Dimethylamino-substituted 7H-Benzo[de]pyrazolo[5,1-a]isoquinolin-7-ones and Their Behavior under Vilsmeier-Haack Conditions

The behavior of dimethylamino-substituted 7H-benzo[de]pyrazolo[5,1-a]isoquinoline-7-ones, synthesized for the first time, under conditions of the Vilsmeier-Haack reaction. It has been shown that, on heating with POCl₃ and DMF, they are converted by electrophilic substitution at the position ortho to the dimethylamino group, followed by cyclization of the iminium adduct to a quinazolinium salt. When an acetyl group is present, the Arnold reaction, leading to the formation of a chloroaryl, accompanies the heterocyclization. The rates and proportion of the reaction products depend on the position of the dimethyl groups relative to the pyrazole ring.     

Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.     

Computation of the Morse Spectrum

The Morse spectrum is a limit set of Lyapunov exponents of periodic pseudo-trajectories. This notion is especially important in the case where a dynamical system has infinitely many periodic trajectories of large period. A method for estimating the Morse spectrum was suggested by the first author in J. Math. Anal. Appl., 252 (2000). This method is based on ideas of symbolic dynamics which reduces the study of a dynamical system to the study of a certain graph, called a symbolic image. Within the framework of this method, the computation of the Morse spectrum is connected with searching simple closed paths and extracting contours with suitable characteristics. However, under iterations of the symbolic image, the number of such paths sharply increases, which leads to huge expenses of memory and time. We suggest an algorithm for constructing contours with the maximal and minimal mean values. This algorithm is based on a special version of the simplex method. Numerical tests are also described. Bibliography: 13 titles. Illustrations: 3 figures.     

Discrete mathematics in primary and secondary schools in the United States

This article provides a status report on discrete mathematics in America's schools, including an overview of publications and programs that have had major impact. It discusses why discrete mathematics should be introduced in the schools and the authors' efforts to advocate, facilitate, and support the adoption of discrete mathematics topics in the schools. Their perspective is that discrete mathematics should be viewed not only as a collection of new and interesting mathematical topics, but, more importantly, as a vehicle for providing teachers with a new way to think about traditional mathematical topics and new strategies for engaging their students in the study of mathematics.     

A two-stage parallel branch and bound algorithm for mixed integer programs

Mixed integer programming (MIP) models are extensively usedto aid strategic and tactical decision making in many businesssectors. Solving MIP models is a computationally intensive processand there is a need to develop solution approaches that enablelarger models to be solved within acceptable timeframes. Inthis paper, we describe the implementation of a two-stage parallelbranch and bound (PB & B) algorithm for MIP. In stage 1of the algorithm, a multiple heuristic search is implementedin which a number of alternative search trees are investigatedusing a forest search in the hope of finding a good solutionquickly. In stage 2, the search is reorganized so that the branchesof a chosen tree are investigated in parallel. A new heuristicis introduced, based on a best projection criterion, which evaluatesalternative B & B trees in order to choose one for investigationin stage 2 of the algorithm. The heuristic also serves as away of implementing a quality load balancing scheme for stage2 of the algorithm. The results of experimental investigationsare reported for a range of models taken from the MIPLIB libraryof benchmark problems.     

Effects of vitrification suppression on structure morphology, conductivity and dielectric properties of vanadium phosphate glasses

Vitrification suppression in the (V₂O₅)_1−x (P₂O₅)_x glasses where x=0.10, 0.15, 0.20, and 0.25 was controlled by changing the rate of quenching glasses. The structure variations occurring in the glasses were detected by differential thermal analysis and optical microscope. The results implied the separation and growth of V₂O₅ orthorhombic microcrystal in the samples with x=0.10 and 0.15 whereas other samples did not illustrate remarkable changes in their microstructure. However, in temperature range between 300 and 473 K a semiconducting behavior for all samples appears during the study of electrical conductivity-temperature dependence. A decrease in conductivity values accompanied with some variations in activation energies by reducing quenching rate was observed. The conductivity results suggested that the conduction occurs by the phonon assisted hopping of a small polaron between V⁴⁺ and V⁵⁺ states at relatively higher temperature range above θ_D/2. Whereas at relatively low temperatures the conduction may occur by electron jumping between filled and empty states at Fermi level in the disordered matrix besides polaronic conduction. Reasonable values for the density of localized states, carrier concentration and carrier mobility were estimated and discussed. Also, dielectric constant and dielectric loss were studied as a function of frequency at different temperatures confirming the structure variations in the glass system.     

Dynamics and crystal chemistry of tellurites. II. Composition- and temperature-dependence of the Raman spectra of x(Tl2O)+(1−x) Te2O glasses: evidence for a phase separation?

Immiscibility effects are suggested to be inherent in tellurite glasses with weak (low valence) cations. This hypothesis is used to explain the structural evolution of the x(Tl₂O)+(1−x)Te₂O glass system as a function of the x value and during temperature-induced crystallisation processes. The results of Raman measurements support the hypothesis.     

Two different synthetic routes involving the reaction of dodecylamine or nicotinamide with crystalline lamellar vanadylphosphate

The crystalline lamellar compound, VOPO₄·2H₂O, was employed as host to react with a long monoamine aliphatic chain, dodecylamine, and with an aromatic derivative, nicotinamide, using two distinct synthetic approaches: in the solid state and from aqueous solution. The resulting compounds were characterized by elemental analysis, infrared spectroscopy, X-ray diffractometry, thermogravimetry and SEM microscopy. From X-ray diffraction patterns, the calculated increase of the interlayer distance was 2.05 nm for the dodecylamine, containing product, which is in agreement with the intercalation process, and was observed with both reactions routes. On the contrary, the guest nicotinamide molecule was not inserted into the lamellar cavity. The reaction in the solid state caused a small modification of the phosphate microstructure, in comparison with the solution procedure. The aliphatic amine molecules are oriented in a bilayer inside the host cavity by forming an angle of 67° with the inorganic lamella. The thermal decomposition for both series of synthesized compounds did not demonstrate any difference in behavior.     

Small Values of the Maximum for the Integral of Fractional Brownian Motion

We consider the integral of fractional Brownian motion (IFBM) and its functionals ξ _T on the intervals (0,T) and (?T,T) of the following types: the maximum M _T , the position of the maximum, the occupation time above zero etc. We show how the asymptotics of P(ξ _T <1)=p _T ,T→∞, is related to the Hausdorff dimension of Lagrangian regular points for the inviscid Burgers equation with FBM initial velocity. We produce computational evidence in favor of a power asymptotics for p _T . The data do not reject the hypothesis that the exponent θ of the power law is related to the similarity parameter H of fractional Brownian motion as follows: θ=?(1?H) for the interval (?T,T) and θ=?H(1?H) for (0,T). The point 0 is special in that IFBM and its derivative both vanish there.