on families of bounded continuous solutions of some systems of functional difference equations on half intervals some sufficient conditions for the existence of families of bounded continuous solutions of some classes of systems of functional difference equations on the intervals 0 and 0 are given

an evolving model of online bipartite networks abstract understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e commerce services nowadays recently various attempts have been tried to propose different models resulting in either power law or exponential degree distributions however many empirical results show that the user degree distribution actually follows a shifted power law distribution the so called mandelbrot s law which cannot be fully described by previous models in this paper we propose an evolving model considering two different user behaviors random and preferential attachment extensive empirical results on two real bipartite networks delicious and citeulike show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions in addition we introduce a structural parameter p to demonstrate that the hybrid user behavior leads to the shifted power law degree distribution and the region of power law tail will increase with the increment of p the proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks

cylinder buckling the mountain pass as an organizing center we revisit the classical problem of the buckling of a long thin axially compressed cylindrical shell by examining the energy landscape of the perfect cylinder we deduce an estimate of the sensitivity of the shell to imperfections key to obtaining this estimate is the existence of a mountain pass point for the system we prove the existence on bounded domains of such solutions for almost all loads and then numerically compute example mountain pass solutions numerically the mountain pass solution with lowest energy has the form of a single dimple we interpret these results and validate the lower bound against some experimental results available in the literature

stochastic homogenization of the bending plate model abstract we use the notion of stochastic two scale convergence introduced in 32 to solve the problem of stochastic homogenization of the elastic plate in the bending regime

the matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells using the notion of convergence we discuss the limiting behavior of the three dimensional nonlinear elastic energy for thin elliptic shells as their thickness h converges to zero under the assumption that the elastic energy of deformations scales like h with 2 4 we establish that for the given scaling regime the limiting theory reduces to linear pure bending two major ingredients of the proofs are the density of smooth infinitesimal isometries in the space of w2 2 first order infinitesimal isometries and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces

boundary layer analysis of the ridge singularity in a thin plate large deformations of thin elastic plates and shells present a formidable problem in continuum mechanics which is generally intractable except by numerical methods conventional approaches break down in the limit of small plate thickness due to appearance of discontinuities in the solution which require boundary layer treatment we examine a simple case of a plate bent by forces exerted along its boundary so as to create a sharp crease in the limit of infinitely small thickness we find a separable boundary layer solution of the von karman plate equations which is valid along the ridge line we confirm a scaling argument t a witten and hao li europhys lett 23 51 1993 that asserts that the ridge possesses a characteristic radius of curvature r given by the thickness of the sheet h and the length of the ridge x it viz r sim h 1 3 x 2 3 the elastic energy of the ridge scales as e sim kappa x h 1 3 where kappa is the bending modulus of the sheet we determine the dependence of these quantities on the dihedral angle of the ridge pi 2 alpha for all angles r sim alpha 4 3 and e sim alpha 7 3 the framework developed in this paper is suitable for determination of other properties of ridges such as their interaction or behavior under various types of loading we expect these results to have broad importance in describing forced crumpling of thin sheets

derivation of homogenized euler lagrange equations for von karman rods in this paper we study the effects of simultaneous homogenization and dimension reduction in the context of convergence of stationary points for thin nonhomogeneous rods under the assumption of the von karman scaling assuming stationarity conditions for a sequence of deformations close to a rigid body motion we prove that the corresponding sequences of scaled displacements and twist functions converge to a limit point which is the stationary point of the homogenized von karman rod model the analogous result holds true for the von karman plate model

on a nonlinear second order system of difference equations we prove that all positive solutions of the next system of difference equationsx n 1 a y n px n 1 q y n 1 a x n py n 1 q email protected n 0 where parameters a p and q are positive numbers are bounded if one of the following conditions is satisfied p 2 4 or p 1 q q 1 completely describing the boundedness character of the system in this case

domains of undefinable solutions of some equations and systems of difference equations for some classes of difference equations and systems of difference equations we find the sets of initial values for which solutions of these equations and systems are not well defined so called domains of undefinable solutions

