Related papers: Strong Pseudo Primes to Base 2
We give an estimation of the existence density for the $2d$ different primes by using a new and simple algorithm for getting the $2d$ different primes. The algorithm is a kind of the sieve method, but the remainders are the central numbers…
A simple recipe for generating a complete set of mutually unbiased bases in dimension (2j+1)**e, with 2j + 1 prime and e positive integer, is developed from a single matrix acting on a space of constant angular momentum j and defined in…
The number of finite additive 2-bases is known to grow exponentially. While this fact has been established by Marzuola and Miller (2010) using complex analytic techniques embedded in the study of numerical sets, we provide a direct, short…
This paper associates a dual problem to the minimization of an arbitrary linear perturbation of the robust sum function introduced in DOI 10.1007/s11228-019-00515-2. It provides an existence theorem for primal optimal solutions and, under…
Despite modular conditions to guarantee stability for large-scale systems have been widely studied, few methods are available to tackle the case of networks with multiple equilibria. This paper introduces small-gain like sufficient…
We provide new conditions for the Strong Atiyah conjecture to lift to finite group extensions. In particular, we show cocompact special groups satisfy these conditions, so the Strong Atiyah conjecture holds for virtually cocompact special…
In this paper, we show that the subadditive dual of a feasible conic mixed-integer program (MIP) is a strong dual whenever it is feasible. Moreover, we show that this dual feasibility condition is equivalent to feasibility of the conic dual…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
Recently, it was shown that a rich class of second-order (maximally) superintegrable systems has an underpinning Hesse-Frobenius structure, i.e.\ a Frobenius structure that is compatible with a Hessian structure such that the Hessian…
Define $\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\psi_m$ is known for $1\le m \le 8$. Z. Zhang have found a 19-decimal-digit number $Q_{11}=3825\,12305\,65464\,13051$ which is a strong…
We consider a topological space with its subbase which induces a coding for each point. Every second-countable Hausdorff space has a subbase that is the union of countably many pairs of disjoint open subsets. A dyadic subbase is such a…
Assuming the obvious definitions (see paper) we show the a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to…
We consider the capability of $p$ groups of class two and odd prime exponent. We use linear algebra and counting arguments to establish a number of new results. In particular, we settle the 4-generator case, and prove a sufficient condition…
The congruences for Jacobi sums of some lower orders has been treated by many authors in the literature. In this paper we establish the congruences for Jacobi sums of order 2l^2 with odd prime l. These congruences are useful to obtain…
We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such representations is of the expected order of magnitude. We…
Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as…
The proliferation of probable prime tests in recent years has produced a plethora of definitions with the word ``pseudoprime'' in them. Examples include pseudoprimes, Euler pseudoprimes, strong pseudoprimes, Lucas pseudoprimes, strong Lucas…
We explicitly construct the structure of Jacquet modules of parabolically induced representations of even unitary groups and even general unitary groups over a $p$-adic field $F$ of characteristic different than two. As an application, we…
This paper investigates a recently introduced notion of strong variational sufficiency in optimization problems whose importance has been highly recognized in optimization theory, numerical methods, and applications. We address a general…
In this paper we show that a certain subset of the Carmichael numbers contains good Euler pseudoprimes, composite numbers that for many bases survive the Solovay-Strassen primality test. We present a classification of Carmichael numbers,…