scholarly journals A Beurling-Helson type theorem for modulation spaces

2009 ◽  
Vol 7 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Kasso A. Okoudjou
Keyword(s):  
Type Theorem ◽  
Modulation Spaces ◽  
Affine Functions ◽  
Special Case

We prove a Beurling-Helson type theorem on modulation spaces. More precisely, we show that the only𝒞1changes of variables that leave invariant the modulation spacesℳp,q(ℝd) are affine functions on ℝd. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair.

scholarly journals Topological Infinite Gammoids, and a New Menger-Type Theorem for Infinite Graphs

10.37236/6083 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Johannes Carmesin
Keyword(s):  
Type Theorem ◽  
Main Tool ◽  
Infinite Graphs ◽  
Disjoint Paths ◽  
Natural Topology ◽  
Locally Finite ◽  
Finite Graphs ◽  
Locally Finite Graphs ◽  
Vertex Sets ◽  
Special Case

Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid.As our main tool, we prove for any infinite graph $G$ with vertex-sets $A$ and $B$, if every finite subset of $A$ is linked to $B$ by disjoint paths, then the whole of $A$ can be linked to the closure of $B$ by disjoint paths or rays in a natural topology on $G$ and its ends.This latter theorem implies the topological Menger theorem of Diestel for locally finite graphs. It also implies a special case of the infinite Menger theorem of Aharoni and Berger.

scholarly journals A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 980
Author(s):  
Naim Latif Braha ◽  
Toufik Mansour ◽  
Hari Mohan Srivastava
Keyword(s):  
Type Theorem ◽  
Weighted Spaces ◽  
Shape Preserving ◽  
Korovkin Type Theorem ◽  
Stancu Operators ◽  
New Class ◽  
Approximation Operators ◽  
Voronovskaya Type Theorem ◽  
Shape Preserving Properties ◽  
Special Case

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and also study the rate of its convergence. Moreover, we derive several results which are related to the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces. Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators.

scholarly journals A Khintchine-type theorem for affine subspaces

2020 ◽  
pp. 1-19
Author(s):  
Daniel C. Alvey
Keyword(s):  
Hausdorff Dimension ◽  
Euclidean Space ◽  
Hausdorff Measure ◽  
Type Theorem ◽  
Affine Subspaces ◽  
Special Case

We show that affine subspaces of Euclidean space are of Khintchine type for divergence under certain multiplicative Diophantine conditions on the parameterizing matrix. This provides evidence towards the conjecture that all affine subspaces of Euclidean space are of Khintchine type for divergence, or that Khintchine’s theorem still holds when restricted to the subspace. This result is proved as a special case of a more general Hausdorff measure result from which the Hausdorff dimension of [Formula: see text] intersected with an appropriate subspace is also obtained.

Galois corings and groupoids acting partially on algebras

2020 ◽  
pp. 2140003
Author(s):  
S. Caenepeel ◽  
T. Fieremans
Keyword(s):  
Galois Extension ◽  
Galois Theory ◽  
Type Theorem ◽  
Partial Action ◽  
Morita Theory ◽  
Maschke Type Theorem ◽  
Galois Corings ◽  
Partial Galois Extension ◽  
Special Case

Bagio and Paques [Partial groupoid actions: globalization, Morita theory and Galois theory, Comm. Algebra 40 (2012) 3658–3678] developed a Galois theory for unital partial actions by finite groupoids. The aim of this note is to show that this is actually a special case of the Galois theory for corings, as introduced by Brzeziński [The structure of corings, Induction functors, Maschke-type theorem, and Frobenius and Galois properties, Algebr. Represent. Theory 5 (2002) 389–410]. To this end, we associate a coring to a unital partial action of a finite groupoid on an algebra [Formula: see text], and show that this coring is Galois if and only if [Formula: see text] is an [Formula: see text]-partial Galois extension of its coinvariants.

scholarly journals A Note on Confusion between Linear and Affine Functions and the Generalized Forms of Gradient

2021 ◽  
pp. 1-6
Author(s):  
Supriya Malla ◽  
Ganesh Malla
Keyword(s):  
Linear Function ◽  
Matrix Theory ◽  
General Setting ◽  
Affine Function ◽  
Affine Functions ◽  
The One ◽  
Definition Of ◽  
Special Case ◽  
Different Levels ◽  
Simple Exposition

Background: Arguably the most frequently used term in science, particularly in mathematics and statistics, is linear. However, confusion arises from the various meanings of linearity instructed in different levels of mathematical courses. The definition of linearity taught in high school is less correct than the one learned in a linear algebra class. The correlation coefficient of two quantitative variables is a numerical measure of the affinity, not only linearity, of two variables. However, every statistics book loosely says it is a measure of linear relationship. This clearly show that there is some confusion between use of the terms the linear function and affine function. Objective: This article aims at clarifying the confusion between use of the terms linear function and affine function. It also provides more generalized forms of the gradient in different branches of mathematics and show their equivalency. Materials and Methods: We have used the pure analytical deductive methods to proof the statements.  Results: We have clearly presented that gradient is the measure of affinity, not just linearity. It becomes a special case of the derivative in calculus, of the least-squares estimate of the regression coefficient in statistics and matrix theory. The gradient can ­­­­be seen in terms of the inverse of the informative matrix in the most general setting of the linear model estimation. Conclusion: The article has been clearly written to show the distinction between the linear and affine functions in a concise and unambiguous manner. We hope that readers will clearly see various generalizations of the gradient and article itself would be a simple exposition, enlightening, and fun to read.

scholarly journals Modulation spaces as a smooth structure in noncommutative geometry

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
Are Austad ◽  
Franz Luef
Keyword(s):  
Abelian Group ◽  
Spectral Triple ◽  
Modulation Spaces ◽  
Locally Compact Abelian Group ◽  
Smooth Structure ◽  
Locally Compact ◽  
Spectral Triples ◽  
Gabor Analysis ◽  
Time Frequency ◽  
Special Case

AbstractWe demonstrate how to construct spectral triples for twisted group $$C^*$$ C ∗ -algebras of lattices in phase space of a second-countable locally compact abelian group using a class of weights appearing in time–frequency analysis. This yields a way of constructing quantum $$C^k$$ C k -structures on Heisenberg modules, and we show how to obtain such structures using Gabor analysis and certain weighted analogues of Feichtinger’s algebra. We treat the standard spectral triple for noncommutative 2-tori as a special case, and as another example we define a spectral triple on noncommutative solenoids and a quantum $$C^k$$ C k -structure on the associated Heisenberg modules.

Quasilinear Elliptic Equations on Half- and Quarter-spaces

2013 ◽  
Vol 13 (1) ◽  
Author(s):  
E.N. Dancer ◽  
Yihong Du ◽  
Messoud Efendiev
Keyword(s):  
Elliptic Equations ◽  
Type Theorem ◽  
Quasilinear Elliptic Equations ◽  
Positive Zero ◽  
One Dimensional ◽  
Quasilinear Elliptic Problems ◽  
The One ◽  
Quasilinear Elliptic ◽  
Special Case ◽  
Strong Comparison Principle

AbstractWe consider quasilinear elliptic problems of the form Δwhere V is a solution of the one-dimensional problemΔwith z a positive zero of f . Our results extend most of those in the recent paper of Efendiev and Hamel [6] for the special case p = 2 to the general case p > 1. Moreover, by making use of a sharper Liouville type theorem, some of the results in [6] are improved. To overcome the difficulty of the lack of a strong comparison principle for p-Laplacian problems, we employ a weak sweeping principle.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

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