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

asymptotically periodic solutions of second order difference equations abstract in this paper we obtain sufficient conditions for the existence of asymptotically periodic solutions of the second order difference equations of the form r n x n a n f x n b n moreover we give sufficient conditions under which every bounded solution of the above equation is asymptotically periodic our approach allows us to control the degree of approximation

saint venant s problem and semi inverse solutions in nonlinear elasticity saint venant s problem consists in finding elastic deformations of an infinite prismatic body taking given values for the cross sectional resultants of force and moment using the center manifold approach we show that all deformations having sufficiently small bounded strains lie on a finite dimensional manifold in particular the flow on this manifold is described by a set of equations having exactly the form of the classical rod equations moreover the set of semi inverse solutions can be analyzed locally

regularity properties of isometric immersions we show that an isometric immersion y from a two dimensional domain s with c1 boundary to 3 which belongs to the critical sobolev space w2 2 is c1 up to the boundary more generally c1 regularity up to the boundary holds for all scalar functions v w2 2 s which satisfy det 2v 0 if s has only lipschitz boundary we show such v can be approximated in w2 2 by functions vk w1 w2 2 with det 2vk 0

modeling discrete combinatorial systems as alphabetic bipartite networks theory and applications genes and human languages are discrete combinatorial systems dcss in which the basic building blocks are finite sets of elementary units nucleotides or codons in a dna sequence and letters or words in a language different combinations of these finite units give rise to potentially infinite numbers of genes or sentences this type of dcss can be represented as an alphabetic bipartite network abn where there are two kinds of nodes one type represents the elementary units while the other type represents their combinations here we extend and generalize recent analytical findings for abns derived in peruani et al europhys lett 79 28001 2007 and empirically investigate two real world systems in terms of abns the codon gene and the phoneme language network the one mode projections onto the elementary basic units are also studied theoretically as well as in real world abns we propose the use of abns as a means for inferring the mechanisms underlying the growth of real world dcss

on a system of difference equations of odd order solvable in closed form it is shown that the next system of difference equationsx n c ny n 2 k 1 a n b ny n 2 k 1 i 1 k 1y n 2 i 1 x n 2 i y email protected nx n 2 k 1 a email protected nx n 2 k 1 i 1 k 1x n 2 i 1 y n 2 email protected n 0 where a n b n c n a n b n c n email protected n 0 and initial values x i y i email protected 1 2 2k 1 are real numbers is solved in closed form and the behavior of its well defined solutions when all the coefficients in the system are constant is described

convergence of equilibria of three dimensional thin elastic beams a convergence result is proved for the equilibrium configurations of a three dimensional thin elastic beam as the diameter h of the cross section goes to zero more precisely we show that stationary points of the nonlinear elastic functional e whose energies per unit cross section are bounded by ch converge to stationary points of the limit of e h this corresponds to a nonlinear one dimensional model for inextensible rods describing bending and torsion effects the proof is based on the rigidity estimate for low energy deformations by friesecke james and muller 4 and on a compensated compactness argument in a singular geometry in addition possible concentration effects of the strain are controlled by a careful truncation argument

global stability of some symmetric difference equations suppose r 0 1 m n and 1 k1 k2 k2m 1 and let s2m 1 1 2 2m 1 we show that every positive solution to the difference equation yn p2m 12m 1 yn k1r yn k2r yn k2m 1r p2m2m 1 yn k1r yn k2r yn k2m 1r n n0 where p2m 12m 1 x1 x2 x2m 1 r 1rodd2m 1 t1 t2 tr s2m 1t1 t2 trxt1xt2 xtr and p2m2m 1 x1 x2 x2m 1 1 r 2reven2m t1 t2 tr s2m 1t1 t2 trxt1xt2 xtr converges to one this result confirms a quite recent conjecture posed by liu and yang 2010 in 10 we also prove another result regarding a related equation

a theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity the energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by g kirchhoff in 1850 we show that it arises as a 0 limit of three dimensional nonlinear elasticity theory as the thickness of a plate goes to zero a key ingredient in the proof is a sharp rigidity estimate for maps v v u r n u r n we show that the l 2 distance of rv from a single rotation matrix is bounded by a multiple of the l 2 distance from

general form of some rational recursive sequences in this note we study the general form of some rational recursive sequences by some modification of the methods and ideas as well as the transformation from the paper k s berenhaut j d foley and s stevic the global attractivity of the rational difference equation y n y n k y n m1 y n ky n m appl math lett 20 2007 54 58 we give a new proof for the conjectures posed therein

on the sobolev space of isometric immersions we prove that every w 2 2 isometric immersion from a convex regular domain of r 2 into r3 can be approximated in w 2 2 norm by smooth isometric immersions from the same domain into r3

