sharp estimates for solutions of multi bubbles in compact riemann surfaces in this paper we consider a sequence of multibubble solutions u k of the equation 0 1 0 u k k he uk f m he u k d 1 0 in m where h is a c 2 positive function in a compact riemann surface m and k is a constant satisfying lim k k 8m for some positive integer m 1 we prove among other things that k 8m 2 m m j 1h 1 p k j 0 log h p k j 8m 2k p k j k j e k j o e k j where p k j are centers of the bubbles of u k and k j are the local maxima of u k after adding a constant this yields a uniform bound of solutions as k converges to 8m from below provided that 0 log h p k j 8m 2k p k j 0 it generalizes a previous result due to ding jost li and wang 18 and nolasco and tarantello 31 which says that any sequence of minimizers u k is uniformly bounded if k 0 for any maximum point p of the sum of 2 log h and the regular part of the green function where k is the gaussian curvature of m the analytic work of this paper is the first step toward computing the topological degree of 0 1 which was initiated by li 24

a variational principle for finite planar deformation of straight slender elastic beams abstract the objective of this paper is to present a finite element formulation for finite deformation analysis of a slender straight elastic in plane beam the formulation is based on a modified hu washizu variational principle in which exact nonlinear kinematic equations are taken into account only the rotation in the interior of an element needs to be approximated thus the ambiguities concerning the order of polynomial approximations for different field variables e g longitudinal and lateral displacements are avoided the euler lagrange equations of this principle are among others exact kinematic and equilibrium conditions for the beam the solution capabilities are illustrated with numerical examples two different finite elements are examined with 3rd order interpolation polynomials for the rotation and with 5th order polynomials excellent convergence and accuracy of both elements is demonstrated the results indicate that the accuracy of the present elements is not notably influenced by the length of the element and the order of numerical integration if it is greater than a minimal value only one load step was sufficient in calculations to achieve the results

statistical mechanics of classical particles with logarithmic interactions the inhomogeneous mean field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions the results apply to various physical models of translation invariant plasmas gravitating systems as well as to planar fluid vortex motion for attractive interactions a critical behavior occurs which can be classified as an extreme case of a second order phase transition to include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic geometric mean inequality the method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions in addition it also provides us with a new proof of the trudinger moser inequality known from differential geometry in its sharp form

mean field equation of liouville type with singular data topological degree we consider the following mean field equation gv h ev mh ev 1 4 j 1n j qj 1 on m where m is a compact riemann surface with volume 1 h is a positive c1 function on m and and j are constants satisfying j 1 in this paper we derive the topological degree counting formula for noncritical values of we also give several applications of this formula including existence of the curvature 1 metric with conic singularities doubly periodic solutions of electroweak theory and a special case of self gravitating strings 2015 wiley periodicals inc

profile of blow up solutions to the exponential neumann boundary value problem abstract arising in problems of prescribed gaussian and geodesic curvatures we consider a blow up sequence of solutions to the following exponential neumann boundary value problem u n v n x x 2 n e 2 u n in b r u n h n x x n e u n on b r r 2 where denotes the outer unit normal vector to b r r 2 and n 1 we establish a uniform estimate for this blow up sequence of solutions near an isolated singular blow up point we treat two cases n and n separately and obtain two different uniform pointwise estimates

explicit free floating beam element summary a two node free floating beam element capable of undergoing arbitrary large displacements and finite rotations is presented in explicit form the configuration of the beam in three dimensional space is represented by the global components of the position of the beam nodes and an associated set of convected base vectors directors the local constitutive stiffness is derived from the complementary energy of a set of six independent deformation modes each corresponding to an equilibrium state of constant internal force or moment the deformation modes are characterized by generalized strains formed via scalar products of the element related vectors this leads to a homogeneous quadratic strain definition in terms of the generalized displacements whereby the elastic energy becomes at most bi quadratic additionally the use of independent equilibrium modes to set up the element stiffness avoids interpolation of kinematic variables resulting in a locking free formulation in terms of three explicit matrices a set of classic benchmark examples illustrates excellent performance of the explicit beam element copyright 2014 john wiley sons ltd

