scholarly journals Some basic properties and fundamental relations for discrete Muckenhoupt and Gehring classes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
S. S. Rabie ◽  
Jehad Alzabut ◽  
D. O’Regan ◽  
R. P. Agarwal
Keyword(s):  
The Self ◽  
Basic Properties ◽  
Muckenhoupt Class

AbstractIn this paper, we prove some basic properties of the discrete Muckenhoupt class $\mathcal{A}^{p}$ A p and the discrete Gehring class $\mathcal{G}^{q}$ G q . These properties involve the self-improving properties and the fundamental transitions and inclusions relations between the two classes.

Research on the Self-Leveling Mortar Made of Tailings

2012 ◽  
Vol 517 ◽  
pp. 506-509 ◽  
Author(s):  
Yu Chen ◽  
Qiu Yi Li ◽  
Jian Min Liu ◽  
Gong Bing Yue
Keyword(s):  
Water Consumption ◽  
High Strength ◽  
The Self ◽  
Production Costs ◽  
Mineral Admixtures ◽  
Time Loss ◽  
Natural Sand ◽  
Basic Properties

To improve the utilization of tailings, the basic properties of tailings and theirs influence on self-leveling mortar performance are experimental studied in this paper. The results show that the tailings can completely replace the natural sand to produce self-leveling mortar since the advantages of better fluidity, less water consumption, smaller time loss and high strength. The strength decreases with the addition of mineral admixtures, but it can still satisfy the requirements of standard JC/T 985-2005 "Cementitious self-leveling floor mortar ". Moreover, this method reduces pollution and production costs effectively.

scholarly journals On structure of discrete Muchenhoupt and discrete Gehring classes

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
S. H. Saker ◽  
S. S. Rabie ◽  
Ghada AlNemer ◽  
M. Zakarya
Keyword(s):  
The Self ◽  
Power Rule ◽  
Muckenhoupt Class ◽  
New Inequalities

Abstract In this paper, we study the structure of the discrete Muckenhoupt class $\mathcal{A}^{p}(\mathcal{C})$ A p ( C ) and the discrete Gehring class $\mathcal{G}^{q}(\mathcal{K})$ G q ( K ) . In particular, we prove that the self-improving property of the Muckenhoupt class holds, i.e., we prove that if $u\in \mathcal{A}^{p}(\mathcal{C})$ u ∈ A p ( C ) then there exists $q< p$ q < p such that $u\in \mathcal{A}^{q}(\mathcal{C}_{1})$ u ∈ A q ( C 1 ) . Next, we prove that the power rule also holds, i.e., we prove that if $u\in \mathcal{A}^{p}$ u ∈ A p then $u^{q}\in \mathcal{A}^{p}$ u q ∈ A p for some $q>1$ q > 1 . The relation between the Muckenhoupt class $\mathcal{A}^{1}(\mathcal{C})$ A 1 ( C ) and the Gehring class is also discussed. For illustrations, we give exact values of the norms of Muckenhoupt and Gehring classes for power-low sequences. The results are proved by some algebraic inequalities and some new inequalities designed and proved for this purpose.

scholarly journals The Category of Modules on an n-Trivial Extension: the Basic Properties

2020 ◽  
Vol 27 (03) ◽  
pp. 607-620
Author(s):  
Dirar Benkhadra ◽  
Driss Bennis ◽  
J.R. García Rozas
Keyword(s):  
The Self ◽  
Trivial Extension ◽  
Injective Dimension ◽  
Basic Properties ◽  
Category Of Modules ◽  
Extension Ring ◽  
The Right

In this paper we investigate a categorical aspect of n-trivial extension of a ring by a family of modules. Namely, we introduce the right (resp., left) n-trivial extension of a category by a family of endofunctors. Among other results, projective, injective and flat objects of this category are characterized, and two applications are presented at the end of this paper. We characterize when an n-trivial extension ring is k-perfect and establish a result on the self-injective dimension of an n-trivial extension ring.

scholarly journals Self-improving properties of weighted Gehring classes with applications to partial differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
J. Alzabut ◽  
D. O’Regan ◽  
R. P. Agarwal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Homogeneous Spaces ◽  
The Self ◽  
Jensen Inequality ◽  
Integrability Theorem ◽  
Partial Differential ◽  
Extended Space ◽  
Muckenhoupt Class ◽  
Nonincreasing Rearrangement

AbstractIn this paper, we prove that the self-improving property of the weighted Gehring class $G_{\lambda }^{p}$ G λ p with a weight λ holds in the non-homogeneous spaces. The results give sharp bounds of exponents and will be used to obtain the self-improving property of the Muckenhoupt class $A^{q}$ A q . By using the rearrangement (nonincreasing rearrangement) of the functions and applying the Jensen inequality, we show that the results cover the cases of non-monotonic functions. For applications, we prove a higher integrability theorem and report that the solutions of partial differential equations can be solved in an extended space by using the self-improving property. Our approach in this paper is different from the ones used before and is based on proving some new inequalities of Hardy type designed for this purpose.

