Functional Analysis and Its Applications最新文献

The two-dimensional problem of normal oscillations of a pendulum with a cavity completely filled with a viscoelastic fluid described by the generalized Oldroyd model is investigated. After formulating the initial-boundary value problem and its operator representation, the properties of the operators involved are examined. The main spectral problem for these operators is formulated and the structure of the corresponding spectrum is studied. A connection is established between the solution of the formulated problem and the eigenvalue problem for a certain operator pencil. Based on this connection, additional information about the structure of the spectrum is obtained. Statements concerning the asymptotic behavior of the eigenvalues are derived and the basis properties of the system of eigenvectors are studied.

In this short paper, we announce results on a new construction of higher operads in the sense of Batanin. Our construction is based on a new concept of a generalised Joyal disk. We introduce a funny product on the category of generalised (d)-disks, which makes it possible to generalise the lattice path operad. For each (dge 1), the generalised lattice path operad (mathcal{L}^d) is a colored symmetric operad with the category of unary operations (Theta_d). Our goal in this paper is to depict a ((d+1))-operad (mathbf{seq}_d) inside the desymmetrisation (mathrm{des}(mathcal{L}^d)). Tamarkin’s operad (mathbf{seq}) is a solution for (d=1). We succeed in constructing such an operad (mathbf{seq}_d) for (d=2,3), and prove that it is contractible in the topological and dg condensations. For (d>3), an explicit construction is also provided, but the proof that it is indeed a ((d+1))-operad (as well as proving its topological and dg contractibility) relies on combinatorial conjectures which are still open. The symmetrisation theorem is applied to (mathbf{seq}_d), which potentially gives rise to a (E_{d+1})-algebra structure on (d)-categorical deformation complexes.

We show that if (f) is a nonlinear convex increasing function on (mathbb{R}), (A) is a (C^*)-algebra, and the continuous functional calculus of (f) on (A_{mathrm{sa}}) preserves the order of the elements in (A_{mathrm{sa}}), then (A) is commutative.

In this paper, we find conditions under which the known definitions of iterated integrals of finite-dimensional Gaussian processes could be used to construct integrals of the infinite-dimensional analogues of these processes. In the context of the rough paths theory, our results allow us to carry the existing constructions of finite-dimensional Gaussian rough paths over to the infinite-dimensional case. Using more abstract terms, we define a continuous linear map between the space of Gaussian chaoses generated by some Gaussian processes and the space of chaoses generated by the infinite-dimensional analogues of these processes.

In 2014, the author showed that in the three-dimensional spherical space, alongside the three classical types of flexible octahedra constructed by Bricard, there exists a new type of flexible octahedra, which was called exotic. In the present paper, we give a geometric construction for exotic flexible octahedra, describe their configuration spaces, and calculate their volumes. We show that the volume of an exotic flexible octahedron is nonconstant during the flexion, and, moreover, the volume remains nonconstant if we replace any set of vertices of the octahedron with their antipodes. So exotic flexible octahedra are counterexamples to the Modified Bellows Conjecture proposed by the author in 2015.

In this paper, we establish some nonexistence results of a quasilinear elliptic inequality

and a system of quasilinear elliptic inequalities

where (nabla_lambda=(lambda_1partial_{x_1},lambda_2partial_{x_2},dots,lambda_Npartial_{x_N})) and (lambda_i), (i=1,2,dots,N) are some functions. Here, (p,widetilde{p}>1), (q, widetilde{q}geq 0), and (w,h, widetilde{w}, widetilde{h} in L^1_{mathrm{loc}}(mathbb R^N)) are nonnegative functions satisfying some growth conditions at infinity. In particular, our results can be seen as a generalization of some results of Mitidieri and Pokhozhaev from the Laplace operator to the (Delta_lambda)-Laplacian.

In this paper, we study a special class of interval translation mappings introduced in 2007 by H. Bruin. We prove that a typical map of infinite type is uniquely ergodic and provide an upper bound for the Hausdorff dimension of the parameter set that gives rise to the interval translation mappings of infinite type. Moreover, we prove that such interval translation mappings have sublinear combinatorial complexity.

We study the spectrum of the Dirichlet problem for the Laplace operator in a thin-walled domain shaped as an upright faceted cup with a regular polygon as the base. We obtain restrictions on the relative thickness of the bottom that ensure localization of the first few eigenfunctions in a neighborhood of the vertices of the base.

We present a seemingly overlooked property of the Moutard transformation considered by Novikov and Taimanov for matrix pairs of generalized analytic functions.

The construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications in soliton theory. Commuting operators of rank 1 were found by Krichever. The problem of constructing operators of rank (l>1) has not been solved in the general case. In all known examples of operators of rank (l>1), the spectral curves are hyperelliptic curves. In this paper, the first examples of operators of rank 2, corresponding to trigonal spectral curves of genus 3, are constructed.