scholarly journals lsjk—a C++ library for arbitrary-precision numeric evaluation of the generalized log-sine functions

2005 ◽  
Vol 172 (1) ◽  
pp. 45-59 ◽  
Author(s):  
M.Yu. Kalmykov ◽  
A. Sheplyakov
Keyword(s):  
Arbitrary Precision ◽  
Sine Functions

scholarly journals Basis properties of the p , q -sine functions

2015 ◽  
Vol 471 (2174) ◽  
pp. 20140642 ◽  
Author(s):  
Lyonell Boulton ◽  
Gabriel J. Lord
Keyword(s):  
Shift Operators ◽  
The Family ◽  
The Subject ◽  
Infinite Multiplicity ◽  
Sine Functions

We improve the currently known thresholds for basisness of the family of periodically dilated p , q -sine functions. Our findings rely on a Beurling decomposition of the corresponding change of coordinates in terms of shift operators of infinite multiplicity. We also determine refined bounds on the Riesz constant associated with this family. These results seal mathematical gaps in the existing literature on the subject.

Algorithm 349: polygamma functions with arbitrary precision [S14]

1969 ◽  
Vol 12 (4) ◽  
pp. 213-214 ◽  
Author(s):  
Georges Schwachheim
Keyword(s):  
Polygamma Functions ◽  
Arbitrary Precision

scholarly journals Fast and Rigorous Arbitrary-Precision Computation of Gauss--Legendre Quadrature Nodes and Weights

2018 ◽  
Vol 40 (6) ◽  
pp. C726-C747 ◽  
Author(s):  
Fredrik Johansson ◽  
Marc Mezzarobba
Keyword(s):  
Arbitrary Precision ◽  
Legendre Quadrature

Recurrent Neural Networks with Small Weights Implement Definite Memory Machines

2003 ◽  
Vol 15 (8) ◽  
pp. 1897-1929 ◽  
Author(s):  
Barbara Hammer ◽  
Peter Tiňo
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Experimental Studies ◽  
Activation Function ◽  
Transition Function ◽  
Recurrent Network ◽  
Point Of View ◽  
Recurrent Networks ◽  
Contraction Parameter ◽  
Arbitrary Precision

Recent experimental studies indicate that recurrent neural networks initialized with “small” weights are inherently biased toward definite memory machines (Tiňno, Čerňanský, & Beňušková, 2002a, 2002b). This article establishes a theoretical counterpart: transition function of recurrent network with small weights and squashing activation function is a contraction. We prove that recurrent networks with contractive transition function can be approximated arbitrarily well on input sequences of unbounded length by a definite memory machine. Conversely, every definite memory machine can be simulated by a recurrent network with contractive transition function. Hence, initialization with small weights induces an architectural bias into learning with recurrent neural networks. This bias might have benefits from the point of view of statistical learning theory: it emphasizes one possible region of the weight space where generalization ability can be formally proved. It is well known that standard recurrent neural networks are not distribution independent learnable in the probably approximately correct (PAC) sense if arbitrary precision and inputs are considered. We prove that recurrent networks with contractive transition function with a fixed contraction parameter fulfill the so-called distribution independent uniform convergence of empirical distances property and hence, unlike general recurrent networks, are distribution independent PAC learnable.

Computing periodic orbits with arbitrary precision

2011 ◽  
Vol 84 (1) ◽  
Author(s):  
Alberto Abad ◽  
Roberto Barrio ◽  
Ángeles Dena
Keyword(s):  
Periodic Orbits ◽  
Arbitrary Precision

Micro/mini computer program for calculating the square root of rationals at arbitrary precision

1983 ◽  
Vol 29 (3) ◽  
pp. 237-244 ◽  
Author(s):  
J. Demsky ◽  
M. Schlesinger ◽  
R.D. Kent
Keyword(s):  
Computer Program ◽  
Square Root ◽  
Arbitrary Precision

Extensions of Zeta Functions ? Examples and a Study of the Double Sine Functions

2005 ◽  
Vol 86 (1-2) ◽  
pp. 179-201
Author(s):  
Nobushige Kurokawa ◽  
Masato Wakayama
Keyword(s):  
Zeta Functions ◽  
Sine Functions

Blending Approximations with Sine Functions

1992 ◽  
pp. 1-19 ◽  
Author(s):  
G. Baszenski ◽  
F.-J. Delvos ◽  
S. Jester
Keyword(s):  
Sine Functions

scholarly journals Free Vibration Exploration of Rotating FGM Porosity Beams under Axial Load considering the Initial Geometrical Imperfection

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Nguyen Thi Giang
Keyword(s):  
Finite Element ◽  
Compressive Load ◽  
Shear Deformation Theory ◽  
Parameter Study ◽  
Compression Load ◽  
Large Structures ◽  
Geometrical Imperfection ◽  
Compressive Loads ◽  
Vibration Responses ◽  
Sine Functions

In practice, some components in large structures such as the connecting rods between the rotating parts in the engines, turbines, and so on, can model as beam structures rotating around the fixed axis and subject to the axial compression load; therefore, the study of mechanical behavior to these structures has a significant meaning in practice. This paper analyzes the vibration responses of rotating FGM beams subjected to axial compressive loads, in which the beam is resting on the two-parameter elastic foundation, taking into account the initial geometrical imperfection. Finite element formulations are established by using the new shear deformation theory type of hyperbolic sine functions and the finite element method. The materials are assumed to be varied smoothly in the thickness direction of the beam based on the power-law function with the porosity. Verification problems are conducted to evaluate the accuracy of the theory, proposed mechanical structures, and the calculation programs coded in the MATLAB environment. Then, a parameter study is carried to explore the effects of geometrical and material properties on the vibration behavior of FGM beams, especially the influences of the rotational speed and axial compressive load.

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