scholarly journals The problem of normal oscillations of a viscous stratified fluid with an elastic membrane

2021 ◽  
Vol 31 (2) ◽  
pp. 311-330
Author(s):  
D.O. Tsvetkov
Keyword(s):  
Half Plane ◽  
Model Problem ◽  
Stratified Fluid ◽  
Elastic Membrane ◽  
Spatial Problem ◽  
Scalar Model ◽  
Oscillation Spectrum ◽  
Complex Half Plane ◽  
The Right ◽  
Location Zone

Normal oscillations of a viscous stratified fluid partially filling an arbitrary vessel and bounded above by an elastic horizontal membrane are studied. In this case, we consider a scalar model problem that reflects the main features of the vector spatial problem. The characteristic equation for the eigenvalues of the model problem is obtained, the structure of the spectrum and the asymptotics of the branches of the eigenvalues are studied. Assumptions are made about the structure of the oscillation spectrum of a viscous stratified fluid bounded by an elastic membrane for an arbitrary vessel. It is proved that the spectrum of the problem is discrete, located in the right complex half-plane symmetrically with respect to the real axis, and has a single limit point $+\infty$. Moreover, the spectrum is localized in a certain way in the right half-plane, the location zone depends on the dynamic viscosity of the fluid.

scholarly journals Continued Fractions and Conformal Mappings for Domains with Angel Points

2018 ◽  
Vol 7 (4.7) ◽  
pp. 409
Author(s):  
Pyotr N. Ivanshin ◽  
. .
Keyword(s):  
Unit Disk ◽  
Half Plane ◽  
Continued Fraction ◽  
Root Function ◽  
Conformal Mappings ◽  
Thin Domains ◽  
Root Functions ◽  
Mapping Sequence ◽  
Complex Half Plane ◽  
The Right

Here we construct the conformal mappings with the help of the continued fraction approximations. We first show that the method of [19] works for conformal mappings of the unit disk onto domains with acute external angles at the boundary. We give certain illustrative examples of these constructions. Next we outline the problem with domains which boudary possesses acute internal angles. Then we construct the method of rational root approximation in the right complex half-plane. First we construct the square root approximation and consider approximative properties of the mapping sequence in Theorem 1. Then we turn to the general case, namely, the continued fraction approximation of the rational root function in the complex right half-plane. These approximations converge to the algebraic root functions , , , . This is proved in Theorem 2 of the aricle. Thus we prove convergence of this method and construct conformal approximate mappings of the unit disk onto domains with angles and thin domains. We estimate the convergence rate of the approximation sequences. Note that the closer the point is to zero or infinity and the lower is the ratio k/N the worse is the approximation. Also we give the examples that illustrate the conformal mapping construction.  

scholarly journals Further properties of the Bergman spaces of slice regular functions

2015 ◽  
Vol 15 (4) ◽  
Author(s):  
Fabrizio Colombo ◽  
J. Oscar González-Cervantes ◽  
Irene Sabadini
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Half Plane ◽  
Bergman Kernel ◽  
Bergman Spaces ◽  
Reflection Principle ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Complex Half Plane ◽  
Schwarz Reflection Principle

AbstractWe continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind. In this paperwe mainly consider the Bergman theory of the second kind, by providing an explicit description of the Bergman kernel in the case of the unit ball and of the half space. In the case of the unit ball, we study the Bergman-Sce transform. We also show that the two Bergman theories can be compared only if suitableweights are taken into account. Finally,we use the Schwarz reflection principle to relate the Bergman kernel with its values on a complex half plane.

scholarly journals Analyticity of semigroups on the right half-plane

2017 ◽  
Vol 448 (2) ◽  
pp. 750-766 ◽  
Author(s):  
Mark Elin ◽  
Fiana Jacobzon
Keyword(s):  
Half Plane ◽  
The Right

Coronary Intimal Thickening Begins in Fetuses and Progresses in Pediatric Population and Adolescents to Atherosclerosis

Angiology ◽  
2019 ◽  
Vol 71 (1) ◽  
pp. 62-69 ◽  
Author(s):  
Roberto Guerri-Guttenberg ◽  
Rocío Castilla ◽  
Gabriel Cao ◽  
Francisco Azzato ◽  
Giuseppe Ambrosio ◽  
...  
Keyword(s):  
Smooth Muscle ◽  
Coronary Artery ◽  
Pediatric Population ◽  
Elastic Membrane ◽  
Lipid Deposition ◽  
Intimal Thickening ◽  
Histomorphometric Analysis ◽  
Young Population ◽  
The Right ◽  
Immunohistochemical Studies

