The topological product structure of systems of Lebesgue spaces

1991 ◽  
Vol 290 (1) ◽  
pp. 527-543 ◽  
Author(s):  
Jan J. Dijkstra ◽  
Jerzy Mogilski
2018 ◽  
Author(s):  
William A. Shirley ◽  
Brian P. Kelley ◽  
Yohann Potier ◽  
John H. Koschwanez ◽  
Robert Bruccoleri ◽  
...  

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.


2020 ◽  
Vol 24 ◽  
Author(s):  
Hubert Hettegger ◽  
Andreas Hofinger ◽  
Thomas Rosenau

: 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.


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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila

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.


2021 ◽  
Vol 19 (1) ◽  
pp. 77-86
Author(s):  
Xiangjun Kong ◽  
Pei Wang ◽  
Jian Tang

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.


2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang

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.


Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero

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.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiao Zhang ◽  
Feng Liu

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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