Cameron–Liebler line classes in PG(n,4)

We derive a new existence condition for Cameron–Liebler line classes in \(PG(3,q)\) . As an application, we obtain the characterization of Cameron–Liebler line classes in \(PG(n,4),\,n\ge 3\) .     

On Gaussian Nikolskii–Besov classes

Doklady Mathematics - In this note we study Nikolskii–Besov classes of functions of fractional smoothness on finitedimensional and infinite-dimensional spaces with Gaussian measures. We prove...     

Generalized Cameron–Storvick theorem and its applications

The goal of this paper is to establish a more generalized Cameron–Storvick theorem with respect to the conditional generalized integral transform (CGIT) and the generalized first variation. Many results and formulas for Cameron–Storvick theorems established in previous papers are included. We first introduce a CGIT and a generalized first variation of functionals by using the concept of the Gaussian process and bounded linear operators. We then give the existence of them for the exponential functionals on function space. We next establish a generalized Cameron–Storvick theorem. Finally, we describe some applications.     

Rozansky–Witten invariants via Atiyah classes

Recently, L. Rozansky and E. Witten associated to any hyper-Kähler manifold X a system of weights (numbers, one for each trivalent graph) and used them to construct invariants of topological 3-manifolds. We give a simple cohomological definition of these weights in terms of the Atiyah class of X (the obstruction to the existence of a holomorphic connection). We show that the analogy between the tensor of curvature of a hyper-Kähler metric and the tensor of structure constants of a Lie algebra observed by Rozansky and Witten, holds in fact for any complex manifold, if we work at the level of cohomology and for any Kähler manifold, if we work at the level of Dolbeault cochains. As an outcome of our considerations, we give a formula for Rozansky–Witten classes using any Kähler metric on a holomorphic symplectic manifold.     

Invariant functions in Denjoy–Carleman classes

Let V be a real finite dimensional representation of a compact Lie group G. It is well known that the algebra of G-invariant polynomials on V is finitely generated, say by σ ₁, . . . , σ _p . Schwarz (Topology 14:63–68, 1975) proved that each G-invariant C ^∞-function f on V has the form f = F(σ ₁, . . . , σ _p ) for a C ^∞-function F on . We investigate this representation within the framework of Denjoy–Carleman classes. One can in general not expect that f and F lie in the same Denjoy–Carleman class C ^M (with M = (M _k )). For finite groups G and (more generally) for polar representations V, we show that for each G-invariant f of class C ^M there is an F of class C ^N such that f = F(σ ₁, . . . , σ _p ), if N is strongly regular and satisfies

Hirzebruch–Milnor classes of complete intersections

We prove a new formula for the Hirzebruch–Milnor classes of global complete intersections with arbitrary singularities describing the difference between the Hirzebruch classes and the virtual ones. This generalizes a formula for the Chern–Milnor classes in the hypersurface case that was conjectured by S. Yokura and was proved by A. Parusiński and P. Pragacz. It also generalizes a formula of J. Seade and T. Suwa for the Chern–Milnor classes of complete intersections with isolated singularities.     

Dixmier classes on generalized Segal–Bargmann–Fock spaces

We give criteria for the membership of Toeplitz operators and products of Hankel operators, with symbols of a certain type, in the Dixmier class, and formulas for their Dixmier trace, on a variety of weighted Segal–Bargmann–Fock spaces on the complex plane.     

Operator-Lipschitz functions in Schatten–von Neumann classes

This paper resolves a number of problems in the perturbation theory of linear operators, linked with the 45-year-old conjecure of M. G. Kreĭn. In particular, we prove that every Lipschitz function is operator-Lipschitz in the Schatten–von Neumann ideals S ^α , 1 < α < ∞. Alternatively, for every 1 < α < ∞, there is a constant c _α > 0 such that

The Cameron–Martin Theorem for (p-)Slepian Processes

We show a Cameron–Martin theorem for Slepian processes \(W_t:=\frac{1}{\sqrt{p}}(B_t-B_{t-p}), t\in [p,1]\), where \(p\ge \frac{1}{2}\) and \(B_s\) is Brownian motion. More exactly, we determine the class of functions \(F\) for which a density of \(F(t)+W_t\) with respect to \(W_t\) exists. Moreover, we prove an explicit formula for this density. p-Slepian processes are closely related to Slepian processes. p-Slepian processes play a prominent role among others in scan statistics and in testing for parameter constancy when data are taken from a moving window.     

