Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...
It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension
In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...
Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...
The “Multivariate Ring Learning with Errors” problem was presented as a generalization of Ring Learning with Errors (RLWE), introducing efficiency improvements with respect to the RLWE counterpart thanks to its multivariate structure. Nevertheless, the rec ...
In a number of cases the minimal polynomials of the images of unipotent elements of non-prime order in irreducible representations of the exceptional algebraic groups in good characteristics are found. It is proved that if p > 5 for a group of type E-8 and ...
Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...
Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...
Let k be a global field of characteristic not 2, and let f is an element of k[X] be an irreducible polynomial. We show that a non-degenerate quadratic space has an isometry with minimal polynomial f if and only if such an isometry exists over all the compl ...
Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...
This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...
We investigate the problem of distributed sensors' failure detection in networks with a small number of defective sensors, whose measurements differ significantly from neighbouring sensor measurements. We build on the sparse nature of the binary sensor fai ...
Let W be a vector space over an algebraically closed field k. Let H be a quasisimple group of Lie type of characteristic p not equal char(k) acting irreducibly on W. Suppose also that G is a classical group with natural module W, chosen minimally with resp ...
We review the main features and results of thermal leptogenesis within the type I seesaw mechanism, the minimal extension of the Standard Model explaining neutrino masses and mixing. After presenting the simplest approach, the vanilla scenario, we discuss ...
The analysis of theories with non-minimal coupling of Higgs field to gravity revealed that they enter into strong coupling regime above certain Higgs-dependent cutoff, which may be considerably below the Planck scale. Assuming that the effective theory, co ...
A general formalism for the maximal symmetrization and reduction of fields (MSRFs) is proposed and applied to wave functions in solid-state nanostructures. Its primary target is to provide an essential tool for the study and analysis of the electronic and ...
The paper introduces a cubic-phase-function based method to estimate interference phase in digital holographic interferometry. The proposed method relies on piecewise polynomial approximation of phase by dividing an arbitrary row/column of the complex reco ...
We generalize the basic results of Vinberg's theta-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. To this end we clarify the relationship between the little Weyl group and the (standard) Weyl group. We ded ...
Aliasing in images is often considered as a nuisance. Artificial low frequency patterns and jagged edges appear when an image is sampled at a too low frequency. However, aliasing also conveys useful information about the high frequency content of the image ...
We show how to enlarge the νMSM (the minimal extension of the Standard Model by three right-handed neutrinos) to incorporate inflation and provide a common source for electroweak symmetry breaking and for right-handed neutrino masses. In addition to inflat ...
