scholarly journals Space of chord diagrams on spherical curves

2019 ◽  
Vol 30 (12) ◽  
pp. 1950060 ◽  
Author(s):  
Noboru Ito
Keyword(s):  
Knot Theory ◽  
Reidemeister Move ◽  
Plane Curves ◽  
Type I ◽  
Main Result Theorem ◽  
Chord Diagrams ◽  
Result Theorem ◽  
Ambient Isotopy ◽  
Definition Of

In this paper, we give a definition of [Formula: see text]-valued functions from the ambient isotopy classes of spherical/plane curves derived from chord diagrams, denoted by [Formula: see text]. Then, we introduce certain elements of the free [Formula: see text]-module generated by the chord diagrams with at most [Formula: see text] chords, called relators of Type (I) ((SI[Formula: see text]I), (WI[Formula: see text]I), (SI[Formula: see text]I[Formula: see text]I), or (WI[Formula: see text]I[Formula: see text]I), respectively), and introduce another function [Formula: see text] derived from [Formula: see text]. The main result (Theorem 1) shows that if [Formula: see text] vanishes for the relators of Type (I) ((SI[Formula: see text]I), (WI[Formula: see text]I), (SI[Formula: see text]I[Formula: see text]I), or (WI[Formula: see text]I[Formula: see text]I), respectively), then [Formula: see text] is invariant under the Reidemeister move of type RI (strong RI[Formula: see text]I, weak RI[Formula: see text]I, strong RI[Formula: see text]I[Formula: see text]I, or weak RI[Formula: see text]I[Formula: see text]I, respectively) that is defined in [N. Ito and Y. Takimura, [Formula: see text] and weak [Formula: see text] homotopies on knot projections, J. Knot Theory Ramifications 22 (2013) 1350085 14 pp].

scholarly journals Independent inner functions in the classical domains

1987 ◽  
Vol 29 (2) ◽  
pp. 229-236
Author(s):  
Tomasz M. Wolniewicz
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Isometric Embedding ◽  
Symmetric Domain ◽  
Type I ◽  
Bounded Symmetric Domains ◽  
Inner Functions ◽  
Main Result Theorem ◽  
Complemented Subspace ◽  
Result Theorem

Let Bn denote the unit ball and Un the unit polydisc in Cn. In this paper we consider questions concerned with inner functions and embeddings of Hardy spaces over bounded symmetric domains. The main result (Theorem 2) states that for a classical symmetric domain D of type I and rank(D) = s, there exists an isometric embedding of Hl(Us) onto a complemented subspace of Hl(D). This should be compared with results of Wojtaszczyk [13] and Bourgain [3, 4] which state that H1(Bn) is isomorphic to Hl(U) while for n>m, Hl(Un) cannot be isomorphically embedded onto a complemented subspace of H1(Um). Since balls are the only bounded symmetric domains of rank 1 and they are of type I, Theorem 2 shows that if rank(D1) = 1, rank(D2) > 1 then H1(D1) is not isomorphic to H1(D2). It is natural to expect this to hold always when rank(D1 ≠ rank(D2) but unfortunately we were not able to prove this.

Idempotent-Separating Extensions Of Inverse Semigroups

1969 ◽  
Vol 9 (1-2) ◽  
pp. 211-217 ◽  
Author(s):  
H. D'Alarcao
Keyword(s):  
Inverse Semigroup ◽  
Main Tool ◽  
Inverse Semigroups ◽  
Main Result Theorem ◽  
Result Theorem ◽  
Standard Terminology ◽  
Points Of View ◽  
Definition Of

Extensions of semigroups have been studied from two points of view; ideal extensions and Schreier extension. In this paper another type of extension is considered for the class of inverse semigroups. The main result (Theorem 2) is stated in the form of the classical treatment of Schreier extensions (see e.g.[7]). The motivation for the definition of idempotentseparating extension comes primarily from G. B. Preston's concept of a normal set of subsets of a semigroup [6]. The characterization of such extensions is applied to give another description of bisimple inverse ω-semigroups, which were first described by N. R. Reilly [8]. The main tool used in the proof of Theorem 2 is Preston's characterization of congruences on an inverse semigroup [5]. For the standard terminology used, the reader is referred to [1].

