Related papers: Odd transgression for Courant algebroids
We introduce a novel class of rotation invariants of two dimensional curves based on iterated integrals. The invariants we present are in some sense complete and we describe an algorithm to calculate them, giving explicit computations up to…
We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
Odd fluids are a class of fluids characterized by non-zero antisymmetric transport coefficient tensors induced by broken time-reversal symmetry. In our previous work, a mesoscale simulation model for two-dimensional isotropic odd fluids was…
We establish several Witten type rigidity and vanishing theorems for twisted Toeplitz operators on odd dimensional manifolds. We obtain our results by combining the modular method, modular transgression and some careful analysis of odd…
In this paper, we find explicit formulas for higher order derivatives of the inverse tangent function. More precisely, we study polynomials which are induced from the higher-order derivatives of arctan(x). Successively, we give generating…
This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
Traditional lens design is a numerical and forward process based on ray tracing and aberration theory. This method has limitations because the initial configuration of the lens has to be specified and the aberrations of the lenses have to…
Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and…
This paper, the last in a series of three, studies vector bundles on an elliptic surface whose determinant has odd intersection number with a general fiber and uses this study to calculate certain coefficients of Donaldson polynomials.
The proof of the theorem concerning to the inverse cyclotomic Discrete Fourier Transform algorithm over finite field is provided.
Wall-crossing phenomena are ubiquitous in many problems of algebraic geometry and theoretical physics. Various ways to encode the relevant information and the need to track the changes under the variation of parameters lead to rather…
We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from the variation of a natural action…
We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach…
The inverse problem of finding the coefficient $\g$ in the equation $\dot{u}=A(t)u+\g(t)u+f(t)$ from the extra data of the form $\phi(t)=u(t),w$ is studied. The problem is reduced to a Volterra equation of the second kind. Applications are…
This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint…
Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. The results are applied to solve a boundary value problem in a…