Inverse and saturation theorems for linear combination of modified Baskakov operators

In this paper, we consider linear combinations of modified Baskakov operators. By use of several lemmas, we obtain the inverse theorem (Theorem 1.1) and the saturation (Theorem 1.2) for those linear combinations.     

Synthesis and Reactions of Some New Pyrrolylfuro[2,3‐d]Pyrimidines and Pyrrolopyrazinofuropyrimidines

5‐Amino‐4‐methyl‐2‐phenyl‐6‐substitutedfuro[2,3‐d]pyrimidines ( 2a‐c ) were reacted with 2,5‐dimethoxytetrahydrfuran to afford the pyrrolyl derivatives 3a‐c . Compound 3a was chosen as intermediate for the synthesis of poly fused heterocycles incorporated furopyrimidines moiety 4–11 . Some of the synthesized compounds were screened for their antibacterial and antifungal activities.     

Germanium growth on Br-terminated Si(1 0 0)

The consequences of Ge deposition on Br-terminated Si(1 0 0) were studied with scanning tunneling microscopy at ambient temperature after annealing at 650 K. One monolayer of Br was sufficient to prevent the formation of Ge huts beyond the critical thickness of 3 ML. This is possible because Br acts as a surfactant whose presence lowered the diffusivity of Ge adatoms. Hindered mobility was manifest at low coverage through the formation of short Ge chains. Further deposition resulted in the extension and connection of the Ge chains and gave rise to the buildup of incomplete layers. The deposition of 7 ML of Ge resulted in a rough surface characterized by irregularly shaped clusters. A short 800 K anneal desorbed the Br and allowed Ge atoms to reorganize into the more energetically favorable “hut” structures produced by conventional Ge overlayer growth on Si(1 0 0).     

Sequential Importance Sampling Algorithms for Dynamic Stochastic Programming

This paper gives a comprehensive treatment of EVPI-based sequential importance sampling algorithms for dynamic (multistage) stochastic programming problems. Both theory and computational algorithms are discussed. Under general assumptions it is shown that both an expected value of perfect information (EVPI) process and the corresponding marginal EVPI process (the supremum norm of the conditional expectation of its generalized derivative) are nonanticipative nonnegative supermartingales. These processes are used as importance criteria in the class of sampling algorithms treated in the paper. When their values are negligible at a node of the current sample problem scenario tree, scenarios descending from the node are replaced by a single scenario at the next iteration. On the other hand, high values lead to increasing the number of scenarios descending from the node. Both the small sample and asymptotic properties of the sample problem estimates arising from the algorithms are established, and the former are evaluated numerically in the context of a financial planning problem. Finally, current and future research is described. Bibliography: 49 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 94–129.     

Quantum General Relativity,Torsion and Uncertainty Relations

It is shown that in gravitational theories with torsion one is led to commutation rules corresponding to Landau-Peierls type uncertainty relations.     

Estimating a reduced rank regression model for non-normal variables

A method using third order moments for estimating the regression coefficients as well as the latent state scores of the reduced-rank regression model when the latent variable(s) are non-normally distributed is presented in this paper. It is shown that the factor analysis type indeterminacy of the regression coefficient matrices is eliminated. A real life example of the proposed method is presented. Differences of this solution with the reduced-rank regression eigen solution are discussed.     

Stationary turbulent closure via the Hopf functional equation

Exact closed-form solutions are exhibited for the Hopf equation for stationary incompressible 3D Navier-Stokes flow, for the cases of homogeneous forced flow (including a solution with depleted nonlinearity) and inhomogeneous flow with arbitrary boundary conditions. This provides an exact method for computing two- and higher-point moments, given the mean flow.