AKUTZU-WADATI LINK POLYNOMIALS FROM FEYNMAN-KAUFFMAN DIAGRAMS

1989 ◽  
Vol 04 (13) ◽  
pp. 3351-3373 ◽  
Author(s):  
MO-LIN GE ◽  
LU-YU WANG ◽  
KANG XUE ◽  
YONG-SHI WU
Keyword(s):  
Knot Theory ◽  
Jones Polynomial ◽  
Feynman Diagrams ◽  
Cpt Symmetry ◽  
Group Representations ◽  
Reidemeister Moves ◽  
S Matrix ◽  
Ambient Isotopy ◽  
Definition Of ◽  
Bracket Polynomials

By employing techniques familiar to particle physicists, we develop Kauffman’s state model for the Jones polynomial, which uses diagrams looking like Feynman diagrams for scattering, into a systematic, diagrammatic approach to new link polynomials. We systematize the ansatz for S matrix by symmetry considerations and find a natural interpretation for CPT symmetry in the context of knot theory. The invariance under Reidemeister moves of type III, II and I can be imposed diagrammatically step by step, and one obtains successively braid group representations, regular isotopy and ambient isotopy invariants from Kauffman’s bracket polynomials. This procedure is explicitiy carried out for the N=3 and 4 cases. N being the number of particle labels (or charges). With appropriate symmetry ansatz and with annihilation and creation included in the S matrix, we have obtained link polynomials which generalize the definition of the Akutzu-Wadati polynomials from closed braids to any oriented knots or links with explicit invariance under Reidemeister moves.

scholarly journals A 5′ splice site mutation affecting the pre-mRNA splicing of two upstream exons in the collagen COL1A1 gene. Exon 8 skipping and altered definition of exon 7 generates truncated proα1(I) chains with a non-collagenous insertion destabilizing the triple helix

1994 ◽  
Vol 302 (3) ◽  
pp. 729-735 ◽  
Author(s):  
J F Bateman ◽  
D Chan ◽  
I Moeller ◽  
M Hannagan ◽  
W G Cole
Keyword(s):  
Splice Site ◽  
De Novo ◽  
Donor Site ◽  
Mrna Splicing ◽  
Splice Donor Site ◽  
Sequence Motif ◽  
Type I ◽  
Splice Donor ◽  
Site Mutation ◽  
Definition Of

A heterozygous de novo G to A point mutation in intron 8 at the +5 position of the splice donor site of the gene for the pro alpha 1(I) chain of type I procollagen, COL1A1, was defined in a patient with type IV osteogenesis imperfecta. The splice donor site mutation resulted not only in the skipping of the upstream exon 8 but also unexpectedly had the secondary effect of activating a cryptic splice site in the next upstream intron, intron 7, leading to re-definition of the 3′ limit of exon 7. These pre-mRNA splicing aberrations cause the deletion of exon 8 sequences from the mature mRNA and the inclusion of 96 bp of intron 7 sequence. Since the mis-splicing of the mutant allele product resulted in the maintenance of the correct codon reading frame, the resultant pro alpha 1(I) chain contained a short non-collagenous 32-amino-acid sequence insertion within the repetitive Gly-Xaa-Yaa collagen sequence motif. At the protein level, the mutant alpha 1(I) chain was revealed by digestion with pepsin, which cleaved the mutant procollagen within the protease-sensitive non-collagenous insertion, producing a truncated alpha 1(I). This protease sensitivity demonstrated the structural distortion to the helical structure caused by the insertion. In long-term culture with ascorbic acid, which stimulates the formation of a mature crosslinked collagen matrix, and in tissues, there was no evidence of the mutant chain, suggesting that during matrix formation the mutant chain was unable to stably incorporated into the matrix and was degraded proteolytically.

scholarly journals A note on the paper "Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Aissam Ichatouhane
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Optimality Condition ◽  
Short Proof ◽  
Necessary Optimality Condition ◽  
Main Result Theorem ◽  
Correct Formulation ◽  
Result Theorem ◽  
Infinite Programming ◽  
Interval Valued

A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066, 2020). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to refute some results on which the main result (Theorem 4.5) is based. For the convinience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5 and give also a short proof.

scholarly journals Functional Metagenomics of a Biostimulated Petroleum-Contaminated Soil Reveals an Extraordinary Diversity of Extradiol Dioxygenases

