Dynamic instability of a non-uniform beam modeled in a two-degree-of-freedom system

The behaviour of a non-uniform beam loaded by a parallel or tangential compressive force respectively is analyzed by exploiting a two-degree-of-freedom dynamic model. The same system has been analyzed previously by Lee and Reissner from a static point of view and by Neer and Baruch by a dynamic approach using a one-degree-of-freedom model. The previous analyses revealed only part of the phenomena by the present approach.Here, for the tangential force a classical flutter instability is obtained and for the parallel force only static instability is possible.     

Realizability of words in mosaic labyrinths

In this paper we study mosaic labyrinths with the help of words generated by them in the alphabet of labels attached to arcs and vertices of a labyrinth. We consider the problem of the characterization of words generated by a labyrinth. We propose a constructive recognition criterion, it defines whether a word is generated by a labyrinth or not. We establish conditions under which a word can be generated by a unique labyrinth, by a finite number of labyrinths, or by infinitely many labyrinths.     

Well-posedness by perturbations of mixed variational inequalities in Banach spaces

In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a mixed variational inequality problem in a Banach space. We establish some metric characterizations of the well-posedness by perturbations. We also show that under suitable conditions, the well-posedness by perturbations of a mixed variational inequality problem is equivalent to the well-posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem. Also, we derive some conditions under which the well-posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution.     

Universal contingent claims in a general market environment and multiplicative measures: Examples and applications

We present and further develop the concept of a universal contingent claim introduced by the author in 1995. This concept provides a unified framework for the analysis of a wide class of financial derivatives.A universal contingent claim describes the time evolution of a contingent payoff. In the simplest case of a European contingent claim, this time evolution is given by a family of nonnegative linear operators, the valuation operators. For more complex contingent claims, the time evolution that is given by the valuation operators can be interrupted by discrete or continuous activation of external influences that are described by, generally speaking, nonlinear operators, the activation operators. For example, Bermudan and American contingent claims represent discretely and continuously activated universal contingent claims with the activation operators being the nonlinear maximum operators.We show that the value of a universal contingent claim is given by a multiplicative measure introduced by the author in 1995. Roughly speaking, a multiplicative measure is an operator-valued (in general, an abstract measure with values in a partial monoid) function on a semiring of sets which is multiplicative on the union of disjoint sets. We also show that the value of a universal contingent claim is determined by a, generally speaking, impulsive semilinear evolution equation.     

Continuous Frames, Function Spaces, and the Discretization Problem

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function spaces can be identified as such spaces. We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame. This is done by generalizing the coorbit space theory developed by Feichtinger and Gröchenig. As an important tool the concept of localization of frames is extended to continuous frames. As a byproduct we give a partial answer to the question raised by Ali, Antoine, and Gazeau whether any continuous frame admits a corresponding discrete realization generated by sampling.     

Nonuniqueness for Willmore Surfaces of Revolution Satisfying Dirichlet Boundary Data

In this note Willmore surfaces of revolution with Dirichlet boundary conditions are considered. We show two nonuniqueness results by reformulating the problem in the hyperbolic half plane and solving a suitable initial value problem for the corresponding elastic curves. The behavior of such elastic curves is examined by a method provided by Langer and Singer to reduce the order of the underlying ordinary differential equation. This ensures that these solutions differ from solutions already obtained by Dall’Acqua, Deckelnick and Grunau. We will additionally provide a Bernstein-type result concerning the profile curve of a Willmore surface of revolution. If this curve is a graph on the whole real numbers it has to be a Möbius transformed catenary. We show this by a corollary of the above-mentioned method by Langer and Singer.     

Schrödinger Operator Perturbed by Operators Related to Null Sets

We discuss the Schrödinger operator with positive singular perturbations given by operators which act in the space constructed by a positive measure supported by a null set. We construct examples when perturbations are given by the one-dimensional Laplacian on a segment.     

On Solvability of Lie Rings with an Automorphism of Finite Order

A new criterion for a Lie ring with a semisimple automorphism of finite order to be solvable is proved. It generalizes the effective version of Winter's criterion obtained earlier by Khukhro and Shumyatsky and by Bergen and Grzeszczuk in replacing the ideal generated by a certain set by the subring generated by this set. The proof is inspired by the original theorem of Kreknin on solvability of Lie rings with regular automorphisms of finite order and is conducted mostly in terms of Lie rings graded by a finite cyclic group.     

