums are reported for the first time finally using a simple energy criterion exact dynamic buckling loads for vanishing but nonzero damping are readily obtained

dynamic stability of a tapered cantilever beam on an elastic foundation subjected to a follower force the equation of motion in matrix form of a tapered cantilever euler beam subjected to a follower force at the free end is formulated based on the lagrangian approach and the assumed mode method the beam is resting on a winkler type elastic foundation the effects of the presence of viscous damping in the foundation which makes the foundation viscoelastic and the presence of internal damping in the beam on the critical flutter loads are examined separately to evaluate their relative importance as expected internal damping of the beam tends to drastically reduce the critical flutter loads for a beam of uniform cross section for tapered beams the effects are however dependent on the taper ratio of the beam as well as the modulus of the elastic foundation the critical flutter loads of both tapered beams and beams of uniform cross section are found to be unaffected by the presence of viscous damping in the elastic foundation the effect of varying the modulus of the elastic foundation on the critical flutter loads is also discussed in the paper

energy based dynamic buckling estimates for autonomous dissipative systems the dynamic buckling global response of a nonlinear 3 degree of freedom dissipative model under a step loading of infinite duration is thoroughly discussed geometrically imperfect models with symmetric or antisymmetric imperfections losing their static stability through a limit point and an asymmetric bifurcation point respectively are considered emphasis is given to the combined effect of nonlinearities geometric and or material and damping exact approximate and lower upper bound estimates based on energy criteria for establishing the dynamic buckling response of such autonomous models without solving the highly nonlinear initial value problem are assessed the reliability and efficiency of the proposed readily obtained estimates is illustrated via numerical simulation the accuracy of which is checked using energy balance considerations certain interesting byproducts associated with a postlimit point bifurcation and breakdown of the symmetry of deformation are also revealed

elastic stability of non uniform columns abstract a simple and efficient method is proposed to investigate the elastic stability of three different tapered columns subjected to uniformly distributed follower forces the influences of the boundary conditions and taper ratio on critical buckling loads are investigated the critical buckling loads of columns of rectangular cross section with constant depth and linearly varied width t 1 constant width and linearly varied depth t 2 and double taper t 3 are investigated among the three different non uniform columns considered taper ratio has the greatest influence on the critical buckling load of column t 3 and the lowest influence on that of column t 1 the types of instability mechanisms for hinged hinged and cantilever non uniform columns are divergence and flutter respectively however for clamped hinged and clamped clamped non uniform columns the type of instability mechanism for column t 1 is divergence while that for columns t 2 and t 3 is divergence only when the taper ratio of the columns is greater than certain critical values and flutter for the rest value of taper ratio when the type of instability mechanism changes from divergence to flutter there is a finite jump for the critical buckling load the influence of taper ratio on the elastic stability of cantilever column t 3 is very sensitive for small values of the taper ratio and there also exist some discontinieties in the critical buckling loads of flutter instability for a hinged hinged non uniform column t 2 or t 3 with a rotational spring at the left end of the column when the taper ratio is less than the critical value the instability mechanism changes from divergence to flutter as the rotational spring constant is increased for a clamped elastically supported non uniform column when the taper ratio is greater than the critical value the instability mechanism changes from flutter to divergence as the translational spring constant is increased

integer solution for linear complementarity problem we consider the problem of finding an integer solution to a linear complementarity problem we introduce the class i of matrices for which the corresponding linear complementarity problem has an integer complementary solution for every vector q for which it has a solution strong principal unimodularity forms a sufficient condition for inclusion in the class i it is also shown to be necessary for some well known classes of matrices including the class of positive semidefinite matrices this is used in deriving necessary and sufficient conditions for a convex quadratic program to have an integer optimal solution for all b and c for which it has an optimal solution characterizations are also derived for some other well known classes of matrices in linear complementarity to belong to the class i in the end a peeling algorithm for finding integer solution for linear complementarity problems is given and related results are derived

