scholarly journals FROM RIBBON CATEGORIES TO GENERALIZED YANG–BAXTER OPERATORS AND LINK INVARIANTS (AFTER KITAEV AND WANG)

2013 ◽  
Vol 24 (01) ◽  
pp. 1250126 ◽  
Author(s):  
SEUNG-MOON HONG

We consider two approaches to isotopy invariants of oriented links: one from ribbon categories and the other from generalized Yang–Baxter (gYB) operators with appropriate enhancements. The gYB-operators we consider are obtained from so-called gYBE objects following a procedure of Kitaev and Wang. We show that the enhancement of these gYB-operators is canonically related to the twist structure in ribbon categories from which the operators are produced. If a gYB-operator is obtained from a ribbon category, it is reasonable to expect that two approaches would result in the same invariant. We prove that indeed the two link invariants are the same after normalizations. As examples, we study a new family of gYB-operators which is obtained from the ribbon fusion categories SO (N)2, where N is an odd integer. These operators are given by 8 × 8 matrices with the parameter N and the link invariants are specializations of the two-variable Kauffman polynomial invariant F.

1925 ◽  
Vol s2-69 (276) ◽  
pp. 703-729
Author(s):  
W. N. F. WOODLAND

1. Those species of Proteocephalid Cestodes in which the testes are situated in the cortex may be described as of the Monticellia type. Of this type there are three conditions : (a) the Monticellia condition in which the testes, uterus, ovary, and vitellaria are all situated in the cortex; (b) the Rudolphiella condition in which the testes and vitellaria alone are in the cortex, the other organs being entirely or almost entirely in the medulla ; and (c) the Marsypocephalus condition in which the testes alone are in the cortex, all other organs being medullary. Fuhrmann's genus Goezeella is synonymous with Monticellia if we ignore the characters of the scolex as features of generic value. 2. The anatomy of two species of Marsypocephalus is described: Marsypocephalus rectangulus Wedl, 1862, and Marsypocephalus heterobranchus, n.sp., from Nile Siluroid fishes. 3. It is concluded that the cortical situation of the testes and other organs is a taxonomic feature of generic value only (as in Pseudophyllidea in the case of the vitellaria) and La Rue's new family of the Monticellidae, created to include Monticellia-like forms, is not accepted. Monticellia, Rudolphiella, and Marsypocephalus are thus regarded as new genera in the Proteocephalidae. 4. The facts that the ‘Corallobothrium’ type of scolex is found in all of the three genera Monticellia (as amended by me and including ‘Goezeella’ siluri, Fuhrmann), Rudolphiella, and Proteocephalus (as amended by me and including ‘Corallobothrium’ solidum, Fritsch), and that in the Caryophyllaeidae, Bothriocephalidae, and Cyclophyllidea (cf. e.g. Taenia solium and Taenia saginata) minor scolex characters are evidently only features of specific value, compel us to delete such genera as Corallobothrium, Choanoscolex, Acanthotaenia, and my own recent genus Gangesia and to regard them as synonyms of Proteocephalus (La Rue's genus ‘Ophiotaenia’, syn. ‘Crepidobothrium’, not being accepted). Fuhrmann's Goezeella siluri becomes Monticellia siluri, and Fritach's Corallobothrium solidum becomes Proteocephalus solidus. The genera of the Proteocephalidae are thus four in number: Proteocephalus , Monticellia, Rudolphiella , and Marsypocep, halus, and these are formally or informally redefined. The two species of Marsypocephalus are diagnosed. 5. The ‘Taenia malopteruri’ of Fritsch, 1886, is not of the Monticellia type, as suggested by La Rue. Its structure is of the usual Proteocephalid type, save that the scolex possesses a rostellum and a broad band of hooklets and is covered with spinelets. It is renamed Proteocephalus malopteruri. 6. A new species of Clestobothrium--Clestobothrium clarias, from Clarias anguillaris Günth-is described. It is of interest, not only as being the third (second ?) species known of the genus, but because it affords one more illustration of the fact that the characters of the scolex cannot be used for diagnoses of genera. For this reason also, Lönnberg's genus Ptychobothrium (1889) becomes synonymous with Diesing's genus Polyonchobothrium (1884).


Zootaxa ◽  
2018 ◽  
Vol 4524 (1) ◽  
pp. 77 ◽  
Author(s):  
KEIJI BABA ◽  
SHANE T. AHYONG ◽  
KAREEN E. SCHNABEL