On a lower bound for the extinction time of surfaces moved by mean curvature

This paper considers a generalized evolution of a compact closed (hyper)-surface moved by its mean curvature. By a comparison of a shrinking ball the surface extincts in a finite time. An estimate of the extinction time from above is given by L. C. Evans and J. Spruck. In this paper we give an estimate from blow. In fact we proved that the extinction time is estimated from below by to times the square of the volume of a set enclosed by the initial surface over the initial area of the surface. The constant two is optimal.Partly supported by the Inamori Foundation     

Proof of the Branner-Hubbard conjecture on Cantor Julia sets

By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove that a component of the filled-in Julia set of any polynomial is a point if and only if its forward orbit contains no periodic critical components. It follows immediately that the Julia set of a polynomial is a Cantor set if and only if each critical component of the filled-in Julia set is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992. This work was supported by the National Natural Science Foundation of China     

A class of Finsler metrics with isotropic S-curvature

In this paper, we study a class of Finsler metrics defined by a Riemannian metric and a 1-form. We characterize these metrics with isotropic S-curvature. Supported by a NNSFC grant (10671214) and by the NSF project of CQ CSTC. Supported by a NNSFC grant (10671214), a NSF grant (DMS-0810159) and the C. K. Chao Foundation for Advanced Research     

Weber problems with mixed distances and regional demand

We consider a location problem where the distribution of the existing facilities is described by a probability distribution and the transportation cost is given by a combination of transportation cost in a network and continuous distance. The motivation is that in many cases transportation cost is partly given by the cost of travel in a transportation network whereas the access to the network and the travel from the exit of the network to the new facility is given by a continuous distance.      

Variational approach to scattering of plane elastic waves by diffraction gratings

The scattering of a time‐harmonic plane elastic wave by a two‐dimensional periodic structure is studied. The grating profile is given by a Lipschitz curve on which the displacement vanishes. Using a variational formulation in a bounded periodic cell involving a nonlocal boundary operator, existence of solutions in quasiperiodic Sobolev spaces is investigated by establishing the Fredholmness of the operator generated by the corresponding sesquilinear form. Moreover, by a Rellich identity, uniqueness is proved under the assumption that the grating profile is given by a Lipschitz graph. The direct scattering problem for transmission gratings is also investigated. In this case, uniqueness is proved except for a discrete set of frequencies. Copyright © 2010 John Wiley & Sons, Ltd.     

Randomized system trajectories

The notion of system trajectory of a time-varying input-output, dynamical system is reviewed. By introducing a probability measure on a class of such systems a stochastic system, the randomized system, is defined. The randomized system has a trajectory induced by the trajectories of the original systems. A theorem is proved giving fairly general conditions under which the randomized system trajectory is generated by a strongly continuous semigroup of bounded linear operators in a Banach space. An example is presented for a system represented by a quadratic integral operator.Research supported in part by National Science Foundation under Grant No. ECS-8005960.     

Information loss and entropy increase

The statistical entropy is shown to increase due to information loss introduced by a substitution of the total distribution function of a given system by (i) a product of distribution functions of lower orders and by (ii) a new distribution function transformed from the original one by an integral equation such as appearing in the theory of stochastic processes.     

The axioms for implication in orthologic

We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice. This work is supported by the Research Project MSM 6198959214 by Czech Goverment.     

Enhanced and reduced natural convection using magnetic fluid in a square cavity

Natural convection using a magnetic fluid was studied in a square cavity under the influence of a permanent magnet. The aim was to explore the degree by which heat transfer may be controlled, enhanced or reduced, by investigating a set of different distances of a permanent magnet to the cavity. These distances of the magnet were set such that the cavity was in some cases fully dominated by buoyancy or by the magnetic body force and in other cases partly dominated by either of both body forces in different parts of the fluid. The effect on heat transfer was characterised by an averaged Nusselt number, Rayleigh and magnetic Rayleigh number. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Automation and group structures in certain economic adjustment mechanisms

It is shown that the economic adjustment mechanism developed by Hurwicz and his associates has the structure of automata. It is then shown that certain price adjustment mechanisms, having an acceptability condition, impose a group structure upon the automaton. This condition is a bilinear invariance implied by a budget constraint. Then the automaton is defined by a subgroup, depending on agents' tastes, technologies and strategies, and by the representations of the subgroup imposed by the automaton.     

Singular Double Porosity Model

We consider the linear parabolic equation describing the transport of a contaminant in a porous media crossed by a net of infinitely thin fractures. The permeability is very high in the fractures but very low in the porous blocks. We derive the homogenized model corresponding to a net of infinitely thin fractures, by means of the singular measures technique. We assume that these singular measures are supported by hyperplanes of codimension one. We prove in a second step that this homogenized model could be obtained indistinctly either by letting the fracture thickness, in the standard double porosity model, tend to zero, or by homogenizing a model with infinitely thin fractures.