conditional stability of solitary waves propagating in elastic rods abstract the problem of dynamic stability of solitary wave solutions of the equations describing bending oscillations of inextensible elastic rods is treated the governing equations describe sufficiently large displacements though we are restricted to small strains we show that under the condition of well posedness of the initial value problem in some specific sense the family of solitary wave solutions of the mentioned equations is stable for the planar elastic rod the framework of the analysis is largely based on the spectral properties of the linearized hamiltonian h we show that for planar oscillations h is positively semidefinite subject to a certain constraint which implies the stability

classical solutions of nonlinear beam equations existence and stabilization in this paper we consider the large amplitude planar motion of a cantilevered beam with a feedback force and or torque proportional and acting opposite to the velocity angular velocity respectively applied at the free end we derive nonlinear equations of motion for such a beam based upon certain natural geometric assumptions we then prove the existence of classical solutions for these equations and show that all classical solutions are uniformly exponentially stable

effect algebras with state operator state operators on convex effect algebras in particular effect algebras of unital jc algebras jw algebras and convex mv algebras are studied and their relations with conditional expectations in algebraic sense as well as in the sense of probability on mv algebras are shown

orthomodularity and quadratic transformations in probabilistic theories of physics a characterization of orthomodularity of a set of effects is given in terms of a triangle closedness of this set this leads to a simple probabilistic characterization of observables with a boolean range quadratic transformations on expectation functionals of observables are studied in order to investigate the derivability of the heisenberg inequality and the form of the lower bound of such an inequality for a pair of observables

spectral resolutions in dedekind σ complete l groups abstract using recent results on a generalized form of the loomis sikorski theorem a dvurecenskij loomis sikorski theorem for complete mv algebras and l groups j austral math soc ser a 68 2000 261 277 d mundici tensor product and the loomis sikorski theorem for mv algebras adv appl math 22 1999 227 248 it is shown that a unital dedekind complete l group is a compatible rickart comgroup in the sense of d j foulis d j foulis spectral resolutions in a rickart comgroup rep math phys 54 2004 229 250 in particular elements in unital dedekind complete l groups and consequently elements in mv algebras admit uniquely defined spectral resolutions similar to spectral resolutions of self adjoint operators a functional calculus and spectra of elements are considered in relation with the loomis sikorski representation by functions

sequential quantum measurements a quantum effect is an operator a on a complex hilbert space h that satisfies 0 a i we denote the set of quantum effects by e h the set of self adjoint projection operators on h corresponds to sharp effects and is denoted by p h we define the sequential product of a b e h by a b a1 2ba1 2 the main purpose of this article is to study some of the algebraic properties of the sequential product many of our results show that algebraic conditions on a b imply that a and b commute for the usual operator product for example if a b satisfies certain distributive or associative laws then ab ba moreover if a b p h then ab ba and a b b or b a b if and only if ab ba b a natural definition of stochastic independence is introduced and briefly studied

solving large scale linear multicommodity flow problems with an active set strategy and proximal accpm in this paper we propose to solve the linear multicommodity flow problem using a partial lagrangian relaxation the relaxation is restricted to the set of arcs that are likely to be saturated at the optimum this set is itself approximated by an active set strategy the partial lagrangian dual is solved with proximal accpm a variant of the analytic center cutting plane method the new approach makes it possible to solve huge problems when few arcs are saturated at the optimum as appears to be the case in many practical problems

multi multiplier ambient space formulations of constrained dynamical systems with an application to elastodynamics various formulations of the equations of motion for both finite and infinite dimensional constrained lagrangian dynamical systems are studied the different formulations correspond to different ways of enforcing constraints through multiplier fields all the formulations considered are posed on ambient spaces whose members are unrestricted by the need to satisfy constraint equations but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied the stability properties of the invariant set within its ambient space are shown to be different in each case we use the specific model problem of linearized incompressible elastodynamics to compare properties of three different ambient space formulations we establish the well posedness of one formulation in the particular case of a homogeneous isotropic body subject to specified tractions on its boundary

