scholarly journals A Method for Constructing a Gray Map for a Group Based on Its Semidirect-product Structure

2018 ◽  
Vol 26 (0) ◽  
pp. 345-349
Author(s):  
Ko Sakai ◽  
Yutaka Sato
Keyword(s):  
Semidirect Product ◽  
Product Structure ◽  
Gray Map

scholarly journals Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category

Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Laurent Poinsot
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Semidirect Product ◽  
Hopf Algebras ◽  
Formal Series ◽  
Product Structure ◽  
Locally Finite ◽  
Commutative Algebras ◽  
Affine Groups ◽  
Formal Power

A locally finite category is defined as a category in which every arrow admits only finitely many different ways to be factorized by composable arrows. The large algebra of such categories over some fields may be defined, and with it a group of invertible series (under multiplication). For certain particular locally finite categories, a substitution operation, generalizing the usual substitution of formal power series, may be defined, and with it a group of reversible series (invertible under substitution). Moreover, both groups are actually affine groups. In this contribution, we introduce their coordinate Hopf algebras which are both free as commutative algebras. The semidirect product structure obtained from the action of reversible series on invertible series by anti-automorphisms gives rise to an interaction at the level of their coordinate Hopf algebras under the form of a smash coproduct.

H-Semidirect Products

1987 ◽  
Vol 30 (4) ◽  
pp. 402-411 ◽  
Author(s):  
Georg Peschke
Keyword(s):  
Semidirect Product ◽  
Loop Space ◽  
Product Structure ◽  
Homotopy Classes ◽  
Semidirect Products ◽  
Cw Complex ◽  
Path Component

AbstractThe concept of H-semidirect product structure on a grouplike space is introduced. It is shown that the loop space ΩX of any based CW-complex X is the H-semidirect product of the identity path-component of ΩX with π1,X. The set of free homotopy classes of maps into a Hsemidirect product inherits the structure of a semidirect product. This leads to new results concerning the nilpotency of homotopy classes of maps into a group-like space.

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 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 On the group of unit-valued polynomial functions

2021 ◽  
Author(s):  
Amr Ali Al-Maktry
Keyword(s):  
Commutative Ring ◽  
Semidirect Product ◽  
Polynomial Functions ◽  
Dual Numbers ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Canonical Representations ◽  
Finite Commutative Ring

AbstractLet R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units $${{\mathcal{F}}}(R)^\times $$ F ( R ) × is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on $$R[x]/(x^2)=R[\alpha ]$$ R [ x ] / ( x 2 ) = R [ α ] , the ring of dual numbers over R, and show that the group $${\mathcal{P}}_{R}(R[\alpha ])$$ P R ( R [ α ] ) , consisting of those polynomial permutations of $$R[\alpha ]$$ R [ α ] represented by polynomials in R[x], is embedded in a semidirect product of $${{\mathcal{F}}}(R)^\times $$ F ( R ) × by the group $${\mathcal{P}}(R)$$ P ( R ) of polynomial permutations on R. In particular, when $$R={\mathbb{F}}_q$$ R = F q , we prove that $${\mathcal{P}}_{{\mathbb{F}}_q}({\mathbb{F}}_q[\alpha ])\cong {\mathcal{P}}({\mathbb{F}}_q) \ltimes _\theta {{\mathcal{F}}}({\mathbb{F}}_q)^\times $$ P F q ( F q [ α ] ) ≅ P ( F q ) ⋉ θ F ( F q ) × . Furthermore, we count unit-valued polynomial functions on the ring of integers modulo $${p^n}$$ p n and obtain canonical representations for these functions.

Topological Left Amenability of Semidirect Products

1981 ◽  
Vol 24 (1) ◽  
pp. 79-85 ◽  
Author(s):  
H. D. Junghenn
Keyword(s):  
Large Class ◽  
Semidirect Product ◽  
Locally Compact ◽  
Semidirect Products ◽  
Topological Semigroups

AbstractLet S and T be locally compact topological semigroups and a semidirect product. Conditions are determined under which topological left amenability of S and T implies that of , and conversely. The results are used to show that for a large class of semigroups which are neither compact nor groups, various notions of topological left amenability coincide.

scholarly journals Natural product fragment combination to performance-diverse pseudo-natural products

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Michael Grigalunas ◽  
Annina Burhop ◽  
Sarah Zinken ◽  
Axel Pahl ◽  
José-Manuel Gally ◽  
...  
Keyword(s):  
Natural Products ◽  
Product Design ◽  
Natural Product ◽  
Chemical Space ◽  
Biological Evaluation ◽  
Product Structure ◽  
Biologically Relevant ◽  
Biologically Relevant Chemical Space

AbstractNatural product structure and fragment-based compound development inspire pseudo-natural product design through different combinations of a given natural product fragment set to compound classes expected to be chemically and biologically diverse. We describe the synthetic combination of the fragment-sized natural products quinine, quinidine, sinomenine, and griseofulvin with chromanone or indole-containing fragments to provide a 244-member pseudo-natural product collection. Cheminformatic analyses reveal that the resulting eight pseudo-natural product classes are chemically diverse and share both drug- and natural product-like properties. Unbiased biological evaluation by cell painting demonstrates that bioactivity of pseudo-natural products, guiding natural products, and fragments differ and that combination of different fragments dominates establishment of unique bioactivity. Identification of phenotypic fragment dominance enables design of compound classes with correctly predicted bioactivity. The results demonstrate that fusion of natural product fragments in different combinations and arrangements can provide chemically and biologically diverse pseudo-natural product classes for wider exploration of biologically relevant chemical space.

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