Solution of a class of stochastic linear-convex control problems using deterministic equivalents

In this paper, we identify a new class of stochastic linearconvex optimal control problems, whose solution can be obtained by solving appropriate equivalent deterministic optimal control problems. The term linear-convex is meant to imply that the dynamics is linear and the cost function is convex in the state variables, linear in the control variables, and separable. Moreover, some of the coefficients in the dynamics are allowed to be random and the expectations of the control variables are allowed to be constrained. For any stochastic linear-convex problem, the equivalent deterministic problem is obtained. Furthermore, it is shown that the optimal feedback policy of the stochastic problem is affine in its current state, where the affine transformation depends explicitly on the optimal solution of the equivalent deterministic problem in a simple way. The result is illustrated by its application to a simple stochastic inventory control problem.This research was supported in part by NSERC Grant A4617, by SSHRC Grant 410-83-0888, and by an INRIA Post-Doctoral Fellowship.     

C-terminal processing of yeast Spt7 occurs in the absence of functional SAGA complex

Background  

Spt7 is an integral component of the multi-subunit SAGA complex that is required for the expression of ~10% of yeast genes. Two forms of Spt7 have been identified, the second of which is truncated at its C-terminus and found in the SAGA-like (SLIK) complex.     

Verlauf der Fluidtemperaturen im Querstromrohrbündel

A new analytical method is presented for the determination of temperature distribution and effectiveness of heat transfer in different cross-flow arrangements. As an improvement over the known analytical solutions simplified energy balance equations are used. This simplification consists only in their notation but not in representation of the exact energy balance. The demanded accuracy of the thermal analysis is achieved by proper selection of a mean value of fluid temperature outside the tube. For each tubei in the bundle a mean value ? _i of the dimensionless fluid temperature outside the tube is introduced according to $$\vartheta _i = \omega \vartheta _{i + {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + (1 - \omega )\vartheta _{i - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} $$ where ? _i?1/2 and ? _i+1/2 are the local temperatures in front and behind thei-th tube, respectively. With symbol ω a weight coefficient is denoted $$\omega = {1 \mathord{\left/ {\vphantom {1 {(1 - e^{ - NTU_{{ \bot \mathord{\left/ {\vphantom { \bot n}} \right. \kern-\nulldelimiterspace} n}} } )}}} \right. \kern-\nulldelimiterspace} {(1 - e^{ - NTU_{{ \bot \mathord{\left/ {\vphantom { \bot n}} \right. \kern-\nulldelimiterspace} n}} } )}} - {n \mathord{\left/ {\vphantom {n {NTU_ \bot }}} \right. \kern-\nulldelimiterspace} {NTU_ \bot }}$$ The number of tube rows in the bundle isn and the number of transfer units of the outside stream is NTU_⊥. Through the introduction of the weight coefficient ω, the mathematical operations related to calculation of the temperature field are radically simplified. This enabled the development of the procedure, valid for three codirected cross-flow arrangements (Fig. 1) and any numbern of the rows.     

Eine Methode der thermischen Berechnung von Gegen- und Gleichstrom-Spiralwärmeaustauschern

Zusammenfassung Eine neue Methode zur thermischen Berechnung wird entwickelt, die die Berücksichtigung der tatsächlichen Stromführung erlaubt. Es wird eine spezielle Spirale als Erzeugende der zylindrischen Oberfläche im geometrischen Modell eines Spiralwärmeaustauschers (SWA) betrachtet. Anstelle einer archimedischen Spirale wird die Erzeugende durch eine Spirale dargestellt, die auf der Basis der Evolvente eines gleichseitigen regelmäßigen Vielecks entsteht. Das Ergebnis ist, daß der SWA hypothetisch in viele Sektionen aufgeteilt ist. Die Folge dieser Änderung sind konstante Koeffizienten in einem linearen gewöhnlichen Differentialgleichungssystem. Die Austrittstemperaturen werden aus diesem System mit Hilfe der Laplace-Transformierten für jede Sektion getrennt bestimmt und durch Randbedingungen miteinander verknüpft.

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Method of thermal calculation for rating countercurrent and cocurrent spiral heat exchangers

A new method of thermal calculation is developed which takes the actual flow arrangement into account. A special spiral is considered as a trace of the cylindrical surface in the geometrical model of a Spiral Heat Exchanger (SHE). Instead of an Archimedic spiral, the trace is formed on the other spiral, which is drawn by involution of a regular manysided figure. As a result SHE is hypothetically divided into many sections. The consequences of this change are constant coefficients in a linear ordinary differential equation system. The sought temperatures are determined from this system by using Laplace's transform for each section separately and coupled by boundary conditions.