limitations on the smooth confinement of an unstretchable manifold we prove that an m dimensional unit ball dm in the euclidean space rm cannot be isometrically embedded into a higher dimensional euclidean ball brd rd of radius r 1 2 unless one of two conditions is met 1 the embedding manifold has dimension d 2m 2 the embedding is not smooth the proof uses differential geometry to show that if d 2m and the embedding is smooth and isometric we can construct a line from the center of dm to the boundary that is geodesic in both dm and in the embedding manifold rd since such a line has length 1 the diameter of the embedding ball must exceed 1

on the difference equation xn 1 pxn s xn tqxn s xn t abstract in this paper we address the difference equation x n 1 px n s x n t qx n s x n t n 0 1 with positive initial conditions we establish a sufficient condition for the global asymptotic stability of the positive equilibrium of this equation

existence uniqueness and attractivity of prime period two solution for a difference equation of exponential form abstract in this paper we study the existence uniqueness and attractivity of prime period two solution of the difference equation x n 1 a bx n 1 e x n where a b are positive constants and the initial values x 1 x 0 are positive numbers

global stability and asymptotics of some classes of rational difference equations in this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable using a berg s result we also find asymptotics of some solutions of these equations

on the n dimensional dirichlet problem for isometric maps we exhibit explicit lipschitz maps from r n to r n which have almost everywhere orthogonal gradient and are equal to zero on the boundary of a cube we solve the problem by induction on the dimension n

topological crossovers in the forced folding of self avoiding matter abstract we study the scaling properties of forced folding of thin materials of different geometry the scaling relations implying the topological crossovers from the folding of three dimensional plates to the folding of two dimensional sheets and further to the packing of one dimensional strings are derived for elastic and plastic manifolds these topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry elasto plastic materials such as paper sheets during the fast folding under increasing confinement force are expected to obey the scaling force diameter relation derived for elastic manifolds however in experiments with paper strips of different geometry we observed the crossover from packing of one dimensional strings to folding two dimensional sheets only because the fractal dimension of the set of folded elasto plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn

eventual periodicity of some systems of max type difference equations the periodicity of the next system of max type difference equations xn 1 max1 i1 m1f1i1xn ki1 1 1 1 xn ki1 2 1 2 xn ki1 l 1 l n xn t1s 1 xn 2 max1 i2 m2f2i2xn ki2 1 2 1 xn ki2 2 2 2 xn ki2 l 2 l n xn t2s 2 xn l max1 il mlflilxn kil 1 l 1 xn kil 2 l 2 xn kil l l l n xn tls l n n0n n0 where s l mj tj kij h j n j h 1 l j h 1 l 1 2 l 1 2 l is a permutation of 1 2 l 1 2 l and fjij 0 l n0 0 fjij 0 l n0 0 j 1 l j 1 l ij 1 mj ij 1 mj is studied it is shown that under some conditions posed on functions fjijfjij all positive solutions of the system are eventually periodic with period ts for some t nt n

asymptotic behavior of the positive solutions of an exponential type system of difference equations in this paper we study the existence of a unique positive equilibrium the boundedness persistence and global attractivity of the positive solutions of a system of the following two difference equations x n 1 ax n by n 1 e x n y n 1 cy n dx n 1 e y n n 0 1 where a b c d are positive constants and the initial values x 1 x 0 y 1 y 0 are positive numbers

quantitative immersability of riemann metrics and the infinite hierarchy of prestrained shell models we propose results that relate the following two contexts for each n we identify conditions for the validity of the scaling h 2n in terms of the vanishing of riemann curvatures of g up to appropriate orders and in terms of the matched isometry expansions we also establish the asymptotic behaviour of the minimizing immersions as h rightarrow 0

invertibility and non invertibility in thin elastic structures the nonlinear elastic energy of a thin film of thickness h is given by a functional eh friesecke james and muller derived the limits as h 0 of the functionals h eh for 3 in this article we study the invertibility properties of almost minimizers of these functionals and more generally of sequences with equiintegrable energy density we show that they are invertible almost everywhere away from a thin boundary layer near the film surface moreover we obtain an upper bound for the width of this layer and a uniform upper bound on the diameter of preimages we construct examples showing that these bounds are sharp in particular for all 3 there exist lipschitz continuous low energy deformations which are not locally invertible

study of the asymptotic behavior of the solutions of three systems of difference equations of exponential form in this paper we study the boundedness the persistence and the asymptotic behavior of the positive solutions of the following systems of two difference equations of exponential form xn 1 a be yn c yn 1 y n 1 d e xn f xn 1

