Defect and Equivalence of Unitary Matrices. The Fourier Case. Part II

2019 ◽  
Vol 26 (01) ◽  
pp. 1950003 ◽  
Author(s):  
Wojciech Tadej
Keyword(s):  
Prime Number ◽  
Unitary Operator ◽  
Real Space ◽  
Finite Abelian Groups ◽  
Unitary Matrices ◽  
First Order ◽  
Case Part ◽  
Fourier Matrix

Consider the real space 𝔻U of directions one can move in from a unitary N × N matrix U without disturbing its unitarity and the moduli of its entries in the first order. dimℝ (𝔻U) is called the defect of U and denoted D(U). We give an account of Alexander Karabegov’s theory where 𝔻U is parametrized by the imaginary subspace of the eigenspace, associated with λ = 1, of a certain unitary operator ℐU on 𝕄N, and where D(U) is the multiplicity of 1 in the spectrum of ℐU. This characterisation allows us to establish the dependence of D(U(1) ⊗ … ⊗ U(r)) on D(U(k))’s, to derive formulas expressing D(F) for a Fourier matrix F of the size being a power of a prime number, as well as to show the multiplicativity of D(F) with respect to Kronecker factors of F if their sizes are pairwise relatively prime. Also partly due to the role of symmetries of U in the determination of the eigenspaces of ℐU we study the ‘permute and enphase’ symmetries and equivalence of Fourier matrices, associated with arbitrary finite abelian groups. This work is published as two papers — the first part [1] and the current second one.

Defect and Equivalence of Unitary Matrices. The Fourier Case. Part I

2018 ◽  
Vol 25 (04) ◽  
pp. 1850020 ◽  
Author(s):  
Wojciech Tadej
Keyword(s):  
Unitary Operator ◽  
Real Space ◽  
Finite Abelian Groups ◽  
Unitary Matrices ◽  
The Real ◽  
First Order ◽  
Case Part ◽  
Fourier Matrix

Consider the real space 𝔻U of directions one can move in from a unitary N × N matrix U without disturbing its unitarity and the moduli of its entries in the first order. dimℝ (𝔻U) is called the defect of U and denoted D(U). We give an account of Alexander Karabegov’s theory where 𝔻U is parametrized by the imaginary subspace of the eigenspace, associated with λ = 1, of a certain unitary operator IU on 𝕄N, and where D(U) is the multiplicity of 1 in the spectrum of IU. This characterization allows us to establish the dependence of D(U(1) ⊗ … ⊗U(r)) on D(U(k))’s, to derive formulas expressing D(F) for a Fourier matrix F of the size being a power of a prime, as well as to show the multiplicativity of D(F) with respect to Kronecker factors of F if their sizes are pairwise relatively prime. Also partly due to the role of symmetries of U in the determination of the eigenspaces of IU we study the ‘permute and enphase’ symmetries and the equivalence of Fourier matrices, associated with arbitrary finite abelian groups. This work is divided in two parts — the present one and the second appearing in the next issue of OSID [1].

Determination of the low-temperature structure of hexamethylbenzene

2005 ◽  
Vol 61 (2) ◽  
pp. 200-206 ◽  
Author(s):  
John A. Stride
Keyword(s):  
Low Temperature ◽  
Temperature Phase ◽  
Temperature Structure ◽  
Thermally Induced ◽  
First Order ◽  
Neutron Powder Diffraction Data ◽  
First Order Phase Transition ◽  
First Order Phase

The low-temperature structure of hexamethylbenzene has been determined from neutron powder diffraction data and found to differ from the room-temperature phase predominantly by a translation of molecular planes to a form a cubic close-packed type structure. By performing measurements as a function of temperature, the role of thermally induced agitation of the molecular units in the first-order phase transition is clearly demonstrated.

scholarly journals On the Role of Mesoentropy in Thermodynamics of First Order Phase Transformations in Alloys

2015 ◽  
Vol 16 (1) ◽  
pp. 20-27
Author(s):  
A. Shirinyan
Keyword(s):  
Size Distribution ◽  
Energy Functional ◽  
Size Distribution Function ◽  
First Order ◽  
General Variation ◽  
The Difference ◽  
First Order Phase ◽  
New Phase

A thermodynamics of a new phase formation in a binary alloy, taking into account the chemical depletion and the size distribution of new phase nuclei giving the energy input at high temperatures, is considered. It is shown the principal possibility of obtaining of the size distribution function for nuclei in the framework of a general variation procedure for the Gibbs free energy functional. The ‘chemical depletion’ related to the difference of compositions of the new phase embryo and the solution of the solid metastable alloy is discussed. The role of the ‘mesoentropy’ for the determination of whole energy of first order phase transformation is manifested.

