Role of molecular symmetries in magneto-spatial dispersional change of the refractive index in fluids

Variations in refractive index due to the (B⁰ · k) effect are calculated for a circularly polarized light wave. The effect is related with the mechanism of nonlinear electron distortion in a field B⁰ described by an i-tensor of rank 4 and the reorientation mechanism represented by the product of two c-tensors, of ranks 3 and 1. The magnetic classes of molecules admitting of these mechanisms are determined.     

Pion and strangeness puzzles

The dependence of pion and strangeness production on the number of participant nucleons and collision energy is discussed for central A+A collisions. A possible interpretation of the experimental results assuming transition to QGP is sketched within a simple statistical approach.     

The electronic structure of the oxygen double-bridged μμ′-dioxo-bis(oxodichloroaquo)dimolybdate (V)-ion by SCCC MO method

Results of SCCC MO calculations for the dimeric oxygen double-bridged [Mo₂O₄Cl₄(H₂O)₂]^2–ion are reported. On the basis of these results the previously reported spectra and magnetic properties may be explained. The strong direct molybdenum — molybdenum interaction in the Mo₂O ₄ ²⁺ core was proved to exist.

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Zusammenfassung Die Ergebnisse von SCCC MO-Rechnungen für das zweikernige Ion [Mo₂O₄Cl₄(H₂O)₂]^2– mit zweifacher Sauerstoffbrücke werden mitgeteilt. Danach können die früher angeführten magnetischen und spektralen Eigenschaften dieses Ions verstanden werden. Die Existenz starker unmittelbarer Molybdän-Molybdän Wechselwirkungen innerhalb des Mo₂O ₄ ²⁺ Kerns wird nachgewiesen.

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Résumé Résultats de calculs SCCCMO pour l'ion dimère Mo₂O₄Cl₄(H₂O) ₂ ^2– . Sur la base de ces résultats les propriétés spectrales et magnétiques précédemment obtenues peuvent être expliquées. L'existence d'une forte interaction directe molybdène-molybdène dans le coeur Mo₂O ₄ ²⁺ est clairement démontrée.

     

Complexity of linear programming

The complexity of linear programming is discussed in the “integer” and “real number” models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation.Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has unbounded complexity in the real number model. We conjecture that there exists no polynomial-time algorithm for the linear inequalities problem in the real number model. We also conjecture that linear inequalities are strictly harder than linear equalities in all “reasonable” models of computation.     

A note on scalar Hertz potentials for gyrotropic media

The scalar Hertz potentials are generalized to the case of electromagnetic fields in gyrotropic media. Expressions for electromagnetic fields in terms of two potentials are presented and the system of differential equations for the potentials is derived. The result are summarized in the form of a theorem. The case of a stratified gyrotropic medium with parameters varying along the distinguished axis has been considered also. Scalar “superpotentials” satisfying a fourth-order partial differential equation are introduced. They allow expressions for electromagnetic fields to be found in terms of one scalar superpotential only. Basic results on scalar Hertz potentials in isotropic media are recalled. The research reported in this paper was carried out during S. Przeździecki's leave of absence from the Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokryzyska 21, PL-00-049 Warszawa, Poland.     

ВЛИЯНИЕ ПРЕДВАРИТЕЛ ЬНОГО ОСВЕЩЕНИЯ ha ХАРАКТЕРИСТИКИ МЕДН ОЗАКИСНЫХ ВЫПРЯМИТЕ ЛЕЙ

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Colored,spinning classical particle in an external non-abelian gauge field

We derive classical non-relativistic equations of motion for a colored, spinning point-like particle in an external SU(2) gauge field from Dirac equation. We find that in addition to the classical spin and color spin vector, S, I, it is necessary to introduce a new classical dynamical variable [J^ab], a, b = 1, 2, 3, describing a mixing of the spin and color. The constraint relations between [J^ab], S, I are also found.     

Ensemble of linear models for predicting drug properties

We propose a new classification method for the prediction of drug properties, called random feature subset boosting for linear discriminant analysis (LDA). The main novelty of this method is the ability to overcome the problems with constructing ensembles of linear discriminant models based on generalized eigenvectors of covariance matrices. Such linear models are popular in building classification-based structure-activity relationships. The introduction of ensembles of LDA models allows for an analysis of more complex problems than by using single LDA, for example, those involving multiple mechanisms of action. Using four data sets, we show experimentally that the method is competitive with other recently studied chemoinformatic methods, including support vector machines and models based on decision trees. We present an easy scheme for interpreting the model despite its apparent sophistication. We also outline theoretical evidence as to why, contrary to the conventional AdaBoost ensemble algorithm, this method is able to increase the accuracy of LDA models.