Applications of Affine Systems of Walsh Type to Generate Smooth Basis

The question on affine Riesz basis of Walsh affine systems is considered. An affine Riesz basis is constructed, generated by a continuous periodic function that belongs to the space on the real line, which has a derivative almost everywhere; in connection with the construction of this example, we note that the functions of the classical Walsh system suffer a discontinuity and their derivatives almost vanish everywhere. A method of regularization (improvement of differential properties) of the generating function of Walsh affine system is proposed, and a criterion for an affine Riesz basis for a regularized generating function that can be represented as a sum of a series in the Rademacher system is obtained.

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Affine Bessel sequences and Nikishin’s example

Filomat ◽

10.2298/fil1704963m ◽

2017 ◽

Vol 31 (4) ◽

pp. 963-966 ◽

Cited By ~ 1

Author(s):

V.A. Mironov ◽

A.M. Sarsenbi ◽

P.A. Terekhin

Keyword(s):

Hilbert Space ◽

Periodic Function ◽

Spectral Theory ◽

Continuous Periodic Function ◽

Affine Systems ◽

Convergence In Measure ◽

Affine System ◽

Bessel Sequences

We study affine Bessel sequences in connection with the spectral theory and the multishift structure in Hilbert space. We construct a non-Besselian affine system fun(x)g1 n=0 generated by continuous periodic function u(x). The result is based on Nikishin?s example concerning convergence in measure. We also show that affine systems fun(x)g1 n=0 generated by any Lipchitz function u(x) are Besselian.

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Almost everywhere convergence of sequences of Cesàro and Riesz means of integrable functions with respect to the multidimensional Walsh system

Acta Mathematica Sinica English Series ◽

10.1007/s10114-013-1766-3 ◽

2013 ◽

Vol 30 (2) ◽

pp. 311-322 ◽

Cited By ~ 3

Author(s):

György Gát

Keyword(s):

Walsh System ◽

Riesz Means ◽

Almost Everywhere Convergence ◽

Almost Everywhere ◽

Integrable Functions ◽

Convergence Of Sequences

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On almost everywhere convergence and divergence of Marcinkiewicz-like means of integrable functions with respect to the two-dimensional Walsh system

Journal of Approximation Theory ◽

10.1016/j.jat.2011.09.010 ◽

2012 ◽

Vol 164 (1) ◽

pp. 145-161 ◽

Cited By ~ 3

Author(s):

György Gát

Keyword(s):

Walsh System ◽

Two Dimensional ◽

Almost Everywhere Convergence ◽

Almost Everywhere ◽

Integrable Functions ◽

Convergence And Divergence

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An Extended Generalized q-Extensions for the Apostol Type Polynomials

Abstract and Applied Analysis ◽

10.1155/2018/2937950 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13 ◽

Cited By ~ 1

Author(s):

Letelier Castilla ◽

William Ramírez ◽

Alejandro Urieles

Keyword(s):

Generating Function ◽

Bernstein Polynomials ◽

Bernoulli Polynomials ◽

Stirling Numbers ◽

Euler Polynomials ◽

Genocchi Polynomials ◽

Differential Properties

Through a modification on the parameters associated with generating function of the q-extensions for the Apostol type polynomials of order α and level m, we obtain some new results related to a unified presentation of the q-analog of the generalized Apostol type polynomials of order α and level m. In addition, we introduce some algebraic and differential properties for the q-analog of the generalized Apostol type polynomials of order α and level m and the relation of these with the q-Stirling numbers of the second kind, the generalized q-Bernoulli polynomials of level m, the generalized q-Apostol type Bernoulli polynomials, the generalized q-Apostol type Euler polynomials, the generalized q-Apostol type Genocchi polynomials of order α and level m, and the q-Bernstein polynomials.

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Semi-Orthogonal Binary Spline Wavelets in Incompressible Fluid Dynamics

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.249-250.164 ◽

2012 ◽

Vol 249-250 ◽

pp. 164-169

Author(s):

Steve Wai Chan ◽

King Fai Lai ◽

Mansoor Syed

Keyword(s):

Fluid Dynamics ◽

Dynamical Systems ◽

Incompressible Fluid ◽

Generating Function ◽

Riesz Basis ◽

Spline Function ◽

Refinable Functions ◽

Spline Wavelets ◽

Derivatives Of

Jia and coworkers [1] have shown that with =M_N and  ̃=M_1as a pair of locally supported refinable functions, one can construct a function, _N(N being an odd integer) given by _N≔∑_(j=0)^N▒〖((-1)^j)/2 [M_(N+1) (j)+M_N (j+1) ] M_N (2∙-j)〗. Here M_N is a binary spline function of degree N. For r =0, 1, 2, …, N-1, the set {2^(j/2) _N^((r) ) (2^j∙-j);j,k ϵ Z} is a Riesz basis for L_2 (R). This base involves the first N-1 derivatives of the generating function and therefore is useful for dynamical systems with derivative constraints.