projected newton methods and optimization of multicommodity flows a superlinearly convergent newton like method for linearly constrained optimization problems is adapted for solution of multicommodity network flow problems of the type arising in communication and transportation networks we show that the method can be implemented approximately by making use of conjugate gradient iterations without the need to compute explicitly the hessian matrix preliminary computational results suggest that this type of method is capable of yielding highly accurate solutions of nonlinear multicommodity flow problems far more efficiently than any of the methods available at present

the norm 1 property of a quantum observable a normalized positive operator measure x e x has the norm 1 property if e x 1 whenever e x o this property reflects the fact that the measurement outcome probabilities for the values of such observables can be made arbitrarily close to one with suitable state preparations some general implications of the norm 1 property are investigated as case studies localization observables phase observables and phase space observables are considered

compatibility and decompositions of effects compatibility relations in effect algebras and their connections with refinements of the orthogonal partitions of unity are studied properties of blocks as maximal sets of compatible elements are discussed some special kinds of effect algebras are characterized using properties of compatibility using refinements an additional structure on the effect test spaces is introduced and used to a characterization of different types of effect algebras

spectral representation of infimum of bounded quantum observables in 2006 gudder math slovaca 56 573 2006 introduced a logic order on bounded quantum observable set s h in 2007 pulmannova and vincekova math slovaca 57 589 2007 proved that for each subset d of s h the infimum of d exists with respect to the logic order in 2008 liu and wu j math phys 49 073521 2008 found a representation of the infimum a b for a b s h and by using the limit methods they gave out a representation for the infimum of d but that representation is complicated in this paper we present a simpler spectral representation for the infimum of d with respect to the logic order

the proximal chebychev center cutting plane algorithm for convex additive functions the recent algorithm proposed by the author for convex nonsmooth optimization is tailored to the case where the objective function is additive we highlight aspects where this specialization differs from ignoring the structure of the objective function to assess the approach we consider two different nonlinear multicommodity flows applications in telecommunications including some comparison with a proximal bundle algorithm

generalized infimum and sequential product of quantum effects the quantum effects for a physical system can be described by the set e h of positive operators on a complex hilbert space h that are bounded above by the identity operator i for a b e h the operation of sequential product a b a1 2ba1 2 was proposed as a model for sequential quantum measurements a nice investigation of properties of the sequential product has been carried over gudder s and nagy g sequential quantum measurements j math phys 42 5212 2001 in this note we extend some results of this reference in particular a gap in the proof of theorem 3 2 in this reference is overcome in addition some properties of generalized infimum a b are studied

a note on the infimum problem of hilbert space effects the quantum effects for a physical system can be described by the set e h of positive operators on a complex hilbert space h that are bounded above by the identity operator i the infimum problem of hilbert space effects is to find under what condition the infimum a b exists for two quantum effects a and b e h the problem has been studied in different contexts by kadison gudder moreland and ando in this note using the method of the spectral theory of operators we give a affirmative answer of a conjecture of s gudder j math phys 37 2637 2642 1996 in addition some properties of generalized infimum a b were considered

lattice properties of quantum effects sufficient conditions for the existence of the infimum a b of two quantum effects a and b are given the existence of a b is characterized for commuting a and b with pure point spectrum properties of a generalized infimum and supremum are studied some previous finite dimensional commutative results are extended to the infinite dimensional and noncommutative case

a representation theorem of infimum of bounded quantum observables in 2006 gudder introduced a logic order on the bounded quantum observable set s h in 2007 pulmannova and vincekova proved that for each subset d of s h the infimum of d exists with respect to this logic order in this paper we present a representation theorem for the infimum of d

comment on a note on the infimum problem of hilbert space effects j math phys 47 102103 2006 we show that the two main results of the article j math phys 47 102103 2006 have very short proofs as direct consequences of the solution to the infimum problem for bounded non negative operators in a hilbert space given by t ando analytic and geometric inequalities and applications mathematical applications vol 478 kluwer academic dordrecht 1999 and a formula for the shorted operator obtained by h kosaki remarks on lebesgue type decomposition of positive operators j oper theory 11 137 143 1984