The chirostyloidean squat lobster genus Gastroptychus Caullery, 1896 is revised and is split into two genera: Gastroptychus sensu stricto (type species, Ptychogaster spinifer A. Milne-Edwards, 1880) and Sternostylus new genus (type species, Ptychogaster formosus Filhol, 1884). Gastroptychus sensu stricto, is restricted to nine species with a sternal plastron, at sternite 3, abruptly demarcated from the preceding sternites (excavated sternum) by a distinct step forming a well-defined transverse or concave anterior margin at the articulation with maxillipeds 3, the maxillipeds 3 widely separated, with the distal parts accommodated in the excavated sternum between the left and right maxillipeds 3 when folded, and the P2–4 dactyli with the terminal spine demarcated by a suture. Sternostylus new genus, represented by 12 species, has the sternite 3 anteriorly bluntly produced medially and steeply sloping anterodorsally to the anterior sternite, with a pair of spines directly behind the anterior margin, the left and right maxillipeds 3 adjacent, and the P2–4 dactyli ending in an indistinctly demarcated corneous spine. The above-mentioned characters of Gastroptychus are consistent with Chirostylidae sensu stricto. Published molecular phylogenies indicate, however, that Sternostylus is the sister group to all the other Chirostylidae, and is designated the type genus of a new family, Sternostylidae. 


2020 ◽  
Vol 98 (10) ◽  
pp. 953-958
Author(s):  
Amin Motamedinasab ◽  
Azam Anbaraki ◽  
Davood Afshar ◽  
Mojtaba Jafarpour

The general parasupersymmetric annihilation operator of arbitrary order does not reduce to the Kornbluth–Zypman general supersymmetric annihilation operator for the first order. In this paper, we introduce an annihilation operator for a parasupersymmetric harmonic oscillator that in the first order matches with the Kornblouth–Zypman results. Then, using the latter operator, we obtain the parasupercoherent states and calculate their entanglement, uncertainties, and statistics. We observe that these states are entangled for any arbitrary order of parasupersymmetry and their entanglement goes to zero for the large values of the coherency parameter. In addition, we find that the maximum of the entanglement of parasupercoherent states is a decreasing function of the parasupersymmetry order. Moreover, these states are minimum uncertainty states for large and also small values of the coherency parameter. Furthermore, these states show squeezing in one of the quadrature operators for a wide range of the coherency parameter, while no squeezing in the other quadrature operator is observed at all. In addition, using the Mandel parameter, we find that the statistics of these new states are subPoissonian for small values of the coherency parameter.


2020 ◽  
Vol 7 (8) ◽  
pp. 200456 ◽  
Author(s):  
Pritom J. Bora ◽  
T. R. Suresh Kumar ◽  
Daniel Q. Tan

MXene, the new family of two-dimensional materials having numerous nanoscale layers, is being considered as a novel microwave absorption material. However, MXene/functionalized MXene-loaded polymer nanocomposites exhibit narrow reflection loss (RL) bandwidth (RL less than or equal to −10 dB). In order to enhance the microwave absorption bandwidth of MXene hybrid-matrix materials, for the first time, macroscopic design approach is carried out for TiO 2 -Ti 3 C 2 T x MXene and Fe 3 O 4 @TiO 2 -Ti 3 C 2 T x MXene hybrids through simulation. The simulated results indicate that use of pyramidal meta structure of MXene can significantly tune the RL bandwidth. For optimized MXene hybrid-matrix materials pyramid pattern, the bandwidth enhances to 3–18 GHz. Experimental RL value well matched with the simulated RL. On the other hand, the optimized Fe 3 O 4 @TiO 2 -Ti 3 C 2 T x hybrid exhibits two specific absorption bandwidths (minimum RL value - −47 dB). Compared with other two-dimensional nanocomposites such as graphene or Fe 3 O 4 -graphene, MXene hybrid-matrix materials show better microwave absorption bandwidth in macroscopic pattern.


2018 ◽  
Vol 27 (02) ◽  
pp. 1850014 ◽  
Author(s):  
Seongjeong Kim

In [Przytyski and Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1989) 115–139], Przytyski and Traczyk introduced an algebraic structure, called a Conway algebra, and constructed an invariant of oriented links, which is a generalization of the Homflypt polynomial invariant. On the other hand, in [Kauffman and Lambropoulou, New invariants of links and their state sum models, arXiv:1703.03655v2 [math.GT] 15 Mar 2017], Kauffman and Lambropoulou introduced new 4-variable invariants of oriented links, which are obtained by two computational steps: in the first step, we apply a skein relation on every mixed crossing to produce unions of unlinked knots. In the second step, we apply another skein relation on crossings of the unions of unlinked knots, which introduces a new variable. In this paper, we will introduce a generalization of the Conway algebra [Formula: see text] with two binary operations and we construct an invariant valued in [Formula: see text] by applying those two binary operations to mixed crossings and pure crossing, respectively. The 4-variable invariant of Kauffman and Lambropoulou with a specific condition is derived from the invariant valued in [Formula: see text]. Moreover, the generalized Conway algebra gives us an invariant of oriented links, which satisfies nonlinear skein relations.


