scholarly journals Strong 1-boundedness of unimodular orthogonal free quantum groups

2021 ◽  
Vol 24 (02) ◽  
pp. 2150012
Author(s):  
Floris Elzinga
Keyword(s):  
Quantum Groups ◽  
Analogous Result ◽  
The Other ◽  
Fundamental Representation ◽  
Boundedness Property ◽  
Defining Relations ◽  
Symplectic Matrix ◽  
Bounded Set ◽  
Pauli Matrices ◽  
Derivatives Of

Recently, Brannan and Vergnioux showed that the orthogonal free quantum group factors [Formula: see text] have Jung’s strong [Formula: see text]-boundedness property, and hence are not isomorphic to free group factors. We prove an analogous result for the other unimodular case, where the parameter matrix is the standard symplectic matrix in [Formula: see text] dimensions [Formula: see text]. We compute free derivatives of the defining relations by introducing self-adjoint generators through a decomposition of the fundamental representation in terms of Pauli matrices, resulting in [Formula: see text]-boundedness of these generators. Moreover, we prove that under certain conditions, one can add elements to a [Formula: see text]-bounded set without losing [Formula: see text]-boundedness. In particular, this allows us to include the character of the fundamental representation, proving strong [Formula: see text]-boundedness.

Energy Approximation

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Main Lemma ◽  
The Other ◽  
Coarse Scale ◽  
Continuous Solutions ◽  
Material Derivative ◽  
Energy Variation ◽  
Energy Approximation ◽  
The Difference ◽  
Derivatives Of

This chapter presents the equations and calculations for energy approximation. It establishes the estimates (261) and (262) of the Main Lemma (10.1) for continuous solutions; these estimates state that we are able to accurately prescribe the energy that the correction adds to the solution, as well as bound the difference between the time derivatives of these two quantities. The chapter also introduces the proposition for prescribing energy, followed by the relevant computations. Each integral contributing to the other term can be estimated. Another proposition for estimating control over the rate of energy variation is given. Finally, the coarse scale material derivative is considered.

scholarly journals II. Compounds isomeric with the sulphocyanic ethers.—I. On the mustard oil of the ethyl series

1868 ◽  
Vol 16 ◽  
pp. 254-258
Keyword(s):  
Royal Society ◽  
The Other ◽  
Mustard Oil ◽  
Other Hand ◽  
Derivatives Of

The results of my researches on the chloroform-derivatives of the primary monamines, which, as I have shown, are isomeric with the nitriles, could not fail to direct my attention to allied groups of bodies, with the view of discovering similar isomerisms. In a note communicated to the Royal Society some months ago, I expressed the expectations which even then appeared to be justified in the following manner:—“In conclusion, I may be permitted to announce as everv probable the existence of a series of bodies isomeric with the sulphocyanides. Already M. Cloëz has shown that the action of chloride of cyanogen on ethylate of potassium gives rise to the formation of an ethylic cyanate possessing properties absolutely different from those belonging to the cyanate discovered by M. Wurtz. On comparing, on the other hand the properties of the methylic and ethylic sulphocyamdes with those of the sulphocyanides of allyl and phenyl, it can scarcely be doubted that we have here the representatives of two groups entirely different, and that the terms of the methyl- and ethyl-series which correspond to oil of mustard, and to the sulphocyanide of phenyl, still remain to be discovered. Experiments with which I am now engaged will show whether these bodies cannot be obtained by the action of the iodides of methyl and ethyl on sulphocyanide of silver."

The synthesis of the isomeric N-methyl derivatives of murexine

1981 ◽  
Vol 34 (8) ◽  
pp. 1739 ◽  
Author(s):  
CC Duke ◽  
JV Eichholzer ◽  
JK Macleod
Keyword(s):  
Imidazole Ring ◽  
The Other ◽  
Pharmacological Activities ◽  
Tautomeric Forms ◽  
Methyl Derivatives ◽  
Paramagnetic Ions ◽  
Nucella Emarginata ◽  
Derivatives Of

The two isomeric N-methyl derivatives of murexine have been synthesised by independent routes and shown to be different from an 'N- methylmurexine' reportedly isolated from the mollusc Nucella emarginata. 1H n.m.r. studies have shown a marked difference in the extent of binding to paramagnetic ions of the two N-methyl derivatives of murexine in water while pharmacological results show substantially different pharmacological activities of the two isomers. Both results can be rationalized in terms of the observed activities being associated with the presence of one or the other of the tautomeric forms of the imidazole ring.