existence and multiplicity result for the singular toda system abstract we consider the toda system on a compact surface g u 1 2 1 h 1 e u 1 h 1 e u 1 d v g 1 2 h 2 e u 2 h 2 e u 2 d v g 1 4 j 1 j 1 j p j 1 u 2 2 2 h 2 e u 2 h 2 e u 2 d v g 1 1 h 1 e u 1 h 1 e u 1 d v g 1 4 j 1 j 2 j p j 1 where h i are smooth positive functions i are positive real parameters p j are given points on and i j are numbers greater than 1 we give existence and multiplicity results using variational and morse theoretical methods it is the first existence result when some of the i j s are allowed to be negative

an improved geometric inequality via vanishing moments with applications to singular liouville equations we consider a class of singular liouville equations on compact surfaces motivated by the study of electroweak and self dual chern simons theories the gaussian curvature prescription with conical singularities and onsager s description of turbulence we analyse the problem of existence variationally and show how the angular distribution of the conformal volume near the singularities may lead to improvements in the moser trudinger inequality and in turn to lower bounds on the euler lagrange functional we then discuss existence and non existence results

extended variational formulations and f e models for nonlinear beams under nonconservative loading abstract for nonconservative mechanical systems classical variational principles do not hold true hence the principle of incremental virtual work is usually taken as a convenient foundation for finite element solution methods 2 8 9 recent results on the so called inverse problem of calculus of variations however lead to extended variational formulations which can be provided even for nonconservative systems in the present paper this approach is used for the particular case of a nonlinear beam subjected to a co planar follower static loading suitable finite element models are deduced from the extended variational principle and their numerical performance is assessed by means of some meaningful examples

constant q curvature metrics in arbitrary dimension working in a given conformal class we prove existence of constant q curvature metrics on compact manifolds of arbitrary dimension under generic assumptions the problem is equivalent to solving a nth order non linear elliptic differential or integral equation with variational structure where n is the dimension of the manifold since the corresponding euler functional is in general unbounded from above and below we use critical point theory jointly with a compactness result for the above equation

the two dimensional lazer mckenna conjecture for an exponential nonlinearity abstract we consider the problem of ambrosetti prodi type u e u s 1 h x in u 0 on where is a bounded smooth domain in r 2 1 is a positive first eigenfunction of the laplacian under dirichlet boundary conditions and h c 0 we prove that given k 1 this problem has at least k solutions for all sufficiently large s 0 which answers affirmatively a conjecture by lazer and mckenna a c lazer p j mckenna on the number of solutions of a nonlinear dirichlet problem j math anal appl 84 1981 282 294 for this case the solutions found exhibit multiple concentration behavior around maxima of 1 as s

asymptotic behavior of condensate solutions in the chern simons higgs theory we study the asymptotic behavior of condensate solutions in the chern simons higgs model as the chern simons coupling parameter tends to zero using the variational method we prove that there exist condensate solutions which show concentration phenomena

scalar curvatures on sn soit m n g une variete de riemann compacte de dimension n 3 et r x une fonction lisse sur m n on etudie si r x peut etre la courbure scalaire d une metrique g qui est conforme point par point a la metrique originale g

existence and non existence results for the su 3 singular toda system on compact surfaces we consider the su 3 singular toda system on a compact surface g u1 2 1 h1eu1 h1eu1dvg 1 2 h2eu2 h2eu2dvg 1 4 m 1m 1m pm 1 u2 2 2 h2eu2 h2eu2dvg 1 1 h1eu1 h1eu1dvg 1 4 m 1m 2m pm 1 where hi are smooth positive functions on i r pm and im 1 we give both existence and non existence results under some conditions on the parameters i and im existence results are obtained using variational methods which involve a geometric inequality of new type non existence results are obtained using blow up analysis and localized poho aev type identities

