Related papers: Higher order constraints for the ($\beta$-deformed…

We consider Hessian quotient equations in Riemannian setting related to a problem posed by Delano\"e and Urbas. We prove unobstructed second order a priori estimate for the real Hessian quotient equation via the maximum principle argument…

We characterize the action of isotropic pseudodifferential operators on functions in terms of their action on Hermite functions. We show that an operator $A : S(\mathbb{R}) \to S(\mathbb{R})$ is an isotropic pseudodifferential operator of…

We derive Gamow vectors from S-matrix poles of higher multiplicity in analogy to the Gamow vectors describing resonances from first-order poles. With these vectors we construct a density operator that describes resonances associated with…

We show that if every module W for a vertex operator algebra V satisfies the condition that the dimension of W/C_1(W) is less than infinity, where C_1(W) is the subspace of W spanned by elements of the form u_{-1}w for u in V of positive…

We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of $(\alpha, \beta)$-derivation to $(\alpha, \beta)$-higher derivation and demonstrate that a filter of a hereditary…

When training large models, such as neural networks, the full derivatives of order 2 and beyond are usually inaccessible, due to their computational cost. Therefore, among the second-order optimization methods, it is common to bypass the…

In this note, the notion of cotorsion classes is introduced into the higher homological algebra. Our results motivate the definition, showing that this notion of $n$-cotorsion classes satisfies usual properties one could expect. In…

Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…

One can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

This short but self-contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen, sub or super-additivity type inequalities are…

This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…

In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…

We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…

We generalize our results of \cite{AP2} and \cite{AP3} to the case of maximal dissipative operators. We obtain sharp conditions on a function analytic in the upper half-plane to be operator Lipschitz. We also show that a H\"older function…

Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…

We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target…

In the paper, we investigate weighted composition operators on Bergman spaces of a half-plane. We characterize weighted composition operators which are hermitian and those which are complex symmetric with respect to a family of…

This paper completes the construction of arbitrary order conformally invariant differential operators in higher spin spaces. Jan Slov\'{a}k has classified all conformally invariant differential operators on locally conformally flat…