Cleavage Reactions of 5-Arylazo Derivatives of 1-Methyl-2-benzyl-2-imidazolin-4-ones

1975 ◽  
Vol 30 (7-8) ◽  
pp. 603-605 ◽  
Author(s):  
Nazmi Abdel Latif Kassab ◽  
Abdel Hamid Harhash ◽  
Sanna Osman Abd Allah
Keyword(s):  
Sodium Hydroxide Solution ◽  
Aqueous Sodium Hydroxide ◽  
The Other ◽  
Ring Cleavage ◽  
Prolonged Heating ◽  
Aqueous Sodium Hydroxide Solution ◽  
Aqueous Sodium ◽  
Triazine Derivatives ◽  
Cleavage Reactions ◽  
Derivatives Of

The 5-arylazo-1-methyl-2-benzyl-2-imidazolin-4-ones (1 a-c) undergo ring cleavage with 1% aqueous sodium hydroxide solution affording α-arylhydrazono-phenacetyl-sarcosine amide (2). Prolonged heating of 1 and 2 with the same reagent yields the cyanamide (3). On the other hand, when 1 a-c were refluxed with acetic acid the triazinones (4) were obtained. The latter adds one mole of Grignards reagent to yield the 5-hydroxy-1,2,4-triazine derivatives (5).

Application of Maple on Solving the Differential Problem of Rational Functions

2013 ◽  
Vol 479-480 ◽  
pp. 855-860
Author(s):  
Chii Huei Yu
Keyword(s):  
Problem Solving ◽  
Research Methods ◽  
Research Method ◽  
Rational Functions ◽  
The Other ◽  
Mathematical Software ◽  
Differential Problem ◽  
Binomial Theorem ◽  
Other Hand ◽  
Derivatives Of

This paper uses the mathematical software Maple as the auxiliary tool to study the differential problem of four types of rational functions. We can obtain the closed forms of any order derivatives of these rational functions by using binomial theorem. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

scholarly journals An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives

2020 ◽  
Vol 8 (2) ◽  
pp. 590-601
Author(s):  
Melani Barrios ◽  
Gabriela Reyero
Keyword(s):  
Exact Solution ◽  
Variational Problem ◽  
Lagrange Equation ◽  
Integral Form ◽  
Variational Problems ◽  
The Other ◽  
Isoperimetric Problems ◽  
Caputo Derivatives ◽  
Fractional Variational Problems ◽  
Derivatives Of

In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputofractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the basic and isoperimetric problems, one in an integral form, and the other that depends only on the Caputo derivatives. The advantage is that Caputo derivatives are more appropriate for modeling problems than the Riemann-Liouville derivatives and makes the calculations easier to solve because, in some cases, its behavior is similar to the behavior of classical derivatives. Finally, anew exact solution for a particular variational problem is obtained.

Anxiety and Two Cognitive Forms of Resistance to the Idea of Death

1966 ◽  
Vol 18 (2) ◽  
pp. 359-364 ◽  
Author(s):  
Stephen L. Golding ◽  
George E. Atwood ◽  
Richard A. Goodman
Keyword(s):  
Semantic Differential ◽  
The Other ◽  
Fear Of Death ◽  
General Factor ◽  
Significant Relationships ◽  
Defense Model ◽  
Derivatives Of ◽  
Affective Orientation