concentration phenomena for a fourth order equation with exponential growth the radial case we let be a smooth bounded domain of r4 and a sequence of functions vk k n c0 such that limk vk 1 in cloc0 we consider a sequence of functions uk k n c4 such that 2uk vke4uk in for all k n we address in this paper the question of the asymptotic behavior of the uk s when k the corresponding problem in dimension 2 was considered by brezis and merle and li and shafrir among others where a blow up phenomenon was described and where a quantization of this blow up was proved surprisingly as shown by adimurthi struwe and the author in adimurthi f robert and m struwe concentration phenomena for liouville equations in dimension four j eur math soc in press available on http www math unice fr frobert a similar quantization phenomenon does not hold for this fourth order problem assuming that the uk s are radially symmetrical we push further the analysis of the mentioned work we prove that there are exactly three types of blow up and we describe each type in a very detailed way

the bandwidth minimization problem for cyclic caterpillars with hair length 1 is np complete in this paper we show that the bandwidth minimization problem remains np complete for cyclic caterpillars with hair length 1 cyclic caterpillars with hair length 1 are graphs in which the removal of all pendant vertices results in a simple cycle

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

blow up phenomena for the liouville equation with a singular source of integer multiplicity abstract we are concerned with the existence of blowing up solutions to the following boundary value problem u a x e u 4 n 0 in u 0 on where is a smooth and bounded domain in r 2 such that 0 a x is a positive smooth function n is a positive integer and 0 is a small parameter here 0 defines the dirac measure with pole at 0 we find conditions on the function a and on the domain under which there exists a solution u blowing up at 0 and satisfying a x e u 8 n 1 as 0

rigid body considerations for non linear finite element analysis the purpose of the paper is to demonstrate how the concept of rigid body motions can be employed to derive the external stiffness matrix for an initially stressed finite element

a simple fem formulation for large deflection 2d frame analysis based on position description this study presents a simple formulation to treat large deflections by the finite element method the proposed formulation does not use the displacement concept it considers position as the main unknown variable of the problem the strain determination is performed directly from the proposed position concept a non dimensional space is created and relative curvature and fibers length are calculated for both reference and deformed configurations and used to directly compute the strain energy at general points this procedure is very simple and presents good results as shown in the example section the simplicity of the resulting formulation may be considered as its main attribute two dimensional frame problems are analyzed by the proposed formulation

numerical results from large deflection beam and frame problems analysed by means of elliptic integrals numerical evaluations of elliptic integral solutions of some large deflection beam and frame problems are presented the values are given in tabular form with up to six significant figures the numerical technique used for evaluating the elliptic integrals is described

convergence rate location and z2 condition for fully bubbling solutions to su n 1 toda systems abstract it is well known that the study of su n 1 toda systems is important not only to chern simons models in physics but also to the understanding of holomorphic curves harmonic sequences or harmonic maps from riemann surfaces to c p n one major goal in the study of su n 1 toda system on riemann surfaces is to completely understand the asymptotic behavior of fully bubbling solutions in this article we use a unified approach to study fully bubbling solutions to general su n 1 toda systems and we prove three major sharp estimates important for constructing bubbling solutions the closeness of blowup solutions to entire solutions the location of blowup points and a z 2 condition

the liouville equation with singular data a concentration compactness principle via a local representation formula abstract for a bounded domain r 2 we establish a concentration compactness result for the following class of singular liouville equations u e u 4 j 1 m j p j in where pj j 0 and pj denotes the dirac measure with pole at point pj j 1 m our result extends brezis merle s theorem comm partial differential equations16 1991 1223 1253 concerning solution sequences for the regular liouville equation where the dirac measures are replaced by lp data p 1 in some particular case we also derive a mass quantization principle in the same spirit of li shafrir indiana univ math j 43 1994 1255 1270 our analysis was motivated by the study of the bogomol nyi equations arising in several self dual gauge field theories of interest in theoretical physics such as the chern simons theory self dual chern simons theories lecture notes in physics vol 36 springer verlag berlin 1995 and the electroweak theory selected papers on gauge theory of weak and electromagnetic interactions world scientific singapore

