Error estimates in the determination of rigid body displacements in protein crystals

We report the estimation of random errors in the refinement of the rigid body displacements of the -helices of the enzyme 6-phosphogluconate dehydrogenase. Least-squares refinement of the TLS parameters of the helices has been carried out using X-ray reflection data of 2.1 Å resolution, resulting in anR-factor of 19.5%. Standard deviations were estimated from the normal matrix. The results show that the translational mean-square displacements of nearly all the helices are significant at this resolution. However the libration parameters are only significant when the helices have at least four turns. Screw-rotation tensor values cannot be determined at this resolution.     

Luikov equations applicable to sublimation-drying

Present paper presents a derivation of Luikov equations applicable to sublimation-drying. The physical situation and transfer mechanism are elucidated clearly. The coefficients appearing in Luikov equations are given in a more explicit way. Some formulation mistakes in recent publications are indicated.

---

Anwendung der Luikov-Gleichungen auf die Sublimationstrocknung

Zusammenfassung Die Untersuchung bezieht sich auf eine Ableitung der Luikov-Gleichungen, mittels deren sich der Vorgang der Sublimationstrocknung analysieren läßt. Physikalische Anfangssituation und Austauschmechanismen werden klar herausgestellt und die in den Luikov-Gleichungen auftretenden Koeffizienten in expliziter Weise angegeben. Ferner erfolgt Hinweis auf Formulierungsfehler in jüngeren Veröffentlichungen.

---

Nomenclature C M _v/V _f, concentration of vapor, kg/m³ - c _pv specific heat of vapor at constant pressure, J/kg K - c _pw specific heat of adsorbed water at constant pressure, J/kg K - c _s specific heat of solid skeleton, J/kg K - C _s M _s/V _f, concentration of solid skeleton, kg/m³ - C _w M _w/V _f, concentration of adsorbed water, kg/m³ - f V _w/V _f, volumetric fraction of adsorbed water - j _F mass flux of vapor by diffusion (Fick) transfer, kg/m² s - j _D mass flux of vapor by filtration (Darcy) transfer, kg/m² s - j _v total mass flux of vapor, kg/m² s - k permeability, m² - M _s mass of solid skeleton, kg - M _v mass of vapor in pores, kg - M _w mass of adsorbed water, kg - P pressure, Pa - q heat flux, W/m² - R gas constant, J/kg K - T temperature, K - V _f volume of the framework of porous medium, m³ - V _v volume of vapor in porous medium, m³ - V _w volume of the absorbed water, m³ Greek symbols /(c _p), effective thermal diffusivity, m²/s - _m effective vapor diffusivity in porous medium, m²/s - _p R T /, Luikov pressure diffusivity, m²/s - +f, porosity of the porous medium - effective thermal conductivity of porous body, W/m K - dynamic viscosity of vapor, kg/m s - kinematic viscosity, m²/s - Ck/=k/, Luikov filtration motion coefficient, s - V _v/V _f, volumetric fraction of vapor - density of absorbed water, kg/m³ - (c _p) M _v c _pv+M _s c _s+M _w c _pw /V _f=Cc _pv+C _s c _s+fc _pw, effective product of density and specific heat of humid porous body, J/m³K     

Diffusion mit überlagerter reibungsbehafteter Strömung

Zusammenfassung Es wird eine allgemeine Differentialgleichung für den Massen- oder Mengenstrom im Fall einer Überlagerung von Diffusion und reibungsbehafteter Strömung, d.h. bei gleichzeitiger Änderung des Gesamtdruckes und der Partialdrücke über den Weg, für den stationären (und quasistationären) Fall abgeleitet. Die sich ergebenden gekoppelten Differentialgleichungen können näherungsweise analytisch gelöst werden.Bei den Überlagerungen wurde allein von Gas-(Fickscher) Diffusion ausgegangen. Unberücksichtigt blieben auch sekundäre Diffusionströme, so durch Druck- u. Thermodiffusion und in anderen Kraftfeldern. Damit wird an zwei Beispielen — einseitige Diffusion (Verdunstung) und Adsorption in porösen Stoffen — gezeigt, daß die Annahme reibungsfreier konvektiver Ausgleichsströmungen bei der Diffusion in porösen Körpern mit engen Poren nicht zulässig ist. Vielmehr treten am Ort der Entstehung des Diffusionsstromes (Verdunstungsspiegel) bzw. in der Adsorptionsfront Änderungen des Gesamtdruckes auf, die zu zusätzlichen Strömungen führen und Rückwirkungen auf den Massenstrom besitzen. Neben der Höhe der Konzentrationen ist für die Größe des Effektes allein das Verhältnis der Transportkoeffizienten für Strömung und Diffusion maßgebend. Der Effekt macht sich bei hohen Konzentrationen der diffundierenden Komponente deutlich bemerkbar, bei niedrigen ist er — wie zu erwarten — zu vernachlässigen.

