A new convenient synthesis of trisubstituted 1,3-dioxole-4-carboxylates from methyl 2-diazo-3-oxobutyrate and aldehydes

The interaction between methyl 2-diazo-3-oxobutyrate and the carbonyl group of aliphatic, aromatic, and α,β-unsaturated aldehydes under bis(hexafluoroacetoacetonato)copper(II) catalysis furnishes 1,3-dioxole-4-carboxylates in preparatively useful yields. The apparent 1,3-dipolar cycloaddition reaction of the metal carbene complex is remarkably free of competing processes.     

Simple upper bounds for partition functions

We tweak Siegel’s method to produce a rather simple proof of a new upper bound on the number of partitions of an integer into an exact number of parts. Our approach, which exploits the delightful dilogarithm function, extends easily to numerous other counting functions. This work was supported by PSC/CUNY Research Awards (# 67261-00 36 and # 68327-00 37).     

Treatment of advanced divertor configurations in the flux-coordinate independent turbulence code GRILLIX

Advanced divertor configurations modify the magnetic geometry of the divertor to achieve a combination of strong magnetic flux expansion, increased connection length and higher divertor volume—to improve detachment stability, neutral/impurity confinement and heat-channel broadening. In this paper, we discuss the modification of the flux-coordinate independent (FCI) turbulence code GRILLIX to treat generalized magnetic geometry, to allow for the investigation of the effect of magnetic geometry on turbulent structures in the edge and scrape-off layer (SOL). The development of grids and parallel operators from numerically defined magnetic equilibria is discussed, as is the application of boundary conditions via penalization, with the finite-width method generalized to treat complex non-conformal boundaries. Initial testing of hyperbolic (advection) and parabolic (diffusion) test cases are presented for the Snowflake scenario.     

Stress-optical analysis of fluids

Summary Recent advances in Rheology have emphasized the necessity of measuring the stress distribution in flowing viscoelastic fluids which is qualitatively different from the one in Newtonian liquids. The use of flow-birefringence for this purpose has advantages. The concept of the stress-optical coefficient, well known in the stress optical analysis of solids, can be also applied to fluid flow. The extinction angle determines the recoverable shear strain,s a parameter in the flow of viscoelastic fluids. This would mean that mechanical and optical flow phenomena are caused primarily by stresses, not by the rate of shear. Experimental results presented confirm this postulate.     

Operators that attain their minima

In this paper we study the theory of operators on complex Hilbert spaces, which attain theirminima in the unit sphere. We prove someimportant results concerning the characterization of the N*, and also AN* operators, see respectively Definition 1.1 and Definition 1.4. The injective property plays an important role in these operators, and shall be established by these classes.     

Revisiting Rademacher's Formula for the Partition Function p(n

We provide a new proof of Rademacher's celebrated exact formula for the partition function. Along the way we present a simple treatment of an integral which is ubiquitous in the theory of nonanalytic automorphic forms.     

Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey

A method for solving the inverse kinematic problem of determining the velocity characteristic of a medium from a vertical seismic survey, is proposed. It is based on the combined use of the eikonal equation and spline methods of approximation for multivariable functions. The problem is solved by assuming a horizontally stratified medium; no assumptions about the number of layers and their thickness are made. First, using the data of the first arrival times of the seismic signal from several shotpoints, which are registered by detectors located in the vertical borehole, a spline approximating the function of first arrival time of the signal from source points to any point in the Earth subsurface is constructed. Then with the help of the eikonal equation, the characteristic of the medium around the borehole is determined. Numerical experiments on the model and the real data show high efficiency of the proposed method.     

Fe- and Cu-oxides supported on γ-Al2O3 as catalysts for the selective catalytic reduction of NO with ethanol. Part I: catalyst preparation,characterization, and activity

Fe- and Cu-oxides supported on γ-alumina (γ-Al₂O₃; metal loading of 3 mass %) were investigated as alternative catalysts to the conventional Ag-based system in the selective catalytic reduction of NO with ethanol (EtOH-SCR). The catalysts were characterized by elemental analysis, N₂ sorption, X-ray diffraction, temperature-prgrammed desorption of NH₃, temperature-programmed reduction with H2, diffuse reflectance UV-VIS (DR-UV-VIS) spectroscopy, and compared with 3 mass % Ag/γ-Al₂O₃ as a reference catalyst. Catalytic experiments were carried out between 423 K and 773 K in the steady state and by temperature-programmed surface reaction (TPSR) experiments. For all catalysts, the highest NO conversion (900 ppm (ppm = parts of the mixture component per million parts of all mixture components) NO, 900 ppm EtOH, 0.5 vol. % H₂O, 4 vol. % O₂ in He) was found at 573 K. While 84 % of NO were converted over the Ag-based catalysts, only 20–60 % NO conversion was observed for the Fe- and Cu-containing catalysts. Total oxidation of ethanol as an unwanted side reaction occurs over 3 mass % Cu on γ-Al₂O₃ already at 573 K, whereas the highest activity of 3 mass % Fe on γ-Al₂O₃ for this conversion was reached at 743 K. For lower temperatures, partial oxidation of ethanol leads to organic by-products which can act as active intermediates in EtOH-SCR. TPSR experiments show that ethanol reacts over both the Fe- and the Cu-based catalysts to organic by-products, such as ethene or acetaldehyde, which affect the EtOH-SCR reaction.