conformal deformation of metrics on s 2 soit d un domaine lisse de s 2 et k une fonction lisse definie sur d alors pour que le probleme aux limites de neumann u k exp 2u 1 sur d u n 0 sur d ait une solution u on a a quand aire d max x d k x 0

energy quantization for a singular super liouville boundary value problem in this paper we develop the blow up analysis and establish the energy quantization for solutions to super liouville type equations on riemann surfaces with conical singularities at the boundary in other problems in geometric analysis the blow up analysis usually strongly utilizes conformal invariance which yields a noether current from which strong estimates can be derived here however the conical singularities destroy conformal invariance therefore we develop another more general method that uses the vanishing of the pohozaev constant for such solutions to deduce the removability of boundary singularities

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

asymptotic blow up analysis for singular liouville type equations with applications abstract we generalize the pointwise estimates obtained in 2 19 and 34 concerning blow up solutions of the liouville type equation u x 2 w x e u in with r 2 open and bounded 1 and w any lipschitz continuous function which satisfies 0 a w b we focus to the case left open in 2 and 34 where the parameter n whose analysis is much more involved as we need to resolve the difficulty of a genuinely non radial behaviour of blow up solutions in the worst situation there is no chance in general to resolve the profile in the form of a solution of a liouville equation in r 2 instead we need to adopt iterated blow up arguments next we refine our blow up analysis to cover a class of planar liouville type problems see 1 27 1 28 below arising from the study of cosmic strings cfr 28 35 in this context we are able to distinguish between a single blow up radial profile and the case of multiple blow up profiles typical of non radial solutions as a consequence we obtain a radial symmetry result which is interesting in itself but also contributes towards the sharp solvability issue for the planar problem 1 27 1 28

finding the minimum bandwidth of an interval graph abstract an assignment of unique integers to the vertices of a graph is called a linear layout the bandwidth minimization problem bandwidth is the following given a graph g v e and an integer k determine whether there exists a linear layout of g such that the maximum difference between adjacent vertices is bounded by k interval graphs are the intersection graphs of a family of intervals of the real line bandwidth remains np complete even when restricted to special subclasses of trees we show that bandwidth can be solved in time o n2 for interval graphs moreover for a given interval graph a linear layout with minimum bandwidth can be constructed in time o n2logn as a by product we get that this construction can be done for proper interval graphs in time o nlog n m

blowing up solutions to an anisotropic emden fowler equation with a singular source we consider the following anisotropic emden fowler equation with a singular source div a x v e2a x ev 4 a p pin v 0on where p r2 constant 0 n a x is a positive smooth function and p denotes the dirac measure with pole at point p if p is a local maximum point of a x we construct a family of solutions ve with arbitrary m bubbles concentrating at p and the quantity e2 a x eve 8 m 1 a p

convected systems for curved structural elements this paper presents a new approach to the use of the updated lagrangian formulation with convected systems the development of this new method is similar to the updated lagrangian formulation presented by bathe et al 4 the main difference is that here the tensors are written in their components in the curvilinear convected system while bathe ramm and wilson employ cartesian components a special form of the natural approach5 is also introduced in this formulation to simplify the element computations the matrices of a two dimensional curved beam column element are derived as an example of this new formulation finally a numerical evaluation is performed to evaluate critically the new curved element and the method proposed here

bubbling solutions for the liouville equation with a singular source non simple blow up abstract we are concerned with the existence of blowing up solutions to the following boundary value problem u e u 4 n 0 in u 0 on where is a smooth and bounded domain in r 2 such that 0 n is a positive number close to an integer n n 1 from the right side 0 defines the dirac measure with pole at 0 and 0 is a small parameter we assume that is n 1 symmetric and the regular part of the green s function satisfies a nondegeneracy condition both assumptions are verified if is the unit ball and we find a solution which exhibits a non simple blow up profile as 0