postbuckling behavior of a clamped elastically supported planar structure under follower force the behavior of a geometrically nonlinear planar two member structure clamped at one end and elastically supported at the other under follower force is studied the characteristics of forces in the members of the structure during loading vs the rigidity of the supporting spring are discussed the changes of bending moment at which the system elements interact the lateral displacement and tangent slope angle vs loading force are presented the critical instability divergence mechanism of a double bar column is compared with the corresponding single column

criteria for occurrence of flutter instability before buckling the occurrence of utter instability through a hopf bifurcation before static buckling in regions of divergence in nonconservative nonself adjoint dissipative systems is thoroughly discussed using a qualitative analysis this region where both ziegler s and static criterion may fail to predict the actual critical load is de ned via two values bounds of the nonconservativenessloadingparameter the upperboundcorresponds to 0 5 being invariant with respect to all other parameters whereas the lower bound corresponds to a double critical divergence point beyond which there are no adjacent equilibria the location of the last point lying always between 0 and 0 5 depends on a stiffness parameter it is also found that the region of nonexistence of adjacent equilibria becomes maximum minimum when the double critical point corresponds to 0 5 0 the interaction of vanishing damping with various parameters leads to new phenomena related to point and periodic attractors as well as to a new type of dynamic bifurcation

on hidden z matrices and the linear complementarity problem abstract in this paper we explore various matrix theoretic aspects of the hidden z class and demonstrate how the concept of principal pivot transform can be effectively used to extend many existing results in fact we revisit various results obtained for hidden z class by mangasarian cottle and pang in context of solving linear complementarity problems as linear programs we identify hidden z matrices of special category and discuss the number of solutions of the associated linear complementarity problems we also present game theoretic interpretation of various results related to hidden z class and obtain proofs following the game theoretic approach of raghavan for a subclass of z matrices

on the transpose of a pseudomonotone matrix and the lcp abstract in the study of linear complementary problem it is known that pseudomonotone matrices belong to the class p 0 q 0 in this note we show that under certain conditions such as invertibility or normality the transpose of a pseudomonotone matrix belongs to the class q 0

on pseudomatroid property of matrices abstract a necessary and sufficient condition for a matrix to have pseudomatroid property is presented pseudosymmetric matrices which possess pseudomatroid property are introduced as a generalization of quasisymmetric matrices considered by a bouchet a duchamp linear algebra and appl 146 1991 67 78 principal unimodularity and perfect balancedness of these matrices are investigated a result on nonbinary pseudomatroids is presented in the end

the principal pivoting method revisited the principal pivoting method ppm for the linear complementarity problem lcp is shown to be applicable to the class of lcps involving the newly identified class of sufficient matrices

some perturbation results for the linear complementarity problem it has been shown previously that the linear complementarity problem is stable when the defining matrix is positive semidefinite and when locally the set of solutions is nonempty and bounded we enlarge the class of matrices for which this is true and also demonstrate how the boundedness condition leads to other stability type questions

nonlinear dynamic buckling of discrete structural systems under impact loading abstract nonlinear dynamic buckling of discrete dissipative or nondissipative nonlinearly elastic structural systems geometrically perfect or imperfect under impact loading is thoroughly examined applying the law of impulse momentum one can determine analytically the initial conditions valid immediately after impact thereafter the response of the system is governed by a set of autonomous highly nonlinear ordinary differential equations using an efficient and qualitative analysis exact and lower upper bound dynamic buckling estimates very useful for structural design purposes are established without integrating the aforementioned nonlinear initial value problem the analysis is supplemented by a variety of numerical results of a two degrees of freedom dissipative model from these results it is clearly shown how the point attractor response of the system is changed after a sudden jump to dynamic buckling occurring through a global dynamic bifurcation