gaussian curvature as an identifier of shell rigidity in the paper we deal with shells with non zero gaussian curvature we derive sharp korn s first linear geometric rigidity estimate and second inequalities on that kind of shell for zero or periodic dirichlet neumann and robin type boundary conditions we prove that if the gaussian curvature is positive then the optimal constant in the first korn inequality scales like h and if the gaussian curvature is negative then the korn constant scales like h 4 3 where h is the thickness of the shell these results have a classical flavour in continuum mechanics in particular shell theory the korn first inequalities are the linear version of the famous geometric rigidity estimate by friesecke et al for plates in arch ration mech anal 180 2 183 236 2006 where they show that the korn constant in the nonlinear korn s first inequality scales like h 2 extended to shells with nonzero curvature we also recover the uniform korn poincare inequality proven for boundary less shells by lewicka and muller in annales de l institute henri poincare c non linear anal 28 3 443 469 2011 in the setting of our problem the new estimates can also be applied to find the scaling law for the critical buckling load of the shell under in plane loads as well as to derive energy scaling laws in the pre buckled regime the exponents 1 and 4 3 in the present work appear for the first time in any sharp geometric rigidity estimate

confining thin elastic sheets and folding paper crumpling a sheet of paper leads to the formation of complex folding patterns over several length scales this can be understood on the basis of the interplay of a nonconvex elastic energy which favors locally isometric deformations and a small singular perturbation which penalizes high curvature based on three dimensional nonlinear elasticity and by using a combination of explicit constructions and general results from differential geometry we prove that in agreement with previous heuristic results in the physics literature the total energy per unit thickness of such folding patterns scales at most as the thickness of the sheet to the power 5 3 for the case of a single fold we also obtain a corresponding lower bound

atomic to continuum passage for nanotubes a discrete saint venant principle and error estimates we consider general infinite nanotubes of atoms in mathbb r 3 where each atom interacts with all the others through a two body potential at the equilibrium the positions of the atoms satisfy a euler lagrange equation when there are no exterior forces and for a suitable geometry a particular family of nanotubes is the set of perfect nanotubes at the equilibrium when exterior forces are applied on the nanotube we compare the nanotube to nanotubes of the previous family in part i of the paper this quantitative comparison is formulated in our first main result as a discrete saint venant principle as a corollary we also give a liouville classification result our saint venant principle can be derived for a large class of potentials including the lennard jones potential when the perfect nanotubes at the equilibrium are stable the approach is designed to be applicable to nanotubes that can have general shapes like for instance carbon nanotubes or dna under the oversimplified assumption that all the atoms are identical in part ii of the paper we derive from our saint venant principle a macroscopic mechanical model for general nanotubes we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting but no bending we establish error estimates between the discrete and the continuous solution more precisely we give two error estimates one at the microscopic level and one at the macroscopic level

heterogeneous thin films of martensitic materials we study the effective behavior of heterogeneous thin films with three competing length scales the film thickness and the length scales of heterogeneity and material microstructure we start with three dimensional nonhomogeneous nonlinear elasticity enhanced with an interfacial energy of the van der waals type and derive the effective energy density as all length scales tend to zero with given limiting ratios we do not require any a priori selection of asymptotic expansion or ansatz in deriving our results depending on the dominating length scale the effective energy density can be identified by three procedures averaging homogenization and thin film limit we apply our theory to martensitic materials with multi well energy density and use a model example to show that the shape memory behavior can crucially depend on the ratios of these length scales we comment on the effective conductivity of linear composites and also on multilayers made of shape memory and elastic materials

justification of the nonlinear kirchhoff love theory of plates as the application of a new singular inverse method in the framework of isotropic homogeneous nonlinear elasticity for a st venant kirchhoff material we consider a three dimensional plate of thickness and periodic in the two other directions using a new method that we call the singular inverse method we prove the existence of a solution rescaled uniformly in for small forces and at the same time we prove the rigorous convergence of this rescaled solution to the solution of the nonlinear kirchhoff love plate model we also state a 3d 2d error estimate

