Superposition of the Nadai and prandtl solutions for the system of two-dimensional ideal plasticity

A general algorithm is presented for transforming the exact solutions of the system of plane ideal plasticity of the Mises medium by using the superposition principle for solutions which arises as a corollary of the fact that the original system admits an infinite-dimensional symmetry group. As an example, there is considered the relation between the known exact solutions: the Prandtl solution for a thin layer compressed by rough solid plates and the Nadai solution for the radial distribution of stresses in a convergent channel in the shape of a flat wedge.     

Additivity of quasi-measures

We prove that quasi-measures on compact Hausdorff spaces are countably additive. Contained in this result is a proof that every quasi-measure decomposes uniquely into a measure and a quasi-measure that has no smaller measure beneath it. We also show that it is consistent with the usual axioms of set-theory that quasi-measures on compact Hausdorff spaces are -additive. Finally, we construct an example that places strong restrictions on other forms of additivity.

     

Factorization of an integrally closed ideal in two-dimensional regular local rings

Let be a two-dimensional regular local ring with algebraically closed residue field and be an -primary integrally closed ideal in . Let be the set of Rees valuations of and be the residue field of the valuation ring associated with . Assume that is any minimal reduction of . We show that if is the product of the distinct simple -primary integrally closed ideals in , then is generated by the image of over for all , and the converse of this is also true.

     

Existence of solutions for the two-dimensional stationary Euler system for ideal fluids with arbitrary force

We generalize a theorem by J.-M. Coron (see [Sur la stabilisation des fluides parfaits incompressibles bidimensionnels, in: Séminaire Équations aux Dérivées Partielles, École Polytechnique, Centre de Mathématiques, 1998–1999, exposé VII]) and prove the existence of steady states of the Euler system for inviscid incompressible fluids with an arbitrary force term, in a plane bounded domain not necessarily simply connected, if one allows the fluid to pass through a prescribed region of the boundary, which satisfies the necessary condition that each connected component of the boundary is met by it.     

On the Additivity of the Minkowski Functionals

In this work, we investigate the additivity of the Minkowski functionals associated to a cone in a linear vector space. As an application we discuss the equivalence of the classical Caristi fixed point theorem in metric spaces and its vectorial version in cone metric spaces.     

Additivity properties of operator ranges

In the present paper we study different conditions regarding the sum of operator ranges. In particular, we find conditions on operators A, B   which imply that R(A+B)=R(A)+R(B)$R(A+B)=R(A)+R(B)$ and derive some results concerning projections.     

On the motion of a rigid body in a two-dimensional ideal flow with vortex sheet initial data

A famous result by Delort about the two-dimensional incompressible Euler equations is the existence of weak solutions when the initial vorticity is a bounded Radon measure with distinguished sign and lies in the Sobolev space H⁻¹$H^{-1}$. In this paper we are interested in the case where there is a rigid body immersed in the fluid moving under the action of the fluid pressure. We succeed to prove the existence of solutions à la Delort in a particular case with a mirror symmetry assumption already considered by Lopes Filho et al. (2006) [11], where it was assumed in addition that the rigid body is a fixed obstacle. The solutions built here satisfy the energy inequality and the body acceleration is bounded. When the mass of the body becomes infinite, the body does not move anymore and one recovers a solution in the sense of Lopes Filho et al. (2006) [11].     

The Poincaré series of a simple complete ideal of a two-dimensional regular local ring

The aim of this work is to introduce both a classical and a motivic Poincaré series associated with a residually rational simple complete m-primary ideal ℘ of a two-dimensional regular local ring (R,m). We describe them in terms of the generators of the value semigroup of ℘, and compare them with the Poincaré series arising from a general element f for ℘.     

Weakening Additivity in Adjoining Closures

In this paper, we weaken the conditions for the existence of adjoint closure operators, going beyond the standard requirement of additivity/co-additivity. We consider the notion of join-uniform (lower) closure operators, introduced in computer science, in order to model perfect lossless compression in transformations acting on complete lattices. Starting from Janowitz’s characterization of residuated closure operators, we show that join-uniformity perfectly weakens additivity in the construction of adjoint closures, and this is indeed the weakest property for this to hold. We conclude by characterizing the set of all join-uniform lower closure operators as fix-points of a function defined on the set of all lower closures of a complete lattice.     

Orthogonality and Additivity Modulo Z

Let E be a real inner product space of dimension at least 2. Suppose ? : E → ? satisfies If there exist a neighbourhood U of the origin and γ ∈ (0, 1/4) such that ?(U) ? (?γ,γ) + ?, then there exist a real constant c and a continuous linear functional g : E → ? such that Suppose Φ : E → ? satisfies If there exist a neighbourhood U of the origin and β ∈ (0, +∞) such that ¦Φ(x)¦ ≤ β?(Φ(x)) for every x ∈ U, then either Φ vanishes on E? {0} or there exist additive functions a : ? → ? and A : E → ?, a real constant c and a continuous linear functional g : E → ? such that      

Additivity of the crossing number of graphs with connectivity 2

We prove that the crossing number of graphs with connectivity 2 has in certain cases an additive property analogous to that of crossing number of graphs with connectivity ≤1.     

Additivity of tunnel number for small knots

We show that for small knots , and that for small knots . Received: March 10, 1997.     

Additivity of integrals on generalized measure spaces

It is proved that the integral is additive on simple summable functions of a generalized measure space.     

Additivity of n-Multiplicative Maps on Alternative Rings

Let ? and ?′ be alternative rings. We study the additivity of n-multiplicative isomorphisms from ? onto ?′ and of n-multiplicative derivations of ?. We prove that, if ? contains a family of nontrivial idempotents satisfying Martindale's conditions, then these two maps are additives.     

Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface

We establish the complete integrability of a nonlinear dynamical system associated with the hydrodynamic Navier-Stokes equations for the flow of an ideal two-dimensional liquid with a free surface over the horizontal bottom. We show that this dynamical system is naturally connected with the nonlinear kinetic Boltzmann-Vlasov equation for a one-dimensional flow of particles with a point potential of interaction between particles.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 1, pp. 86–90, January, 1993.