more on positive subdefinite matrices and the linear complementarity problem abstract in this article we consider positive subdefinite matrices psbd recently studied by j p crouzeix et al siam j matrix anal appl 22 2000 66 and show that linear complementarity problems with psbd matrices of rank 2 are processable by lemke s algorithm and that a psbd matrix of rank 2 belongs to the class of sufficient matrices introduced by r w cottle et al linear algebra appl 114 115 1989 231 we also show that if a matrix a is a sum of a merely positive subdefinite copositive plus matrix and a copositive matrix and a feasibility condition is satisfied then lemke s algorithm solves lcp q a this supplements the results of jones and evers

integral solutions of linear complementarity problems we characterize the class of integral square matrices m having the property that for every integral vector q the linear complementarity problem with data m q has only integral basic solutions these matrices called principally unimodular matrices are those for which every principal nonsingular submatrix is unimodular as a consequence we show that if m is rank symmetric and principally unimodular and q is integral then the problem has an integral solution if it has a solution principal unimodularity can be regarded as an extension of total unimodularity and our results can be regarded as extensions of well known results on integral solutions to linear programs we summarize what is known about principally unimodular symmetric and skew symmetric matrices

dynamic stability criteria of nonlinear elastic damped undamped systems under step loading the nonlinear dynamic stability of simple nonlinearly elastic systems with or without viscous damping under step loading of infinite or finite duration is discussed the analysis refers to discrete structural systems with one or two degrees of freedom which under the action of the same loading applied statically lose their stability by snapping considering the stability of motion in the large in the sense of lagrange conditions for a bounded or an unbounded motion and thereby dynamic buckling criteria are properly established for one degree of freedom systems it is found that regardless of the length of time of loading application as well as regardless of whether or not damping is included the motion ceases to be bounded when the phase point velocity vanishes using this criterion exact or approximate lower bound dynamic buckling loads for damped or undamped systems under step loading of infinite or finite duration can be obtained without solving the strongly nonlinear differential equation of motion

integral equation formulation and analysis of the dynamic stability of damped beams subjected to subtangential follower forces abstract this paper presents a mathematical model based on integral equations for numerical investigations of stability analyses of damped beams subjected to subtangential follower forces a mathematical formulation based on euler bernoulli beam theory is presented for beams with variable cross sections on a viscoelastic foundation and subjected to lateral excitation conservative and non conservative axial loads using the boundary element method and radial basis functions the equation of motion is reduced to an algebro differential system related to internal and boundary unknowns generalized formulations for the deflection the slope the moment and the shear force are presented the free vibration of loaded beams is formulated in a compact matrix form and all necessary matrices are explicitly given the load frequency dependence is extensively investigated for various parameters of non conservative loads of internal and viscous dampings and for various positions of the concentrated foundation for an undamped beam a dynamic stability analysis is illustrated numerically based on the coalescence criterion the flutter load and instability regions with respect to various parameters are identified the effects of internal and viscous dampings on the critical flutter load are examined separately and relative effects are evaluated the dynamic responses before near and after the flutter are investigated a simple and quite general methodological approach is presented comprehensive numerical tests for flutter analysis are reported and discussed

two characterizations of sufficient matrices abstract two characterizations are given for the class of sufficient matrices defined by cottle pang and venkateswaran the first is a direct translation of the definition into linear programming terms the second can be thought of as a generalization of a theorem of t d parsons on p matrices

instability of lightly damped linear nonconservative systems in computing the critical load for a linear nonconservative system one needs to construct the load frequency curve from the characteristic equation that contains asymmetric matrices based on the finite element formulation traditionally this requires repeated solution of complex eigenvalues from the characteristic equation at many load levels which is extremely time consuming in practice small damping of the rayleigh type is assumed a bieigenvalue curve is adopted to approximate the load frequency curve for the first few modes of interest such a curve can be uniquely determined once the derivatives of the frequency with respect to the load parameter have been calculated for a preset load level after the bieigenvalue curve is established the critical load can be computed by setting its first derivative equal to zero the effectiveness of the present method is demonstrated in the numerical study