on a class of elliptic problems in r symmetry and uniqueness results in the plane r 2 we classify all solutions for an elliptic problem of liouville type involving a radial weight function as a consequence we clarify the origin of the non radially symmetric solutions for the given problem as established by chanillo and kiessling for a more general class of liouville type problems we show that rather than radial symmetry the solutions always inherit the invariance of the problem under inversion with respect to suitable circles this symmetry result is derived with the help of a shrinking sphere method

nontopological n vortex condensates for the self dual chern simons theory we prove the existence of nontopological n vortex solutions for an arbitrary number n of vortex points for the self dual chern simons higgs theory with t hooft periodic boundary conditions we use a shadowing type lemma to glue together any number of single vortices obtained as a perturbation of a radially symmetric entire solution of the liouville equation 2003 wiley periodicals inc

comparison of two linearization schemes for the nonlinear bending problem of a beam pinned at both ends the nonlinear bending problem of a constant cross section simply supported beam pinned at both ends and subject to a uniformly distributed load q x is analyzed in detail the numerical integration of the two point boundary value problem bvp derived for the nonlinear timoshenko beam is tackled through two different linearization schemes the multi step transversal linearization mtrl and the multi step tangential linearization mtnl proposed by viswanath and roy 2007 the fundamentals of these linearization techniques are to replace the nonlinear part of the governing odes through a set of conditionally linearized ode systems at the nodal grid points along the neutral axis ensuring the intersection between the solution manifolds transversally in the mtrl and tangentially in the mtnl in this paper the solution values are determined at grid points by means of a centered finite differences method with multipoint linear constraints keller 1969 and a simple iterative strategy the analytical solution for this kind of bending problem including the extensional effects can be worked out by integration of the governing two point bvp equations monleon et al 2008 finally the comparison of analytical and numerical results shows the better ability of mtnl with the proposed iterative strategy to reproduce the theoretical behavior of the beam for each load step because the restraint of equating derivatives in mtnl leads to further closeness between solution paths of the governing odes and the linearized ones in comparison with mtrl this result is opposed to the conclusion reached in viswanath and roy 2007 where the relative errors produced by mtrl are said to be smaller than the mtnl ones for the simply supported beam and the tip loaded cantilever beam problems

uniqueness and symmetry results for solutions of a mean field equation on 2 via a new bubbling phenomenon motivated by the study of gauge field vortices we consider a mean field equation on the standard two sphere involving a dirac distribution supported at a point p of s 2 as needed for the applications we show that solutions concentrate exactly at p for some limiting value of a given parameter we use this fact to obtain symmetry about the axis op and uniqueness property for the solution the presence of the dirac measure makes such a task particularly delicate indeed we need to rule out the possibility that after blow up in a suitable scale the solution sequence may admit a double peak profile described in terms of appropriate limiting problems for instance we need to account for the presence of non axially symmetric solutions in such limiting problems in this process we establish a symmetry result about a maximal circle through p and its antipodal point p that applies to more general situations where the full axial symmetry cannot be expected

a sup inf type inequality for conformal metrics on riemann surfaces with conical singularities abstract a sup inf type inequality is proved for the regular part of conformal factors for riemannian metrics on surfaces with conical singularities of positive order 0 the proof is based on the explicit representation formula for solutions of the singular liouville equation and generalizes to the singular case an argument by i shafrir

on multivortices in the electroweak theory ii existence of bogomol nyi solutions in ℝ2 in this paper we study the bogomol nyi equations of the electroweak theory in the full plane we will show that for any distribution of the vortices there exists a two parameter family of gauge distinct solutions moreover we also establish some sharp decay rate estimates for these solutions

a sup inf inequality for some nonlinear elliptic equations involving exponential nonlinearities let u be a solution of the equation u v x eu in a domain r2 where 0 a v b and v is lipschitz continuous we prove that sup u can be controlled in terms of inf u more precisely supku inf u c a b k v l for any compact subset k this extends an earlier result of shafrir who obtained a similar conclusion when v 1

