相关论文: The 8k-3 Instanton

he octonion offset linear canonical transform can be defined as a time shifted and frequency modulated version of the octonion linear canonical transform, a more general framework of most existing signal processing tools. In this paper, we…

We establish a dimension formula for the unreduced singular instanton homology of dual knots $\widetilde{K}_{p/q}\subset S^3_{p/q}(K)$ for a knot $K\subset S^3$: $$ \dim I^\sharp(S^3_{p/q}(K),\widetilde{K}_{p/q},\omega; \mathbb{K}) = 2q…

We study the perfect $3$-colorings on 4-regular graphs of order 8.

Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…

We give a uniform description of the decomposition of the unipotent variety of a classical group in arbitrary characteristic into pieces (considered in a non-uniform way in the earlier parts of this paper).

This is the second part of our study of epimorphisms with source a thick generalized $m$-gon and target a thin generalized $m$-gon. We classify the case $m = 8$ when the polygons are finite (in the first part [15] we handled the cases $m =…

The study of axion models and quantum corrections to their potential has experienced great progress by phrasing the axion potential in terms of a 3-form field eating up the 2-form field dual to the axion. Such reformulation of the axion…

In this paper, we present a refined version of the (classical) Stein inequality for the Fourier transform, elevating it to a new level of accuracy. Furthermore, we establish extended analogues of a more precise version of the Stein…

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly K\"ahler manifold. The cone over the sine-cone on a nearly K\"ahler manifold…

I show that the general implicit-function problem (or parametrized fixed-point problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this…

We suggest and describe the protocol of measurements providing completely probabilistic representation of all parameters of biphoton polarization qutrits, i.e providing explicit expressions for all parameters of qutrits via the…

In a recent paper, the first author and his collaborator developed a method to compute an upper bound of the dimension of instanton Floer homology via Heegaard Diagrams of 3-manifolds. For a knot inside S3, we further develop an algorithm…

We apply the Fourier transform technique and a modified version of E. Stein's interpolation theorem communicated by L. Grafakos, to obtain sharp $L^p$-$L^q$ estimates for the Radon transform and more general convolution-type fractional…

For noninteracting particles moving in a Gaussian random potential, there exists a disagreement in the literature on the asymptotic expression for the density of states in the tail of the band. We resolve this discrepancy. Further we…

Formulas are developed for the eight basis matrices {T^+,T^-,T^3,V^+,V^-,U^+,U^-,U^3} of the finite dimensional (p,q)-irreducible representation of SU(3). Two computer programs, one in an interpretive language and one in a compiled…

A new approach to building explicit time-marching stencil computation schemes for the transient 2D acoustic wave equation is implemented. It is based on using Poisson's formula and its three time level modification combined with polynomial…

In this note, we present a systematic method to explicitly compute the determinants and inverses for some generalized Hilbert matrices associated with orthogonal systems with explicit representations. We expressed the determinant, the…

We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…

We present an elementary way of recovering a well-known criterion of K-stability for Fano reductive group compactifications.

We study $H$-instanton bundles on the infinite family of smooth three-dimensional varieties $X_e=\mathbb{P}(\mathcal{O}_{\mathbb{P}^2} \oplus \mathcal{O}_{\mathbb{P}^2}(e))$, for $e \geq 0$. We provide two distinct monadic descriptions of…