divergence and flutter of a cantilever rod with an intermediate spring support abstract the equation of motion in matrix form of a cantilever euler beam subject to a tipconcentrated follower force at the free end is formulated based on the lagrangian approach and the assumed mode method the non conservative nature of the system is identified by the non symmetric matrix in the equation of motion the beam is assumed to rest on an intermediate spring support jump phenomenon for the critical follower load is found to occur for both variations in the support location as well as the stiffness of the spring support detailed history of the changes in the load frequency diagram due to variation in the support location and the stiffness of the spring support is presented to explain the occurrence of the jump phenomenon an interesting finding is that the rod is found to be extremely unstable for a certain combination of spring stiffness and support location for a cantilever rod

stability analysis of stochastically parametered nonconservative columns nonconservatively loaded columns which have stochastically distributed material property values and stochastic loadings in space are considered young s modulus and mass density are treated to constitute random fields the support stiffness coefficient and tip follower load are considered to be random variables the fluctuations of external and distributed loadings are considered to constitute a random field the variational formulation is adopted to get the differential equation and boundary conditions the non self adjoint operators are used at the boundary of the regularity domain the statistics of vibration frequencies and modes are obtained using the standard perturbation method by treating the fluctuations to be stochastic perturbations linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed bounds for the statistics of vibration frequencies are obtained the critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought then the frequency equation is employed to transform the eigenvalue statistics to critical load statistics specialization of the general procedure to beck leipholz and pfluger columns is carried out for pfluger column nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics

even more with the lemke complementarity algorithm this note presents a new termination result for the lemke linear complementarity algorithm that unifies two previous results special cases include linear complementarity problems satisfying the evers condition and those whosem matrix is copositive plus

the linear complementarity problem under asymptotic analysis in this work we study the classical linear complementarity problem lcp by describing the asymptotic behavior of the approximate solutions to its variational inequality formulation thus some properties satisfied by the directions which are limits of the normalized unbounded approximate solutions will be established based on this analysis various equivalent conditions guaranteeing the existence of solutions to lcp are given in particular the sufficient condition of gowda and pang expressed in terms of the solutions to augmented linear complementarity problems is written in a way that is more easily verifiable our approach allows us to deal with garca a matrices semimonotone copositive q pseudomonotone matrices among others in a unified framework furthermore we introduce a larger class of matrices for which many of the results including a sensitivity one due to gowda and pang are still valid in addition some conditions ensuring the boundedness of the solution set are also provided and some estimates for the asymptotic cone of the solution set for different classes of matrices are given as well hence the present approach sheds new light and offers an alternative to view classical results

semidirect products of semigroups two alternative characterizations of semidirect products of semigroups are given characterizations are provided of such products that are groups regular semigroups and inverse semigroups respectively

on strongly degenerate complementary cones and solution rays in this paper we show that ifa is a matrix in the class of matricese d for ad r n d 0 introduced by garcia then the boundary of the set ofq r n for which the linear complementarity problem q a has a solution is equal to the union of all strongly degenerate cones of i a this is a generalization of a similar result for copositive plus matrices observed by cottle we also study some related questions

notes on sufficient matrices abstract we give some constructive characterizations for sufficient matrices and present some matrix classes whose elements are identified as column sufficient matrices in particular we give the structure of column row sufficient matrices which leads to efficient testing methods for column row sufficiency

total dual integrality and integral solutions of the linear complementarity problem abstract this paper deals with the problem of finding an integer solution to a linear complementarity problem lcp chandrasekaran et al 1 introduced the class i of integral matrices for which the corresponding lcp has an integer solution for every integral vector q for which it has a solution and proved that for some well known matrix classes principal unimodularity forms a necessary and sufficient condition for inclusion in the class i in this paper we identify some more well known matrix classes for which principal unimodularity forms a necessary and sufficient condition for inclusion in the class i the concept of total dual integrality is utilized to obtain a necessary and sufficient condition for existence of an integer solution to lcp with a hidden k matrix we interconnect the concept of hilbert basis with principal unimodularity of a matrix and the corresponding complementary cones a necessary and sufficient condition is given for the existence of an integer solution of a linear fractional programming problem by using its lcp formulation

