classification of systems of nonlinear ordinary differential equations with superposition principles a system of n first order nonlinear ordinary differential equations x t f x t is said to admit a superposition principle if its general solution can be written as a function of a finite number m of particular solutions and n constants such a system can be associated with the nonlinear action of a lie group g on a space m we show that indecomposable systems of ode s with supersposition principles are obtained if and only if the lie algebras l0 l corresponding to the isotropy group h of a point and the group g respectively define a transitive primitive filtered lie algebra l l0 using known results from the theory of transitive primitive lie algebras we deduce that l0 must be a maximal subalgebra of l and that g must be an affine group a simple lie group or the direct product of two identical simple lie groups affine groups lead to linear equations the other types to nonlinear equations with polynomial or rational nonlinearities equations corresponding to the classical complex lie algebra

deformation of characteristic curves of the plane ideal plasticity equations by point symmetries abstract the hyperbolic system of plane ideal plasticity equations under the saint venant mises yield criterion is considered its characteristics curves are deformed by the action of admitted group of point transformations that permits to construct a new analytical solution the mechanical sense of obtained characteristic fields is discussed the general algorithm of the relation of solutions of quasilinear hyperbolic system of two homogeneous equations of two independent variables is proposed

two dimensional lattice vesicles and polygons we consider a lattice model of two dimensional vesicles in which the boundary of the vesicle is the perimeter of a self avoiding polygon embeddable in the square lattice with fixed boundary length m we incorporate an osmotic pressure difference by associating a fugacity with the area enclosed by the polygon we derive rigorous results concerning the behaviour of the associated free energy and the form of the phase diagram by deriving exact values ofthe numbers of polygons with m edges which enclose area n and analysing the resulting series we obtain the free energy the phase boundary and various scaling exponents and amplitudes numerically

statistics of lattice animals the authors investigate the large n behaviour of the number of lattice animals with n vertices having alpha cycles per vertex they prove concavity and continuity properties for the corresponding growth constant and in particular show that lattice trees are exponentially scarce in the set of lattice animals they also consider the corresponding generating function and prove a number of theorems which bound it and set other limits on its possible behaviour

wirtinger type integral inequalities for interval valued functions abstract this study presents some wirtinger type integral inequalities for interval valued functions by means of the generalized hukuhara differentiability and the pompeiu hausdorff metric these integral inequalities generalize their respective versions for real valued functions numerical examples that illustrate the applicability of the theory developed herein are also provided

symmetry group analysis of an ideal plastic flow in this paper we study a finite dimensional lie point symmetry group of a system describing an ideal plastic plane flow in two dimensions in order to find analytical solutions the infinitesimal generators that span this lie algebra are given we completely classify the subalgebras of codimension up to two into conjugacy classes under the action of the symmetry group based on invariant forms we use ansatze to compute symmetry reductions in such a way that the obtained solutions simultaneously cover many invariant and partially invariant solutions we calculate solutions of algebraic trigonometric inverse trigonometric and elliptic type some solutions depending on one or two arbitrary functions of one variable have also been found in some cases the shape of a potentially feasible extrusion die corresponding to the solution is deduced these tools could be used to thin curve undulate or shape a ring in an ideal plastic material

monte carlo study of self avoiding surfaces two models of self avoiding surfaces on the cubic lattice are studied by monte carlo simulations both the first model with fluctuating boundary and the second one with a fixed boundary are found to belong to the universality class of branched polymers the algorithms as well as the methods used to extract the critical exponents are described in detail the results are compared to other recent estimates in the literature

recent advances on the discretizable molecular distance geometry problem the molecular distance geometry problem mdgp consists in finding an embedding in r 3 of a nonnegatively weighted simple undirected graph with the property that the euclidean distances between embedded adjacent vertices must be the same as the corresponding edge weights the discretizable molecular distance geometry problem dmdgp is a particular subset of the mdgp which can be solved using a discrete search occurring in continuous space its main application is to find three dimensional arrangements of proteins using nuclear magnetic resonance nmr data the model provided by the dmdgp however is too abstract to be directly applicable in proteomics in the last five years our efforts have been directed towards adapting the dmdgp to be an ever closer model of the actual difficulties posed by the problem of determining protein structures from nmr data this survey lists recent developments on dmdgp related research

