Remarks on the Scattering Result of Nonlinear Schroedinger Equations

0 Introduction 　　In this paper, we give another proof of the scattering result of the following Cauchy problem in the energy space     

Cohomology of the Lie algebra ℌ2: Experimental results and conjectures

The cohomology with trivial coefficients of the Lie algebra ? of Hamiltonian vector fields in the plane and of its maximal nilpotent subalgebra L ₁? is considered. The cohomology H ₂(L ₁?) is calculated, and some far-reaching conjectures concerning the cohomology of the Lie algebras mentioned above and based on an extensive experimental material are formulated.     

On the action of the Iwahori–Hecke algebra on modular invariants

We compute the action of the modular Iwahori–Hecke algebra on the ring of invariants of the mod p cohomology of elementary p-groups under Borel subgroup of the general linear group. Applications include a direct proof of the structure of the universal Steenrod algebra and a new proof of a key result on the structure of the Takayasu modules.     

Interpolating Blaschke products and the ideals of the algebra H∂

To each vector-function f, f H(Z²) one can associate two ideals of the algebra. In the note one characterizes those functions f for which some interpolation Blaschke product is contained in I(f) (or J (f)). One also characterizes those functions u, u H such that if for some f, then u I(f) (in the corona theorem a similar statement is proved for the case u =1).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 196–201, 1983.     

Remarks on existence and uniqueness of Cournot–Nash equilibria in the non-potential case

This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot–Nash equilibria for games with a continuum of players with both attractive and repulsive effects. We mainly address separable situations but for which the game does not have a potential, contrary to the variational framework of Blanchet and Carlier (Optimal transport and Cournot–Nash equilibria, 2012). We also present several numerical simulations which illustrate the applicability of our approach to compute Cournot–Nash equilibria.     

Extensions of the disc algebra and of Mergelyanʼs theorem

We investigate the uniform limits of the set of polynomials on the closed unit disc $\overline{D}$ with respect to the chordal metric χ. More generally, we examine analogous questions replacing $\mathbb{C}\cup \{\infty \}$ by other metrizable compactifications of $\mathbb{C}$.     

ℤ/2ℤ Invariants of the free fermion algebra

By using quantum vertex operators we study the invariance of the rank n free-fermion vertex algebra under the action of the group ?∕2? and obtain its minimal generating set. When n = 1, it is well known that this subalgebra is isomorphic to the Virasoro vertex algebra with central charge 1∕2. In the n = 2 case we show that invariant subalgebra is isomorphic to a simple quotient of a certain W-algebra, which we explicitly construct. For n≥3, our approach leads to a rediscovery of the spinor representation of the a?ne vertex algebra associated to the Lie algebra 𝔰𝔬(n) of I. Frenkel.     

On ℤp-graded identities and cocharacters of the Grassmann algebra

Let p be an odd prime number, F a field of characteristic zero, and let Ebe the unitary Grassmann algebra generated by the infinite-dimensionalF-vector space L. We determine the bases of the ?_p-graded identities.Moreover we compute the ?_p-graded codimension and cocharacter sequences for the algebra E endowed with any ?_p-grading such that L is a homogeneous subspace.     

Remarks on Maximal Attractors for the Compressible Navier-Stokes Equations of Viscous and Heat Conductive Fluid

This paper is concerned with the existence of maximal attractors in Hi (i = 1, 2,4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn(n = 2,3).     

Remarks on the Global Attractor of the Weakly Dissipative Benjamin－Ono Equation

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Cones in the space Lp (1 ≤ p ≤ ∞) and minimax problems of mathematical statistics

The structure of cones in the spaces L_p(l p ) and their application to minimax problems of statistical assumptions are considered.Translated from Staticheskie Metody, pp. 28–30, 1978.     

Solvability of the 3D rotating Navier–Stokes equations coupled with a 2D biharmonic problem with obstacles and gradient restriction

A coupled system by the 3D rotating Navier–Stokes equations with a mixed boundary condition and a 2D biharmonic problem with two obstacles and the gradient restriction is investigated in this paper. Using the Schauder’s fixed point theorem, we show the existence of a strong solution for a sufficiently large viscosity ν and sufficiently small data.