on a subclass of p0 abstract in 1966 fiedler and ptak wrote the first systematic investigation of the matrix class p 0 consisting of all real square matrices with nonnegative principal minors in this note we focus on a particular subclass of p 0 that has arisen within the field of linear complementarity theory namely the class su of sufficient matrices our principal result is that su contains another class p we conjecture that the latter two classes are in fact the same

on the classes of fully copositive and fully semimonotone matrices abstract in this paper we consider the class c 0 f of fully copositive and the class e 0 f of fully semimonotone matrices we show that c 0 f matrices with positive diagonal entries are column sufficient we settle a conjecture made by murthy and parthasarathy to the effect that a c 0 f q 0 matrix is positive semidefinite by providing a counterexample we finally consider e 0 f matrices introduced by cottle and stone math program 27 1983 191 213 and partially address stone s conjecture to the effect that e 0 f q 0 p 0 by showing that e 0 f d c matrices are p 0 where d c is the doverspike class of matrices

the linear complimentarity problem sufficient matrices and the criss cross method specially structured linear complementarity problems lcps and their solution by the criss cross method are examined the criss cross method is known to be finite for lcps with positive semidefinite bisymmetric matrices and with p matrices it is also a simple finite algorithm for oriented matroid programming problems recently cottle pang and venkateswaran identified the class of column row sufficient matrices they showed that sufficient matrices are a common generalization of p and psd matrices cottle also showed that the principal pivoting method with a clever modification can be applied to row sufficient lcps in this paper the finiteness of the criss cross method for sufficient lcps is proved further it is shown that a matrix is sufficient if and only if the criss cross method processes all the lcps defined by this matrix and all the lcps defined by the transpose of this matrix and any parameter vector

structure properties of w matrices abstract we continue an investigation of the class w of real square matrices a matrix belongs to w if and only if certain pairs of its complementary cones intersect in the zero vector only we show that a w matrix with no zero diagonal entries is a p 0 matrix each principal minor is nonnegative and a w matrix with no nonzero diagonal entries is a nonnegative matrix which either is monomial or has a zero column lastly we show how these two results impose certain necessary conditions on the structure of a w matrix

global stabilty analysis of a classical non conservative system under a follower load abstract the bifurcations critical conditions and global stability of the classical two degree of freedom ziegler s dissipative model under a partial follower load are thoroughly discussed with the aid of a complete non linear dynamic analysis attention is mainly focused on the range of values of the non conservativeness loading parameter for which adjacent equilibria do not exist various characteristic findings are established by studying the nature of the jacobian matrix eigenvalues associated with the above non linear autonomous dissipative system it is found that the system exhibits stable hopf bifurcations global stability for the entire region of non adjacent equilibria while the classical linear stability analysis leads to flutter instability local instability moreover in an explicit general form the significant effect of damping on the critical dynamic bifurcation load is established on the basis of the latter the critical loads for the case of vanishing damping are found to be completely different from those of the classical local stability analysis all findings of this analysis are checked against numerical solution of the equations of motion

vibration and stability of a cantilever column subject to a follower force passing through a fixed point abstract the paper describes the stability and natural vibration of column loaded by a force passing through a fixed point it is proved that the system is conservative and its loss of stability occurs via divergence on the other hand a change in modes occurring along the fundamental eigencurve which modifies its slope from positive to negative with the increasing load is found theoretically and confirmed by the modal analysis for that reason the system is proposed to be called the divergence pseudo flutter system experimental results concerning the natural vibration frequency agreed well with the numerical ones