Zootaxa ◽  
2018 ◽  
Vol 4415 (3) ◽  
pp. 452 ◽  
Author(s):  
P. R. PUGH ◽  
C.W. DUNN ◽  
S.H.D. HADDOCK

A new species of calycophoran siphonophore, Tottonophyes enigmatica gen. nov, sp. nov., is described. It has a unique combination of traits, some shared with prayomorphs (including two rounded nectophores) and some with clausophyid diphyomorphs (the nectophores are dissimilar, with one slightly larger and slightly to the anterior of the other, and both possess a somatocyst). Molecular phylogenetic analyses indicate that the new species is the sister group to all other diphyomorphs. A new family, Tottonophyidae, is established for it. Its phylogenetic position and distinct morphology help clarify diphyomorph evolution. The function and homology of the nectophoral canals and somatocyst is also re-examined and further clarification is given to their nomenclature.


1968 ◽  
Vol 46 (10) ◽  
pp. 1235-1251 ◽  
Author(s):  
George J. Hollenberg ◽  
Isabella A. Abbott

Eleven new taxa are described from California; two species, in addition, have new varieties added to them; and two species are given new circumscriptions to include a number of entities previously known under other names. New species are described in Percursaria (Chlorophyta), in Feldmannia (Phaeophyta), and in eight genera (Membranella, Porphyra, Rhododiscus, Peyssonelia, Prionitis, Blinksia, Besa and Rhodoglossum) of Rhodophyta. Two monotypic genera of Rhodophyta are described for the first time. One, Membranella nitens, is added to the Bangiales, and the other, Blinksia californica, is the type for a new family, the Blinksiaceae (Gigartinales). Half of the species of red algae are crustose non-corallinaceous species.


1993 ◽  
Vol 113 (2) ◽  
pp. 401-411
Author(s):  
M. A. Hennings

Recently Kauffman[2, 3] has classified the (strongly) spin-preserving solutions of the Yang—Baxter equation, and in particular discussed two solutions. One of these can be used to obtain the Jones polynomial, while the other (with care) leads to the Alexander polynomial. In this paper we shall complete this analysis, and shall describe all strongly spin-preserving invertible solutions of the Yang-Baxter equation which lead to link invariants. Having done this, we investigate what sort of link invariants can be obtained from these solutions. It turns out that these invariants are precisely those which have been described in Hennings [l].


1970 ◽  
Vol 9 (1) ◽  
Author(s):  
Maria Mocarz-Kleindienst

Why Do New Translations Come into Being? Mikhail Bulgakov’s The Master and Margarita in a New Polish TranslationLiterary works tend to be amongst the most often translated texts. A perfect example is Mikhail Bulgakov’s novel The Master and Margarita: over the previous two years (2016—2017) three new translations thereof into Polish appeared, one of them being a translation by Leokadia, Grzegorz, and Igor Przebinda. In this paper, the main reasons for the publication of this new, “family” translation were discussed. The question about the need for makeing new translations was accompanied by other questions: how are such texts translated what strategies are used by the translator?, to what extent does he or she take account of the assumed expectations of contemporary readers? In the presentation, two research perspectives were proposed. The first of them is the translator’s viewpoint, for whom the newly done translation is a domesticated translation. The other perspective, the researcher’s one, consist in analyzing the translated text itself, in particular with regard to the applied translation strategies (exoticization vs. adaptation), indicating the differences between the latest translation and the previous ones (first by Irena Lewandowska and Witold Dąbrowski, and second by Andrzej Drawicz). The analysis of the translated text along with the accompanying paratexts in the form of numerous footnotes leads one to a conclusion that exoticization is a dominant strategy.KEY WORDS: domestication, exoticization, Master and Margarita, Mikhail Bulgakov


2019 ◽  
Vol 93 (04) ◽  
pp. 389-423 ◽  
Author(s):  
Robert H. Cowie

AbstractThis catalogue is concerned with the closely related angiostrongylid generaAngiostrongylus,Gallegostrongylus,RodentocaulusandStefanskostrongylus. Three species,Angiostrongylus cantonensis,A. costaricensisandA. vasorum, have attracted most attention because of their importance in human and domestic animal disease. Many of the remaining species are poorly known and the number of valid taxa is unclear. The catalogue lists all nomenclaturally available and unavailable genus-group and species-group names that have been applied to the above genera and the species included in them, indicating their current nomenclatural status and providing the rigorous nomenclatural basis for future work. The catalogue lists 14 published and nomenclaturally available genus-group names, with the above four treated as valid, the other ten being junior synonyms. There are 42 published species-group names: 36 are valid, two are junior synonyms, four are nomenclaturally unavailable. One additional species, described inChabaudistrongylus(synonym ofAngiostrongylus), is listed asincertae sedisin Angiostrongylidae. Also listed are two unpublished collection names. The catalogue provides bibliographic details for all published names, and for available names provides locations of type material, details of type localities, geographic distributions and details of type and other hosts, both definitive and intermediate, to the extent known. The catalogue is a work of nomenclature, not a revisionary taxonomic work. No new names or new combinations are proposed. The apparently new family-group synonymy of Cardionematinae with Angiostrongylidae is introduced, as are four genus-group synonymies, three withAngiostrongylusand one withStefaskostrongylus.


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