on the system of difference equations x n x n 1 y n 2 a y n 2 b y n 1 y n y n 1 x n 2 c x n 2 d x n 1 we show that the following system of difference equations x n x n 1 y n 2 a y n 2 b y n 1 y n y n 1 x n 2 c x n 2 d x n 1 n n 0 where parameters a b c d as well as initial values x 2 x 1 y 2 y 1 are real numbers is solvable in closed form and by using obtained formulas we give some results on the long term behavior of their solutions we also give natural explanations and considerably extend some recent results in the literature

finite element approximation of large bending isometries a finite element scheme for the approximation of large isometric deformations with minimal bending energy is devised and analyzed the convergence to a stationary point and energy decreasing property of an iterative algorithm for the numerical solution of the scheme is proved numerical experiments illustrate the performance of the iteration and show that the discretization leads to accurate approximations for large vertical loads and compressive boundary conditions

on some periodic systems of max type difference equations we show that all positive solutions to the system of max type difference equations xn 1 max1 i m1f1ixn ki 1 1 1 xn ki 2 1 2 xn ki l 1 l n xn s 1 xn 2 max1 i m2f2ixn ki 1 2 1 xn ki 2 2 2 xn ki l 2 l n xn s 2 xn l max1 i mlflixn ki 1 l 1 xn ki 2 l 2 xn ki l l l n xn s l n n0 where s l mj ki t j n j t 1 l and for a fixed j i 1 mj and where the functions fji 0 l n0 0 j 1 l i 1 mj satisfy some conditions are eventually periodic with not necessarily prime period s a related result for the corresponding system of min type difference equations is also proved

the global attractivity of a higher order rational difference equation abstract this paper studies global asymptotic stability for positive solutions to the equation y n y n k y n l y n m y n k y n l y n m 1 y n k y n l y n k y n m y n l y n m n 0 1 with y m y m 1 y 1 0 and 1 k l m the paper also includes a listing of possible semi cycle structures for various k l m the results generalize several others in the recent literature

convergence of equilibria of thin elastic plates under physical growth conditions for the energy density abstract the asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied as the thickness h of the plate goes to zero more precisely it is shown that critical points of the nonlinear elastic functional e h whose energies per unit thickness are bounded by ch 4 converge to critical points of the limit of h 4 e h this is proved under the physical assumption that the energy density w f blows up as det f 0

the von karman equations the stress function and elastic ridges in high dimensions the elastic energy functional of a thin elastic rod or sheet is generalized to the case of an m dimensional manifold in n dimensional space we derive potentials for the stress field and curvatures and find the generalized von karman equations for a manifold in elastic equilibrium we perform a scaling analysis of an m 1 dimensional ridge in an m n 1 dimensional manifold a ridge of linear size x in a manifold with thickness h x has a width w h1 3x2 3 and a total energy e hm x h m 5 3 where is a stretching modulus we also prove that the total bending energy of the ridge is exactly five times the total stretching energy these results match those of a lobkovsky phys rev e 53 3750 1996 for the case of a bent plate in three dimensions

blister patterns and energy minimization in compressed thin films on compliant substrates this paper is motivated by the complex blister patterns sometimes seen in thin elastic films on thick compliant substrates these patterns are often induced by an elastic misfit that compresses the film blistering permits the film to expand locally reducing the elastic energy of the system it is therefore natural to ask what is the minimum elastic energy achievable by blistering on a fixed area fraction of the substrate this is a variational problem involving both the elastic deformation of the film and substrate and the geometry of the blistered region it involves three small parameters the nondimensionalized thickness of the film the compliance ratio of the film substrate pair and the mismatch strain in formulating the problem we use a small slope foppl von karman approximation for the elastic energy of the film and a local approximation for the elastic energy of the substrate for a one dimensional version of the problem we obtain matching upper and lower bounds on the minimum energy in the sense that both bounds have the same scaling behavior with respect to the small parameters the upper bound is straightforward and familiar it is achieved by periodic blistering on a specific length scale the lower bound is more subtle since it must be proved without any assumption on the geometry of the blistered region for a two dimensional version of the problem our results are less complete our upper and lower bounds only match in their scaling with respect to the nondimensionalized thickness not in the dependence on the compliance ratio and the mismatch strain the lower bound is an easy consequence of our one dimensional analysis the upper bound considers a two dimensional lattice of blisters and uses ideas from the literature on the folding or crumpling of a confined elastic sheet our main two dimensional result is that in a certain parameter regime the elastic energy of this lattice is significantly lower than that of a few large blisters 2015 wiley periodicals inc