criteria for occurrence of flutter instability before buckling in nonconservative dissipative systems the occurrence of flutter instability through a hopf bifurcation before static buckling in regions of divergence in nonconservative nonself adjoint dissipative systems is thoroughly discussed using a qualitative analysis this region where both ziegler s and static criterion may fail to predict the actual critical load is defined via two values bounds of the nonconservativeness loading parameter the upper bound corresponds to 0 5 being invariant with respect to all other parameters whereas the lower bound corresponds to a double critical divergence point beyond which there are no adjacent equilibria the location of the last point lying always between 0 and 0 5 depends on a stiffness parameter it is also found that the region of nonexistence of adjacent equilibria becomes maximum minimum when the double critical point corresponds to 0 5 0 the interaction of vanishing damping with various parameters leads to new phenomena related to point and periodic attractors as well as to a new type of dynamic bifurcation

the role of prestressing in establishing regions of instability for a compound column under conservative or non conservative load the influence of prestressing of a non linear two member column on its natural vibration and stability is studied the perturbation method is used for solving the problem regions of divergence and flutter instabilities for a column has been determined on the basis of courses of eigencurves in relation to prestress rate discontinuities of the critical force have been observed for the border value of the prestress leading to the instability of the column without the external load although each prestress lowers the critical force it can be used for passive vibration control

the linear complementarity problem and a subclass of fully semimonotone matrices abstract in this paper we investigate a subclass w of the n n real matrices a matrix m belongs to w if and only if certain pairs of its complementary cones intersect only in the zero vector we show that w u where u is the class of matrices m for which lcp q m the linear complementarity problem has a unique solution whenever q belongs in the interior of the union of its complementary cones membership in w can be established by solving 2n 1 systems of linear equations finally several sufficient conditions are given on a matrix in w so that it possesses nonnegative principal minors

the influence of an intermediate support on the stability behaviour of cantilever beams subjected to follower forces abstract a non uniform undamped beam which is simply supported at one end resting on an elastically flexible support at an intermediate abscissa q is examined the beam is subjected to a generic set of follower forces along the axis so that beck leipholz and hauger problems can be easily recovered as particular cases in all these systems a location for the intermediate support exists which corresponds to passage from flutter to divergence

free vibrations and the stability of a geometrically non linear column loaded by a follower force directed towards the positive pole abstract a slender system built as a geometrically non linear system and subjected to specific load by a follower force directed towards the positive pole is discussed the load is induced by heads composed of circular profile elements the problem of stability and free vibration was formulated on the basis of hamilton s principle and then owing to its non linearity solved using the straightforward expansion method this paper provides example results of numerical computations concerning the influence of selected parameters characterizing the considered column including pre stressing on the stability and free vibration the accuracy of the adopted mathematical model is also proved on the basis of experimental studies

flutter and divergence instability of nonconservative beams and plates for a conservative system the only possible instability is of divergence type for a nonconservative system however instability can be of divergence flutter or both depending on the amount of nonconservativeness in this paper we study the instability of a cantilevered beam and a simply supported plate subjected to a combination of fixed and follower forces a nonconservative parameter is introduced to provide all possible combinations of these forces for the beam instability changes from divergence to flutter at a critical value of this parameter for values of the parameter above the critical value the flutter instability remains as the only instability pattern in contrast to implications in the literature for the plate the instability is governed by flutter for a certain range of the nonconservative parameter even though divergence instability still exists the range depends on the geometry aspect ratio and material property poisson s ratio of the plate

principal pivot transforms of some classes of matrices in this paper we study and characterize various classes of matrices that are defined based on principal pivot transforms we show that matrices in these classes have nonnegative principal minors

bifurcations in a two degree of freedom elastic system with follower forces abstract the stability and bifurcations of a two degree of freedom elastic system subjected to follower forces are studied attention is mainly concentrated on local behavior small amplitude motions about a centre equilibrium for the parameter values in the neighborhood of some point on the stability boundaries by using centre manifold theory and some codimension two bifurcations it is shown that a number of distinct bifurcations may occur in such a system according to the ratio of two damping coefficients numerical integrations of the full equations of motion have been performed to confirm the analytical aspects of the local solutions as well as to understand some aspects of the global behavior of the solutions

