Related papers: Higher order constraints for the ($\beta$-deformed…
Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively…
We derive a family of high-order, structure-preserving approximations of the Riemannian exponential map on several matrix manifolds, including the group of unitary matrices, the Grassmannian manifold, and the Stiefel manifold. Our…
Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation…
The Lie group SE(3) of isometric orientation preserving transformation is used for modeling multibody systems, robots, and Cosserat continua. The use of these models in numerical simulation and optimization schemes necessitates the…
We study the Virasoro constraints for moduli spaces of representations of quiver with relations by Joyce's vertex algebras. Using the framed Virasoro constraints, we construct a representation of half of the Virasoro algebra on the…
Let $\mathfrak g(G,\lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $\lambda\neq-1$ and an additive subgroup $G$ of $\mathbb C$. For a total order on $G$ that is compatible with addition,…
We give the sufficient conditions for the vector-valued Kurokawa-Mizumoto congruence related to the Klingen-Eisenstein series to hold. And we give a reinterpretation for differential operators on automorphic forms by the representation…
We present theory for general partial derivatives of matrix functions on the form $f(A(x))$ where $A(x)$ is a matrix path of several variables ($x=(x_1,\dots,x_j)$). Building on results by Mathias [SIAM J. Matrix Anal. Appl., 17 (1996), pp.…
We show that a recently introduced fifth-order bi-Hamiltonian equation with a differentially constrained arbitrary function by A. de Sole, V.G. Kac and M. Wakimoto is not a new one but a higher symmetry of a third-order equation. We give an…
Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the…
Let $H$ be a positive semi-definite matrix partitioned in $\beta\times \beta$ Hermitian blocks, $H=[A_{s,t}]$, $1\le s,t,\le \beta$. Then, for all symmetric norms, {equation*} \| H \| \le \| \sum_{s=1}^{\beta} A_{s,s} \|. {equation*} The…
Tarski initiated a logic-based approach to formal geometry that studies first-order structures with a ternary betweenness relation (\beta) and a quaternary equidistance relation (\equiv). Tarski established, inter alia, that the first-order…
Inspired by results of A. Bergamasco on perturbations of vector fields defined on the two-dimensional torus, and of J. Delgado and M. Ruzhansky on properties of invariant operators with respect to an elliptic operator defined on a closed…
Contractive selfadjoint extensions of a Hermitian contraction $B$ in a Hilbert space ${\mathfrak H}$ with an exit in some larger Hilbert space ${\mathfrak H}\oplus{\mathcal H}$ are investigated. This leads to a new geometric approach for…
We use the Kontsevich--Miwa transform to relate the Virasoro constraints on integrable hierarchies with the David-Distler-Kawai formalism of gravity-coupled conformal theories. The derivation relies on evaluating the energy-momentum tensor…
In this paper, we study a class of infinitesimal deformations of the centerless higher rank Heisenberg-Virasoro algebras. Explicitly, the universal central extensions, derivations and isomorphism classes of these algebras are determined.
We present a combination of raising, explicit variable dependency representation, the liberalized delta-rule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our…
In this paper a theory of Hecke operators for higher order modular forms is established. The definition of cusp forms and attached L-functions is extended beyond the realm of parabolic invariants. The role of representation theoretic…
We present four infinite families of mutually commuting difference operators which include the deformed elliptic Ruijsenaars operators. The trigonometric limit of this kind of operators was previously introduced by Feigin and Silantyev.…
We study star operations for Iwahori-Hecke algebras and invariant hermitian forms for finite dimensional modules over (graded) affine Hecke algebras with a view towards a unitarity algorithm.