scholarly journals On Computing the Instability Index of a Non-Self-Adjoint Differential Operator Associated with Coating and Rimming Flows

2011 ◽  
Vol 43 (1) ◽  
pp. 367-388 ◽  
Author(s):  
Almut Burchard ◽  
Marina Chugunova
Keyword(s):  
Differential Operator ◽  
Instability Index ◽  
Rimming Flows

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions

Applicability of Instability Index for In vitro Protein Stability Prediction

2019 ◽  
Vol 26 (5) ◽  
pp. 339-347 ◽  
Author(s):  
Dilani G. Gamage ◽  
Ajith Gunaratne ◽  
Gopal R. Periyannan ◽  
Timothy G. Russell
Keyword(s):  
Protein Stability ◽  
Caulobacter Crescentus ◽  
Effect Of Temperature ◽  
Instability Index ◽  
Dipeptide Composition ◽  
Experimental Conditions ◽  
The Stability ◽  
Vitro Protein

Background: The dipeptide composition-based Instability Index (II) is one of the protein primary structure-dependent methods available for in vivo protein stability predictions. As per this method, proteins with II value below 40 are stable proteins. Intracellular protein stability principles guided the original development of the II method. However, the use of the II method for in vitro protein stability predictions raises questions about the validity of applying the II method under experimental conditions that are different from the in vivo setting. Objective: The aim of this study is to experimentally test the validity of the use of II as an in vitro protein stability predictor. Methods: A representative protein CCM (CCM - Caulobacter crescentus metalloprotein) that rapidly degrades under in vitro conditions was used to probe the dipeptide sequence-dependent degradation properties of CCM by generating CCM mutants to represent stable and unstable II values. A comparative degradation analysis was carried out under in vitro conditions using wildtype CCM, CCM mutants and two other candidate proteins: metallo-β-lactamase L1 and α -S1- casein representing stable, borderline stable/unstable, and unstable proteins as per the II predictions. The effect of temperature and a protein stabilizing agent on CCM degradation was also tested. Results: Data support the dipeptide composition-dependent protein stability/instability in wt-CCM and mutants as predicted by the II method under in vitro conditions. However, the II failed to accurately represent the stability of other tested proteins. Data indicate the influence of protein environmental factors on the autoproteolysis of proteins. Conclusion: Broader application of the II method for the prediction of protein stability under in vitro conditions is questionable as the stability of the protein may be dependent not only on the intrinsic nature of the protein but also on the conditions of the protein milieu.

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

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