self avoiding surfaces with knotted boundaries the authors consider orientable self avoiding surfaces with genus g embedded in the hypercubic lattice they consider a surface which has a boundary component and non zero genus and devise a construction which will reduce the genus of the surface this result enables them to study embeddings of surfaces in the three dimensional lattice where a surface of genus g may have a boundary component which is a knot of genus g or g they prove that the growth constants of these surfaces are independent of the knot type of the boundary component and they derive inequalities between the associated critical exponents

self avoiding surfaces the set of self avoiding random surfaces sn h with n plaquettes and h boundary components is considered the concatenation of the surfaces in sn h and new constructions which either increase or decrease the number of boundary components of a surface are studied these constructions make it possible to prove the existence of growth constants beta h for the cardinality sn h of sn h for each h or 1 in two dimensions and h or 0 in d or 3 dimensions the authors prove that beta h beta 1 for all h or 1 in d or 2 dimensions in addition they prove that beta 0 or 3 dimensions and that in two dimensions beta 1 beta where beta is the growth constant of the set sn the set of all self avoiding surfaces in two dimensions finally by postulating the existence of a critical exponent phi h for each set sn h by assuming that sn h approximately n phi h beta nh they derive bounds on phi h from the constructions defined on the surface in sn h

some symmetry group aspects of a perfect plane plasticity system in this paper all the known classical solutions of a plane perfect plasticity system under the saint venant tresca von mises yield criterion are associated with some group of point symmetries the equations of slip line families for all solutions are constructed which allows one to explicitly determine the boundaries of the plastic areas it is shown how one can determine the compatible velocity solution for known stresses by considering symmetries some invariant solutions of velocities for prandtl stresses are constructed the mechanical sense of the obtained velocity fields is discussed to the blessed memory of our teacher d d ivlev

self avoiding random surfaces monte carlo study using oct tree data structure self avoiding random surfaces on a cubic lattice are studied by extensive monte carlo sampling the surfaces have an empty boundary and the topology of a 2 sphere an oct tree data structure allows good statistics to be obtained for surfaces whose plaquette number is up to an order of magnitude greater than in previous investigations the new simulation strategy is explained in detail and compared with previous ones the critical plaquette fugacity mu 1 and the entropic exponent theta are determined by maximum likelihood methods and by logarithmic plots of the average surface area versus fugacity the latter approach which produces results having much better convergence by taking advantage of the scaling properties of several runs at various fugacities leads to the estimates mu 1 729 or 0 036 and theta 1 500 or 0 026 linear regression estimates for the radius of gyration exponent give v 0 509 or 0 004 while the asymptotic ratio of surface area over average volume enclosed approaches a finite value 3 18 or 0 03 the results give strong corroborating evidence that this long controversial problem belongs to the universality class of branched polymers

symmetry groups of non stationary planar ideal plasticity this paper is a study of the lie groups of point symmetries admitted by a system describing a non stationary planar flow of an ideal plastic material for several types of forces involved in the system the infinitesimal generators which generate the lie algebra of symmetries have been obtained in the case of a monogenic force the classification of one and two dimensional subalgebras into conjugacy classes under the action of the group of automorphisms has been accomplished the method of symmetry reduction is applied for certain subalgebra classes in order to obtain invariant solutions

euclidean distance geometry and applications euclidean distance geometry is the study of euclidean geometry based on the concept of distance this is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in euclidean space realizing those given distances we survey the theory of euclidean distance geometry and its most important applications with special emphasis on molecular conformation problems

on the estimation of unknown distances for a class of euclidean distance matrix completion problems with interval data abstract we consider some euclidean distance matrix completion problems whose structure is inspired by molecular conformation problems some matrix distances are given precisely or in terms of intervals and other values are unknown we present theoretical results that can be useful in methods to estimate the possible values of the unknown matrix distances

