The topological product structure of systems of Lebesgue spaces

1991 ◽  
Vol 290 (1) ◽  
pp. 527-543 ◽  
Author(s):  
Jan J. Dijkstra ◽  
Jerzy Mogilski
Keyword(s):  
Product Structure ◽  
Topological Product ◽  
Lebesgue Spaces

Unzipping Natural Products: Improved Natural Product Structure Predictions by Ensemble Modeling and Fingerprint Matching

2018 ◽  
Author(s):  
William A. Shirley ◽  
Brian P. Kelley ◽  
Yohann Potier ◽  
John H. Koschwanez ◽  
Robert Bruccoleri ◽  
...  
Keyword(s):  
Natural Products ◽  
Open Source ◽  
Natural Product ◽  
Gene Cluster ◽  
Public Domain ◽  
Product Structure ◽  
Fingerprint Matching ◽  
Ensemble Modeling ◽  
Chemical Structures ◽  
Source Gene

This pre-print explores ensemble modeling of natural product targets to match chemical structures to precursors found in large open-source gene cluster repository antiSMASH. Commentary on method, effectiveness, and limitations are enclosed. All structures are public domain molecules and have been reviewed for release.

On the Reaction of 2,5-Dihydroxy-[1,4]-benzoquinone with Diamines – Strain-induced Reactivity Effects

2020 ◽  
Vol 24 ◽  
Author(s):  
Hubert Hettegger ◽  
Andreas Hofinger ◽  
Thomas Rosenau
Keyword(s):  
Nucleophilic Substitution ◽  
Product Structure ◽  
Carbonyl Groups ◽  
Reaction Products ◽  
Double Bonds ◽  
Oh Groups ◽  
Natural Geometry ◽  
Quinoid Structure ◽  
Bond Localization

: The regioselectivity of the reaction of 2,5-dihydroxy-[1,4]-benzoquinone (DHBQ) with diamines could not be explained satisfactorily so far. In general, the reaction products can be derived from the tautomeric ortho-quinoid structure of a hypothetical 4,5-dihydroxy-[1,2]-benzoquinone. However, both aromatic and aliphatic 1,2-diamines form in some cases phenazines, formally by diimine formation on the quinoid carbonyl groups, and in other cases the corresponding 1,2- diamino-[1,2]-benzoquinones, by nucleophilic substitution of the OH groups, the regioselectivity apparently not following any discernible pattern. The reactivity was now explained by an adapted theory of strain-induced bond localization (SIBL). Here, the preservation of the "natural" geometry of the two quinoid C–C double bonds (C3=C4 and C5=C6) as well as the N–N distance of the co-reacting diamine are crucial. A decrease of the annulation angle sum (N–C4–C5 + C4–C5–N) is tolerated well and the 4,5-diamino-ortho-quinones, having relatively short N–N spacings are formed. An increase in the angular sum is energetically unfavorable, so that diamines with a larger N–N distance afford the corresponding ortho-quinone imines. Thus, for the reaction of DHBQ with diamines, exact predictions of the regioselectivity, and the resulting product structure, can be made on the basis of simple computations of bond spacings and product geometries.

scholarly journals ON THE COMPLEXITY OF CLASSIFYING LEBESGUE SPACES

2020 ◽  
pp. 1-35
Author(s):  
TYLER A. BROWN ◽  
TIMOTHY H. MCNICHOLL ◽  
ALEXANDER G. MELNIKOV
Keyword(s):  
Lebesgue Spaces

scholarly journals $L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Acoustic Waves ◽  
Maximal Regularity ◽  
Bubble Radius ◽  
Fourier Multipliers ◽  
Cylindrical Domain ◽  
Lebesgue Spaces ◽  
Regularity Problem ◽  
Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

scholarly journals Quasi-ideal Ehresmann transversals: The spined product structure

2021 ◽  
Vol 19 (1) ◽  
pp. 77-86
Author(s):  
Xiangjun Kong ◽  
Pei Wang ◽  
Jian Tang
Keyword(s):  
Structure Theorem ◽  
Product Structure ◽  
Abundant Semigroup ◽  
Spined Product ◽  
Equivalent Conditions

Abstract In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

scholarly journals A note on maximal singular integrals with rough kernels

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiao Zhang ◽  
Feng Liu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Maximal Operators ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Homogeneous Mapping ◽  
Recent Developments ◽  
Maximal Singular Integrals ◽  
Maximal Singular Integral

Abstract In this note we study the maximal singular integral operators associated with a homogeneous mapping with rough kernels as well as the corresponding maximal operators. The boundedness and continuity on the Lebesgue spaces, Triebel–Lizorkin spaces, and Besov spaces are established for the above operators with rough kernels in $H^{1}({\mathrm{S}}^{n-1})$ H 1 ( S n − 1 ) , which complement some recent developments related to rough maximal singular integrals.

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