Related papers: Algebraic solution of the Jacobi inverse problem a…
Motivated by the necessity to find exact solutions with the elliptic Weierstrass function of the Einstein's equations (see gr-qc/0105022),the present paper develops further the proposed approach in hep-th/0107231, concerning the s.c. cubic…
We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that the Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. We…
Previous work by the authors (this journal, \vol{60} (2008), 1009-1044) produced equations that hold on certain loci of the Jacobian of a cyclic $C_{rs}$ curve. A curve of this type generalizes elliptic curves, and the equations in question…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
Novikov's conjecture on the Riemann-Schottky problem: {\it the Jacobians of smooth algebraic curves are precisely those indecomposable principally polarized abelian varieties (ppavs) whose theta-functions provide solutions to the…
We compute an explicit closed formula for the Hilbert polynomial of the Jacobian algebra $M(f)$ of a reduced surface $X:f=0$ in $\mathbb P^3$ in terms of the graded Betti numbers of the algebra $M(f)$. When $X$ has only isolated…
We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of the system from the spectra of two configurations.…
We consider Abel maps for regular smoothing of nodal curves with values in the Esteves compactified Jacobian. In general, these maps are just rational, and an interesting question is to find an explicit resolution. We translate this problem…
Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie…
We show how the Abel-Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivative of the Abel-Jacobi map is just the St\"{a}ckel matrix,…
The Jacobian Conjecture states that any locally invertible polynomial system in C^n is globally invertible with polynomial inverse. C. W. Bass et al. (1982) proved a reduction theorem stating that the conjecture is true for any degree of…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
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).
Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing…
The tree formula, which relates proper and connected vertices, is shown to be the solution to a Hamilton-Jacobi equation.
It is shown that corresponding to Plebansky equation of symmetry posses the infinite set of solutions, which we present in explicit form. This fact leads to conclusion about possibility to find series solutions of the Plebansky equation in…
We investigate Non-Linear Plane-Wave solutions of the classical Minkowskian Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves Gauss' law for the $SU(3)$ theory, we derive solutions which consist of Jacobi…