On Schrödinger-Virasoro type Lie conformal algebras

In this paper, two classes of Schrödinger-Virasoro type Lie conformal algebras TSV(a,b) and TSV(c) which are non-simple are introduced for some a, b, c∈?. Moreover, central extensions, conformal derivations and free conformal modules of rank 1 of TSV(a,b) and TSV(c) are determined.     

Purity in the category of S-posets

In this paper, purity of S-posets over a pomonoid S is investigated. We first study some basic properties of absolutely po-pure S-posets. Among other results, it is proved that every regular injective S-poset is absolutely po-pure, and every absolutely po-pure inequationally compact S-poset is regular injective. Then, using the notion of semi-finitely presented S-poset based on the finitely induced S-poset congruence, we find an equivalent condition for an S-poset to be 1-po-pure in a regular extension. Finally, a characterization of an absolutely 1-po-pure S-poset is presented.     

On a Class of Non-local Operators in Conformal Geometry

In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.     

On the normalized eigenvalue problems for nonlinear elliptic operators

This paper solves the following form of normalized eigenvalue problem:

     

Analytic Extension of Functions from Analytic Hilbert Spaces

Let M be an invariant subspace of Hv2. It is shown that for each f∈M⊥, f can be analytically extended across (?)Bd\σ(Sz1,…, Szd).     

New segmented poly(ester‐urethane)s from renewable resources

The physical and mechanical properties of aliphatic homopolyesters from monomers obtainable from renewable resources, namely, 1,3‐propanediol and succinic acid, were improved by their combination with aromatic urethane segments capable of establishing strong intermolecular hydrogen bonds. Segmented poly(ester‐urethane)s were synthesized from dihydroxy‐terminated oligo(propylene succinate)s chain‐extended with 4,4′‐diisophenylmethane diisocyanate. The newly synthesized materials were exhaustively characterized by ¹H NMR spectroscopy, size exclusion chromatography, differential scanning calorimetry, dynamic mechanical analysis, and with respect to their main static mechanical properties, an Instron apparatus was used. The average repeat number of the hard segments, evaluated by NMR, ranged from 4 to 9, whereas that of the flexible segments was about 14. The degree of crystallinity, glass‐transition temperature, melting point, tensile strength, elongation, and Young's modulus were influenced by the ratio between hard and soft segments of the segmented copolymer in a predictable way. The results demonstrated that poly(ester‐urethane)s from 1,3‐propanediol and succinic acid are promising thermoplastics. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 630–639, 2001     

A method for establishing generalized variational principle

A method for establishing generalized variational principle is proposed in this paper. It is based on the analysis of mechanical meaning and it can be applied to problems in which the variational principles are needed but no corresponding variational principle is available. In this paper, the Hu-Washizu ’s generalized variational principle and the Hu’s generalized principle of complementary energy are derived from the mechanical meaning instead of from the generalization of the principle of minimum potenlial energy and the correct proofs of these two generaleed variational principles are given. It is also proved that this is wrong if one beleives that σ_ij, e_ij and ui are independent variables each other based on the reason that these three kinds of variables are all contained in these two generalized variational principles. The condition of using these two variational principles in a correct manner is also explained.     

Singular point perturbation of an odd operator in ℤ2-Graded space

In the paper we study supersymmetric models for point interaction perturbations of operators of Dirac type and their spectral properties. Such models are considered in the class of odd self-adjoint operators in ℤ₂-graded Pontryagin space. We present in detail the previously considered realization method of strongly singular perturbation by means of their embedding into the theory of self-adjoint extensions. We describe odd self-adjoint extensions of odd symmetric operators with deficiency indices (1,1) in ℤ₂-graded Pontryagin space and squares of such extensions using Krein’s formula for the resolvent. The results obtained are refined in application to singular perturbations of odd self-adjoint differential operators. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 924–940, December, 1999.