Related papers: Notes on the lens integral pentagon identity
In this paper we study McShane's identity in real and complex hyperbolic spaces and obtain various generalizations of the identity for representations of surface groups into the isometry groups of rank one symmetric spaces. Our methods…
We obtain some Bailey pairs associated with indefinite quadratic forms with the $\beta_n$ connected to a finite sum. A new general identity is given, which provides identities for $q$-hypergeometric series, including mock theta functions.
In the article the problem of the integrable classification of nonlinear lattices depending on one discrete and two continuous variables is studied. By integrability we mean the presence of reductions of a chain to a system of hyperbolic…
Plane mirror can make one object into two for observers on the object's side. Yet, there seems no way to achieve the same effect for observers from all directions. In this letter, we will design a new class of gradient index lenses from…
We construct three-dimensional N=1 QED with N_f flavors using branes of type IIB string theory. This theory has a mirror, which can be realized using the S-dual brane configuration. As in examples with more supersymmetry, the Higgs branch…
In this paper, a general integral identity for a twice differentiable functions is derived. By using of this identity, the author establishes some new Hermite-Hadamard type and Simpson type inequalities for differentiable…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
We give a survey on results related to the Berglund-H\"ubsch duality of invertible polynomials and the homological mirror symmetry conjecture for singularities.
In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
We construct integrable pseudopotentials with an arbitrary number of fields in terms of generalized hypergeometric functions. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of…
An invariant of three-dimensional orientable manifolds is built on the base of a solution of pentagon equation expressed in terms of metric characteristics of Euclidean tetrahedra.
Criteria for experimental observation of multi-dimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and…
Imaging is of great importance in everyday life and various fields of science and technology. Conventional imaging is achieved by bending light rays originating from an object with a lens. Such ray bending requires space-variant structures,…
In the paper we provide some polynomial identities for finite-dimensional algebras. A list of well known single polynomial identities is exposed and the classification of all $2$-dimensional algebras with respect to these identities is…
In this paper we observe that information theoretical concepts are valuable tools for extracting information from images and, in particular, information on image symmetries. It is shown that the problem of detecting reflectional and…
It is well known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a Killing field on R^3. In this paper, we find…
In this paper, we consider the lens hyperbolic gamma solution to the star-star relation and the flipping relation from three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $S^3_b/\mathbb{Z}_r$. We explore that a certain limit…
We study relations between reflections in (positive or negative) points in the complex hyperbolic plane. It is easy to see that the reflections in the points q_1,q_2 obtained from p_1,p_2 by moving p_1,p_2 along the geodesic generated by…