Related papers: Very good and very bad field generators

In this article, we study skew cyclic codes over ring $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and $v^{3}=v$. We describe generator polynomials of skew cyclic codes over this ring and…

We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…

We develop the theory of pretty good quantum fractional revival in arbitrary sized subsets of a graph, including the theory for fractional cospectrality of subsets of arbitrary size. We use this theory to give conditions under which a…

This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A=k[X_1, X_2, \ldots, X_n]$ is a polynomial ring over a field $k$. The Complete Intersection conjecture states that, for any ideal $I$ in $A$,…

Let K be a field of positive characteristic. When V is a linear variety in K^n and G is a finitely generated subgroup of K^*, we show how to compute the intersection of V and G^n effectively using heights. We calculate all the estimates…

The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The resulting leads to a valid affine quantization of the particle in a box field theory, which points toward…

This paper first presents a theory for generative adversarial methods that does not rely on the traditional minimax formulation. It shows that with a strong discriminator, a good generator can be learned so that the KL divergence between…

We describe the K-ring of the classifying space of the generalized quaternion group in terms of generators and the minimal set of relations. We also compute the order of the main generator in the truncated rings.

All quantum random number generators based on measuring value indefinite observables are at least three-dimensional because the Kochen-Specker Theorem and the Located Kochen-Specker Theorem are false in dimension two. In this article, we…

Polynomials whose coefficients, roots, and critical points lie in the ring of rational integers are called nice polynomials. In this paper, we present a general method for investigating such polynomials. We extend our results from the ring…

J. G. Thompson showed that a finite group G is solvable if and only if every two -generated subgroup is solvable. Recently, Grunevald, Kunyavskii, Nikolova, and Plotkin have shown that the analogue holds for finite-dimensional Lie algebras…

Denote by $P_k$ the graded polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_k]$ over the prime field of two elements, $\mathbb F_2$, with the degree of each $x_i$ being 1. We study the Peterson hit problem of determining a minimal set of…

Within a superfield approach, we formulate a simple quantum generating equation of the field - antifield formalism. Then, we derive the Schroedinger equation with the Hamiltonian whose $\Delta$ - exact part serves as a generator to the…

We suggest a new mass generation mechanism for gauge fields. The quantum field theory constructed in this paper is nonabelian, gauge invariant and asymptotically free.

A subfield $K$ of $\bar{\mathbb{Q}}$ is $large$ if every smooth curve $C$ over $K$ with a rational point has infinitely many rational points. A subfield $K$ of $\bar{\mathbb{Q}}$ is $big$ if for every positive integer $n$, $K$ contains a…

A new mechanism for mass generation of gauge fields is proposed in this paper. By introducing two sets of gauge fields and making the variatons of these two sets of gauge fields compensate each other under local gauge transformations, the…

Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of…

In this paper we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field K.

We establish the correspondence between, on one side, the possible gaugings and massive deformations of half-maximal supergravity coupled to vector multiplets and, on the other side, certain generators of the associated very extended…

We initiate a way of generating models by the computer, satisfying both experimental and theoretical constraints. In particular, we present a framework which allows the generation of effective field theories. We use Generative Adversarial…