Some Thoughts on the Aesthetics of Retribution

2004 ◽  
Vol 17 (2) ◽  
pp. 233-254
Author(s):  
Theodore Y. Blumoff
Keyword(s):  
Emotional Reactivity ◽  
Criminal Liability ◽  
Prima Facie ◽  
Necessary Condition ◽  
Negative Component ◽  
First Order ◽  
The People ◽  
Criminal Intent

There is a tendency among those who identify themselves as subjectivists on the issue of defining criminal intent to dismiss or minimize the role of actual non-trivial harm in the determination of criminal liability and punishment. That is to say, they are those who argue that an individual’s subjective intent is a sufficient indication of potential dangerousness and culpability to justify punishment. In this essay, the author presents a view, based on Adam Smith’s recognition of the “irregularity of the sentiments,” that actual physical harm matters; that it reflects the negative component of the two great motivators, pleasure and pain; and that it can release the worst sort of emotional reactivity: retribution. The infliction of a non-trivial first order harm can invoke a deeply felt aesthetic reaction which, in turn, reflects our natural (and cognitively “irregular”) human sentiments. Trying to dispense with harm as a feature in our understanding of criminality seems prima facie absurd. Awareness of the sentiment, as Smith understood, helps temper the worst parts of our nature: that which hopes to crush the people and ideas we find threatening. Ironically, the existence of and need for harm as a necessary condition of criminality heightens our awareness of the limitations of reason in dealing with victims of crime. We are not simply cognitive creatures.

A Molecular Approach to Immunoscintigraphy: A Study of the T-Antigen Conformation on the Surface of Tumors

1987 ◽  
Vol 26 (01) ◽  
pp. 1-6 ◽  
Author(s):  
S. Selvaraj ◽  
M. R. Suresh ◽  
G. McLean ◽  
D. Willans ◽  
C. Turner ◽  
...  
Keyword(s):  
Monoclonal Antibodies ◽  
Tumor Cell ◽  
T Antigen ◽  
Human Carcinomas ◽  
Animal Tumor ◽  
Synthetic Antigens

The role of glycoconjugates in tumor cell differentiation has been well documented. We have examined the expression of the two anomers of the Thomsen-Friedenreich antigen on the surface of human, canine and murine tumor cell membranes both in vitro and in vivo. This has been accomplished through the synthesis of the disaccharide terminal residues in both a and ß configuration. Both entities were used to generate murine monoclonal antibodies which recognized the carbohydrate determinants. The determination of fine specificities of these antibodies was effected by means of cellular uptake, immunohistopathology and immunoscintigraphy. Examination of pathological specimens of human and canine tumor tissue indicated that the expressed antigen was in the β configuration. More than 89% of all human carcinomas tested expressed the antigen in the above anomeric form. The combination of synthetic antigens and monoclonal antibodies raised specifically against them provide us with invaluable tools for the study of tumor marker expression in humans and their respective animal tumor models.

Antithrombin-mediated Inhibition of Factor Vlla-Tissue Factor Complex by the Synthetic Pentasaccharide Representing the Heparin Binding Site to Antithrombin

1996 ◽  
Vol 76 (01) ◽  
pp. 005-008 ◽  
Author(s):  
Jean Claude Lormeau ◽  
Jean Pascal Herault ◽  
Jean Marc Herbert
Keyword(s):  
Binding Site ◽  
Tissue Factor ◽  
Residual Activity ◽  
Coagulation Factors ◽  
Heparin Binding ◽  
Experimental Conditions ◽  
First Order ◽  
Heparin Binding Site ◽  
Coagulant Activity

SummaryWe examined the effect of the synthetic pentasaccharide representing the minimal binding site of heparin to antithrombin on the antithrombin-mediated inactivation of factor Vila bound to tissue factor. This effect was compared to the effect of unfractionated heparin. Using purified recombinant human coagulation factors and either a clotting or an amidolytic assay for the determination of the residual activity of factor Vila, we showed that the pentasaccharide was an efficient antithrombin-dependent inhibitor of the coagulant activity of tissue factor-factor Vila complex. In our experimental conditions, assuming a mean MW of 14,000 for heparin, the molar pseudo-first order rate constants for ATIII-mediated FVIIa inhibition by ATIII-binding heparin and by the synthetic pentasaccharide were found to be similar with respective values of 104,000 ± 10,500 min-1 and 112,000 ± 12,000 min-1 (mean ± s.e.m., n = 3)

On The Mechanism Of Heparin-Induced Potentiation Of Platelet Aggregation

1981 ◽  
Author(s):  
M Yamamoto ◽  
K Watanabe ◽  
Y Ando ◽  
H Iri ◽  
N Fujiyama ◽  
...  
Keyword(s):  
Platelet Aggregation ◽  
Platelet Activation ◽  
Coagulation Factors ◽  
Marked Enhancement ◽  
Matrix Bound ◽  
Induced Aggregation ◽  
Aggregation Of Platelets ◽  
Plasma Heparin