point attractors and dynamic buckling of autonomous systems under step loading abstract in this study the dynamic response of autonomous mainly dissipative multi d o f systems under step loading is re examined based on the geometrical point of view of the theory of non linear dynamical systems and the rapidly developing theory of attractors the investigation focuses on limit point like systems with snapping as their salient feature it is found that dynamic buckling through a saddle or its neighborhood although leading to a large amplitude motion may be associated with a point attractor response on the pre buckling fixed point depending on the amount of damping considered in close conjunction with the motion channel geometry and the total potential characteristics of all stable and complementary equilibria for such systems only a straightforward fully non linear dynamic analysis can provide valid information on the global dynamic stability since the shape of the total potential hypersurface may become very complicated rendering energy aspects practically not applicable a 2 d o f model simulating an asymmetric suspended roof is comprehensively analyzed to capture the above findings and a parametric investigation is carried out revealing a variety of new dynamic response types and leading to a more accurate insight of the stability of motion in the large

bifurcations associated with a double zero and a pair of pure imaginary eigenvalues interactive static and dynamic bifurcations associated with a nonlinear autonomous system and the stability properties of various solutions are explored attention is focused on the vicinity of a compound critical point where the jacobian of the system exhibits a double zero eigenvalue of index one and a pair of pure imaginary eigenvalues the system under consideration has three independent parameters and depending on the route followed in the parameter space the system may exhibit static bifurcations hopf bifurcations secondary hopf bifurcations and bifurcations into two or three dimensional tori the general analysis is based on a perturbation method which combines an intrinsic harmonic balancing technique with a certain unification procedure this approach leads to bifurcation equations and simplified differential equations governing the local dynamics in the vicinity of the compound critical point a control system is analyzed for illustration

finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading a nonlinear finite element analysis of elastic structures which can be studied by a 3d beam theory subjected to conservative as well as to nonconservative forces is presented the stability behaviour of the system is studied by means of an eigenvalue analysis the stiffness matrix of the eigenvalue problem is asymmetric i e non self adjoint system the flutter and divergence modes of instability as well as the values of the critical load are identified for a number of numerical examples belonging to the benchmark tests proposed by nafems 1990 the results demonstrate the reliability of this finite element formulation in particular the effect of damping on the stability behaviour of such structures is investigated and the destabilizing effect of small damping is underlined finally the need to define a number of benchmark tests for nonlinear nonconservative analyses in presence of damping is included

the existence of regions of divergence instability for nonconservative systems under follower forces abstract in this investigation the existence of regions of divergence instability for an elastically restrained column under a follower compressive force at its end is discussed necessary and sufficient conditions for the existence of regions of divergence instability are established the boundary between flutter and divergence instability passes always through a double critical point where the first and second static buckling eigenmodes coincide the eigenvalues buckling loads of nonself adjoint problems of this type are positive and distinct for the entire region of divergence instability except at its boundary where the first and second eigenvalues coincide at this boundary where the buckling mechanism changes from divergence to flutter and vice versa a sudden increase in the critical load occurs with the flutter load always being higher than the corresponding divergence load

the structure of q inverse semigroups abstract as a generalization of quasi inverse semigroups in the class of regular semigroups we consider the q inverse semigroups which are idempotent connected abundant semigroups with regular bands in this paper a construction theorem of q inverse semigroups is given by using the wreath product of some semigroups it is proved that a semigroup s is a q inverse semigroup if and only if s is a spined product of an l inverse semigroup and an r inverse semigroup thus the structure of q inverse semigroups is fully described and the results on quasi inverse semigroups obtained by m yamada in 1973 are extended and amplified

on some classes of linear complementarity problems with matrices of order n and rank n 1 in this paper we generalize a fundamental result observed by b c eaves on the nature of solutions constructed by lemke s algorithm applied to solve the linear complementarity problem q m initiating it with the positive vector d rn we use this generalization and identify two subclasses of the class of n n matrices m of rank n 1 for which the set of q rn such that the lcp q m has a solution is convex we also present algorithms to compute a solution to q m if one exists for these classes of matrices