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Given an isolated, quasi-homogeneous singularity $X$ we prove that there is a group isomorphism between the group of rank one reflexive sheaves on $X$ and the free abelian group generated by $\mathbb{C}^*$-divisors, modulo linear…
We construct the full linearisation functor which takes a graded bundle of degree $k$ (a particular kind of graded manifold) and produces a $k$-fold vector bundle. We fully characterise the image of the full linearisation functor and show…
For plane frameworks with reflection or rotational symmetries, where the group action is not necessarily free on the vertex set, we introduce a phase-symmetric orbit rigidity matrix for each irreducible representation of the group. We then…
The work is devoted to constructing a wide class of differential-functional dynamical systems, whose rich algebraic structure makes their integrability analytically effective. In particular, there is analyzed in detail the operator Lax type…
It has been understood that correlation functions of multi-trace operators in ${\cal N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to…
We show that the qualitative picture of the phase diagram which includes the non-uniform chiral phase and 2SC superconducting phase is independent of the considered regularization schemes. We also demonstrate that the quantitative results…
In cross-section-space probability table constructions, reaction-channel levels are reconstructed on fixed total-subgroup nodes and probabilities. Although the standard full-matching reconstruction is uniquely determined, it does not in…
This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function…
To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the tilting operation preserves several homological invariants…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the…
Extensive work has been done on the group classification of systems of equations in the literature. This paper identifies the gap in the literature which concerns the group classification of systems of two autonomous nonlinear second-order…
In this work we present a coupled-cluster theory for the propagation of multireference electronic systems initiating at general quantum mechanical states. Our formalism is based on the infinitesimal analysis of modified cluster operators,…
We develop a formalism with two different UV cutoff scales, one for space and one for time, appropriate for the richer structure of non-Lorentz invariant quantum field theories. In this formalism there are two different beta-functions for…
The randomly pinned planar flux line array is supposed to show a phase transition to a vortex glass phase at low temperatures. This transition has been examined by using a mapping onto a 2D XY-model with random an\-iso\-tropy but without…
Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are…
In the modeling of complex biological systems, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully…
The design of isophoric phased arrays composed of two-sized square-shaped tiles that fully cover rectangular apertures is dealt with. The number and the positions of the tiles within the array aperture are optimized to fit desired…
A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…
We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the Unitarity Flow Conjecture, which states that the…