A class of integral transforms which are projections

We consider all convolution tranforms onL ²() which are projections, and determine their ranges and null-spaces; it turns out that all are orthogonal projections. By modification of the kernel, integral transforms are defined which are oblique projections, and their angle of inclination is approximated using finite dimensional spaces. Several families of such projections are treated and results for the angle of inclination as function of the parameters are displayed. In some cases an exact formula has been obtained.     

A certain class of functions that are univalent in an annulus

In the class F₁ of functions f(), regular and univalent in the annulus ={<||<1} and satisfying the conditions ¦f()¦ < 1 and f() 0 for , ¦f()¦=1 ¦¦=1, for f(l)=1, one finds the set of the values D(A)=f(A): f for an arbitrary fixed point A. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 82–92, 1985.     

Degeneracy of holomorphic curves in surfaces

Let X be a complex projective algebraic manifold of dimension 2 and let D1,…,Du be distinct irreducible divisors on X such that no three of them share a common point. Let f: C→X\(U1≤i≤uDi) be a holomorphic map. Assume that u≥4 and that there exist positive integers n1,…,nu, c such that ninj(Di.Dj) = c for all pairs i, j. Then f is algebraically degenerate, i.e. its image is contained in an algebraic curve on X.     

A new class of nonexpansive type mappings and fixed points

In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.27. march 80     

A note on asymptotic inference in a class of non-stationary processes

In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation.     

Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC

In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type BC. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds G/K over one of the skew fields F=R,C,H. We write the product formula of these spherical functions in an explicit form which allows analytic continuation with respect to the parameters. In each of the three cases, we obtain a series of hypergroup algebras which include the commutative convolution algebras of K-biinvariant functions on G as special cases. The characters are given by the associated hypergeometric functions.     

A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory

Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear model constitutive laws. We obtain laws previously used to model a variety of hard and soft nonlinear elastic responses. A natural extension of the latter leads to a novel class of model constitutive laws where the stress and strain are given parametrically in terms of elliptic functions. Such models allow a change in the concavity of the stress-strain law. Such behavior can be observed in the compression of polycrystalline materials or in the unloading regimes of superelastic nickel-titanium.     

Marino—Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces

In this work, we study a class of Euler functionals defined in Banach spaces, associated with quasilinear elliptic problems involving p-Laplace operator (p > 2). First we obtain perturbation results in the spirit of the remarkable paper by Marino and Prodi (Boll. U.M.I. (4) 11(Suppl. fasc. 3): 1–32, 1975), using the new definition of nondegeneracy given in (Ann. Inst. H. Poincaré: Analyse Non Linéaire. 2:271–292, 2003). We also extend Morse index estimates for minimax critical points, introduced by Lazer and Solimini (Nonlinear Anal. T.M.A. 12:761–775, 1988) in the Hilbert case, to our Banach setting. Mathematics Subject Classification (1991) 58E05, 35B20, 35J60, 35J70     

A class of completely continuous operators in a Hilbert space of entire functions of exponential type

Any positive Borel measure in Rⁿ which satisfies the conditionsup {xRⁿ¦ ¦x–y¦1}< generates a Hermitian bilinear form in the Hilbert space of entire functionsf: CⁿC¹ of exponential type not exceeding which are square-summable on Rⁿ. In this paper a criterion is given for the complete continuity of this form.Translated from Matematicheskie Zametki, Vol. 6, No. 2, pp. 173–179, August, 1969.     

粘弹性方程的非协调变网格有限元方法

讨论了粘弹性方程的Crouzeix-Raviart型非协调变网格有限元方法,在不需要引入传统分析中Riesz投影的情况下得到了最优误差估计.     

A method for accelerating the iterative solution of a class of Fredholm integral equations

The present paper extends the synthetic method of transport theory to a large class of integral equations. Convergence and divergence properties of the algorithm are studied analytically, and numerical examples are presented which demonstrate the expected theoretical behavior. It is shown that, in some instances, the computational advantage over the familiar Neumann approach is substantial.This authors acknowledge with pleasure conversations with Paul Nelson. Thanks are due also to Janet E. Wing, whose computer program was used in making the calculations reported in Section 8.This work was performed in part under the auspices of USERDA at the Los Alamos Scientific Laboratory of the University of California, Los Alamos, New Mexico.     

A new type of integral equations related to the co-area formula (Reduction of dimension in multi-dimensional integral equations)

Some classes of multi-dimensional integral equations of the second kind are introduced which admit an equivalent reduction to integral equations for functions depending on a smaller number of independent variables. This reduction is performed by factorization of the integral operator based on the co-area formulas.     

A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type

In this paper, we proved a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type and a property (E.A) introduced in [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188]. Our theorem generalizes Theorem 2.2 of [M. Aamri, D. El Moutawakil, Common fixed points under contractive conditions in symmetric spaces, Appl. Math. E-Notes 3 (2003) 156-162] and Theorem 2 of [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188].     

Characterisation of homogeneous polynomials which are constant on complex-tangential curves in the boundary of the unit ball of

We prove that a complex-tangential curve γ in the boundary of the unit ball of having the property that there exists a homogeneous polynomial P such that P=1 on γ has constant curvature. This implies that a homogeneous polynomial P having the property that there exists a closed complex-tangential curve γ (respectively a totally real 2-dimensional submanifold) in the boundary of the unit ball of such that P=1 on γ (respectively |P|=1 on γ) reduces to a monomial by a unitary chage of variables. These results represent a positive answer to conjectures of H. O. Kim.     

A framization of the Hecke algebra of type B

We introduce a framization of the Hecke algebra of type B. For this framization, we construct a faithful tensorial representation and two linear bases. We also construct a Markov trace on such an algebra, and from this trace we derive isotopy invariants for framed and classical knots and links in the solid torus.     

A N. Bourbaki type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory T.     

A strong solution of a high-order mixed type partial differential equation with integral conditions

In this article, we study a mixed problem with integral boundary conditions for a high-order partial differential equation of mixed type. We prove the existence and uniqueness of a strong solution. The proof is based on energy inequality and on the density of the range of the operator generated by the considered problem.