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Bezeichnungen b, b Kanalbreite (Kanalhöhe),b gemessen entlang dem Radius, der vom Anfang der Spirale ausgeht, undb gemessen senkrecht zu einer der beiden den Kanal begrenzenden Kurven - C _ijl Konstante Gl. (13) - E Einheitsmatrix - F(), F _i () verallgemeinerte Temperaturfunktion (Vektor und seine Komponenten) - Laplace-Transformierte vonF - h ₀ Höhe des SWA - k Wärmedurchgangskoeffizient - L Operator der Laplace-Transformation - m ₀ Anzahl der Seiten des regelmäßigen Vielecks - M Matrix im Gleichungssystem (8), Gl. (9) - n Anzahl der Kanäle - r, =r/b Radius, reduzierter Radius, reduzierter Krümmungs-radius, Koeffizienten im Gleichungssystem (6), (7) - r _m Radiusvektor der Kanäle im Sektorm mit den Komponenten ₁= ₁/b, ₂=r ₂/b ₃=r ₃/b, ..., _m =r _m /b - R = _I / _II Quotient der WärmekapazitätenW - s Bildvariable der Laplace-Transformation - t Fluidtemperatur - dimensionslose Temperatur des Fluids I - , Parameter im MatrixM (), Gl. (9) - dimensionslose Temperatur des Fluids II - Radius der archimedischen Spirale - Winkel - , geometrische Koordinaten - dimensionslose Temperaturänderungen (Betriebscharakteristik des Wärmeaustauschers) - Anzahl der Ubertragungseinheiten - = verallgemeinerter Winkel - )I betr. Fluid I - )II betr. Fluid II - ein betr. Eintritt des Fluids Verzeichnis der Abkürzungen SWA Spiralwärmeaustauscher - S-A archimedische Spirale - S-ERV Spirale aus der Evolvente eines regelmäßigen Vielecks     

Syntheses and characterizations of bis(trialkoxysilyl)oligoimides. II. Syntheses and characterizations of fluorinated crosslinkable oligoimides with low refractive indices

Novel crosslinkable fluorinated oligoimides were prepared in two steps. The first involved the synthesis of oligoimides terminated with nadic or allylic double bonds, and the second step was materialized either by a radical addition of mercaptotrialkoxysilane derivatives onto nadic double bonds or a hydrosilylation reaction of hydrogenotrialkoxysilane derivative onto allylic double bonds. Three kinds of crosslinking of the trialkoxysilane end groups were studied. The first kind entailed a thermal self‐crosslinking of trialkoxysilane groups. The second process of crosslinking incorporated a bicomponent system—the crosslinked agent was 1,1,1‐tris(4‐hydroxyphenyl)ethane (TRIOH). The trialkoxysilane groups reacted with the hydroxyl–phenol groups of TRIOH to give thermally stable phenoxysilane bonds as well as a crosslinking network. The last method was also a bicomponent system; the oxalic acid was added into an oligoimide solution where by thermal treatment water was created. The water molecules hydrolyzed the trialkoxysilane groups into silanol groups that polycondensed into a crosslinked network following a sol–gel process. The mechanism of the different crosslinking reactions was investigated by Fourier transform infrared spectroscopy and solid‐state ²⁹Si NMR. The self‐crosslinked material prepared from precursor α,ω‐trimethoxysilyl fluorinated oligomer (M_n = 5500 g · mol^?1) exhibited a 10 wt % loss temperature under air higher than 420 °C and a low birefringence (Δn = 0.008) at 1.300 μm. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2602–2619, 2001     

On the role of the pairing modes in the (h92 ⊗ 3−) multiplet of 209Bi

A unified picture of the low lying states of ²⁰⁹Bi is attempted in terms of surface and pairing vibrations as well as particle and hole degrees of freedom.     

Spurious Center of Mass Effects in Electroweak Decays

The microscopic treatment of the spurious motion of the center of mass in nuclear many-body systems is reviewed. In this talk we present and compare the results of using the counterterms which are needed to fulfill the translational and Galilean invariances, and those obtained by using collective variables. The formalism is applied to the calculation of matrix elements of electroweak operators, as those which are active in the (^-, e^-) conversion process.