multi step transversal and tangential linearization methods applied to a class of nonlinear beam equations a novel and continuously parameterized form of multi step transversal linearization mtrl method is developed and numerically explored for solving nonlinear ordinary differential equations governing a class of boundary value problems bvps of relevance in structural mechanics a similar family of multi step tangential linearization mtnl methods is also developed and applied to such bvp s within the framework of mtrl and mtnl a bvp is treated as a constrained dynamical system i e a constrained initial value problem ivp while the mtrl requires the linearized solution manifold to transversally intersect the nonlinear solution manifold at a chosen set of points across the axis of the independent variable the essential difference of the present mtrl method from its previous version roy d kumar r 2005 a multistep transversal linearization mtl method in nonlinear structural dynamics j sound vib 17 829 852 is that it has the flexibility of treating nonlinear damping and stiffness terms as time variant damping and stiffness terms in the linearized system the resulting time variant linearized system is then solved using magnus characterization magnus w 1954 on the exponential solution of differential equations for a linear operator commun pure appl math 7 649 673 towards numerical illustrations response of a tip loaded cantilever beam elastica is first obtained next the response of a simply supported nonlinear timoshenko beam is obtained using a variationally correct vc model for the beam marur s prathap g 2005 nonlinear beam vibration problems and simplification in finite element model comput mech 35 5 352 360 the new model does not involve any simplifications commonly employed in the finite element formulations in order to ease the computation of nonlinear stiffness terms from nonlinear strain energy terms a comparison of results through mtrl and mtnl techniques consistently indicate a superior quality of approximations via the transversal linearization technique while the usage of tangential system matrices is common in nonlinear finite element practices it is demonstrated that the transversal version of linearization offers an easier and more general implementation requires no computations of directional derivatives and leads to a consistently higher level of numerical accuracy it is also observed that higher order versions of mtrl mtnl with lagrangian interpolations may not work satisfactorily and hence spline interpolations are suggested to overcome this problem

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

statistical mechanics approach to some problems in conformal geometry a weak law of large numbers is established for a sequence of systems of n classical point particles with logarithmic pair potential in rn or sn n n which are distributed according to the configurational microcanonical measure e h or rather some regularization thereof where h is the configurational hamiltonian and e the configurational energy when n with non extensive energy scaling e n2e the particle positions become i i d according to a self consistent boltzmann distribution respectively a superposition of such distributions the self consistency condition in n dimensions is some nonlinear elliptic pde of order n pseudo pde if n is odd with an exponential nonlinearity when n 2 this pde is known in statistical mechanics as poisson boltzmann equation with applications to point vortices 2d coulomb and magnetized plasmas and gravitational systems it is then also known in conformal differential geometry where it is the central equation in nirenberg s problem of prescribed gaussian curvature for constant gauss curvature it becomes liouville s equation which also appears in two dimensional so called quantum liouville gravity the pde for n 4 is paneitz equation and while it is not known in statistical mechanics it originated from a study of the conformal invariance of maxwell s electromagnetism and has made its appearance in some recent model of four dimensional quantum gravity in differential geometry the paneitz equation and its higher order n generalizations have applications in the conformal geometry of n manifolds but no physical applications yet for general n interestingly though all the paneitz equations have an interpretation in terms of statistical mechanics

equilibrium considerations of the updated lagrangian formulation of beam columns with natural concepts bathe and co workers 1 2 updated lagrangian formulation is reviewed for a two dimensional beam column element from this review a physical interpretation and properties are derived for the matrices of the method a variant of argyris and co workers 4 5 natural concept is introduced in the updated lagrangian formulation and a new method to derive element matrices arises a detailed derivation of the matrices of the twodimensional beam column element is presented to clarify further the ul formulations explicit expressions for these matrices computed with the use of symbolic manipulation 17 are also presented to illustrate the concepts discussed finally numerical results are shown to compare and evaluate different methods and matrices

