On the induced almost contact structure of a Brieskorn manifold

Geometriae Dedicata -     

On the influence of contact mechanics on friction induced flutter instability

Within this contribution, the general form of perturbation equations for systems of moving elastic bodies is derived and examined with respect to symmetry and definiteness properties. The contact is enforced by a penalty formulation, which is motivated by a constitutive contact model relying on statistical data of the surface. Evaluating Hamilton's Principle and carrying out a linearization about a stationary transport motion, the general perturbation equations are derived. The resulting differential operators are stated and discussed. The findings are exemplified for a rotating cicular Timoshenko beam with frictional contacts. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Waves induced by the longitudinal impact of a rod against a stepped rod in contact with a rigid barrier

The longitudinal elastic central impact of a rod system, consisting of a uniform rod having a pre-impact velocity against a stepped rod which is in a state of rest and interacts by means of unilateral constraints with a rigid barrier, is modelled.     

Multibody elastic contact analysis by quadratic programming

A quadratic programming method for contact problems is extended to a general problem involving contact ofn elastic bodies. Sharp results of quadratic programming theory provide an equivalence between the originaln-body contact problem and the simplex algorithm used to solve the quadratic programming problem. Two multibody examples are solved to illustrate the technique.     

Foliations induced by congruences

Communicated by Klaus Keimel     

Exponential rates of convergence by an iteration technique

The goal of this Note is to introduce a technique leading to a convergence of exponential type for the solution of problems set in cylinders becoming unbounded in some directions. To cite this article: M. Chipot, K. Yeressian, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Dependence structure between LIBOR rates by copula method

This paper discusses the correlation structure between London Interbank Offered Rates (LIBOR) by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela (1997) and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.     

Optimal design of profit sharing rates by FFT

This paper addresses the calculation of a fair profit sharing rate for participating policies with a minimum interest rate guaranteed. The bonus credited to policies depends on the performance of a basket of two assets: a stock and a zero coupon bond and on the guarantee. The dynamics of the instantaneous short rates are driven by a Hull and White model, whereas the stocks follow a double exponential jump-diffusion model. The participation level is determined such that the return retained by the insurer is sufficient to hedge the interest rate guaranteed. Given that the return of the total asset is not lognormal, we rely on a Fast Fourier Transform to compute the fair value of bonus and guarantee options.     

Random induced subgraphs of Cayley graphs induced by transpositions

In this paper we study random induced subgraphs of Cayley graphs of the symmetric group induced by an arbitrary minimal generating set of transpositions. A random induced subgraph of this Cayley graph is obtained by selecting permutations with independent probability, λ_n. Our main result is that for any minimal generating set of transpositions, for probabilities where and δ>0, a random induced subgraph has a.s. a unique largest component of size . Here x(?_n) is the survival probability of a Poisson branching process with parameter λ=1+?_n.     

Equivalences induced by graded bimodules

Let k be a commutative ringG a finite groupR and S fully G-graded k-algebras. In this paper we investigate Morita equivalences, derived equivalences and stable equivalences of Morita type between R and S, which are induced by G-graded R, 5-bimodules or complexes of G-graded bimodules. Such equivalences occur naturally in the case of group algebras in certain reduction steps for Broue's conjecture, and we show how they can be lifted from equivalences between R ₁ and S ₁.     

Filtrations induced by continuous functions

In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to Rⁿ${\mathbb{R}}^n$. A natural question arises, whether these approaches are equivalent or not. In this paper we study this problem and prove that, while the answer to the previous question is negative in the general case, the approach by continuous functions is not restrictive with respect to the other, provided that some natural stability and completeness assumptions are made. In particular, we show that every compact and stable 1-dimensional filtration of a compact metric space is induced by a continuous function. Moreover, we extend the previous result to the case of multi-dimensional filtrations, requiring that our filtration is also complete. Three examples show that we cannot drop the assumptions about stability and completeness. Consequences of our results on the definition of a distance between filtrations are finally discussed.     

Analysis of unbonded contact problems by means of quadratic programming

Two-body, elastic, unbonded contact problems are formulated as quadratic programming problems. Uniqueness theorems of quadratic programming theory are applied to show that the solution of a contact problem, if one exists, is unique and can be readily found by the modified simplex method of quadratic programming. A solution technique that is compatible with finite-element methods is developed, so that contact problems with complex boundary configurations can be routinely solved. A number of classical and nonclassical problems are solved. Good agreement is found for problems with previously known solutions.     

Some tight contact foliations can be approximated by overtwisted ones

A contact foliation is a foliation endowed with a leafwise contact structure. In this remark we explain a turbulisation procedure that allows us to prove that tightness is not a homotopy invariant property for contact foliations.     

Globally stable vaccine-induced eradication of horizontally and vertically transmitted infectious diseases with periodic contact rates and disease-dependent demographic factors in the population

Within the framework of SEIR-like epidemic models, we studied the conditions for the stable eradication of some families of vertically and horizontally transmitted infectious diseases in the case of periodically varying contact rate. By means of Floquet’s theory, we found a condition for the eradication solution to be locally asymptotically stable. We then demonstrated that the same condition guarantees also that this vaccine-induced disease-free solution is globally asymptotically stable. A model with interacting populations is also considered. In the final part of this work, we extended the model by taking into account the variation of population size, the impact of disease-related deaths and reduction of fertility.     

Convex structures induced by Chebyshev systems

Recent developments have clarified that some tools of Convex Geometry are closely related to separation theorems obtained in the field of Functional Inequalities. This phenomenon has motivated the investigation of convex structures induced by Chebyshev systems. The present note characterizes such a possible structure, completely describing its combinatorial invariants.     

Graphs induced by iterated function systems

For an iterated function system (IFS) of similitudes, we define two graphs on the representing symbolic space. We show that if the self-similar set \(K\) has positive Lebesgue measure or the IFS satisfies the weak separation condition, then the graphs are hyperbolic; moreover the hyperbolic boundaries are homeomorphic to the self-similar sets.