Related papers: The big theta
Analogue to commutants in the theory of associative algebras, one can construct a new subalgebra of vertex algebra known as a vertex algebra commutant. In this paper, for the adjoint representation $V$ of Lie algebra $sl(2,\C)$, we describe…
In this note we show that McGee's {\omega}-inconsistency result can be derived from L\"ob's theorem.
We derive Hessian estimates for convex solutions to quadratic Hessian equation by a compactness argument.
We solve tensor balancing, rescaling an Nth order nonnegative tensor by multiplying N tensors of order N - 1 so that every fiber sums to one. This generalizes a fundamental process of matrix balancing used to compare matrices in a wide…
This paper provides a construction of the unipotent representations for classical complex groups in terms of the Theta correspondence as introduced and studied by R. Howe. The K-type structure of unipotent representations is obtained as a…
We use the methods developed in our papers on moments and divisor correlations to derive heuristically the conjectural ratios formula for two zetas over two zetas.
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
We describe in detail the quantum tunneling of massive particles from Kerr black hole by using complex trajectories, which are solutions to the Hamilton's equations of motion with imaginary proper time. The trajectories are smooth and cover…
We establish an explicit relationship between the partition function of certain special cubic Hodge integrals and the generalized Brezin--Gross--Witten (BGW) partition function, which we refer to as the Hodge-BGW correspondence. As an…
We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\mathcal{X}$, the algorithm provides a set of…
An embedding of arbitrary Heyting algebra H into a reduct from the variety of Kuznetsov-Muravitsky algebras is constructed. An algebraic proof is given that this reduct belongs to the variety of Heyting algebras generated by H.
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through…
We introduce a new big I-function for certain GIT quotients W//G using the quasimap graph space from infinitesimally pointed $\mathbb{P}^1$ to the stack quotient [W/G]. This big I-function is expressible by the small I-function introduced…
In this paper, we use methods of exponential sums to derive a formula for estimating effective upper bounds of $|\zeta'(1/2+it)|$. Different effective upper bounds can be obtained by choosing different parameters.
In this paper we propose a homotopy method to compute the largest eigenvalue and a corresponding eigenvector of a nonnegative tensor. We prove that it converges to the desired eigenpair when the tensor is irreducible. We also implement the…
The generalization of squeezing is realized in terms of the Virasoro algebra. The higher-order squeezing can be introduced through the higher-order time-dependent potential, in which the standard squeezing operator is generalized to…
We explain how the gluing of a closed piece of the tensor-triangular spectrum with its open complement hinges on the support of the Tate ring.
Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…
In \cite{LV}, Howard's construction of big Heegner points on modular curves was extended to general Shimura curves over the rationals. In this paper, we relate the higher weight specializations of the big Heegner points of \emph{loc.cit.}…