absolute continuity for operator valued completely positive maps on c algebras motivated by applicability to quantum operations quantum information and quantum probability we investigate the notion of absolute continuity for operator valued completely positive maps on c algebras previously introduced by parthasarathy in athens conference on applied probability and time series analysis i springer verlag berlin 1996 pp 34 54 we obtain an intrinsic definition of absolute continuity we show that the lebesgue decomposition defined by parthasarathy is the maximal one among all other lebesgue type decompositions and that this maximal lebesgue decomposition does not depend on the jointly dominating completely positive map we obtain more flexible formulas for calculating the maximal lebesgue decomposition and we point out the nonuniqueness of the lebesgue decomposition as well as a sufficient condition for uniqueness in addition we consider radon nikodym derivatives for absolutely continuous completely positive maps that in general are unbounded positive self adjoint ope

a partitioning algorithm for the network loading problem this paper proposes a benders like partitioning algorithm to solve the network loading problem the approach is an iterative method in which the integer programming solver is not used to produce the best integer point in the polyhedral relaxation of the set of feasible capacities rather it selects an integer solution that is closest to the best known integer solution contrary to previous approaches the method does not exploit the original mixed integer programming formulation of the problem the effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems the method is compared to alternative approaches proposed in the literature and appears to be efficient for computing good upper bounds

progress made in solving the multicommodity flow problem during the past few years steady progress has been made in solving the multicommodity flow problem using emnet a primal partitioning network simplex algorithm this paper describes a recent improvement made to emnet which permits it to dramatically reduce the solution time for multicommodity flow problems with large numbers of side constraints it is now possible to efficiently solve extremely large multicommodity flow problems when this new idea is coupled with the resource directive decomposition heuristic as found in emnet commercial problems with the number of constraints ranging up to 600 000 are routinely solved by emnet

primal convergence from dual subgradient methods for convex optimization when solving a convex optimization problem through a lagrangian dual reformulation subgradient optimization methods are favorably utilized since they often find near optimal dual solutions quickly however an optimal primal solution is generally not obtained directly through such a subgradient approach unless the lagrangian dual function is differentiable at an optimal solution we construct a sequence of convex combinations of primal subproblem solutions a so called ergodic sequence which is shown to converge to an optimal primal solution when the convexity weights are appropriately chosen we generalize previous convergence results from linear to convex optimization and present a new set of rules for constructing the convexity weights that define the ergodic sequence of primal solutions in contrast to previously proposed rules they exploit more information from later subproblem solutions than from earlier ones we evaluate the proposed rules on a set of nonlinear multicommodity flow problems and demonstrate that they clearly outperform the ones previously proposed

lower and upper probabilities in the distributive lattice of subsystems the set of subsystems of a finite quantum system with variables in together with logical connectives is a distributive lattice with regard to this lattice the where is the projector to obeys a supermodularity inequality and it is interpreted as a lower probability in the sense of the dempster shafer theory and not as a kolmogorov probability it is shown that the basic concepts of the dempster shafer theory lower and upper probabilities and the dempster multivaluedness are pertinent to the quantum formalism of finite systems

partial order of quantum effects the set of effects is not a lattice with respect to its natural order projection operators do have the greatest lower bounds and the least upper bounds in that set but there are also other incomparable effects which share this property however the coexistence the commutativity and the regularity of a pair of effects are not sufficient for the existence of their infima and suprema the structure of the range of an observable as a normalized pov measure can vary from that of a commutative boolean to a noncommutative non boolean subset of effects

convergence of a second order scheme for the nonlinear dynamical equations of elastic rods a second order energy preserving finite difference scheme to approximate the partial differential equations governing planar twist free motions of inextensible unshearable elastic rods is presented and analyzed

coexistency on hilbert space effect algebras and a characterisation of its symmetry transformations the hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in ludwig s formulation of quantum mechanics each effect represents a quantum fuzzy event the relation of coexistence plays an important role in this theory as it expresses when two quantum events can be measured together by applying a suitable apparatus this paper s first goal is to answer a very natural question about this relation namely when two effects are coexistent with exactly the same effects the other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence in particular we will see that they can differ quite a lot from usual standard automorphisms which appear for instance in ludwig s theorem as a byproduct of our methods we also strengthen a theorem of moln ar

