Related papers: Discriminant Formulas and Applications
Chen and Cheung [C.-P. Chen, W.-S. Cheung, Sharpness of Wilker and Huygens type inequalities, J. Inequal. Appl. 2012 (2012) 72, \url{http://dx.doi.org/10.1186/1029-242X-2012-72}] established sharp Wilker and Huygens-type inequalities. These…
An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…
We prove the equivalence between two explicit expressions for two-point Witten-Kontsevich correlators obtained by M. Bertola, B. Dubrovin, D. Yang and by P. Zograf.
We settled a conjecture of Feigin, Wang and Yoshinaga, appeared in the preprint "Integral expressions for derivations of multiarrangements" (arXiv: 2309.01287v2).
Pausinger recently investigated a special determinant involving prime numbers. In this short note we point out that this type of determinants was already known in linear algebra and its computation is unrelated to prime numbers.
We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable…
In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-functions, thereby extending Guo's results to arbitrary…
The work studies some Difference equations, which are connected with Mejer's function.
We extend the classical Landesman-Lazer results to the setting of second order Hamilton-Jacobi-Bellman equations. A number of new phenomena appear.
The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.
We give a formula for matrix exponentials and partial fraction decompositions.
In this paper we generalize the notion of discriminant for symmetric matrices and some results about it to the case of symmetric spaces.
We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…
We prove a conjectured relationship among resultants and the determinants arising in the formulation of the method of moving surfaces for computing the implicit equation of rational surfaces formulated by Sederberg. In addition, we extend…
Let $K$ be a field. In this article, we derive a formula for the discriminant of a sequence $\{r_{A,n}+c r_{A,n-1}\}$ of polynomials. Here, $c \in K$ and $\{r_{A,n} \}$ is a sequence of polynomials satisfying a certain recurrence relation…
We give a simple formula for some determinants, and an analogous formula for pfaffians, both of which are polynomial identities. The second involve some expressions that interpolate between determinants and pfaffians. We give several…
A conjecture concerning some pairs of interfering estimates for some integrals is formulated in three equivalent versions. Its importance for the the Paley problem for plurisubharmonic functions and for certain classes of extremal problems…
This note provides formula for determinant and inverse of r-circulant matrices with general sequences of third order. In other words, the study combines many papers in the literature.
Some identities of Chebyshev polynomials are deduced from Waring's formula on symmetric functions. In particular, these formulae generalize some recent results of Grabner and Prodinger.