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Inversor of digits $Q^∗_2$-representative of numbers

Matematychni Studii ◽

10.30970/ms.55.1.37-43 ◽

2021 ◽

Vol 55 (1) ◽

pp. 37-43

Author(s):

M. V. Pratsiovytyi ◽

Ya. V. Goncharenko ◽

N. V. Dyvliash ◽

S. P. Ratushniak

Keyword(s):

Closed Interval ◽

Binary Representation ◽

Almost Everywhere ◽

Self Similar ◽

Differential Properties

We consider structural, integral, differential properties of function defined by equality$$I(\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=\Delta^{Q_2^*}_{[1-\alpha_1][1-\alpha_2]...[1-\alpha_n]...}, \quad \alpha_n\in A\equiv\{0,1\}$$for two-symbol polybasic non-self-similar representation of numbers of closed interval $[0;1]$ that is a generalization of classic binary representation and self-similar two-base $Q_2$-representation.For additional conditions on the sequence of bases, singularity of the function and self-affinity of the graph are proved.Namely, the derivative is equal to zero almost everywhere in the sense of Lebesgue measure.The integral of the function is calculated.

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Microstructural Characterization of Au-Ge-Ni based ohmic contacts to GaAs/AlGaAs modfet device

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100126433 ◽

1987 ◽

Vol 45 ◽

pp. 326-327

Author(s):

A.K. Rai ◽

A.K. Petford-Long ◽

A. Ezis ◽

D.W. Langer

Keyword(s):

Contact Resistance ◽

Ohmic Contact ◽

Ohmic Contacts ◽

Microstructural Characterization ◽

Almost Everywhere ◽

Spacer Layer ◽

Good Contact ◽

The Relationship ◽

Lower Contact

Considerable amount of work has been done in studying the relationship between the contact resistance and the microstructure of the Au-Ge-Ni based ohmic contacts to n-GaAs. It has been found that the lower contact resistivity is due to the presence of Ge rich and Au free regions (good contact area) in contact with GaAs. Thus in order to obtain an ohmic contact with lower contact resistance one should obtain a uniformly alloyed region of good contact areas almost everywhere. This can possibly be accomplished by utilizing various alloying schemes. In this work microstructural characterization, employing TEM techniques, of the sequentially deposited Au-Ge-Ni based ohmic contact to the MODFET device is presented.The substrate used in the present work consists of 1 μm thick buffer layer of GaAs grown on a semi-insulating GaAs substrate followed by a 25 Å spacer layer of undoped AlGaAs.

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HUBUNGAN HIGIENE SANITASI DENGAN KANDUNGAN ESCHERICHIA COLI PADA ES BATU INDUSTRI RUMAH TANGGA DI TEPI JALAN WAHID HASYIM 2 KECAMATAN SEMPAJA KOTA SAMARINDA TAHUN 2015

KESMAS UWIGAMA: Jurnal Kesehatan Masyarakat ◽

10.24903/kujkm.v2i1.301 ◽

2018 ◽

Vol 2 (1) ◽

pp. 43

Author(s):

Suwignyo Suwignyo ◽

Abdul Rachim ◽

Arizal Sapitri

Keyword(s):

Escherichia Coli ◽

Data Analysis ◽

Random Sampling ◽

Preliminary Test ◽

Raw Material ◽

Almost Everywhere ◽

Ice Cube ◽

Processing And Storage ◽

And Storage ◽

Cluster Random Sampling

Ice is a water that cooled below 0 °C and used for complement in drink. Ice can be found almost everywhere, including in the Wahid Hasyim Sempaja Roadside. From the preliminary test, obtained 5 samples ice cube were contaminated by Escherichia coli. The purpose of this study was to determine relationship between hygiene and sanitation with presence of Eschericia coli in ice cube of home industry at Wahid Hasyim Roadside Samarinda. This research used quantitative with survey methode. The population in this study was all of the seller in 2nd Wahid Hasyim Roadside. Sample was taken by Krejcie and Morgan so the there were 44 samples and used Cluster Random Sampling. The instruments are questionnaries, observation and laboratory test. Data analysis was carried out univariate and bivariate (using Fisher test p= 0.05). The conclusion of this study there are a relation between chosing raw material (p=0,03) and saving raw material (p=0,03) with presence of Eschericia coli. There was no relation between processing raw material into ice cube with presence of Eschericia coli (p=0,15).Advice that can be given to ice cube should maintain hygiene and sanitation of the selection, processing and storage of ice cube.

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