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We give a new method to calculate the universal cohomology classes of coincident root loci. We show a polynomial behavior of them and apply this result to prove that generalized Pl\"ucker formulas are polynomials in the degree, just as the…
In this paper we present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were…
In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is $(4-\alpha)$, where $\alpha…
In this paper we introduce a technique to degenerate K3 surfaces and linear systems through fat points in general position on K3 surfaces. Using this degeneration we show that on generic K3 surfaces it is enough to prove that linear systems…
Using the possibility of computationally determining points on a finite cover of a unirational variety over a finite field, we determine all possibilities for direct Gorenstein linkages between general sets of points in P^3 over an…
Let F be a closed orientable surface. We give an explicit formula for the number mod 2 of quadruple points occurring in any generic regular homotopy between any two regularly homotopic embeddings e,e':F -> R^3. The formula is in terms of…
We establish multiple recurrence results for pretentious measure-preserving multiplicative actions along generalized Pythagorean triples, that is, solutions to the equation $ax^2 + b y^2 = c z^2$. This confirms the ergodic-theoretic form of…
In this paper, the third-order Jacobsthal generalized quaternions are introduced. We use the well-known identities related to the third-order Jacobsthal and third-order Jacobsthal-Lucas numbers to obtain the relations regarding these…
We present several new quadrature formulas in the triangle for exact integration of polynomials. The points were computed numerically with a cardinal function algorithm which imposes that the number of quadrature points $N$ be equal to the…
This paper provides a detailed description of various reduction schemes in rigid body dynamics. Analysis of one of such nontrivial reductions makes it possible to order the cases already found and to obtain new generalizations of the…
Generalised Pythagorean triples are integer tuples $(x,y,z)$ satisfying the equation $E_{a,b,c}: ax^2+by^2+cz^2=0$. A significant amount of research has been devoted towards understanding generalised Pythagorean triples and, in particular,…
Let f: C --> P^3 be a general curve of genus g, mapped to P^3 via a general linear series of degree d; and let Q be a general (and thus smooth) quadric. In this paper, we show that the points of intersection f(C) \cap Q give a general…
We give a formula for the Hodge numbers of hypersurfaces in $\mathbb P^{4}$ with ordinary triple points.
We determine the integral homology of PSL4(Z) in degrees at most 5 and determine its p-part in higher degrees for the primes p>=5. Our method applies to other arithmetic groups; as illustrations we include descriptions of the integral…
We study the existence of components with the expected number of moduli of the Hilbert scheme of integral nodal curves $C \subset \mathbb {P}^r$ with prescribed degree, arithmetic genus and number of singular points.
The purpose of this article is to bring together the third-order Jacobsthal numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and…
The directed percolation (DP) hypothesis for stochastic, range-4 cellular automata with acceptance rule $y \le\sum_{j=-4}^4 s_{i-j} \le 6$, in cases of $y < 6$ was investigated in one and two dimensions. Simulations, mean-field…
The computation of the dimension of linear systems of plane curves through a bunch of given multiple points is one of the most classic issues in Algebraic Geometry. In general, it is still an open problem to understand when the points fail…
The graded Betti numbers of the minimal free resolution (and also therefore the Hilbert function) of the ideal of a fat point subscheme Z of P^2 are determined whenever Z is supported at any 6 or fewer distinct points. All results hold over…
One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has…