scholarly journals On uniform regularity and strong regularity

Optimization ◽  
2018 ◽  
Vol 68 (2-3) ◽  
pp. 549-577 ◽  
Author(s):  
R. Cibulka ◽  
J. Preininger ◽  
T. Roubal
Keyword(s):  
Strong Regularity

A note on the strong regularity of Nrlund means

1983 ◽  
Vol 94 (2) ◽  
pp. 261-263
Author(s):  
J. R. Nurcombe
Keyword(s):  
Strong Convergence ◽  
Complex Numbers ◽  
Strong Regularity ◽  
Image Position

Let (pn), (qn) and (un) be sequences of real or complex numbers withThe sequence (sn) is strongly generalized Nrlund summable with index 0, to s, or s or snsN, p, Q ifand pnv=pnvpnv1, with p10. Strong Nrlund summability N, p was first studied by Borweing and Cass (1), and its generalization N, p, Q by Thorp (6). We shall say that (sn) is strongly generalized convergent of index 0, to s, and write snsC, 0, Q if sns and where sn=a0+a1++an. When qn all n, this definition reduces to strong convergence of index , introduced by Hyslop (4). If as n, the sequence (sn) is summable (, q) to s sns(, q).

scholarly journals A New Symmetric Key Cryptographic Algorithm using Paley Graphs and ASCII Values

2021 ◽  
Vol 297 ◽  
pp. 01046
Author(s):  
Zhour Oumazouz ◽  
Driss Karim
Keyword(s):  
Brute Force ◽  
Strong Regularity ◽  
Quadratic Residues ◽  
Cryptographic Algorithm ◽  
Paley Graph ◽  
Encryption And Decryption ◽  
Symmetric Key ◽  
Brute Force Attack ◽  
The Moment ◽  
Paley Graphs

The main objective of the study conducted in this article is to introduce a new algorithm of encryption and decryption of a sensitive message after transforming it into a binary message. Our proposed encryption algorithm is based on the study of a particular graph constructed algebraically from the quadratic residues. We have exploited the Paley graph to introduce an abstract way of encryption of such message bit according to the other message bits by the intermidiate study of the neighborhood of a graph vertex. The strong regularity of the Paley graphs and the unknown behavior of the quadratic residues will play a very important role in the cryptanalysis part which allows to say that the brute force attack remains for the moment the only way to obtain the set of possible messages.

scholarly journals On strong regularity of relations

1994 ◽  
Vol 119 (2) ◽  
pp. 151-155
Author(s):  
Josef Šlapal
Keyword(s):  
Strong Regularity

scholarly journals Strong Regularity in Arbitrary Rings

1952 ◽  
Vol 4 ◽  
pp. 51-53 ◽  
Author(s):  
Tetsuo Kandô
Keyword(s):  
Matrix Ring ◽  
Strong Regularity ◽  
Full Matrix ◽  
Regular Ideal ◽  
Strongly Regular ◽  
Full Matrix Ring

An element a of a ring R is called regular, if there exists an element x of R such that a×a = a, and a two-sided ideal a in R is said to be regular if each of its elements is regular B. Brown and N. H. McCoy [1] has recently proved that every ring R has a unique maximal regular two-sided ideal M(R), and that M(R) has the following radical-like property: (i) M(R/M(R)) = 0; (ii) if a is a two-sided ideal of R, then M(a) = a ∩ M(R); (iii) M(Rn) = (M(R))n, where Rn denotes a full matrix ring of order n over R. Arens and Kaplansky [2] has defined an element a of R to be strongly regular when there exists an element x of R such that a2x = a. We shall prove in this note that replacing “regularity” by “strong regularity,” we have also a unique maximal strongly regular ideal N(R), and shall investigate some of its properties.

scholarly journals The Manifold of Elliptical Galaxies

1987 ◽  
Vol 127 ◽  
pp. 79-88
Author(s):  
S. Djorgovski
Keyword(s):  
Galaxy Formation ◽  
Surface Brightness ◽  
Velocity Dispersion ◽  
Elliptical Galaxies ◽  
Morphological Parameters ◽  
Strong Regularity ◽  
Fundamental Plane ◽  
Global Properties ◽  
Error Bars ◽  
Intrinsic Scatter

Global properties of elliptical galaxies, such as the luminosity, radius, projected velocity dispersion, projected luminosity density, etc., form a two-dimensional family. This “fundamental plane” of elliptical galaxies can be defined by the velocity dispersion and mean surface brightness, and its thickness is presently given by the measurement error-bars only. This is indicative of a strong regularity in the process of galaxy formation. However, all morphological parameters which describe the shape of the distribution of light, and reflect dynamical anisotropies of stars, are completely independent from each other, and independent of the fundamental plane. The M/L ratios show only a small intrinsic scatter in a luminosity range spanning some four orders of magnitude; this suggests a constant fraction of the dark matter contribution in elliptical galaxies.

Pseudo-Strong Regularity Around a Set

2002 ◽  
Vol 50 (1) ◽  
pp. 33-47 ◽  
Author(s):  
M.A. Fiol ◽  
E. Garriga
Keyword(s):  
Strong Regularity

Wind Power Forecasting Based on Improved Biased Wavelet Neural Network

2014 ◽  
Vol 915-916 ◽  
pp. 1532-1535
Author(s):  
Yu Han Mao
Keyword(s):  
Neural Network ◽  
Wind Power ◽  
Prediction Accuracy ◽  
Forecast Model ◽  
Wavelet Neural Network ◽  
Strong Regularity ◽  
Power Prediction ◽  
Wind Power Prediction ◽  
Wind Power System ◽  
Power Sequence

Wind power prediction is the key to grid-connected wind power system. In this paper, first of all, we decompose and reconstruct the power sequence by wavelet analysis, and reduce the noise of the detail signal, to obtain the strong-regularity subsequence. We adapt the biased wavelet neural network rolling forecast model for the processed sequence to obtain seven days of rolling forecast results through several amendments. For the sequence of 5 minutes interval the prediction accuracy is 98.63%, for the sequence of 15 minutes interval the prediction accuracy is 99.88%.

Sparse Tensor Product Approximation for Radiative Transfer

2007 ◽  
Author(s):  
Gisela Widmer ◽  
Ralf Hiptmair
Keyword(s):  
Radiative Transfer ◽  
Tensor Product ◽  
Degrees Of Freedom ◽  
Convergence Result ◽  
Superior Performance ◽  
Discrete Ordinates ◽  
Strong Regularity ◽  
Scattering Media ◽  
Translation Invariant ◽  
Tensor Product Approximation

The stationary monochromatic radiative transfer equation is stated in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. In order to overcome the high dimensionality of the problem, we propose and analyse a new multiscale Galerkin Finite Element discretizaton that, under strong regularity assumptions on the solution, reduces the complexity of the problem to the number of degrees of freedom in space only (up to logarithmic terms). The sparse tensor product approximation adapts the idea of so-called ‘Sparse Grids’ for the product space of functions on the physical domain and the unit sphere. We present some details of the sparse tensor product construction including a convergence result that shows that, assuming strong regularity of the solution, the method converges with essentially optimal asymptotic rates while its complexity grows essentially only as that for a linear transport problem. Numerical experiments in a translation invariant setting in non-scattering media agree with predictions of theory and demonstrate the superior performance of the sparse tensor product method compared to the discrete ordinates method.

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