EXCEL-orientated procedure for calculating the values of special functions with interval argument assigned on the hyperbolic form

Aim of the work is to propose the main terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form. The results of the work. The methods of presenting the interval values in the hyperbolic form and the rules of addition, subtraction, multiplication, and division of this values were considered. The procedures of calculating the function values, whose arguments can be degenerate or interval values were described. Namely, the direct and the reverse functions of the linear trigonometry, the direct and the reverse functions of the hyperbolic trigonometry, exponential function, arbitrary exponential function and power function, Gamma-function, incomplete Gamma-function, digamma-function, trigamma-function, tetragamma-function, pentagamma-function, Beta-function and its partial derivatives, integral exponential function, integral logarithm, dilogarithm, Frenel integrals, sine integral, cosine integral, hyperbolic sine integral, hyperbolic cosine integral. The basic terms of the EXCEL-orientated procedures for calculating the values of elementary and special functions with interval argument that is assigned on the hyperbolic form were proposed. The numerical examples were provided, that illustrate the application of the proposed methods.

Can We Prescribe the Physical Parameters of Multiple Black Holes?

The parabolic-hyperbolic form of the constraints and superposed Kerr-Schild black holes have already been used to provide a radically new initialization of binary black hole configurations. The method generalizes straightforwardly to multiple black hole systems. This paper is to verify that each of the global Arnowitt-Deser-Misner quantities of the constructed multiple black hole initial data can always be prescribed, as desired, in advance of solving the constraints. These global charges are shown to be uniquely determined by the physical parameters of the involved individual Kerr-Schild black holes.

Black hole initial data by numerical integration of the parabolic–hyperbolic form of the constraints

The parabolic–hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is fourth-order accurate (in the spatial directions) while “time”-integration is made by using the method of lines with a fourth-order order accurate Runge–Kutta scheme. The proper implementation of the applied numerical method is verified by convergence tests and monitoring the relative and absolute errors is determined by comparing numerically and analytically known solutions of the constraints involving boosted and spinning vacuum single black hole configurations. The main part of our investigations is, however, centered on the construction of initial data for distorted black holes which, in certain cases, have non-negligible gravitational wave content. Remarkably, the applied new method is unprecedented in that it allows to construct initial data for highly boosted and spinning black holes, essentially for the full physical allowed ranges of these parameters. In addition, the use of the evolutionary form of the constraints is free from applying any sort of boundary conditions in the strong field regime.

Limits of canonical forms on towers of Riemann surfaces

We prove a generalized version of Kazhdan’s theorem for canonical forms on Riemann surfaces. In the classical version, one starts with an ascending sequence {\{S_{n}\rightarrow S\}} of finite Galois covers of a hyperbolic Riemann surface S, converging to the universal cover. The theorem states that the sequence of forms on S inherited from the canonical forms on {S_{n}}’s converges uniformly to (a multiple of) the hyperbolic form. We prove a generalized version of this theorem, where the universal cover is replaced with any infinite Galois cover. Along the way, we also prove a Gauss–Bonnet-type theorem in the context of arbitrary infinite Galois covers.

A Pragmatic Analysis: Implications of Lexical Choices in Translating Quranic Rhetoric

An increasing interest in the translation of the meaning of the Quran has recently been developed due to the various conflicts in the name of religion that dominate mass and social media. The Quran features amongst the most read books in the world. However, roughly all the existing translations contain flaws in terms of content, style and culture. This study addresses the challenges of achieving pragmatic equivalence of five English translations of the Quran by comparing them with their original one to determine the degree of faithfulness of the overall message, focusing on the Quranic phraseology that alludes to something or someone without directly stating it. The study is mainly concerned with assessing the degree of accuracy and fidelity in conveying the meaning of some Arabic literary devices into English. The question of whether figurative Quranic words or phrases are pragmatically mistranslated is still debatable. This article contributes to the debate of accuracy and fluency of the selected versions of the Quran in English by shedding light upon specific pragmatic features that create a special effect in the Quranic text by assessing the degree of deviation from SL message if any. Analysis revealed that the five selected English versions of the Quran have fallen short of accurately conveying the non-literal use of Quranic expressions such as Metonymy, Synecdoche, Allusion, Nonverbal signals, Euphemistic phrases, and Hyperbolic form. The findings suggested that translating the Quran requires more than acquiring linguistic skills to create the same impact and maintain the same spirit in the target language. The results also indicated that inconsistency of conveying the meaning of the Quranic rhetoric is due in parts to non-success in checking authentic exegesis as a source of elucidation, explanation or interpretation for clear understanding. This study serves as a platform for further research on translating Quranic rhetorical tools through highlighting the shortcomings and the strengths of some samples from the Quran.

Weaponizing Victimhood

This chapter analyzes a rhetoric of “weaponized victimhood” and its crucial role in uniting disparate factions of the contemporary American Right. Weaponized victimhood speaks to a felt sense of loss of power and esteem among social groups facing challenges to their traditionally privileged status positions. This expression of grievance takes on a hyperbolic form through assertions that groups such as whites, men, and Christians face great social oppression. These groups are portrayed as victims of such projected threats as a “War on Christmas” and “feminazi” activists. Such victimization narratives circulate across various types of conservative news and right-wing media—from Fox News to alt-right and men’s rights websites. A common rhetoric of victimization cultivates a shared affective sensibility among groups ranging from avowed white supremacists to anti-feminists to others reacting against a perceived challenge to their social power and standing.

Complexiton solutions for complex KdV equation by optimal Homotopy Asymptotic Method

In this article an innovative technique named as Optimal Homotopy Asymptotic Method has been explored to treat system of KdV equations computed from complex KdV equation. By developing special form of initial value problems to complex KdV equation, three different types of semi analytic complextion solutions fromcomplexKdVequation have been achieved. First semi analytic position solution received fromtrigonometric form of initial value problem, second is semi analytic negation solution received by hyperbolic form of initial value problem and third one is special type of semi analytic solution expressed by the combination of trigonometric and hyperbolic functions. It was proved that only first order OHAM solution is accurate to the closed-form solution.

On the Evolutionary Form of the Constraints in Electrodynamics

The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity, it is shown, regardless of the signature and dimension of the ambient space, that the “divergence of a vector field”-type constraint can always be put into linear first order hyperbolic form for which the global existence and uniqueness of solutions to an initial-boundary value problem are guaranteed.