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71.
72.
We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive. 相似文献
73.
74.
Pavel G. Todorov 《Rendiconti del Circolo Matematico di Palermo》1988,37(3):369-383
We examine certain non-linear extremal problems for two-dimensional Riemann-Stieltjes integrals \(\varphi (z) \equiv \int {_D \int {g(z,\zeta )d\mu (\zeta ),} \zeta \in D \equiv [\zeta |\left| \zeta \right|} \leqslant 1]\) ,z∈Δ≡[z‖|z|<1] whereg(z, ζ) is a continuous function in (z, ζ)∈[Δ×D] and an analytic function forz∈Δ and μ(ζ) is a unit mass measure onD. In particular, if the mass is distributed on the segment [a, b], we obtain the well-known Ruscheweyh results for the one-dimensional Riemann-Stieltjes integrals \(\varphi (z) \equiv \int_a^b {g(z,t)d\mu (t),z \in \Delta } \) . In particular, ifg(z,σ)≡z/(1—zσ), we determine the maximal domain of univalence and the radii of starlikeness and convexity of order α, ?∞<α<1, of the corresponding functions ?(z). A particular study is made of the functions of classesS 1(D) andS 2(D) which is similar to the study of the functions of the corresponding classesS 1(C) andS 2(C) of Schwarz analytic functions. In addition to obtaining maximal domains of univalence, we also determine the unique extremal functions for each of the functional studied. 相似文献
75.
Ilija N. Cvijetić Miloš P. Pešić Miljana D. Todorov Branko J. Drakulić Ivan O. Juranić Tatjana Ž. Verbić Mire Zloh 《Structural chemistry》2018,29(2):423-434
Aryldiketo acids (ADKs) exhibit the variety of biological activities, mainly due to large affinity toward divalent metal ions. Metal complexation ability of ADKs, as well as interactions with proteins, depend on tautomeric form present in solution. The main aim of this study was to fully explore the tautomeric preferences of 4-phenyl-2,4-dioxobutanoic acid (4PDA), as ADKs representative, in aqueous media at different pH values. 1D and 2D NMR spectroscopy in combination with quantum chemical calculations was applied in order to better understand the tautomeric preferences of 4PDA. The data in highly acidic media are especially interesting since there are no such findings in the literature due to low solubility of ADKs in molecular form. At low pH values, where 4PDA is unionized, the most abundant tautomeric form is enol with keto group closer to phenyl ring. At higher pH values, mixture of two 4PDA ionic forms coexists in solution. Their ratio calculated according to NMR data fits the values predicted using two experimentally determined pK a values. Based on the complexity of 1H NMR spectrum of monoanionic 4PDA form, coexistence of two stable rotamers was assumed. In an alkaline media, 4PDA is mostly present in dianionic form. As π-electrons of dianion are delocalized over an entire keto-enol moiety, spectral distinction between tautomers was not possible. Quantum chemical calculations were used to predict relative stability of tautomers. The predictions were in good accordance with experimental results only in case when explicit water molecule was included in calculations. 相似文献
76.
T. S. Todorov 《International Journal of Theoretical Physics》1975,14(5):295-298
The mathematical definition of superselection rules in the case when observables are described by unbounded operators in a fixed Hilbert space (for instance, in the frame of Wightman's axioms) is examined. The additional condition \(P_{H_q } D \subset D\) (whereD is the common domain of definition of the operators,H q is theqth sector, and \(P_{H_q } \) is the projection onH q ) is found to be sufficient in order to preserve-as in the case of bounded observables—the one-to-one correspondence between reducing subspacesH q and projections \(P_{H_q } \) from the commutantA′ of the algebraA of observables. This additional condition is equivalent to the physical requirement that every physical vector state can be uniquely represented as a linear combination of physical states, each belonging to some sector. 相似文献
77.
Conclusions A cluster analysis enabled to determine groups of countries with similar distribution of physics publications by subfield. Though percentage data are used, clusters form around the major producers. Values of ratios between distinct subfields provide a straightforward picture of national preferences in physics research.In some countries (e.g. [23]) the subfield distribution could be confronted with equally structurized manpower figures. For practical decisions, however, it may be necessary to elaborate on better defined narrow specialties (cf. the hitherto tackled in [18, 3]). A full-scale distribution assessment within all of physics is again suitable for bringing fresh arguments to discussions on criteria for priority choice [24] fitted to the needs of individual countries. 相似文献
78.
Nickola Stefanov Todorov 《International Journal of Theoretical Physics》1980,19(10):725-740
On the basis of the discussion in our previous work (T1) and the reexamination of the concept of entropy of a pure quantum state it is shown that a natural explanation of the process of entropy increase exists. A new definition of an entropy operator is given and it is shown that there is not any increase of entropy when one confines oneself to the usual formalism of quantum mechanics and uses this definition. Some other attempts of proving theH theorem are briefly discussed. 相似文献
79.
V. B. Petkova G. M. Sotkov I. T. Todorov 《Communications in Mathematical Physics》1985,97(1-2):227-255
A formulation of massless QED is studied with a non-singular Lagrangian and conformal invariant equations of motion. It makes use of non-decomposable representations of the conformal groupG and involves two dimensionless scalar fields (in addition to the conventional charged field and electromagnetic potential) but gauge invariant Green functions are shown to coincide with those of standard (massless) QED. Assuming that the (non-elementary) representation ofG for the 5-potential which leaves the equations of motion invariant and leads to the free photon propagator of Johnson-Baker-Adler (JBA) conformal QED remains unaltered by renormalization, we prove that consistency requirements for conformal invariant 2-, 3-, and 4-point Green functions satisfying (renormalized) equations of motion and standard Ward identities lead to either a trivial solution (withe=0) or to a subcanonical dimensiond=1/2 for the charged field.To the memory of Kurt Symanzik 相似文献
80.
G. T. Todorov P. R. Karavassilev N. V. Sabotinov P. K. Telbizov 《Zeitschrift für Physik D Atoms, Molecules and Clusters》1997,39(4):251-255
The rate coefficients for collision induced transitions from a laser level to neighboring levels of active medium particles are theoretically connected with the intensity of the spontaneous emission originating from these levels and its variation due to 100% modulation of the laser oscillation. The levels pertaining to the configuration 4s 2 4p 2(2 P)5p of Se2 are explored at conditions of operation of a positive column He-Se+ laser. Normalized population transfer rate coefficients are defined. Their values are obtained based on the measured spontaneous emission intensity and its variation. The dominating partners for the mixing collisions with excited selenium ions are suggested as Se+, Se and He+ in contrast with the free electrons and helium atoms. 相似文献