weighted barycentric sets and singular liouville equations on compact surfaces given a closed surface we prove a general existence result for some elliptic pde with exponential nonlinearities and negative dirac deltas extending a theory recently obtained for the regular case this is done by global methods since the associated euler functional might be unbounded from below we define a new model space generalizing the so called space of formal barycenters and characterizing up to homotopy equivalence its low sublevels as a result the analytic problem is reduced to a topological one concerning the contractibility of this model space to this aim we prove a new functional inequality in the spirit of chen and li 1991 11 and then employ a min max scheme based on conical construction jointly with the blow up analysis in bartolucci and montefusco 2007 4 after bartolucci and tarantello 2002 brezis and merle 1991 and this study is motivated by abelian chern simons theory in self dual regime or from the problem of prescribing the gaussian curvature with conical singularities generalizing a problem raised in kazdan and warner 1974 24

non linear analysis of thin walled structures using plate elements this paper presents a simple and efficient rectangular thin plate element for elastic geometric non linear analysis of thin walled structures based on the updated lagrangian formulation and small strain hypothesis this element can accurately predict the non linear pre and post buckling load deflection paths of a plate structure using symbolic manipulation the linear and geometric stiffness matrices for the rectangular thin plate element are derived explicitly thereby eliminating the need for numerical integration the element contains 30 degrees of freedom d o f 14 d o f for the in plane membrane action and 16 d o f for the out of plane bending action several examples involving the large deflection behaviour of thin walled structures are presented to demonstrate the accuracy efficiency and versatility of the method

on finding the minimum bandwidth of interval graphs abstract let g v e be an interval graph with v n and e m an o n 2 log n algorithm was proposed in kratsch inform comput 74 140 158 1987 to find the bandwidth of g we show that this algorithm is wrong and provide a corrected version of the same also it was observed in 4 that the bandwidth of a proper interval graph can be computed in o n log n m time we show how this idea can be modified slightly to yield an o n m algorithm

a quantization property for blow up solutions of singular liouville type equations abstract motivated by the study of self dual vortices in gauge field theory cf vortices and monopoles birkhauser boston 1980 solitons in field theory and nonlinear analysis monographs in mathematics springer new york 2001 we consider a concentrating solution sequence u k satisfying u k z 2 k v k z e u k in b 1 z 2 k v k z e u k z 0 weakly in the sense of measures in b 1 where i k r k ii v k c 0 1 b 1 0 a v k b and v k a in b 1 we prove that necessarily 8 n 8 1 8 z the result is sharp as shown by explicit examples and should be compared with that obtained by li shafrir ind univ math j 43 4 1994 1255 concerning the situation where k 0 k n

the existence of non topological multivortex solutions in the relativistic self dual chern simons theory we construct a general type of multivortex solutions of the self duality equations the bogomol nyi equations of 2 1 dimensional relativistic chern simons model with the non topological boundary condition near infinity for such construction we use a perturbation argument around the explicit solutions of the liouville equation

an exponential time 2 approximation algorithm for bandwidth the bandwidth of a graph g on n vertices is the minimum b such that the vertices of g can be labeled from 1 to n such that the labels of every pair of adjacent vertices differ by at most b in this paper we present a 2 approximation algorithm for the bandwidth problem that takes worst case o 1 9797 n o 3 0 6 2 1 7 n time and uses polynomial space this improves both the previous best 2 and 3 approximation algorithms of cygan et al which have o 3 n and o 2 n worst case running time bounds respectively our algorithm is based on constructing bucket decompositions of the input graph a bucket decomposition partitions the vertex set of a graph into ordered sets called buckets of almost equal sizes such that all edges are either incident to vertices in the same bucket or to vertices in two consecutive buckets the idea is to find the smallest bucket size for which there exists a bucket decomposition the algorithm uses a divide and conquer strategy along with dynamic programming to achieve the improved time bound

multiple blow up solutions for an exponential nonlinearity with potential in r 2 abstract we study the following boundary value problem 0 1 u a x u p 1 e u p 0 u 0 in u 0 on where is a bounded domain in r 2 with smooth boundary 0 is a small parameter the function a x 0 is a smooth potential and the exponent p satisfies 0 p 2 we construct a family of solutions to problem 0 1 which blows up as 0 at some points of which stay outside the zero set of a x we relate the number of possible blow up points with the zero set of a x

