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91.
Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,55(2):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献
92.
We study the evolution of strings in the equatorial plane of a Kerr–Newman black hole. Writing the equations of motion and the constraints resulting from Hamilton's principle, three classes of exact solutions are presented, for a closed string, encircling the black hole. They all depend on two arbitrary integration functions and two constants. A process for extracting energy is examined for the case of one of the three families of solutions. This is the analogue of the Penrose process for the case of a particle. 相似文献
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Chiotellis A Tsoukalas C Pelecanou M Papadopoulos A Raptopoulou C Terzis A Pirmettis I Papadopoulos M Chiotellis E 《Inorganic chemistry》2006,45(14):5635-5640
The present paper deals with the synthesis and structural characterization of novel neutral oxorhenium(V) complexes of the general formula ReO[SNO][NN]. The simultaneous action of the tridentate SNO ligand, N-(2-mercaptoacetyl)glycine (1), and the bidentate NN ligand, N-phenylpyridine-2-aldimine (2), on ReOCl3(PPh3)2 leads to the formation of two isomers 4a and 4b of the general formula ReO[SNO][NN], as a result of the different orientations of the NN ligand. In both cases, the SNO donor atoms of the tridentate ligand occupy the three positions in the equatorial plane of the distorted octahedron, whereas the oxo group is always directed toward one of the apical positions. In the first isomer, 4a, the imino nitrogen of the NN ligand occupies the fourth equatorial position and the pyridine type nitrogen is directed trans to the oxo group, while in the second isomer, 4b, the imino nitrogen of the NN ligand occupies the apical position trans to the oxo group and the pyridine type nitrogen completes the equatorial plane of the distorted octahedron. The [SNO][NN] mixed-ligand system was applied in the synthesis of the oxorhenium complex 5 in which the 1-(2-methoxyphenyl)piperazine moiety, a fragment of the true 5-HT1A antagonist WAY 100635, has been incorporated in the NN bidentate ligand (NN is N-{3-[4-(2-methoxyphenyl)piperazin-1-yl]propyl}pyridine-2-aldimine). In this case, high-performance liquid chromatography and NMR showed the existence of one isomer, 5, in which the pyridine nitrogen is trans to the oxo core, as demonstrated by crystal structure analysis. 相似文献
96.
Tzanopoulou S Pirmettis IC Patsis G Raptopoulou C Terzis A Papadopoulos M Pelecanou M 《Inorganic chemistry》2006,45(2):902-909
The reaction of 2-(2'-pyridyl)benzothiazole, [NN], with the ReO(V)(3+) and TcO(V)(3+) cores in the presence of thiophenols, [S] (RC(6)H(4)SH, R = H, 4-CH(3), 4-OCH(3)), as coligands led to the isolation of hexacoordinated complexes of the MO[NN][S](3) type (M = Re, Tc). In all cases, two geometric mer isomers were formed, as evidenced by NMR spectroscopy and confirmed by X-ray crystallography. In both isomers, the coordination geometry about the metal ion is a distorted octahedral defined by the two nitrogen atoms of the bidentate ligand, the three sulfur atoms of the monodentate thiols, and the oxygen atom of the oxo group. The apical positions of the octahedron are occupied by the oxygen of the oxo group and, in one of the isomers, the nitrogen of the pyridyl moiety of 2-(2'-pyridyl)benzothiazole, while, in the second isomer, the imine nitrogen of 2-(2'-pyridyl)benzothiazole. The complexes are stable, neutral, and lipophilic. Complete (1)H and (13)C NMR assignments are reported for all complexes. The synthetic reaction was also successfully transferred at the technetium-99m tracer level by ligand exchange reaction using (99m)Tc-glucoheptonate as precursor in the presence of 2-(2'-pyridyl)benzothiazole and 4-CH(3)C(6)H(4)SH. The structure of the technetium-99m complex was established by high-performance liquid chromatographic comparison with the analogous oxotechnetium and oxorhenium complexes. The 2-(2'-pyridyl)benzothiazole ligand serves as a preliminary model for 2-(4-aminophenyl)benzothiazole, which possesses interesting properties for the development of technetium and rhenium radiopharmaceuticals for tumor imaging and/or radiotherapy as well as in vivo diagnosis of Alzheimer's disease. 相似文献
97.
Lixin Liu Athanase Papadopoulos Weixu Su Guillaume Théret 《Monatshefte für Mathematik》2010,161(3):295-311
We consider some metrics and weak metrics defined on the Teichmüller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call “ε 0-relative \({\epsilon}\)-thick parts”, and whose definition depends on the choice of some positive constants ε 0 and \({\epsilon}\). Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs. 相似文献
98.
A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two results on minimal cograph completions. The first is a characterization that allows us to check in linear time whether a given cograph completion is minimal. The second result is a vertex incremental algorithm to compute a minimal cograph completion H of an arbitrary input graph G in O(|V(H)|+|E(H)|) time. An extended abstract of the result has been already presented at FAW 2008 [D. Lokshtanov, F. Mancini, C. Papadopoulos, Characterizing and computing minimal cograph completions, in: Proceedings of FAW’08-2nd International Frontiers of Algorithmics Workshop, in: LNCS, vol. 5059, 2008, pp. 147158. [1]]. 相似文献
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