X-ray crystal structure and magnetic and photophysical properties of novel copper(II) N-oxide adduct [(4-MPyO)2(CuCl2)2(H2O)(C2H5OH)] (4-MPyO = 4-(4-methoxystyryl)pyridine N-oxide)

A new mixed adduct, (4-MPyO)2(CuCl2)2(H2O)(C2H5OH) [where 4-MPyO is the 4-(4-methoxystyryl)pyridine N-oxide], was obtained for the first time. It has been characterized by X-ray studies, IR, electronic absorption, and emission spectra, lifetime measurements, and variable-temperature magnetic susceptibility measurements in the range 80-300 K. The single-crystal X-ray diffraction shows that the geometry around both of the copper(II) ions can be described as a tetragonal pyramid with a trapezoidal base at the corners of which are two oxygen atoms of N-oxide and two chlorine atoms. The oxygen atoms of either water or ethanol are at the apex of the pyramid. Besides that, two molecules of the adduct form a double-hydrogen-bonded superdimer in which they are connected to each other through hydrogen bonds of the O-H...Cl type as formed between the chlorine atoms and ethanol molecule (Cl...O 3.22 A). The copper(II) atoms are antiferromagnetically coupled within a dimeric unit, and a singlet-triplet separation of 2 J value (1100 cm(-1)) is greater than the value expected from Hatfield's rule for the bridging angles Cu-O-Cu equal 108.9 degrees and 110.2 degrees . By means of the PM3-calculated values of vertical excitation energies, the ligand-to-metal charge-transfer (LMCT) and the metal-to-ligand charge-transfer transitions in the unresolved experimental absorption spectra of I have been revealed. From the large Stokes shift value of emission spectra in solvents of different polarity (more than 6500 cm(-1) in acetonitrile), the charge-transfer (CT) nature of the emissive (LMCT) state of I has been concluded. Biexponential decay of the excited complex in acetonitrile and frozen propanol suggests that the two different CT conformers (0.8, 4.12 ns and 1.99, 15.2 ns, respectively) are present in the excited state in solution while only one CT form is indicated by a monoexponential decay (9.0 micros) in the solid.     

Groups with few characters of small degrees

Letd>1 be a proper divisor of the order of a finite groupG and let σ _d (G) be the sum of squares of degrees of those irreducible characters whose degrees are not divisible byd. It is easy to see thatd divides σ _d (G). The groupsG such that σ _d (G) =d coincide with Frobenius groups whose kernel has indexd (see G. Karpilovsky,Group Representations, Volume 1, Part B, North-Holland, Amsterdam, 1992, Theorem 37.5.5). In this note we study the case σ _d (G) = 2d in some detail. In particular, ifG is a 2-group, it is of maximal class (Remark 3(b)). The author was supported in part by the Ministry of Absorption of Israel.     

A Class of Quasi-linear Equations in Coframe Gravity

We have shown recently that the gravity fieldphenomena can be described by a traceless part of thewave-type field equation. This is an essentiallynon-Einsteinian gravity model. It has an exactsphericallysymmetric static solution, that yields to theYilmaz-Rosen metric. This metric is very close to theSchwarzchild metric. The wave-type field equation cannotbe derived from a suitable variational principle by free variations, as was shown by Hehl and hiscollaborators. In the present work we are looking foranother field equation having the same exactspherically-symmetric static solution. Thedifferential-geometric structure on the manifold endowed with a smoothorthonormal coframe field is described by the scalarobjects of anholonomity and its exterior derivative. Weconstruct a list of the first and second order SO(1,3)-covariants (one- and two-indexedquantities) and a quasi-linear field equation with freeparameters. We fix a part of the parameters by acondition that the field equation is satisfied by aquasi-conformal coframe with a harmonic conformal function .Thus we obtain a wide class of field equations with asolution that yields the Majumdar-P apapetrou metricand, in particular, the Yilmaz-Rosen metric, that is viable in the framework of three classicaltests.     