critical exponents for lattice animals with fixed cyclomatic index the authors derive an inequality between the number of trees and the number of lattice animals with exactly c cycles an c for all positive c if they assume that an c approximately n theta c lambda nc n to infinity c fixed they use this to show that theta c theta o c where theta 0 is the corresponding exponent for trees

discrete time interval optimal control problem abstractthis paper proposes a new approach for the discrete time interval optimal control problem the optimal interval solution of discrete time interval optimal control problem is obtained using

single level constraint interval arithmetic in the present paper we propose a variant of constraint interval arithmetic that operates with a single parameter level in each interval operand of an expression this results in a computationally simple interval arithmetic that has several desirable properties not shared in general by interval operations previously defined in the literature the actualization and usefulness of this approach to fuzzy interval arithmetic is accomplished via alpha levels the evaluation of arithmetic expressions using the proposed single level constrained arithmetic is discussed in detail and we extend this theory to the fuzzy context

surfaces in the hypercubic lattice let sn h g be the number of surfaces with h boundary components and with genus g embedded in the hypercubic lattice then the author proves that for all h or 0 and g or 0 there exists a constant c6 0 in two dimensions such that o e c6 log n 2 beta 1 0n 0 and k3 0 such that in three and more dimensions o e k7 logn 3 beta 1 0n or phi 1 0 2h 4g in three and more dimensions

interval linear systems as a necessary step in fuzzy linear systems this article clarifies what it means to solve a system of fuzzy linear equations relying on the fact that they are a direct extension of interval linear systems of equations already studied in a specific interval mathematics literature we highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals each of which based on a generalization of scalar equality to intervals each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals we also consider the smallest multidimensional intervals containing the solution sets we propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals this unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies

calculating the possible conformations arising from uncertainty in the molecular distance geometry problem using constraint interval analysis abstract the calculation of the 3d structure of a protein molecule is important because it is associated to its biological function nuclear magnetic resonance nmr experiments can provide distance information between atoms that are close enough in a given protein and the problem is how to use these distances to determine the protein structure using the chemistry of proteins and supposing all the distances are precise values it is possible to define an atomic order v 1 v n such that the distances related to the pairs v i 3 v i v i 2 v i v i 1 v i are available and solve the problem iteratively using a combinatorial method called branch and prune bp however due to uncertainty in nmr data the distances associated with pairs v i 3 v i may not be precise which implies that there are many difficulties in applying the bp algorithm to this scenario the use of standard interval arithmetic can be directly applied to the algorithm but it is known that it generates overestimations this paper proposes a new methodology to compute possible conformations on the presence of uncertainties arising from nmr distance measurements using a constraint interval analysis approach some numerical examples are presented

on the universality class of planar self avoiding surfaces with fixed boundary using a modified version of a monte carlo algorithm proposed by sterling and greensite 1983 the authors obtain the exponents theta 1 51 or 0 25 and nu 0 502 or 0 024 for planar self avoiding surfaces with a fixed boundary in three dimensions consistent with the conjectured exact values for branched polymers they show how the modifications are needed to obtain a viable distribution of surfaces

group analysis of an ideal plasticity model a group analysis of a system describing an ideal plastic flow is made in order to obtain analytical solutions the complete lie algebra of point symmetries of this system are given two of the infinitesimal generators that span the lie algebra are original to this paper a classification into conjugacy classes of all one and two dimensional subalgebras is performed invariant and partially invariant solutions corresponding to certain conjugacy classes are obtained using the symmetry reduction method solutions of algebraic trigonometric inverse trigonometric and elliptic type are provided as illustrations and other solutions expressed in terms of one or two arbitrary functions have also been found for some of these solutions a physical interpretation allows one to determine the shape of feasible extrusion dies corresponding to these solutions the corresponding tools could be used to curve rods or slabs or to shape a ring in an ideal plastic material by an extrusion process