All Solutions of a Bitangential Interpolation Problem that Includes Boundary Points

2013 ◽  
Vol 51 (6) ◽  
pp. 4387-4413 ◽  
Author(s):  
Jovan Stefanovski
Keyword(s):  
Interpolation Problem ◽  
Boundary Points ◽  
All Solutions ◽  
Bitangential Interpolation

scholarly journals Solution of a multiple Nevanlinna–Pick problem for Schur functions via orthogonal rational functions

Analysis ◽  
2008 ◽  
Vol 28 (1) ◽  
Author(s):  
Adhemar Bultheel ◽  
Andreas Lasarow
Keyword(s):  
Unique Solution ◽  
Interpolation Problem ◽  
Schur Functions ◽  
Rational Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Orthogonal Rational Functions ◽  
All Solutions ◽  
Pick Problem ◽  
Complex Valued

An interpolation problem of Nevanlinna–Pick type for complex-valued Schur functions in the open unit disk is considered. We prescribe the values of the function and its derivatives up to a certain order at finitely many points. Primarily, we study the case that there exist many Schur functions fulfilling the required conditions. For this situation, an application of the theory of orthogonal rational functions is used to characterize the set of all solutions of the problem in question. Moreover, we treat briefly the case of exactly one solution and present an explicit description of the unique solution in that case.

scholarly journals SCHUR–NEVANLINNA SEQUENCES OF RATIONAL FUNCTIONS

2007 ◽  
Vol 50 (3) ◽  
pp. 571-596 ◽  
Author(s):  
Adhemar Bultheel ◽  
Andreas Lasarow
Keyword(s):  
Unit Circle ◽  
Interpolation Problem ◽  
Schur Functions ◽  
Rational Functions ◽  
The Other ◽  
Complex Numbers ◽  
Orthogonal Rational Functions ◽  
All Solutions ◽  
The One

AbstractWe study certain sequences of rational functions with poles outside the unit circle. Such kinds of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur–Nevanlinna algorithm for Schur functions on the one hand, and to orthogonal rational functions on the unit circle on the other. We shall see that rational functions belonging to a Schur–Nevanlinna sequence can be used to parametrize the set of all solutions of an interpolation problem of Nevanlinna–Pick type for Schur functions.

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

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.

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

scholarly journals Simplified and improved criteria for oscillation of delay differential equations of fourth order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. Moaaz ◽  
A. Muhib ◽  
D. Baleanu ◽  
W. Alharbi ◽  
E. E. Mahmoud
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Interesting Point ◽  
All Solutions ◽  
Special Cases ◽  
Delay Differential ◽  
Noncanonical Operator

AbstractAn interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studying the noncanonical case. Therefore, this study aims to reduce the oscillation conditions of the fourth-order delay differential equations with a noncanonical operator. Moreover, the approach used gives more accurate results when applied to some special cases, as we explained in the examples.

scholarly journals A COVID-19 Lockdown Tabletop Exercise in New Taipei City, Taiwan

2021 ◽  
pp. 1-19
Author(s):  
I-Tien Lo ◽  
Ching-Yuan Lin ◽  
Ming-Tai Cheng
Keyword(s):  
Policy Making ◽  
Large City ◽  
Strategic Plan ◽  
Government Control ◽  
Subject Knowledge ◽  
All Solutions ◽  
Taipei City ◽  
Returning To Work ◽  
Three Stages ◽  
Stage 1

Abstract Objectives: This exercise aimed to validate New Taipei City’s strategic plan for a city lockdown in response to COVID-19. The main goal of all solutions was the principle of “reducing citizen activity and strengthening government control”. Methods: We created a suitable exercise, and creating 15 hypothetical situations for three stages. All participating units designed and proposed policy plans and execution protocols according to each situation. Results: In the course of the exercise, many existing policies and execution protocols were validated to address. Situations occurring in Stage 1, when the epidemic was spreading to the point of lockdown preparations, approaches to curb the continued spread of the epidemic in Stage 2, and returning to work after the epidemic is controlled and lockdown is lifted in Stage 3. Twenty response units participated in the exercise. Although favourable outcomes were obtained, the evaluators provided comments suggesting further improvements. Conclusions: Our exercise demonstrated a successful example to help policy making and revision in a large city over 4 million population during COVID-19 pandemic. It also enhanced participants’ subject knowledge and familiarity with the implementation of a city lockdown. For locations intending to go into lockdown, similar tabletop exercises are an effective verification option.

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