A relationship between affective orientation to death and two cognitive forms of resistance to the idea of death was hypothesized. Affect was measured by the Sarnoff Fear of Death Scale (Sarnoff & Corwin, 1959). One form of resistance was examined by using a perceptual defense model employing neutral- and death-related words; the other was connotative rigidity, a postulated associative inflexibility of death-related concepts. This rigidity was conceived as a clustering of death-related words on the Evaluative (E), Potency (P), and Activity (A) factors of the semantic differential (Osgood, Suci, & Tannenbaum, 1957), and was mathematically expressed as a variance score. Death-related words, presented tachistoscopically, proved significantly more difficult to recognize than neutral words ( p < .01). No significant relationships were demonstrated between affective orientation to death and the two forms of resistance. However, significant correlations between the measures of perceptual defense and connotative rigidity were obtained. In interpreting the results a defense model was used, according to which connotative rigidity and perceptual defense are derivatives of the same general factor.

Cognitive constraints in English lexical blending

2018 ◽  
Vol 25 (1) ◽  
pp. 142-173
Author(s):  
Daniel Kjellander
Keyword(s):  
Neighborhood Effects ◽  
Formation Process ◽  
Word Formation ◽  
The Other ◽  
Word Class ◽  
Transfer Effects ◽  
Cognitive Constraints ◽  
Growing Body ◽  
The Impact ◽  
Derivatives Of

Abstract The complex characteristics of lexical blending have long troubled mainstream word formation research to the extent that it has typically been considered a peripheral issue in linguistics. In recent years this has begun to change, and there is currently a growing body of evidence uncovering the intriguing nature of this word formation process. In the present study, underlying principles and usage-based aspects of lexical blends were examined. Analyses of derivatives of three matrix words, republican, liberal, and vegetarian, revealed the impact of three cognitive constraints on the use of lexical blends: schema transfer effects, neighborhood effects, and effects of the influence from morphological lexicalization. The first constraint fueled blend formation, while the other two displayed a hampering effect on the use of lexical blending. Furthermore, a study of the word class distribution in the datasets showed that there were significant differences in the grammar of lexical blending and compounding, respectively.

Relation of the metabolism of sulfobromophthalein sodium to its blood clearance in the rat

1959 ◽  
Vol 197 (2) ◽  
pp. 292-296 ◽  
Author(s):  
John S. Krebs
Keyword(s):  
Chromatographic Analysis ◽  
The Other ◽  
Blood Clearance ◽  
Chain Sequence ◽  
A Chain ◽  
Derivatives Of

Chromatographic analysis of BSP (sodium phenoltetrabromphthalein disulfonate) excreted into the bile of the rat showed that the BSP had undergone transformation into similarly colored but chemically different compounds. Injection of purified samples of these derived compounds into the rat showed that the compounds were less effectively removed from plasma than BSP but were excreted into bile at almost the same rate as when pure BSP was injected. Chromatographic analysis of bile following injection of the isolated bile-type derivatives of BSP showed that the derivatives were formed, one from the other, in a chain sequence, starting with BSP. Chromatographic analysis of the blood following injection of BSP showed that bile-type derivatives of BSP appeared in the blood and became progressively more predominant with increasing time after injection of the BSP.

scholarly journals A categorical reconstruction of crystals and quantum groups at q = 0

2019 ◽  
Vol 70 (3) ◽  
pp. 895-925
Author(s):  
Craig Smith
Keyword(s):  
Hopf Algebra ◽  
Quantum Group ◽  
Lie Algebra ◽  
Quantum Groups ◽  
Analogous Result ◽  
Crystal Bases ◽  
Direct Sums ◽  
Finite Dimensional ◽  
Monoidal Structure

Abstract The quantum co-ordinate algebra Aq(g) associated to a Kac–Moody Lie algebra g forms a Hopf algebra whose comodules are direct sums of finite-dimensional irreducible Uq(g) modules. In this paper, we investigate whether an analogous result is true when q=0. We classify crystal bases as coalgebras over a comonadic functor on the category of pointed sets and encode the monoidal structure of crystals into a bicomonadic structure. In doing this, we prove that there is no coalgebra in the category of pointed sets whose comodules are equivalent to crystal bases. We then construct a bialgebra over Z whose based comodules are equivalent to crystals, which we conjecture is linked to Lusztig’s quantum group at v=∞.

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