scholarly journals ON BASIS PROPERTY OF SYSTEMS ROOT VECTORS OF A LOADED MULTIPLE DIFFERENTIATION OPERATOR

2020 ◽  
Vol 1 (329) ◽  
pp. 32-37
Author(s):  
N. S. Imanbaev ◽  
◽  
◽  
Keyword(s):  
Basis Property ◽  
Differentiation Operator ◽  
Multiple Differentiation

NON STABILITY ON BASIS PROPERTY OF SYSTEMS ROOT VECTORS OF A LOADED MULTIPLE DIFFERENTIATION OPERATOR

2020 ◽  
pp. 78-83
Author(s):  
N.S. Imanbaev ◽  
Keyword(s):  
Differential Operators ◽  
Boundary Value ◽  
Basis Property ◽  
Differentiation Operator ◽  
A Value ◽  
Multiple Differentiation ◽  
Associated Functions ◽  
Strongly Regular ◽  
Small Change ◽  
Loaded Term

In this paper we consider perturbations of a second order differential equation of the spectral problem with a loaded term, containing a value of the unknown function at the point zero, with regular, but not strongly regular boundary value conditions. Question about basis property of eigen functions and associated functions (E&AF) systems of a loaded multiple differentiation operator is studied. In the case of non-self-adjoint ordinary differential operators, the basis property of systems of eigen functions and associated functions (E&AF), in addition to the boundary value conditions, can be affected by values of coefficients of the differential operator. Moreover, it is known that the basic properties of E&AF can be changed at a small change of values of the coefficients. This fact was first noted in Il’in V.A. In this paper problem non stability on basis property of systems root vectors of a loaded multiple differentiation operator.

scholarly journals On a Problem that Does not Have Basis Property of Root Vectors, Associated with a Perturbed Regular Operator of Multiple Differentiation

2020 ◽  
pp. 568-573
Author(s):  
Nurlan S. Imanbaev
Keyword(s):  
Spectral Problem ◽  
Boundary Value ◽  
Basis Property ◽  
Differentiation Operator ◽  
Boundary Value Condition ◽  
Root Functions ◽  
Multiple Differentiation ◽  
Strongly Regular ◽  
Integral Perturbation ◽  
System Of Root Functions

A spectral problem for a multiple differentiation operator with integral perturbation of boundary value conditions which are regular but not strongly regular is considered in the paper. The feature of the problem is the absence of the basis property of the system of root vectors. A characteristic determinant of the spectral problem is constructed. It is shown that absence of the basis property of the system of root functions of the problem is unstable with respect to the integral perturbation of the boundary value condition

scholarly journals On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
N. S. Imanbaev
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Basis Property ◽  
Differentiation Operator ◽  
Stability And Instability ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Type Boundary ◽  
Eigenfunctions And Associated Functions ◽  
Integral Perturbation

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

FINITELY BASED WORDS

2000 ◽  
Vol 10 (04) ◽  
pp. 457-480 ◽  
Author(s):  
OLGA SAPIR
Keyword(s):  
Sufficient Conditions ◽  
Basis Property ◽  
Free Monoid ◽  
Finite Basis ◽  
Finitely Based ◽  
Finite Basis Property ◽  
Letter Alphabet ◽  
Finite Language ◽  
Rees Quotient ◽  
The Ideal

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.

scholarly journals Antigen-driven EGR2 expression is required for exhausted CD8+ T cell stability and maintenance

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mayura V. Wagle ◽  
Stephin J. Vervoort ◽  
Madison J. Kelly ◽  
Willem Van Der Byl ◽  
Timothy J. Peters ◽  
...  
Keyword(s):  
T Cells ◽  
Transcription Factor ◽  
Cd8 T Cell ◽  
Chronic Stimulation ◽  
Epigenetic State ◽  
Multiple Differentiation ◽  
Cell Stability ◽  
Substantial Interest ◽  
Transcriptional State ◽  
Stimulation Of

AbstractChronic stimulation of CD8+ T cells triggers exhaustion, a distinct differentiation state with diminished effector function. Exhausted cells exist in multiple differentiation states, from stem-like progenitors that are the key mediators of the response to checkpoint blockade, through to terminally exhausted cells. Due to its clinical relevance, there is substantial interest in defining the pathways that control differentiation and maintenance of these subsets. Here, we show that chronic antigen induces the anergy-associated transcription factor EGR2 selectively within progenitor exhausted cells in both chronic LCMV and tumours. EGR2 enables terminal exhaustion and stabilizes the exhausted transcriptional state by both direct EGR2-dependent control of key exhaustion-associated genes, and indirect maintenance of the exhausted epigenetic state. We show that EGR2 is a regulator of exhaustion that epigenetically and transcriptionally maintains the differentiation competency of progenitor exhausted cells.

scholarly journals MULTIPLE DIFFERENTIATION OF PLASMONS OF DIPLOID SPECIES OF SOLANUM

Genetics ◽  
1962 ◽  
Vol 47 (10) ◽  
pp. 1321-1333 ◽  
Author(s):  
Paul Grun ◽  
Mary Aubertin ◽  
Anne Radlow
Keyword(s):  
Diploid Species ◽  
Multiple Differentiation
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