on the supremum and infimum of bounded quantum observables let s h be the set of all bounded self adjoint linear operators on a complex hilbert space h in 2006 gudder math slovaca 56 573 2006 introduced a new order on s h since then the existence conditions and representations of the supremum and infimum of two elements in s h with respect to the order have been intensively studied specifically li and sun j math phys 50 122107 2009 10 1063 1 3272542 obtained simpler representations of a p and a p where a s h and p is an orthogonal projection on h in this note we present more intuitive and concise results on a p and extend the results of li and sun to more general cases moreover some applications of our results are given to show that our results are easier to deal with

an unconstrained hamiltonian formulation for incompressible fluid flow the equations governing the time evolution of an ideal fluid in material coordinates are expressed as an unconstrained canonical hamiltonian system the incompressibility of the flow is consequent upon certain first integrals of the motion the variable conjugate to the configuration field is not the usual linear momentum but is instead a quantity that is related to linear momentum through an auxiliary scalar field whose time derivative is the pressure the definition of the hamiltonian involves a minimization with respect to this auxiliary field the method of derivation may be generally applied to obtain unconstrained hamiltonian descriptions of lagrangian field equations subject to pointwise constraints

a projection and an effect in a synaptic algebra abstract we study a pair p e consisting of a projection p an idempotent and an effect e an element between 0 and 1 in a synaptic algebra a generalization of the self adjoint part of a von neumann algebra we show that some of halmos s theory of two projections or two subspaces including a version of his cs decomposition theorem applies in this setting and we introduce and study two candidates for a commutator projection for p and e

on geometrical properties of preconditioners in ipms for classes of block angular problems one of the most efficient interior point methods for some classes of block angular structured problems solves the normal equations by a combination of cholesky factorizations and preconditioned conjugate gradient for respectively the block and linking constraints in this work we show that the choice of a good preconditioner depends on geometrical properties of the constraint structure in particular the principal angles between the subspaces generated by the diagonal blocks and the linking constraints can be used to estimate ex ante the efficiency of the preconditioner numerical validation is provided with some generated optimization problems an application to the solution of multicommodity network flow problems with nodal capacities and equal flows of up to 64 million variables and up to 7 9 million constraints is also presented these computational results also show that predictor corrector directions combined with iterative system solves can be a competitive option for large instances

an alternating linearization bundle method for convex optimization and nonlinear multicommodity flow problems we give a bundle method for minimizing the sum of two convex functions one of them being known only via an oracle of arbitrary accuracy each iteration involves solving two subproblems in which the functions are alternately represented by their linearizations our approach is motivated by applications to nonlinear multicommodity flow problems encouraging numerical experience on large scale problems is reported

hamiltonian dynamics of an elastica and the stability of solitary waves a method is presented for deriving unconstrained hamiltonian systems of partial differential equations equivalent to given constrained lagrangian systems the method is applied to the theory of planar finite amplitude motions of inextensible and unshearable elastic rods the constraints of inextensibility and unshearability become integrals of motion in the hamiltonian formulation

accpm with a nonlinear constraint and an active set strategy to solve nonlinear multicommodity flow problems this paper proposes an implementation of a constrained analytic center cutting plane method to solve nonlinear multicommodity flow problems the new approach exploits the property that the objective of the lagrangian dual problem has a smooth component with second order derivatives readily available in closed form the cutting planes issued from the nonsmooth component and the epigraph set of the smooth component form a localization set that is endowed with a self concordant augmented barrier our implementation uses an approximate analytic center associated with that barrier to query the oracle of the nonsmooth component the paper also proposes an approximation scheme for the original objective an active set strategy can be applied to the transformed problem it reduces the dimension of the dual space and accelerates computations the new approach solves huge instances with high accuracy the method is compared to alternative approaches proposed in the literature