The prevalence of coronary intimal thickening (IT) was assessed in fetuses and pediatric population. We studied the coronary arteries of 63 hearts obtained from fetuses, infants, children, and adolescents, deceased from noncardiac disease or trauma. Histomorphometric analysis, planimetry, and immunohistochemical studies were conducted. Intimal thickening consisted of proliferation of smooth muscle cells and scarce monocytes embedded in amorphous deposits within the internal elastic membrane (IEM). Intermingled lesions of intimal hyperplasia and parietal nonstenotic plaques were also observed. Intimal thickening was found in 10% of 20 fetuses, in 33.3% of 18 infants, 73.3% of 15 children, and 100% of 10 adolescents. A significant correlation ( r = 0.671, P < 0.001) was found between the extent of IT and age. The IEM was duplicated or interrupted in 43% of patients, showing a positive correlation with the degree of IT ( P = 0.01). Intimal thickening was predominantly found near bifurcation sites in the left anterior descending coronary artery (55.6%) and in zones free of bifurcation in the right coronary artery (75%). In conclusion, the prevalence and extension of IT lesions are higher at older ages within a young population. Intimal thickening may be regarded as the first event occurring in coronary preatherosclerosis, preceding lipid deposition.

scholarly journals A Berezin-type map and a class of weighted composition operators

2017 ◽  
Vol 4 (1) ◽  
pp. 18-31
Author(s):  
Namita Das
Keyword(s):  
Linear Operator ◽  
Bergman Space ◽  
Half Plane ◽  
Composition Operators ◽  
Weighted Composition Operators ◽  
Unitary Operators ◽  
Area Measure ◽  
Weighted Composition ◽  
The Right

Abstract In this paper we consider the map L defined on the Bergman space $L_a^2({{\rm\mathbb{C}}_{\rm{ + }}})$ of the right half plane ℂ+ by $(Lf)(w) = \pi M'(w)\int\limits_{{{\rm\mathbb{C}}_{\rm{ + }}}} {\left( {{f \over {M'}}} \right)} (s){\left| {{b_w}(s)} \right|^2}d\tilde A(s)$ where ${b_{\bar w}}(s) = {1 \over {\sqrt \pi }}{{1 + w} \over {1 + w}}{{2{\mathop{Re}\nolimits} w} \over {{{(s + w)}^2}}}$ , s ∈ ℂ+ and $Ms = {{1 - s} \over {1 + s}}$ . We show that L commutes with the weighted composition operators Wa, a ∈ 𝔻 defined on $L_a^2({{\rm\mathbb{C}}_{\rm{ + }}})$ , as ${W_a}f = (f \circ {t_a}){{M'} \over {M' \circ {t_a}}}$ , $f \in L_a^2(\mathbb{C_ + })$ . Here $${t_a}(s) = {{ - ids + (1 - c)} \over {(1 + c)s + id}} , if a = c + id ∈ 𝔻 c, d ∈ ℝ. For a ∈ 𝔻, define ${V_a}:L_a^2({{\mathbb{C}}_{\rm{ + }}}) \to L_a^2({{\mathbb{C}}_{\rm{ + }}})$ by (Vag)(s) = (g∘ta)(s)la(s) where $la(s) = {{1 - {{\left| a \right|}^2}} \over {{{((1 + c)s + id)}^2}}}$ .We look at the action of the class of unitary operators Va, a ∈ 𝔻 on the linear operator L. We establish that Lˆ = L where $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over L} = \int\limits_{\mathbb{D}} {{V_a}L{V_a}dA(a)}$ and dA is the area measure on 𝔻. In fact the map L satisfies the averaging condition $$\tilde L({w_1}) = \int\limits_{\mathbb{D}} {\tilde L({t_{\bar a}}({w_1}))dA(a),{\rm{for all }}{w_1} \in {{\rm{C}}_{\rm{ + }}}}$$ where $\tilde L({w_1}) = \left\langle {L{b_{{{\bar w}_1}}},{b_{{{\bar w}_1}}}} \right\rangle$.

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