Related papers: Areas Between Cosines

In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic…

Whilst standard field theoretic Cosmic Strings cannot end, Cosmic Superstrings can form three string junctions, at which each string ends. This opens up a new class of possible boundary conditions for such strings and we show that, at least…

We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the $L$ tetromino, and the $T$ tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by…

We present a construction of the superspace of maximally supersymmetric adS_{p+2} x S^{d-p-2} near-horizon geometry based entirely on the supergravity constraints of which the bosonic space is a solution. Besides the geometric superfields,…

We study the production of cosmological axions in the standard scenario in which a global string network forms at the Peccei-Quinn phase transition. We make detailed calculations of the axions produced by string loops (a previously…

We investigated the relation between the two-dimensional minimal gravity (Lee-Yang series) with boundaries and open intersection theory. It is noted that the minimal gravity with boundaries is defined in terms of boundary cosmological…

Using a discrete spectrum proposed for expectation values of canonical variables in black hole coherent states, the semiclassical entropy associated with the Schwarzschild space-time is derived to be the area of the apparent horizon.

We compute the Cox ring of an embedded variety $X \subseteq Z$ within a Mori dream space, under the assumption that the pullback map induces an isomorphism at the level of divisor class groups. We show that the Cox ring of $X$ is the…

Let X->P^(n-1) be an elliptic fibration obtained by resolving the indeterminacy of the projection of a cubic hypersurface Y of P^(n+1) from a line L not contained in Y. We prove that the Mordell-Weil group of the elliptic fibration is…

We introduce extremal affine surface areas in a functional setting. We show their main properties. Among them are linear invariance, isoperimetric inequalities and monotonicity properties. We establish a new duality formula, which shows…

Integrals related to the surface area of arbitrary ellipsoids are derived, evaluated, and compared with each other and existing integrals found in the literature. We clarify the literature on the ellipsoid area problem, which dates back to…

We count the number of irreducible polynomials in several variables of a given degree over a finite field. The results are expressed in terms of a generating series, an exact formula and an asymptotic approximation. We also consider the…

This thesis establishes new quantitative records in several problems of incidence geometry and growth. After the necessary background in Chapters 1, 2 and 3, the following results are proven. Chapter 4 gives new results in the incidence…

Exact solutions of the Einstein-Maxwell equations that describe moving black holes in a cosmological setting are discussed with the aim of discovering the global structure and testing cosmic censorship. Continuation beyond the horizons…

We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over $\mathbb{F}_p$ relates to the class number of the quadratic imaginary number field $\Q(\sqrt{-p})$. In this sense,…

We study sequences of functions of the form F_p^n -> {0,1} for varying n, and define a notion of convergence based on the induced distributions from restricting the functions to a random affine subspace. Using a decomposition theorem and a…

Let $(X,d,p)$ be a pointed metric space. A pretangent space to $X$ at $p$ is a metric space consisting of some equivalence classes of convergent to $p$ sequences $(x_n), x_n \in X,$ whose degree of convergence is comparable with a given…

We construct an uncountable family of finitely generated groups of intermediate growth, with growth functions of new type. These functions can have large oscillations between lower and upper bounds, both of which come from a wide class of…

We study the infinitesimal generators of evolutions of linear mappings on the space of polynomials, which correspond to a special class of Markov processes with polynomial regressions called quadratic harnesses. We relate the infinitesimal…

In this paper, we analyze the existence of algebraic and topological structures in the set of sequences that contain only a finite number of zero coordinates. Inspired by the work of Daniel Cariello and Juan B. Seoane-Sep\'ulveda, our…