Irrational rotations motivate measurable sets

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Irrational rotations motivate measurable sets

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Evaluating practical measurements of fire-induced vent flows with stereoscopic PIV

Stereoscopic particle image velocimetry (SPIV) was applied to a fire-induced doorway flow to provide the velocity field for computations of the mass flow rate of air into an enclosure. For a flow of uniform temperature and concentration, the technique met all of the requirements to provide the best estimate of the mass flow rate. Simultaneous measurements of vertical distributions of velocity and temperature were also conducted with conventional vent flow techniques, bi-directional probes and thermocouples. Correction factors for mass flow rate computations using the conventional techniques were determined based on comparisons to the SPIV results. An average correction factor of unity was determined for the bi-directional probe technique thus further confirming the utilization of velocity distributions acquired using the technique in mass flow rate computations. An average correction factor of 0.69 was determined for mass flow rates computed from vertical temperature distributions inside and outside the enclosure. This agrees with average correction factors determined in previous studies. The results from the present study suggest that the conventional techniques, which are practical and affordable for routine fire testing, may be applied with greater confidence for fires up to 500 kW.     

On the Hartshorne-Speiser-Lyubeznik theorem about Artinian modules with a Frobenius action

Let be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring (associated to and the Frobenius homomorphism , in the indeterminate ) that is both -torsion and Artinian over .

     

Fermentation of “Quick Fiber” produced from a modified corn-milling process into ethanol and recovery of corn fiber oil

Approximately 9% of the 9.7 billion bushels of corn harvested in the United States was used for fuel ethanol production in 2002, half of which was prepared for fermentation by dry grinding. The University of Illinois has developed a modified dry grind process that allows recovery of the fiber fractions prior to fermentation. We report here on conversion of this fiber (Quick Fiber [QF]) to ethanol. QF was analyzed and found to contain 32%wt glucans and 65%wt total carbohydrates. QF was pretreated with dilute acid and converted into ethanol using either ethanologenic Escherichia coli strain FBR5 or Saccharomyces cerevisiae. For the bacterial fermentation the liquid fraction was fermented, and for the yeast fermentation both liquid and solids were fermented. For the bacterial fermentation, the final ethanol concentration was 30 g/L, a yield of 0.44 g ethanol/g of sugar(s) initially present in the hydrolysate, which is 85% of the theoretical yield. The ethanol yield with yeast was 0.096 gal/bu of processed corn assuming a QF yield of 3.04 lb/bu. The residuals from the fermentations were also evaluated as a source of corn fiber oil, which has value as a nutraceutical. Corn fiber oil yields were 8.28%wt for solids recovered following prtetreatment.     

Synthesis and crystal structures of two novel 3,4,5- trimethoxyphenyl derivatives from (Z)-1-[(2′,3′-dinitro-4′-methoxy)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl] ethene

The title compounds, (Z)-1-[(2′,4′-dimethoxy-3′-nitro)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl]ethene, C₁₉H₂₁O₇N (I), and 2-amino-4-methyl-6-(3,4,5-trimethoxy-phenyl)-pyrimidine, C₁₄H₁₇O₃N₃ (II), were obtained unexpectedly from a reaction involving (Z)-1-[(2′,3′-dinitro-4′-methoxy)-phenyl]-2-[(3″,4″,5″-trimethoxy)-phenyl]ethene (IV). The molecular structures of these compounds were obtained by single-crystal X-ray diffraction. Crystallization of I occurs in the centrosymmetric monoclinic space group P2₁/c (No. 14) with a=7.7311(5), b=19.9239(13), c=11.5725(8); and β=92.193(3) and Z=4. Crystallization of II occurs in the centrosymmetric monoclinic space group C2/c (No. 15) with a=21.296(2), b=6.8963(7), c=20.001(2); and β=114.121(6) and Z=8. Details of the synthesis and the structural characterization of the title compounds are presented and discussed.     

The Dirichlet problem for the minimal surface equation in non-regular domains

Summary In this paper we study the Dirichlet problem for the minimal surface equation in a open set Ω without any assumption about the regularity of ϖΩ. We prove an existence theorem using only the pseudoconvexity of Ω.

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Riassunto In questo lavoro studiamo il problema di Dirichlet per l'equazione delle superfici minime in un aperto Ω diR ⁿ sulla cui frontiera non si fa nessuna ipotesi di regolarità. Si ottiene un teorema di esistenza usando la sola pseudoconvessità di Ω.

     

Fermat's theorem as a corollary to the multinomial theorem

The multinomial theorem and a basic property of multinomial coefficients yield a way of counting the number of chains of coloured beads of a fixed length where each colour can be used repeatedly. This coupled with a simple counting argument forms a concise proof of Fermat's theorem.