sign changing blow up solutions for henon type elliptic equations with exponential nonlinearity abstract we study the existence of sign changing solutions with multiple concentration to the following boundary value problem u e 2 x 2 e u e u in u 0 on where 0 is a smooth bounded domain in r 2 containing the origin e 0 is a small parameter in particular we prove that if 1 then a nodal solution exists with a number of mixed positive and negative blow up points up to 4

topological degree for a mean field equation on riemann surfaces we consider the following mean field equations 0 1 where m is a compact riemann surface with volume 1 h is a positive continuous function on m is a real number 0 2 and where is a bounded smooth domain h is a c1 positive function on and based on our previous analytic work 14 we prove among other things that the degree counting formula for 0 1 is given by for 8m 8 m 1 2003 wiley periodicals inc

non linear spatial timoshenko beam element with curvature interpolation the paper presents a spatial timoshenko beam element with a total lagrangian formulation the element is based on curvature interpolation that is independent of the rigid body motion of the beam element and simplifies the formulation the section response is derived from plane section kinematics a two node beam element with constant curvature is relatively simple to formulate and exhibits excellent numerical convergence the formulation is extended to n node elements with polynomial curvature interpolation models with moderate discretization yield results of sufficient accuracy with a small number of iterations at each load step generalized second order stress resultants are identified and the section response takes into account non linear material behaviour green lagrange strains are expressed in terms of section curvature and shear distortion whose first and second variations are functions of node displacements and rotations a symmetric tangent stiffness matrix is derived by consistent linearization and an iterative acceleration method is used to improve numerical convergence for hyperelastic materials the comparison of analytical results with numerical simulations in the literature demonstrates the consistency accuracy and superior numerical performance of the proposed element copyright 2001 john wiley sons ltd

two dimensional euler flows with concentrated vorticities for a planar model of euler flows proposed by tur and yanovsky 2004 we construct a family of velocity fields w e for a fluid in a bounded region with concentrated vorticities e for e 0 small more precisely given a positive integer and a sufficiently small complex number a we find a family of stream functions e which solve the liouville equation with dirac mass source e e 2 e e 4 pa e in e 0 on for a suitable point p p a e the vorticities e e concentrate in the sense that 1 e 4 pa e 8 1 j 1 pa e a j 0 as e 0 j 1 where the satellites a 1 a 1 denote the complex 1 roots of a the point p a e lies close to a zero point of a vector field explicitly built upon derivatives of order 1 of the regular part of green s function of the domain

vanishing pohozaev constant and removability of singularities conformal invariance of two dimensional variational problems is a condition known to enable a blow up analysis of solutions and to deduce the removability of singularities in this paper we identify another condition that is not only sufficient but also necessary for such a removability of singularities this is the validity of the pohozaev identity in situations where such an identity fails to hold we introduce a new quantity called the pohozaev constant which on one hand measures the extent to which the pohozaev identity fails and on the other hand provides a characterization of the singular behavior of a solution at an isolated singularity we apply this to the blow up analysis for super liouville type equations on riemann surfaces with conical singularities because in the presence of such singularities conformal invariance no longer holds and a local singularity is in general non removable unless the pohozaev constant is vanishing

analytical treatment of equilibrium configurations of cantilever under terminal loads using jacobi elliptical functions abstract the paper provides an exact analytical solution for the equilibrium configurations of a cantilever rod subject to inclined force and tip moment acting on its free end the solution is given in terms of jacobi s elliptical functions and illustrated by several numerical examples and several graphical presentations of shapes of deformed cantilevers possible forms of the underlying elastica of a cantilever are discussed in detail and various simple formulas are given for calculating the characteristic dimensions of the elastica for the case when a cantilever is subject only to applied force three load conditions are discussed the follower load problem the load determination problem and the conservative load problem for all cases either a formula or an effective procedure for determining the solution is provided in particular a new efficient procedure is given to determine all possible equilibrium shapes in the case of the conservative load problem