It has been suggested that heparin caused potentiation of aggregation induced by ADP or epinephrine. The exact mechanism of heparin-induced platelet activation, however, remained unknown. In this paper, we have investigated the role of anti-thrombin III ( AT ) in heparin-induced platelet activation using purified AT and AT depleted plasma. When ADP or epinephrine was added to citrated PRP one minute after addition of heparin ( 1 u/ml, porcine intestinal mucosal heparin, Sigma Co. USA ), marked enhancement of platelet aggregation was observed, compared with the degree of aggregation in the absence of heparin. However, in platelet suspensions prepared in modified Tyrode’s solution, heparin exhibited no potentiating effect on platelet aggregation induced by epinephrine or ADP. Potentiation of epinephrine- or ADP-induced platelet aggregation by heparin was demonstrated when purified AT was added to platelet suspensions at a concentration of 20 μg/ml. AT depleted plasma, which was prepared by immunosorption using matrix-bound antibodies to AT, retained no AT, while determination of α1-antitrypsinα2- macroglobulin and fibrinogen in AT depleted plasma produced values which corresponded to those of the original plasma when dilution factor was taken into account. The activities of coagulation factors were also comparable to those of the original plasma. Heparin exhibited potentiating effect on ADP- or epinephrine-induced aggregation of platelets in original plasma, but no effect in AT depleted plasma. When purified AT was added back to AT depleted plasma at a concentration of 20 μg/ml, potentiation of platelet aggregation by heparin was clearly demonstrated.Our results suggest that effect of heparin on platelet aggregation is also mediated by anti-thrombin III.

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

2003 ◽  
Vol 218 (1) ◽  
Author(s):  
K. Chowdhury ◽  
S. Ghosh ◽  
M. Mukherjee
Keyword(s):  
Cytochrome C ◽  
Ab Initio ◽  
Structure Determination ◽  
Direct Method ◽  
Real Space ◽  
Reciprocal Space ◽  
Cytochrome C6 ◽  
Ab Initio Structure ◽  
Space Approach

AbstractThe direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c

ІНТЕРПРЕТАЦІЯ КАТЕГОРІЇ РОЗВИТКУ В СУЧАСНІЙ ПСИХОЛОГІЇ

1970 ◽  
Vol 8 (1) ◽  
pp. 22-30
Author(s):  
Анжеліка Шамне
Keyword(s):  
Cultural Context ◽  
Developmental Psychology ◽  
Structure And Dynamics ◽  
Modern Psychology ◽  
Development Site ◽  
Approaches To Study ◽  
Methodological Approaches ◽  
Self Motion

У статті розглянуто сучасні підходи до інтерпретації категорії розвитку, розкрито теоретичні  та методологічні підходи до вивчення категорії розвитку у сучасній психології, визначено її психологічний  зміст,   моделі,   структуру   та   динаміку.   Категорія   розвитку   розглядається   як   епіцентр   наукової  проблематики у психології та як поняття інтегративного типу. Розвиток проаналізовано як категорію,  явище і проблему психології розвитку в різних аспектах аналізу. Розглянуто місце розвитку в системі  споріднених психологічних понять. У статті також аналізуються психологічні аспекти теоретичних та  методологічних  постнекласичних  тенденцій  вивчення  природи,  характеру  та  визначення  психічного  розвитку. Постнекласична парадигма та плюралістична методологія пізнання визначають розмитість  дисциплінарної мови  та  врахування  ролі  соціокультурного  контексту  при  вивченні  психологічних явищ.  Важливими тенденціями сучасного теоретико-методологічного стану психологічних досліджень розвитку  також є визнання неефективності моністичного підходу до його вивчення, взаємозв'язок теоретичних ідей  та   спроби   створення   метатеоретичних   схем,   постнекласичне   розуміння   розвитку   як   принципово  незавершеного   процесу   саморуху,   актуалізація   антропологічного   діапазону   проблем   та   посилення  спрямованості на роль культурного контексту в дослідженні розвитку людини.  The article deals with the modern approaches to the interpretation of the category of development, reveals  the theoretical and methodological approaches to study of development in modern psychology, its psychological  content, patterns, structure and dynamics. Category of development is viewed as an epicenter of scientific issues in  modern  psychology  and  the  concept  of  the  integrative  type.  Category  of  development  is  considered  as  the  phenomenon  and  the  problem  of  developmental  psychology  in  various  aspects  of  the  analysis.  Analyzed  the  development site in the related psychological concepts. The article analyzes the psychological aspects of theoretical  and methodological postnonclassical contemporary trends in the study of nature, character, and determination of  mental  development.  Postnonclassical  paradigm  and  pluralistic  methodology  of  knowledge  determine  the  disciplinary blurring and increase of the role of the analysis of socio-cultural context in the study of psychological  phenomenon. The important tendencies of modern theoretical and methodological state of psychological researches  of development are facts of inefficiency of the monistic approach to its study, interconnection of theoretical ideas  and   attempts   of  creating   metatheoretical   schemes,   postnonclassical   understanding   of   development   as   a  fundamentally  uncompleted  process  of  self-motion,  actualization  of  anthropological  range  of  problems  and  strengthening of focus on the role of cultural context in research of human development.   

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