Search results for "Inverse trigonometric functions"
showing 5 items of 5 documents
On Carlson"s and Shafer"s inequalities
2014
In this paper the authors re ne the Carlson"s inequalities for inverse cosine function, and the Shafer"s inequalities for inverse tangent function.
Millimeter-Scale and Billion-Atom Reactive Force Field Simulation on Sunway Taihulight
2020
Large-scale molecular dynamics (MD) simulations on supercomputers play an increasingly important role in many research areas. With the capability of simulating charge equilibration (QEq), bonds and so on, Reactive force field (ReaxFF) enables the precise simulation of chemical reactions. Compared to the first principle molecular dynamics (FPMD), ReaxFF has far lower requirements on computational resources so that it can achieve higher efficiencies for large-scale simulations. In this article, we present our efforts on scaling ReaxFF on the Sunway TaihuLight Supercomputer (TaihuLight). We have carefully redesigned the force analysis and neighbor list building steps. By applying fine-grained …
A geometrical constructive approach to infinitesimal analysis: epistemological potential and boundaries of tractional motion
2014
Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the “inverse tangent problem.” Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geome…
Shifting of wrapped phase maps in the frequency domain using a rational number
2016
The number of phase wraps in an image can be either reduced, or completely eliminated, by transforming the image into the frequency domain using a Fourier transform, and then shifting the spectrum towards the origin. After this, the spectrum is transformed back to the spatial domain using the inverse Fourier transform and finally the phase is extracted using the arctangent function. However, it is a common concern that the spectrum can be shifted only by an integer number, meaning that the phase wrap reduction is often not optimal. In this paper we propose an algorithm than enables the spectrum to be frequency shifted by a rational number. The principle of the proposed method is confirmed b…
Functional inequalities for generalized inverse trigonometric and hyperbolic functions
2014
Various miscellaneous functional inequalities are deduced for the so-called generalized inverse trigonometric and hyperbolic functions. For instance, functional inequalities for sums, difference and quotient of generalized inverse trigonometric and hyperbolic functions are given, as well as some Gr\"unbaum inequalities with the aid of the classical Bernoulli inequality. Moreover, by means of certain already derived bounds, bilateral bounding inequalities are obtained for the generalized hypergeometric ${}_3F_2$ Clausen function.