A short proof that hyperspaces of Peano continua are absolute retracts

We give a short proof of Wojdyslawski's famous theorem.

     

The limit state of a layer compressed by rough plates

The possibility of presenting the solution of the problem of the compression of a three-dimensional layer by two rough plates, if use is made of Prandtl's assumption of a linear variation of the shear stresses over the thickness (not depending on the coordinates along the plates), is analysed. The case of an anisotropic material with a yield point obeying Hill's condition is also considered.     

A simplified proof for the limit of a tower over a cubic finite field

Recently Bezerra, Garcia and Stichtenoth constructed an explicit tower F=(Fn)_n?0 of function fields over a finite field Fq³, whose limit λ(F)=limn→∞N(Fn)/g(Fn) attains the Zink bound λ(F)?2(q²−1)/(q+2). Their proof is rather long and very technical. In this paper we replace the complex calculations in their work by structural arguments, thus giving a much simpler and shorter proof for the limit of the Bezerra, Garcia and Stichtenoth tower.     

An elementary proof of the local central limit theorem

We give an elementary proof of the local central limit theorem for independent, non-identically distributed, integer valued and vector valued random variables.Support by a NSF Grant.Supported by an NSERC Grant     

Multivalued maps as a tool in modeling and rigorous numerics

Applications of the fixed point theory of multivalued maps can be classified into several areas: (1) Game theory and mathematical economics; (2) Discontinuous differential equations, differential inclusions, and optimal control; (3) Computing homology of maps; (4) Computer assisted proofs in dynamics; (5) Digital imaging. We give an overview of the most classical and well developed areas of applications (1) and (2), where a multivalued map is used as a generalization of a single-valued continuous map, and we survey more recent applications (3), (4), and (5), where multivalued maps play the role of a numerical tool. Dedicated to Felix Browder on his 80th birthday     

A rigorous proof of the asymptotic expansion of Green's function in the shadow zone for diffraction on a convex body

We prove the asymptotic expansion (for is the wavenumber) of Green's function for diffraction on a convex smooth body, with both the source and the observation point at an arbitrary distance from the boundary. The analysis is conducted for a two-dimensional Dirichlet problem.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 148, pp. 79–88, 1985.I acknowledge the useful comments of V. B. Filippov.     

Postcritical stage of plates buckling beyond the elastic limit

The theory of small elastoplastic deformations is used to construct differential equations for investigating the behavior of plates in the postcritical stage. The problem of the cylindrical bending of a rectangular plate compressed in one direction is solved by way of example.Tartu State University. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 881–886, September–October, 1968.     

On Kersting's proof of the central limit theorem

By an adaptation of a method originally invented by G. Kersting [1] for the calculation of the limiting distribution of Markovian processes the central limit theorem (CLT) is proven. Only the case of equal variances is considered.     

A semigroup proof of a non-ergodic Markov process central limit theorem with third order terms

A semigroup product for linear operators is used to get a central limit theorem with third order terms which applies to all ergodic and non-ergodic discrete time Markov processes with continuous transition probability densities on a compact Hausdorff space.     

A short proof of Motoo's combinatorial central limit theorem using Stein's method

Summary A new proof of Motoo's combinatorial central limit theorem (see Motoo 1957) is given using a method of Stein (1972) and a combinatorial method of Bolthausen (1984). This proof is shorter than Motoo's and other wellknown proofs (see e.g. Hájek 1961).     

Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations

In this paper, we determine numerically a large class of equilibrium configurations of an elastic two-dimensional continuous pantographic sheet in three-dimensional deformation consisting of two families of fibers which are parabolic prior to deformation. The fibers are assumed (1) to be continuously distributed over the sample, (2) to be endowed of bending and torsional stiffnesses, and (3) tied together at their points of intersection to avoid relative slipping by means of internal (elastic) pivots. This last condition characterizes the system as a pantographic lattice (Alibert and Della Corte in Zeitschrift für angewandte Mathematik und Physik 66(5):2855–2870, 2015; Alibert et al. in Math Mech Solids 8(1):51–73, 2003; dell’Isola et al. in Int J Non-Linear Mech 80:200–208, 2016; Int J Solids Struct 81:1–12, 2016). The model that we employ here, developed by Steigmann and dell’Isola (Acta Mech Sin 31(3):373–382, 2015) and first investigated in Giorgio et al. (Comptes rendus Mecanique 2016, doi:10.1016/j.crme.2016.02.009), is applicable to fiber lattices in which three-dimensional bending, twisting, and stretching are significant as well as a resistance to shear distortion, i.e., to the angle change between the fibers. Some relevant numerical examples are exhibited in order to highlight the main features of the model adopted: In particular, buckling and post-buckling behaviors of pantographic parabolic lattices are investigated. The fabric of the metamaterial presented in this paper has been conceived to resist more effectively in the extensional bias tests by storing more elastic bending energy and less energy in the deformation of elastic pivots: A comparison with a fabric constituted by beams which are straight in the reference configuration shows that the proposed concept is promising.     

The nonexistence of expansive homeomorphisms of a class of continua which contains all decomposable circle-like continua

A homeomorphism of a compactum with metric is expansive if there is such that if and , then there is an integer such that . It is well-known that -adic solenoids () admit expansive homeomorphisms, each is an indecomposable continuum, and cannot be embedded into the plane. In case of plane continua, the following interesting problem remains open: For each , does there exist a plane continuum so that admits an expansive homeomorphism and separates the plane into components? For the case , the typical plane continua are circle-like continua, and every decomposable circle-like continuum can be embedded into the plane. Naturally, one may ask the following question: Does there exist a decomposable circle-like continuum admitting expansive homeomorphisms? In this paper, we prove that a class of continua, which contains all chainable continua, some continuous curves of pseudo-arcs constructed by W. Lewis and all decomposable circle-like continua, admits no expansive homeomorphisms. In particular, any decomposable circle-like continuum admits no expansive homeomorphism. Also, we show that if is an expansive homeomorphism of a circle-like continuum , then is itself weakly chaotic in the sense of Devaney.

     

Mechanically homogenized material model for a pack of sheets

In the present contribution we discuss the modeling of a large number of plane metal sheets under compressive forces. The direct approach to this contact problem is based on a finite element (FE) discretization of each sheet and a contact formulation between each adjacent sheet. The numerical problem is highly non-linear and of very large dimension. Therefore it is difficult to be solved by conventional FE-software. We propose to replace the contact model by a homogenized constitutive law, which behaves as a pack of infinitely thin sheets. A coarser discretization as for the contact model can be used. A pack of sheets under pressure normal to the sheet plane serves as a benchmark example. The model is verified and implemented for the 2D case and numerical results of the test case are shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

COGARCH as a continuous-time limit of GARCH(1,1)

COGARCH is an extension of the GARCH time series concept to continuous time, which has been suggested by Klüppelberg, Lindner and Maller [C. Klüppelberg, A. Lindner, R. Maller, A continuous-time GARCH process driven by a Lévy process: Stationarity and second order behaviour, Journal of Applied Probability 41 (2004) 601–622]. We show that any COGARCH process can be represented as the limit in law of a sequence of GARCH(1,1) processes. As a by-product we derive the infinitesimal generator of the bivariate Markov process representation of COGARCH. Moreover, we argue heuristically that COGARCH and the classical bivariate diffusion limit of Nelson [D. Nelson, ARCH models as diffusion approximations, Journal of Econometrics 45 (1990) 7–38] are probably the only continuous-time limits of GARCH.     

Structured continua from a lagrangian point of view

Sunto In questo lavoro si studiano le ipersuperfici di bigrado (p, 2)in P ¹×P ^m ,m3m dispari p1.Tali ipersuperfici per p=1si presentanto in modo naturale nello studio del problema di Torelli per le intersezioni complete di due quadriche trasverse in P ^m .Viene analizzata la loro struttura e dimostrato che per p2il Teorema di Torelli non vale per tali ipersuperfici mentre vale per p=1 (Turin).

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Partially supported by a C.N.R. fellowship at the University of Georgia, Athens, Georgia.