Heterogeneous uncertainties in cholesterol management

Physicians use clinical guidelines to inform judgment about therapy. Clinical guidelines do not address three important uncertainties: (1) uncertain relevance of tested populations to the individual patient, (2) the patient’s uncertain preferences among possible outcomes, and (3) uncertain subjective and financial costs of intervention. Unreliable probabilistic information is available for some of these uncertainties; no probabilities are available for others. The uncertainties are in the values of parameters and in the shapes of functions. We explore the usefulness of info-gap decision theory in patient-physician decision making in managing cholesterol level using clinical guidelines. Info-gap models of uncertainty provide versatile tools for quantifying diverse uncertainties. Info-gap theory provides two decision functions for evaluating alternative therapies. The robustness function assesses the confidence—in light of uncertainties—in attaining acceptable outcomes. The opportuneness function assesses the potential for better-than-anticipated outcomes. Both functions assist in forming preferences among alternatives. Hypothetical case studies demonstrate that decisions using the guidelines and based on best estimates of the expected utility are sometimes, but not always, consistent with robustness and opportuneness analyses. The info-gap analysis provides guidance when judgment suggests that a deviation from the guidelines would be productive. Finally, analysis of uncertainty can help resolve ambiguous situations.     

Irregular Boundary Value Problems with Discontinuous Coefficients and the Eigenvalue Parameter

In this study, a Birkhoff-irregular boundary value problem for linear ordinary differential equations of the second order with discontinuous coefficients and the spectral parameter has been considered. Therefore, at the discontinuous point, two additional boundary conditions (called transmission conditions) have been added to the boundary conditions. The eigenvalue parameter is of the second degree in the differential equation and of the first degree in a boundary condition. The equation contains an abstract linear operator which is (usually) unbounded in the space Lq(−1, 1). Isomorphism and coerciveness with defects 1 and 2 are proved for this problem. The case of the biharmonic equation is also studied.     

Enhanced electro-catalytic degradation of chloroorganic compounds in the presence of ultrasound

The application of finely divided (black) Pd and Pd-Fe powder in the sono-electro-catalytic reduction of chlorophenoxy herbicides (2,4-D) and chlorophenols (2,4-DCP) in aqueous solutions allows for effective destruction of toxic chlorinated aromatic compounds. At 20 degrees C complete conversion of these compounds is observed within 10 min. On bimetallic Pd/Fe catalyst, intermediates due to the oxidation reaction are detected in addition to the products of dechlorination. The bimetallic catalyst appears to be energetically and economically superior to the Pd. In both cases, the reaction times were considerably shortened in comparison with traditional electro-catalytic processes.     

An Application of the Renormalization Group Method to Stable Limit Laws

Let \((X_n)_{n=1}^{\infty }\) be a sequence of independent identically distributed random variables. We study the normalized partial sums and the corresponding renormalization group flow in the space of probability densities. We prove the convergence to stable limit laws under suitable assumptions on the initial density.     

Nonsymmetric bifurcations of solutions of the 2D Navier–Stokes system

We consider the 2D Navier–Stokes system written for the stream function with periodic boundary conditions and construct a set of initial data such that initial critical points bifurcate from 1 to 2 and then to 3 critical points in finite time. The bifurcation takes place in a small neighborhood of the origin. Our construction does not require any symmetry assumptions or the existence of special fixed points. For another set of initial data we show that 3 critical points merge into 1 critical point in finite time. We also construct a set of initial data so that bifurcation can be generated by the Navier–Stokes flow and do not require the existence of an initial critical point.     

Scheduling UET task systems with concurrency on two parallel identical processors

Problems with unit execution time tasks and two identical parallel processors have received a great deal of attention in scheduling theory. In contrast to the conventional models, where each task requires only one processor, we consider a situation when a task may require both processors simultaneously. For problems without precedence constraints we present several polynomial time algorithms which complement recent results of Lee and Cai. We also show that the introduction of precedence constraints leads to NP-hardness results for maximum lateness and mean flow time objective functions. For the maximum lateness problem, a family of algorithms, based upon the idea of modified due dates, is considered. The worst case behaviour of these algorithms is analysed, and it is shown that the same upper bound is tight for each algorithm of this family.