Self-improving properties of discrete Muckenhoupt weights

Analysis ◽  
2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Samir H. Saker ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Algebraic Equation ◽  
Type Inequality ◽  
The Self ◽  
Muckenhoupt Weights ◽  
Discrete Version ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Muckenhoupt Class ◽  
Complete Study

Abstract In this paper, we will provide a complete study of the self-improving properties of the discrete Muckenhoupt class 𝒜 p ⁢ ( 𝒞 ) {\mathcal{A}^{p}(\mathcal{C})} of weights defined on ℤ + {\mathbb{Z}_{+}} . In addition, we will determine the range of the new constants which are related to the original constants via an algebraic equation. For illustration, we will give an example to prove that the results are sharp. The results will be obtained by employing a discrete version of an inequality due to Hardy–Littlewood and a new discrete Hardy-type inequality with negative powers.

Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

2019 ◽  
Vol 42 ◽  
Author(s):  
Lucio Tonello ◽  
Luca Giacobbi ◽  
Alberto Pettenon ◽  
Alessandro Scuotto ◽  
Massimo Cocchi ◽  
...  
Keyword(s):  
Autism Spectrum Disorder ◽  
Problem Behaviors ◽  
Autism Spectrum ◽  
The Self ◽  
Network Structures ◽  
Self Organized ◽  
Critical Equilibrium ◽  
Self Organized Criticality ◽  
Acute Agitation ◽  
Spectrum Disorders

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

The Nature of Rapidly Extracted Phycocyanin from the Blue-Green Alga Plectonema Boryanum

1971 ◽  
Vol 29 ◽  
pp. 366-367
Author(s):  
M. Kessel ◽  
R. MacColl
Keyword(s):  
Self Assembly ◽  
Analytical Ultracentrifugation ◽  
Uranyl Acetate ◽  
The Self ◽  
Major Protein ◽  
Subunit Structure ◽  
Blue Green Alga ◽  
Thin Sections ◽  
Blue Green Algae ◽  
Cacodylate Buffer

The major protein of the blue-green algae is the biliprotein, C-phycocyanin (Amax = 620 nm), which is presumed to exist in the cell in the form of distinct aggregates called phycobilisomes. The self-assembly of C-phycocyanin from monomer to hexamer has been extensively studied, but the proposed next step in the assembly of a phycobilisome, the formation of 19s subunits, is completely unknown. We have used electron microscopy and analytical ultracentrifugation in combination with a method for rapid and gentle extraction of phycocyanin to study its subunit structure and assembly.To establish the existence of phycobilisomes, cells of P. boryanum in the log phase of growth, growing at a light intensity of 200 foot candles, were fixed in 2% glutaraldehyde in 0.1M cacodylate buffer, pH 7.0, for 3 hours at 4°C. The cells were post-fixed in 1% OsO4 in the same buffer overnight. Material was stained for 1 hour in uranyl acetate (1%), dehydrated and embedded in araldite and examined in thin sections.

Interrelationship of the cellular distribution and secretion of regular structure (RS) protein in Bacillus licheniformis nm 105

1992 ◽  
Vol 50 (1) ◽  
pp. 712-713
Author(s):  
Xiaorong Zhu ◽  
Richard McVeigh ◽  
Bijan K. Ghosh
Keyword(s):  
Alkaline Phosphatase ◽  
Bacillus Licheniformis ◽  
Self Assembly ◽  
Gel Electrophoresis ◽  
Culture Supernatant ◽  
Regular Structure ◽  
The Self ◽  
Cellular Distribution ◽  
Structural Protein ◽  
Laboratory Cultures

A mutant of Bacillus licheniformis 749/C, NM 105 exhibits some notable properties, e.g., arrest of alkaline phosphatase secretion and overexpression and hypersecretion of RS protein. Although RS is known to be widely distributed in many microbes, it is rarely found, with a few exceptions, in laboratory cultures of microorganisms. RS protein is a structural protein and has the unusual properties to form aggregate. This characteristic may have been responsible for the self assembly of RS into regular tetragonal structures. Another uncommon characteristic of RS is that enhanced synthesis and secretion which occurs when the cells cease to grow. Assembled RS protein with a tetragonal structure is not seen inside cells at any stage of cell growth including cells in the stationary phase of growth. Gel electrophoresis of the culture supernatant shows a very large amount of RS protein in the stationary culture of the B. licheniformis. It seems, Therefore, that the RS protein is cotranslationally secreted and self assembled on the envelope surface.

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