part metric and its applications in discrete systems this paper applies the part metric method to study some types of higher order symmetric difference equations with several different exponential parameters these difference equations are proved to have unique equilibria and some useful inequalities regarding the difference equation functions are formulated by use of the part metric and a result given by kruse and nesemann 1999 8 some sufficient conditions on the parameters are given to guarantee the global asymptotic stability of the equilibria furthermore by the part metric defined on matrices this approach is also applicable to show the global asymptotic stability of some cyclic discrete dynamic systems the results of this paper are considered a big improvement over many existing results found in the literature

rim curvature anomaly in thin conical sheets revisited this paper revisits one of the puzzling behaviors in a developable cone d cone the shape obtained by pushing a thin sheet into a circular container of radius r by a distance the mean curvature was reported to vanish at the rim where the d cone is supported we investigate the ratio of the two principal curvatures versus sheet thickness h over a wider dynamic range than was used previously holding r and fixed instead of tending toward 1 as suggested by previous work the ratio scales as h r 1 3 thus the mean curvature does not vanish for very thin sheets as previously claimed moreover we find that the normalized rim profile of radial curvature in a d cone is identical to that in a c cone which is made by pushing a regular cone into a circular container in both c cones and d cones the ratio of the principal curvatures at the rim scales as r h 5 2 f yr 2 where f is the pushing force and y is the young s modulus scaling arguments and analytical solutions confirm the numerical results

the kirchhoff theory for elastic pre strained shells abstract applying methods of convergence we introduce and justify a variant of the kirchhoff theory for pre strained shells the effective 2d energy represents bending relative to the desired riemannian metric we also develop the analogue of this theory in the presence of the incompressibility constraint with respect to the metric

coarsening of folds in hanging drapes we consider the elastic energy of a hanging drape a thin elastic sheet pulled down by the force of gravity with fine scale folding at the top that achieves approximately uniform confinement this example of energy driven pattern formation in a thin elastic sheet is of particular interest because the length scale of folding varies with height we focus on how the minimum elastic energy depends on the physical parameters as the sheet thickness vanishes the limiting energy is due to the gravitational force and is relatively easy to understand our main accomplishment is to identify the scaling law of the correction due to positive thickness we do this by i proving an upper bound by considering the energies of several constructions and taking the best and ii proving an ansatz free lower bound which agrees with the upper bound up to a parameter independent prefactor the coarsening of folds in hanging drapes has also been considered in the recent physics literature by using a self similar construction whose basic cell has been called a wrinklon our results complement and extend that work by showing that self similar coarsening achieves the optimal scaling law in a certain parameter regime and by showing that other constructions involving lateral spreading of the sheet do better in other regions of parameter space our analysis uses a geometrically linear foppl von karman model for the elastic energy and is restricted to the case when poisson s ratio is 0 2016 wiley periodicals inc

axial compression of a thin elastic cylinder bounds on the minimum energy scaling law we consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core treating the core as an obstacle we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness and the magnitude of axial compression we focus exclusively on the setting where the radius of the core is greater than or equal to the natural radius of the cylinder we consider two cases the large mandrel case where the radius of the core exceeds that of the cylinder and the neutral mandrel case where the radii of the core and cylinder are the same in the large mandrel case our upper and lower bounds match in their scaling with respect to thickness compression and the magnitude of pre strain induced by the core we construct three types of axisymmetric wrinkling patterns whose energy scales as the minimum in different parameter regimes corresponding to the presence of many wrinkles few wrinkles or no wrinkles at all in the neutral mandrel case our upper and lower bounds match in a certain regime in which the compression is small as compared to the thickness in this regime the minimum energy scales as that of the unbuckled configuration we achieve these results for both the von karman donnell model and a geometrically nonlinear model of elasticity 2017 wiley periodicals inc

eventually constant solutions of a rational difference equation we describe all the solutions of a rational difference equation from putnam s mathematical competition which are eventually equal to its positive equilibrium email protected 1 as a consequence we give a new elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one moreover we show that almost all solutions of the equation are not eventually equal to one

on positive solutions of some classes of max type systems of difference equations global attractivity results on positive solutions of some special cases of the next max type system of difference equations xn i max1 xn l1 i i p1 i j1 1m1 i xn j1 i1 sj1 i1 qj1 i1 xn lri i i pri i jri 1mri i xn jri iri sjri iri qjri iri n n0 where ri n i 1 k k n sjt it 1 k qjt it 0 i 1 k t 1 ri and pj i 0 1 mj i n i 1 k j 1 ri are presented we also present some results on the behavior of positive solutions of the difference equation xn max p1xn 1 pkxn k xn max p1xn 1 pkxn k where pj j 1 k are nonnegative numbers

