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We classify and compute, by means of the six-dimensional embedding formalism in twistor space, all possible three-point functions in four dimensional conformal field theories involving bosonic or fermionic operators in irreducible…

Vertex operators for the deformed Virasoro algebra are defined, their bosonic representation is constructed and difference equation for the simplest vertex operators is described.

Fusion frames have become a major tool in the implementation of distributed systems. The effectiveness of fusion frame applications in distributed systems is reflected in the efficiency of the end fusion process. This in turn is reflected…

We study the fused currents of the deformed Virasoro algebra (DVA). By constructing a homotopy operator we show that for special values of the parameter of the algebra fused currents pairwise coincide on the cohomologies of the Felder…

Partial differential equations (PDEs) govern diverse physical phenomena, yet high-fidelity numerical solutions are computationally expensive and Machine Learning approaches lack generalization. While Scientific Foundation Models (SFMs) aim…

In this paper, we consider Dunkl theory on R^d associated to a finite reflection group. This theory generalizes classical Fourier anal- ysis. First, we give for 1 < p <= 2, sufficient conditions for weighted Lp-estimates of the Dunkl…

We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on…

We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure which associates to every strongly local…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…

Density-corrected density functional theory (DC-DFT) is enjoying substantial success in improving semilocal DFT calculations in a wide variety of chemical problems. This paper provides the formal theoretical framework and assumptions for…

In this paper, we introduce and study frame of operators in quaternionic Hilbert spaces as a generalization of g frames which in turn generalized various notions like Pseduo frames, bounded quasi-projectors and frame of subspaces (fusion…

Understanding, optimizing, and controlling the optical absorption process, exciton gemination, and electron-hole separation and conduction in low dimensional systems is a fundamental problem in materials science. However, robust and…

For any finite dimensional Lie superalgebra $\dot{\mathfrak{g}}$ (maybe a Lie algebra) with an even derivation $d$ and a finite order automorphism $\sigma$ that commutes with $d$, we introduce the $(d,\sigma)$-twisted Affine-Virasoro…

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…

Neural 3D implicit representations learn priors that are useful for diverse applications, such as single- or multiple-view 3D reconstruction. A major downside of existing approaches while rendering an image is that they require evaluating…

In this paper we propose a generalization of deep neural networks called deep function machines (DFMs). DFMs act on vector spaces of arbitrary (possibly infinite) dimension and we show that a family of DFMs are invariant to the dimension of…

This paper discusses the observability of nonlinear Dynamical Systems over Finite Fields (DSFF) through the Koopman operator framework. In this work, given a nonlinear DSFF, we construct a linear system of the smallest dimension, called the…

This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field…

In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension $D$, the four-point function of…