stability of solitary waves in nonlinear composite media the system of equations for planar waves in elastic composite media in the presence of anisotropy is considered in anisotropic case two two parametric families of solitary waves are found in an explicit form in case of the absence of anisotropy these two families coalesce into the unique three parametric family the solitary wave solutions are found to be orbitally stable in a certain range of their phase speeds range of stability both in an anisotropic as well as in an isotropic materials it is also shown that the initial value problem for the governing equations is locally well posed which is needed to prove the stability result the local well posedness of the initial value problem along with stability of solitary waves implies global existence result provided the initial data lie in a neighbourhood of a stable solitary wave this complements the previous results of blow up for this type of equations

quantum probabilities as dempster shafer probabilities in the lattice of subspaces the orthocomplemented modular lattice of subspaces l h d of a quantum system with d dimensional hilbert space h d is considered a generalized additivity relation which holds for kolmogorov probabilities is violated by quantum probabilities in the full lattice l h d it is only valid within the boolean subalgebras of l h d this suggests the use of more general than kolmogorov probability theories and here the dempster shafer probability theory is adopted an operator d h1 h2 which quantifies deviations from kolmogorov probability theory is introduced and it is shown to be intimately related to the commutator of the projectors p h1 p h2 to the subspaces h1 h2 as an application it is shown that the proof of the inequalities of clauser horne shimony and holt for a system of two spin 1 2 particles is valid for kolmogorov probabilities but it is not valid for dempster shafer probabilities the violation of these inequalities in experiments supports the interpretation of quantum proba

infima of hilbert space effects the quantum effects for a physical system are usually described by the set h of positive operators on a hilbert spaceh that are bounded above by the unit operator under a natural order h becomes a partially ordered set that is not a lattice unless dimh 1 a characterization of the pairsa b h such that the infimuma b exists is an open problem called the infimum problem methods of linear algebra are employed to solve the infimum problem when dimh these methods do not appear to generalize to infinite dimensions so the general problem remains open progress toward solution of the general problem is discussed

sharp and unsharp observables on σ mv algebras a comparison with the hilbert space approach we prove that any observable with a standard value space on a probability mv algebra m can be extended from a mapping defined on measurable subsets with values in m to a mapping defined on bounded real valued measurable functions with values in the set of sharp observables associated with m our method of proof is quite different from the method of the proof of analogous result for pov observables on a hilbert space we show that for pov observables with commuting range both approaches give the same results

on the dynamics of rods in the theory of kirchhoff and clebsch we discuss here the dynamical equations of a theory of elastic rods that is due to kmcm ioff 1 2 and cl bsc 3 4 this properly invariant theory is applicable to motions in which the strains relative to an undistorted configuration remain small although rotations may be large it is constructed to be a first order theory i e a theory that is complete to within an error of order two in an appropriate dimensionless measure of thickness curvature twist and extension in a first order theory of thin rods one can treat the rod as inextensible and we do so here at the outset thus at each time t the arc length parameter s for the axial curve t is employed as a material coordinate i e a parameter whose value at a material point is constant in time and not only the resultant of the shearing forces on a cross section but also the tension in the rod are reactive quantities not given by constitutive equations consider for a moment a rod that is naturally prismatic and dynamically symmetric i e a rod that in an undistorted stress free configuration is a cylinder whose directrix although not necessarily a circle bounds a figure with equal principal moments of inertia a motion of the rod is said to be planar and twist flee i e a motion of pure flexure if it is such that t lies at all times in a fixed plane which contains a principal axis of inertia of each cross section for such a motion we employ a fixed cartesian coordinate system on and for consistency with a discussion of more general motions to be given later in this paper we call the abscissa z and the ordinate x we may write fz s t fx s t for the z and x components of the resultant force f at time t on the cross section with arc length coordinate s the motion of the rod may be described by giving the z x coordinates of the points on t as functions of s and t with o s t the counterclockwise angle from the z axis to the tangent of t at s we have

