Complex Analysis and Complexes of Differential Operators

1982 ◽  
pp. 105-195 ◽  
Author(s):  
Mauro Nacinovich
Keyword(s):  
Complex Analysis ◽  
Differential Operators

scholarly journals DIFFUSIVE REPRESENTATIONS FOR THE ANALYSIS AND SIMULATION OF FLARED ACOUSTIC PIPES WITH VISCO-THERMAL LOSSES

2006 ◽  
Vol 16 (04) ◽  
pp. 503-536 ◽  
Author(s):  
TH. HÉLIE ◽  
D. MATIGNON
Keyword(s):  
Finite Order ◽  
Acoustic Waves ◽  
Complex Analysis ◽  
Differential Operators ◽  
Transfer Functions ◽  
Representation Formula ◽  
Input Output ◽  
Numerical Approximations ◽  
Pseudo Differential Operators ◽  
Scattering Matrices

Acoustic waves travelling in axisymmetric pipes with visco-thermal losses at the wall obey a Webster–Lokshin model. Their simulation may be achieved by concatenating scattering matrices of elementary transfer functions associated with nearly constant parameters (e.g. curvature). These functions are computed analytically and involve diffusive pseudo-differential operators, for which we have representation formula and input-output realizations, yielding direct numerical approximations of finite order. The method is based on some involved complex analysis.

scholarly journals Holomorphic functions, relativistic sum, Blaschke products and superoscillations

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Stefano Pinton ◽  
Irene Sabadini
Keyword(s):  
Infinite Order ◽  
Complex Analysis ◽  
Differential Operators ◽  
Entire Functions ◽  
Growth Conditions ◽  
Weak Values ◽  
Blaschke Products ◽  
Independent Field ◽  
Superoscillating Functions ◽  
Band Limited

AbstractSuperoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The notion of superoscillation is a particular case of that one of supershift. In the recent years, superoscillating functions, that appear for example in weak values in quantum mechanics, have become an interesting and independent field of research in complex analysis and in the theory of infinite order differential operators. The aim of this paper is to study some infinite order differential operators acting on entire functions which naturally arise in the study of superoscillating functions. Such operators are of particular interest because they are associated with the relativistic sum of the velocities and with the Blaschke products. To show that some sequences of functions preserve the superoscillatory behavior it is of crucial importance to prove that their associated infinite order differential operators act continuously on some spaces of entire functions with growth conditions.

scholarly journals Systems of Simultaneous Differential Inclusions Implying Function Containment

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1252
Author(s):  
José A. Antonino ◽  
Sanford S. Miller
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Mixed Problem ◽  
Unit Disc ◽  
Differential Inclusions ◽  
Complex Analysis ◽  
Differential Operators ◽  
Derivatives Of ◽  
Differential Subordinations

An important problem in complex analysis is to determine properties of the image of an analytic function p defined on the unit disc U from an inclusion or containment relation involving several of the derivatives of p. Results dealing with differential inclusions have led to the development of the field of Differential Subordinations, while results dealing with differential containments have led to the development of the field of Differential Superordinations. In this article, the authors consider a mixed problem consisting of special differential inclusions implying a corresponding containment of the form D[p](U)⊂Ω⇒Δ⊂p(U), where Ω and Δ are sets in C, and D is a differential operator such that D[p] is an analytic function defined on U. We carry out this research by considering the more general case involving a system of two simultaneous differential operators in two unknown functions.

Singular Perturbations of Differential Operators

2000 ◽  
Author(s):  
S. Albeverio ◽  
P. Kurasov
Keyword(s):  
Singular Perturbations ◽  
Differential Operators

Effect of Calcium ion on the interaction between Thrombin and Heparin. Thermal Denaturation

1977 ◽  
Vol 38 (03) ◽  
pp. 0677-0684 ◽  
Author(s):  
Raymund Machovich ◽  
Péter Arányi
Keyword(s):  
Calcium Ions ◽  
Rate Constants ◽  
Thermal Denaturation ◽  
Time Course ◽  
Complex Analysis ◽  
Heat Inactivation ◽  
Second Phase ◽  
Denaturation Kinetics ◽  
Enzyme Protection ◽  
Enzyme Denaturation

SummaryHeat inactivation of thrombin at 54° C followed first order kinetics with a rate constant of 1.0 min−1 approximately. Addition of heparin resulted in protection against thermal denaturation and, at the same time, rendered denaturation kinetics more complex. Analysis of the biphasic curve of heat inactivation in the presence of heparin revealed that the rate constants of the second phase changed systematically with heparin concentrations. Namely, at 4.5 × 10−6M, 9 × 10−6M, 1.8 × 10−5M and 3.6 × 10−5M heparin concentrations, the rate constants were 0.27 min−1, 0.17 min−1, 0.11 min−1 and 0.06 min−1, respectively.Sulfate as well as phosphate ions displayed also enzyme protection against heat inactivation, however, the same effect was obtained already at a heparin concentration, lower by three orders of magnitude.The kinetics of enzyme denaturation was not affected by calcium ions, whereas in the presence of heparin the inactivation rate of thrombin changed, i. e. calcium ions abolished the biphasic character of time course of thermal denaturation.Thus, the data suggest that calcium ions contribute to the effect of heparin on thrombin.

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