相关论文: A formula for Gau{\ss}-Manin determinants
We present new generalized Jacobson's lemma for generalized Drazin inverses. This extend the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear $\&$ Multilinear Algebra, {\bf 68}(2020), 81--93).
The discriminantal arrangement is the space of configurations of $n$ hyperplanes in generic position in a $k$ dimensional space (see \cite{MS}). Differently from the case $k=1$ in which it corresponds to the well known braid arrangement,…
We describe the group SK_1(R[G]) for group rings R[G] where G is an arbitrary finite group and where the coefficient ring R is a p-adically complete Noetherian integral domain of characteristic zero which admits a lift of Frobenius and…
We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and…
The author introduces a conjecture about Makar-Limanov invariants of affine unique factorization domains over a field of characteristic zero. Then the author finds that the conjecture does not always hold when $\mathbbm{k}$ is not…
We deal with the construction of linear connections associated with second order ordinary differential equations with and without first order constraints. We use a novel method allowing glueing of submodule covariant derivatives to produce…
This is a review article on the Gauss-Manin system associated to the complete intersection singularities of projection. We show how the logarithmic vector fields appear as coefficients to the Gauss-Manin system. We examine further how the…
When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…
Using properties of Gauss and Jacobi sums, we derive explicit formulas for the number of solutions to a diagonal equation of the form $x_1^{2^m}+\dots+x_n^{2^m}=0$ over a finite field of characteristic $p\equiv\pm 3\pmod{8}$. All of the…
This work presents closed formulas for determinant, permanent, inverse, and Drazin inverse of circulant matrices with two non-zero coefficients.
A derivative expansion technique is developed to compute functional determinants of quadratic operators, non diagonal in spacetime indices. This kind of operators arise in general 't Hooft gauge fixed Lagrangians. Elaborate applications of…
We provide an effective uniform upper bond for the number of zeros of the first non-vanishing Melnikov function of a polynomial perturbations of a planar polynomial Hamiltonian vector field. The bound depends on degrees of the field and of…
A noncommutative analogue of the Zariski cancellation problem asks whether $A[x]\cong B[x]$ implies $A\cong B$ when $A$ and $B$ are noncommutative algebras. We resolve this affirmatively in the case when $A$ is a noncommutative finitely…
An operator $H=H_{0}+V$ where $H_{0}=i^{-N} \partial^{N}$ ($N$ is arbitrary) and $V$ is a differential operator of order $N-1$ with coefficients decaying sufficiently rapidly at infinity is considered in the space $L^2(\Bbb R)$. The goal of…
In this paper, we provide the notions of connection $1$-forms and curvature $2$-forms on graphs. We prove a Weitzenb\"ock formula for connection Laplacians in this setting. We also define a discrete Yang-Mills functional and study its…
We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate…
In this note, we investigate the paratrophic determinants attached to the multiplicative semigroup $\mathbb{Z}/N\mathbb{Z}$. We show that, via discrete Fourier, cosine, and sine transforms, these determinants factor into products of group…
Based on the operator formalism that arises from the underlying SU(2) group structure, a formula is derived that provides a description of the generalized Hermite-Laguerre Gauss modes in terms of a Jones vector, traditionally used to…
A formula for the difference of Vassiliev invariants of degree k+1 of two knots all of whose Vassiliev invariants of degree k agree is proven. The proof uses K. Habiro's C-moves and his theorem which relates them to Vassiliev invariants.