Isomorphism classes of Doche–Icart–Kohel curves over finite fields

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in two families of curves introduced by C. Doche, T. Icart and D.R. Kohel.     

Cohen–Macaulayness of two classes of circulant graphs

Journal of Algebraic Combinatorics - Let n be a positive integer and let $$S_n$$ be the set of all nonnegative integers less than n which are relatively prime to n. In this paper, we discuss...     

On the real algebra of Denjoy–Carleman classes

We show that a nonnegative function germ at the origin of belonging to a quasianalytic Denjoy–Carleman class can be written as a sum of two squares of functions which lie in a Denjoy–Carleman class again. When the germ is elliptic we prove that the class is the same, in the general case a loss of regularity is possible. As a consequence we deduce the Artin–Lang property for suitable unions of such quasianalytic classes. The author is a member of GNSAGA of CNR, partially supported by the European Research Training Network RAAG 2002-2006 (HPRN-CT-00271).     

Note on conjectures of Beilinson–Bloch–Kato¶for cycle classes

Conjecures of Beilinson and Bloch–Kato describe the order of zeros of L-functions of motives in terms of motivic cohomology groups and Selmer groups. We restrict our attention to the parts generated by the cycle classes, and give modest evidence for the conjectures. Received: 7 June 1999 / Revised version: 7 September 1999     

Monge–Ampère equations in big cohomology classes

We define non-pluripolar products of an arbitrary number of closed positive (1, 1)-currents on a compact Kähler manifold X. Given a big (1, 1)-cohomology class α on X (i.e. a class that can be represented by a strictly positive current) and a positive measure μ on X of total mass equal to the volume of α and putting no mass on pluripolar sets, we show that μ can be written in a unique way as the top-degree self-intersection in the non-pluripolar sense of a closed positive current in α. We then extend Kolodziedj’s approach to sup-norm estimates to show that the solution has minimal singularities in the sense of Demailly if μ has L ^1+ε -density with respect to Lebesgue measure. If μ is smooth and positive everywhere, we prove that T is smooth on the ample locus of α provided α is nef. Using a fixed point theorem, we finally explain how to construct singular Kähler–Einstein volume forms with minimal singularities on varieties of general type.     

Gamma–closure of some classes of nonstandard convex integrands

Within the framework of the theory of Γ-convergence for convex functionals with nonstandard coercivity and growth conditions, we study the inheritance of some properties (for example, strict convexity, differentiablility, and Δ₂-property) of integrands under taking the Γ-closure. We focus on power integrands |ξ| ^p(x) with variable exponents. The results obtained are also of interest in the case of the Γ-convergence theory for standard functionals. Bibliography: 15 titles.     

English–Vietnamese cross-language paraphrase identification using hybrid feature classes

Journal of Heuristics - Paraphrase identification plays an important role with various applications in natural language processing tasks such as machine translation, bilingual information...     

Vanishing theorems for some classes of Riemann–Cartan manifolds

In this paper, a classification of Riemann–Cartan manifolds based on the orthogonal decomposition of the torsion tensor is given. Problems on the existence of two classes ℘₁ ⨁ ℘₂ and ℘₃ of Riemann–Cartan spaces are discussed.     

Inclusions of Waterman–Shiba spaces into generalized Wiener classes

The characterization of the inclusion of Waterman–Shiba spaces ΛBV^(p)$\Lambda {\mathit{BV}}^{(p)}$ into generalized Wiener classes of functions BV(q;δ)$\mathit{BV}(q;\delta )$ is given. It uses a new and shorter proof and extends an earlier result of U. Goginava.