a note on the logic of bounded quantum observables the set of bounded observables for a quantum system is represented by the set of bounded self adjoint operators s h on a complex hilbert space h and the quantum effects for a physical system can be described by the set e h of positive contractive operators on a complex hilbert space h in this note by the techniques of operator block and spectral we give the simpler representation of a p and obtained the new necessary and sufficient conditions for a p for a s h and p p h where p h is the set of all orthogonal projection operators on h in particular we get that if a p exists then a p e h for a e h and p p h in addition we consider the relations between the existence of a b a b and a b where a b a and b are the positive and negative parts of a b s h

on the infimum of quantum effects the quantum effects for a physical system can be described by the set e h of positive operators on a complex hilbert space h that are bounded above by the identity operator while a general effect may be unsharp the collection of sharp effects is described by the set of orthogonal projections p h e h under the natural order e h becomes a partially ordered set that is not a lattice if dimh 2 a physically significant and useful characterization of the pairs a b e h such that the infimum a b exists is called the infimum problem we show that a p exists for all a e h p p h and give an explicit expression for a p we also give a characterization of when a i a exists in terms of the location of the spectrum of a we present a counterexample which shows that a recent conjecture concerning the infimum problem is false finally we compare our results with the work of ando on the infimum problem

the hamiltonian structure of nonlinear elasticity the material and convective representations of solids rods and plates it is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation for example in the analysis of rotating structures the coupling of the equations for geometrically inexact models obtained by linearization or other approximations with those for rotating rigid bodies can easily lead to misleading artificial softening effects that can significantly alter numerical results see simo and vuquoc 1986c especially equations 3 and 5 in this paper we consider fully nonlinear geometrically exact models for rods plates and shells which take into account shear and torsion as well as the usual bending effects in traditional rod and plate models these models can be obtained either from the three dimensional theory by a systematic use of projection methods see e g antman 1972 and naghdi 1972 or by a direct approach within the context of cosserat continuum remarkably the two approaches lead to essentially the same form of the governing field equations in the present context we have chosen as a model problem a particular rod model which may be regarded as an extension of the classical kirchhoff love model see love 1944 to include shear deformations as in

numerical integration of constrained hamiltonian systems using dirac brackets we study the numerical properties of the equations of motion of constrained systems derived with dirac brackets this formulation is compared with one based on the extended hamiltonian as concrete examples a pendulum in cartesian coordinates and a chain molecule are treated

characterizations of fixed points of quantum operations let a be a general quantum operation an operator b is said to be a fixed point of a if a b b in this note we shall show conditions under which b a fixed point a implies that b is compatible with the operation element of a in particular we offer an extension of the generalized luders theorem

an explicit expression of supremum of bounded quantum observables bounded observables corresponding to a quantum system are usually represented by s h the set of all bounded linear self adjoint operators on a hilbert space h in 2006 gudder introduced a logic order on s h for a b s h a b if and only if there exists c s h such that ac 0 and a c b given a b s h let a b be the least upper bound supremum for a and b with respect to the gudder order in 2007 pulmannova and vincenkova proved that a b exists if and only if a and b have an upper bound for the gudder order in this paper we present some new necessary and sufficient conditions for which a b exists and give an explicit representation of a b if a b exists

improving complexity of structured convex optimization problems using self concordant barriers the purpose of this paper is to provide improved complexity results for several classes of structured convex optimization problems using the theory of self concordant functions developed by nesterov and nemirovski in siam studies in applied mathematics siam publications philadelphia 1994 we describe the classical short step interior point method and optimize its parameters in order to provide the best possible iteration bound we also discuss the necessity of introducing two parameters in the definition of self concordancy and which one is the best to fix a lemma due to den hertog et al in mathematical programming series b 69 1 1995 is improved which allows us to review several classes of structured convex optimization problems and improve the corresponding complexity results

solving nonlinear multicommodity flow problems by the analytic center cutting plane method the paper deals with nonlinear multicommodity flow problems with convex costs a decomposition method is proposed to solve them the approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems each subproblem consists of finding a minimum cost flow between an origin and a destination node in an uncapacited network it is thus formulated as a shortest path problem and solved with dijkstra s d heap algorithm an implementation is described that takes full advantage of the supersparsity of the network in the linear algebra operations computational results show the efficiency of this approach on well known nondifferentiable problems and also large scale randomly generated problems up to 1000 arcs and 5000 commodities