dynamical properties of a class of higher order nonlinear difference equations abstract in this note we consider the dynamical properties of the following higher order nonlinear difference equation x n i 1 v x n i i 1 i 1 v x n i i 1 i 1 v x n i i 1 i 1 v x n i i 1 n 0 1 with x v x v 1 x 1 0 1 0 1 i 0 i 2 3 v our result extends and includes corresponding results in the recent literatures

energy scaling of compressed elastic films three dimensional elasticity and reduced theories we derive an optimal scaling law for the energy of thin elastic films under isotropic compression starting from three dimensional nonlinear elasticity as a consequence we show that any deformation with optimal energy scaling must exhibit fine scale oscillations along the boundary which coarsen in the interior this agrees with experimental observations of folds which refine as they approach the boundary

exploring the random genesis of co occurrence networks using the network random generation models from gustedt 2009 we simulate and analyze several characteristics such as the number of components the degree sequence and the clustering coefficient of the generated networks this is done for a variety of distributions fixed value bernoulli poisson binomial that are used to control the parameters of generation process these parameters are in particular the size of newly appearing sets of objects the number of contexts in which new elements appear initially the number of objects that are shared with parent contexts and the time period inside which a context may serve as a parent context aging the results show that these models allow to fine tune the generation process such that the graphs adopt properties as they can be found in real world graphs

global asymptotic stability in some discrete dynamical systems for a discrete dynamical system xn 1 txn on m rr some general conditions will be specified under which the unique equilibrium is globally asymptotically stable as a special result we obtain the strong negative feedback property established in a m amleh n kruse and g ladas j differ equations appl to appear finally we apply our result to show that the equilibrium x 1 of the putnam difference equation xn 1 xn xn 1 xn 2xn 3xnxn 1 xn 2 xn 3 with positive initial conditions x0 x 3 is globally asymptotically stable

periodicity of a class of nonautonomous max type difference equations abstract in this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x n max f 1 x n k 1 n f m x n k m n x n s n n 0 and x n min f 1 x n k 1 n f m x n k m n x n s n n 0 where 1 k 1 k m m s n and where the functions f i 0 n 0 0 1 i m satisfy some additional conditions these results considerably extend and unify numerous results on max type difference equations existing in the literature

on a system of difference equations abstract we show that the system of difference equations x n 1 ax n 1 by n x n 1 c y n 1 y n 1 x n y n 1 n n 0 where the parameters a b c and initial values x 1 x 0 y 1 y 0 are real numbers can be solved considerably improving the results in the literature

long term behavior of positive solutions of a system of max type difference equations abstract some sufficient conditions which guaranty the attractivity of all positive solutions of the next system of difference equations x n max a y n 1 p j 2 k x n j q j y n max a x n 1 p j 2 k y n j q j n n 0 where a p 0 and q j j 2 k are nonnegative numbers are given the boundedness character of positive solutions of the system is also studied

n body decomposition of bipartite author networks in this paper we present a method to project co authorship networks that accounts in detail for the geometrical structure of scientists collaborations by restricting the scope to three body interactions we focus on the number of triangles in the system and show the importance of multi scientist more than two collaborations in the social network this motivates the introduction of generalized networks where basic connections are not binary but involve arbitrary number of components we focus on the three body case and study numerically the percolation transition

a control theory point of view on beverton holt equation in population dynamics and some of its generalizations abstract this paper is devoted to develop some ad hoc control theory formalism useful for the famous beverton holt equation arising in population dynamics in particular the inverse equation is redefined for a finite set of consecutive samples under the equivalent form of a discrete linear dynamic system whose input sequence is defined by the sequence of carrying capacity gains and the unforced dynamics is directly related to the intrinsic growth rate for that purpose the environment carrying capacity gains are allowed to be time varying and designed for control purposes the controllability property is also investigated on this dynamic extended system as well as the stability equilibrium points and attractor oscillating trajectories the properties of the dynamic system associated with the beverton holt inverse equation allow extrapolate in a simple dual way the above properties to the standard beverton holt equation some generalizations are given for the case when there are extra parameters in the equation or when the system is subject to the presence of additive disturbances in all cases a reference model being also of beverton holt type is proposed to be followed by the control system