A Simple Method to Find All Solutions to the Functional Equation of the Smoothing Transform

Approximate mixed type additive and quartic functional equation

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v35i1.29014 ◽

2017 ◽

Vol 35 (1) ◽

pp. 43 ◽

Cited By ~ 1

Author(s):

Abasalt Bodaghi

Keyword(s):

Functional Equation ◽

Mixed Type ◽

Current Work ◽

Ulam Stability ◽

Normed Spaces ◽

Quartic Functional Equation ◽

All Solutions

In the current work, we introduce a general form of a mixed additive and quartic functional equation. We determine all solutions of this functional equation. We also establish the generalized Hyers-Ulam stability of this new functional equation in quasi-$\beta$-normed spaces.

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A simple method for all solutions of a piecewise linear network

10.1109/iscas.1988.15150 ◽

2003 ◽

Cited By ~ 2

Author(s):

Q. Huang ◽

R. Liu

Keyword(s):

Piecewise Linear ◽

Linear Network ◽

Simple Method ◽

All Solutions

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Linear differential equations with unbounded delays and a forcing term

Abstract and Applied Analysis ◽

10.1155/s1085337504306020 ◽

2004 ◽

Vol 2004 (4) ◽

pp. 337-345 ◽

Cited By ~ 1

Author(s):

Jan Čermák ◽

Petr Kundrát

Keyword(s):

Differential Equation ◽

Functional Equation ◽

Continuous Function ◽

Differential Equations ◽

Asymptotic Behaviour ◽

Functional Equations ◽

Continuous Functions ◽

Positive Continuous Function ◽

All Solutions ◽

Linear Differential

The paper discusses the asymptotic behaviour of all solutions of the differential equationy˙(t)=−a(t)y(t)+∑i=1nbi(t)y(τi(t))+f(t),t∈I=[t0,∞), with a positive continuous functiona, continuous functionsbi,f, andncontinuously differentiable unbounded lags. We establish conditions under which any solutionyof this equation can be estimated by means of a solution of an auxiliary functional equation with one unbounded lag. Moreover, some related questions concerning functional equations are discussed as well.

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On solutions of functional equations with polynomial translations

Creative Mathematics and Informatics ◽

10.37193/cmi.2019.01.08 ◽

2019 ◽

Vol 28 (1) ◽

pp. 53-59

Author(s):

MITROFAN M. CHOBAN ◽

◽

LARISA M. SALI ◽

Keyword(s):

Functional Equation ◽

Special Form ◽

Functional Equations ◽

Homogeneous Equation ◽

Sufficient Conditions ◽

Simple Method ◽

Polynomial Solutions

In this paper, we study polynomial functional equations of the form af(p(x)) + bf(q(x)) = g(x), where p(x), q(x) are given polynomials and g(x) is a given function. Theorems 21 and 22 contain sufficient conditions under which the functional equation has a solution of the special form. In Section 3 we present an algorithm of constructing polynomial solutions of the functional equations. Other non-polynomial solutions depend on solutions of the homogeneous equation af(p(x)) + bf(q(x)) = 0. That case is analyzed in Section 4. Finally, we present a simple method of constructing examples with desirable properties.

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Exogeneous factors are not necessary in attachment, spreading and polarization of hela cells

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100082418 ◽

1978 ◽

Vol 36 (2) ◽

pp. 310-311

Author(s):

W. Liebrich

Keyword(s):

Hela Cells ◽

Calf Serum ◽

Glass Tube ◽

Serum Free Medium ◽

Nacl Solution ◽

Free Medium ◽

Minimum Essential Medium ◽

Serum Free ◽

All Solutions ◽

Glass Support

HeLa cells were grown for 2-3 days in EAGLE'S minimum essential medium with 10% calf serum (S-MEM; Seromed, München) and then incubated for 24 hours in serum free medium (MEM). After detaching the cells with a solution of 0. 14 % EDTA and 0. 07 % trypsin (Difco, 1 : 250) they were suspended in various solutions (S-MEM = control, MEM, buffered salt solutions with or without Me++ions, 0. 9 % NaCl solution) and allowed to settle on glass tube slips (Leighton-tubes). After 5, 10, 15, 20, 25, 30, 1 45, 60 minutes 2, 3, 4, 5 hours cells were prepared for scanning electron microscopy as described by Paweletz and Schroeter. The preparations were examined in a Jeol SEM (JSM-U3) at 25 KV without tilting.The suspended spherical HeLa cells are able to adhere to the glass support in all solutions. The rate of attachment, however, is faster in solutions without serum than in the control. The latter is in agreement with the findings of other authors.

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A simple way for producing holographic filters suitable for image improvement

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100108271 ◽

1978 ◽

Vol 36 (1) ◽

pp. 226-227

Author(s):

K.-H. Herrmann ◽

E. Reuber ◽

P. Schiske

Keyword(s):

Transfer Functions ◽

Diffraction Order ◽

Lateral Position ◽

Simple Method ◽

Spatial Frequencies ◽

Resolution Electron ◽

Wiener Filters ◽

Image Improvement ◽

Optical Reconstruction ◽

Set Up

Aposteriori deblurring of high resolution electron micrographs of weak phase objects can be performed by holographic filters [1,2] which are arranged in the Fourier domain of a light-optical reconstruction set-up. According to the diffraction efficiency and the lateral position of the grating structure, the filters permit adjustment of the amplitudes and phases of the spatial frequencies in the image which is obtained in the first diffraction order.In the case of bright field imaging with axial illumination, the Contrast Transfer Functions (CTF) are oscillating, but real. For different imageforming conditions and several signal-to-noise ratios an extensive set of Wiener-filters should be available. A simple method of producing such filters by only photographic and mechanical means will be described here.A transparent master grating with 6.25 lines/mm and 160 mm diameter was produced by a high precision computer plotter. It is photographed through a rotating mask, plotted by a standard plotter.

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Rotary Beveling for In Situ Thin-Section Microscopy of Cell Cultures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100099192 ◽

1981 ◽

Vol 39 ◽

pp. 550-551

Author(s):

Dean A. Handley ◽

Jack T. Alexander ◽

Shu Chien

Keyword(s):

Cell Growth ◽

Cell Cultures ◽

Molecular Interactions ◽

Convenient Method ◽

Petri Dish ◽

Simple Method ◽

Thin Section Microscopy ◽

Thin Sectioning ◽

Organic Fluids

In situ preparation of cell cultures for ultrastructural investigations is a convenient method by which fixation, dehydration and embedment are carried out in the culture petri dish. The in situ method offers the advantage of preserving the native orientation of cell-cell interactions, junctional regions and overlapping configurations. In order to section after embedment, the petri dish is usually separated from the polymerized resin by either differential cryo-contraction or solvation in organic fluids. The remaining resin block must be re-embedded before sectioning. Although removal of the petri dish may not disrupt the native cellular geometry, it does sacrifice what is now recognized as an important characteristic of cell growth: cell-substratum molecular interactions. To preserve the topographic cell-substratum relationship, we developed a simple method of tapered rotary beveling to reduce the petri dish thickness to a dimension suitable for direct thin sectioning.

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