a specialized interior point algorithm for multicommodity network flows despite the efficiency shown by interior point methods in large scale linear programming they usually perform poorly when applied to multicommodity flow problems the new specialized interior point algorithm presented here overcomes this drawback this specialization uses both a preconditioned conjugate gradient solver and a sparse cholesky factorization to solve a linear system of equations at each iteration of the algorithm the ad hoc preconditioner developed by exploiting the structure of the problem is instrumental in ensuring the efficiency of the method an implementation of the algorithm is compared to state of the art packages for multicommodity flows the computational experiments were carried out using an extensive set of test problems with sizes of up to 700 000 variables and 150 000 constraints the results show the effectiveness of the algorithm

a conic quadratic formulation for a class of convex congestion functions in network flow problems in this paper we consider a multicommodity network flow problem with flow routing and discrete capacity expansion decisions the problem involves trading off congestion and capacity assignment or expansion costs in particular we consider congestion costs involving convex increasing power functions of flows on the arcs we first observe that under certain conditions the congestion cost can be formulated as a convex function of the capacity level and the flow then we show that the problem can be efficiently formulated by using conic quadratic inequalities as most of the research on this problem is devoted to heuristic approaches this study differs in showing that the problem can be solved to optimum by branch and bound solvers implementing the second order cone programming socp algorithms computational experiments on the test problems from the literature show that the continuous relaxation of the formulation gives a tight lower bound and leads to optimal or near optimal integer solutions within reasonable cpu times

nonlinear dynamical theory of the elastica the dynamical behaviour of a slender rod is analyzed here in terms of a generalization of euler s elastica theory the model includes a linear stress strain relation but nonlinear geometric terms properties of the rod may vary along its length and various boundary conditions are considered a rotational inertia term that is neglected in many theories is retained and is essential to the analysis by use of the equivalence of an energy and a sobolev norm and by reformulation of the equations as a semilinear system global existence of solutions is proved for any smooth initial data equilibrium solutions that are stable in the static sense of minimizing the potential energy are then proved to be stable in the dynamic sense due to liapounov

on a characterization of classical and nonclassical probabilities in this paper a comparison of various approaches to the problem of characterization of probabilities is presented the notion of multidimensional probability or s probability is introduced and it is shown that this notion can be profitably used for characterization of probability systems the main results are given in theorems 3 and 4 in theorem 3 the conditions are considered under which a system of s probabilities admits a model on a generalized event space while in theorem 4 the conditions under which the system admits a classical model are considered an interpretation for s probabilities is discussed and it is shown that theorems 3 and 4 allow one to derive the logical structure of events from the observed probabilities

homogeneous analytic center cutting plane methods for convex problems and variational inequalities in this paper we consider a new analytic center cutting plane method in an extended space we prove the efficiency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem the variational inequality problem and the problem of constrained minimization our analysis is valid even for problems whose solution belongs to the boundary of the domain

two metric projection methods for constrained optimization this paper is concerned with the problem min f x mid x in x where x is a convex subset of a linear space h and f is a smooth real valued function on h we propose the class of methods x k 1 p x k alpha k g k where p denotes projection on x with respect to a hilbert space norm cdot g k denotes the frechet derivative of f at x k with respect to another hilbert space norm cdot k on h and alpha k is a positive scalar stepsize we thus remove an important restriction in the original proposal of goldstein 1 and levitin and poljak 2 where the norms cdot and cdot k must be the same it is therefore possible to match the norm cdot with the structure of x so that the projection operation is simplified while at the same time reserving the option to choose cdot k on the basis of approximations to the hessian of f so as to attain a typically superlinear rate of convergence the resulting methods are particularly attrac

