Related papers: Quantization formula for singular reductions
In this paper we classify the isolated singularities of positive solutions to Choquard equation and prove the existence of isolated singular solutions.
We provide a full characterisation of quantum differentiability (in the sense of Connes) on quantum tori. We also prove a quantum integration formula which differs substantially from the commutative case.
Subsequently to the author's preceding paper, we give full proofs of some explicit formulas about factorizations of $K$-$k$-Schur functions associated with any multiple $k$-rectangles.
We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.
We extend the homological method of quantization of generalized Drinfeld--Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.
We prove the precise inversion of adjunction formula for quotient singularities and klt Cartier divisors. As an application, we prove the semi-continuity of minimal log discrepancies for klt hyperquotient singularities.
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
We give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.
We prove a single sum formula for the linearization coefficients of the Bessel polynomials. In two special cases we show that our formula reduces indeed to Berg and Vignat's formulas in their proof of the positivity results about these…
We present an explicit formula for Witten-Kontsevich tau-function.
General formulas of entanglement concentration are derived by using an information-spectrum approach for the i.i.d. sequences and the general sequences of partially entangled pure states. That is, we derive general relations between the…
We prove a result on the singularities of ball quotients $\Gamma\backslash\CC H^n$. More precisely, we show that a ball quotient has canonical singularities under certain restrictions on the dimension $n$ and the underlying lattice. We also…
For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is…
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
We obtained a new formula for $\pi$.
This note contains a short proof of the functional equation for the zeta function.
In this paper, we propose a generalization of a congruence due to Carlitz.
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
This work considers a formal deformation of the quantum disc (it is developed via an application of the Berezin method) and presents an explicit formula for this deformation.