2016 ◽  
Vol 82 (8) ◽  
pp. 2467-2478 ◽  
Author(s):  
Laura Terrón-González ◽  
Guadalupe Martín-Cabello ◽  
Manuel Ferrer ◽  
Eduardo Santero
Keyword(s):  
Contaminated Soil ◽  
Phylogenetic Analyses ◽  
Metagenomic Library ◽  
Type I ◽  
Type Ii ◽  
Extradiol Dioxygenase ◽  
Metagenomic Dna ◽  
Petroleum Contaminated Soil ◽  
Definition Of ◽  
Extradiol Dioxygenases

ABSTRACTA metagenomic library of a petroleum-contaminated soil was constructed in a fosmid vector that allowed heterologous expression of metagenomic DNA. The library, consisting of 6.5 Gb of metagenomic DNA, was screened for extradiol dioxygenase (Edo) activity using catechol and 2,3-dihydroxybiphenyl as the substrates. Fifty-eight independent clones encoding extradiol dioxygenase activity were identified. Forty-one different Edo-encoding genes were identified. The population of Edo genes was not dominated by a particular gene or by highly similar genes; rather, the genes had an even distribution and high diversity. Phylogenetic analyses revealed that most of the genes could not be ascribed to previously defined subfamilies of Edos. Rather, the Edo genes led to the definition of 10 new subfamilies of type I Edos. Phylogenetic analysis of type II enzymes defined 7 families, 2 of which harbored the type II Edos that were found in this work. Particularly striking was the diversity found in family I.3 Edos; 15 out of the 17 sequences assigned to this family belonged to 7 newly defined subfamilies. A strong bias was found that depended on the substrate used for the screening: catechol mainly led to the detection of Edos belonging to the I.2 family, while 2,3-dihydroxybiphenyl led to the detection of most other Edos. Members of the I.2 family showed a clear substrate preference for monocyclic substrates, while those from the I.3 family showed a broader substrate range and high activity toward 2,3-dihydroxybiphenyl. This metagenomic analysis has substantially increased our knowledge of the existing biodiversity of Edos.

Closure Theorem for Analytic Subgroups of Real Lie Groups

1976 ◽  
Vol 19 (4) ◽  
pp. 435-439 ◽  
Author(s):  
D. Ž. Djoković
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Closed Subgroup ◽  
Main Result Theorem ◽  
Closure Theorem ◽  
Result Theorem ◽  
Analytic Subgroup

Let G be a real Lie group, A a closed subgroup of G and B an analytic subgroup of G. Assume that B normalizes A and that AB is closed in G. Then our main result (Theorem 1) asserts that .This result generalizes Lemma 2 in the paper [4], G. Hochschild has pointed out to me that the proof of that lemma given in [4] is not complete but that it can be easily completed.

Proposed Recommended Nutrient Densities for Moderately Malnourished Children

2009 ◽  
Vol 30 (3_suppl3) ◽  
pp. S267-S342 ◽  
Author(s):  
Michael H. Golden
Keyword(s):  
Dietary Intake ◽  
Severe Malnutrition ◽  
Type I ◽  
Type Ii ◽  
Healthy Individuals ◽  
Malnourished Children ◽  
Factorial Approach ◽  
Accelerated Growth ◽  
Moderate Malnutrition ◽  
Definition Of

Recommended Nutrient Intakes (RNIs) are set for healthy individuals living in clean environments. There are no generally accepted RNIs for those with moderate malnutrition, wasting, and stunting, who live in poor environments. Two sets of recommendations are made for the dietary intake of 30 essential nutrients in children with moderate malnutrition who require accelerated growth to regain normality: first, for those moderately malnourished children who will receive specially formulated foods and diets; and second, for those who are to take mixtures of locally available foods over a longer term to treat or prevent moderate stunting and wasting. Because of the change in definition of severe malnutrition, much of the older literature is pertinent to the moderately wasted or stunted child. A factorial approach has been used in deriving the recommendations for both functional, protective nutrients (type I) and growth nutrients (type II).

scholarly journals On radicals of finite near-rings

1984 ◽  
Vol 27 (3) ◽  
pp. 247-259 ◽  
Author(s):  
K. Kaarli
Keyword(s):  
Main Result Theorem ◽  
Result Theorem

In this paper the study of radicals of finite near-rings is initiated. The main result (Theorem 4.3) gives a description of hereditary radicals having hereditary semisimple classes too. Also it is shown that there exist non-hereditary radicals having hereditary semisimple classes.

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