triangular norm based measures and their markov kernel representation abstract we approach the problem whether left continuous triangular norm based valuations called t measures or t probability measures defined on triangular normbased tribes of the unit cube can be disintegrated by markov kernels we prove that each t measure based on a fundamental triangular norm these triangular norms t together with their corresponding triangular conorms s satisfy the functional equation t x y s x y x y can be uniquely represented as a sum of a disintegrable t measure and a hard core which is either identically zero or which is monotonically irreducible i e cannot be disintegrated

some relations of projection and star order in hilbert space abstract we study the star order on b h and show several properties for which the common star lower or star upper bound exists regarding the relationships among operators and projections we give various characterizations of star order and obtain much simpler matrix representations with respect to star order relation

some properties on the star order of bounded operators abstract in this paper we give various characterizations of star order and present some new relationships between the logic order and the star order we present some necessary and sufficient conditions for which the infimum or upper bound exists with respect to given orders

heisenberg inequality and the complex field in quantum mechanics observables a and b satisfy the heisenberg inequality if the product of their variances has a positive lower bound independent of the state of the system in the hilbert space formulation of quantum mechanics it is a consequence of the schwarz inequality that the heisenberg type inequality var a var b 1 4 a b b a 2 holds for any pair of observables a and b represented as self adjoint operators and for any vector state represented as a unit vector if inf a b b a dom a dom b 0 then a and b satisfy the heisenberg inequality in the present paper the derivability of the heisenberg type inequality is analyzed within the general theoretical frame of a sum logic it is shown that any real valued non negative function a f a of observables a and of states which has a symmetry property f a b f a b 2f a 2f b with respect to observables satisfies the heisenberg type inequality f a f b 1 4 f a b f a f b 2 for all observables a and

bundle methods for sum functions with easy components applications to multicommodity network design we propose a version of the bundle scheme for convex nondifferentiable optimization suitable for the case of a sum function where some of the components are easy that is they are lagrangian functions of explicitly known compact convex programs this corresponds to a stabilized partial dantzig wolfe decomposition where suitably modified representations of the easy convex subproblems are inserted in the master problem as an alternative to iteratively inner approximating them by extreme points thus providing the algorithm with exact information about a part of the dual objective function the resulting master problems are potentially larger and less well structured than the standard ones ruling out the available specialized techniques and requiring the use of general purpose solvers for their solution this strongly favors piecewise linear stabilizing terms as opposed to the more usual quadratic ones which in turn may have an adverse effect on the convergence speed of the algorithm so that the overall performance may depend on appropriate tuning of all these aspects yet very good computational results are obtained in at least one relevant application the computation of tight lower bounds for fixed charge multicommodity min cost flow problems

test instances for the multicommodity flow problem an erratum this note is an erratum to babonneau et al 2006 in which some data were incorrectly described in babonneau et al 2006 the accpm method is used to solve the linear multicommodity flow problem on four sets of instances i e the planar and the grid instances some telecommunication problems and some transportation problems from bar gera 2007 http www bgu ac il bargera tntp sioux falls winnipeg barcelona chicago region and philadelphia the mistakes concern the last category of instances the new data and the associated results can now be found in the electronic companion at http or journal informs org this site also provides the full information on test instances in the multicommodity flow problem mcf and the traffic assignment problem to facilitate benchmarking it gives the data and the results using three specific objective functions used in the literature e g bureau of public roads bpr kleinrock or linear for more details on the optimization problem we refer the reader to babonneau et al 2006 and babonneau and vial 2007

removable singularities for solutions of coupled yang mills dirac equations we prove a removable singularity theorem for solutions of coupled yang mills dirac equations on compact four dimensional manifolds we show that a field satisfying the coupled equations with a point singularity is gauge equivalent to a smooth field if the energy functional is finite the hypotheses are very natural only conformally invariant conditions are placed on force field and particle field interacting with the force field it is noticeable that there is no assumption on the derivative of the particle field

on the infimum of bounded quantum observables the set of all bounded observables corresponding to a quantum system is usually represented by s h the set of all bounded linear self adjoint operators on a hilbert space h in 2006 gudder introduced a logic order on s h given a b s h let a b be the greatest lower bound infimum of a and b with respect to the gudder order in this paper we characterize a b using the invariant subspaces of a and b