---

Diffusion of superimposed frictional flow

A general differential equation for a mass and volume flow will be derived for the case of diffusion superimposed frictional flow, that means, at simultaneously varying total and partial pressures along the path, for the stationary and quasi-stationary states. The resulting coupled differential equations can be analytically treated for an approximate solution.The conception was based entirely upon (Fick's) gas diffusion. Secondary diffusional flows were neglected, like pressure and thermal diffusions, or those caused by other potential gradients. Two examples, the diffusion through a stagnant gas film (evaporation by diffusion), and the adsorption in porous material exemplify that assuming a frictionless convective arbitration flow is invalid in the case of diffusion within porous structures of narrow pores. Adequately, at the source of the diffusional flow (mirror of diffusional evaporation), respectively within the adsorption front, changes in total pressure arise, causing additional flows acting upon the mass flow. The scope of the effect depends entirely upon the extents of the concentration and the ratio of transport coefficients of the flow and diffusion. The effect increases noticeably at elevated concentration of the diffusing components, while it gets negligible at lower concentration, as to be expected.

---

Formelzeichen c Konzentration [kmol/m³] - d _p Porendurchmesser - bezogener Diffusionsstrom - f Querschnittsfläche - bezogener Strom - M relative Molmasse - Mengenstromdichte - P Druck - R _a Radius eines kugelförmigen Partikels - s Diffusionsweg - t Zeit - v Geschwindigkeit des konv. Stroms - w _Fr Frontgeschwindigkeit - x Variable des Weges - X Beladung des Adsorbens [kmol/kg] - Z, z Variable, s. Gl. (23), Gl. (29) Griechische Buchstaben (X) Kapazitätsfaktor - Verhältnis der Transportkoeffizienten _lam/ _D - Diffusions- bzw. äquivalenter Transportkoeffizient - freie Weglänge - dynamische Zähigkeit - Tortuositätsfaktor - Dichte - Lage der Adsorptionsfront - Porosität des Adsorbens Indices o Bezugsgröße bzw. vorgegebener Wert der Größe im Gas - e einseitig - D Dampf, diffundierende Komponente - L Luft, aufnehmendes Gas - lam laminare Strömung - s Feststoff - in der Adsorptionsfront     

Growth functions for semi-regular tilings of the hyperbolic plane

This paper studies the growth function, with respect to the generating set of edge identifications, of a surface group with fundamental domainD in the hyperbolic plane ann-gon whose angles alternate between /p and /q. The possibilities ofn,p andq for which a torsion-free surface group can have such a fundamental polygon are classified, and the growth functions are computed. Conditions are given for which the denominator of the growth function is a product of cyclotomic polynomials and a Salem polynomial.This work was supported in part by NSF Research Grants.     

Inner Derivations and Primal Ideals of C*-Algebras

Let A be a C*-algebra. For a A let D(a, A) denote the innerderivation induced by a, regarded as a bounded operator on A,and let d(a, Z(A)) denote the distance of a from Z(A), the centreof A. Let K(A) be the smallest number in [0, ] such that d(a,Z(A)) K(A)||D(a, A)|| for all a A. It is shown that if A isnon-commutative and has an identity then either K(A) = , or K(A) = 1 / 3, or K(A) 1. Necessaryand sufficient conditions for these three possibilities aregiven in terms of the primitive and primal ideals of A. If Ais a quotient of an AW*-algebra then K(A) . Helly's Theorem is used to show that if A is aweakly central C*-algebra then K(A) 1.     

OR Utilization in Nigeria: A Sample Survey

The study presents the results of a mail survey on the utilization of Operational Research (OR) techniques in tackling complex operational problems in the private sector in Nigeria. The survey was mailed to OR practitioners in nearly 1000 companies and was aimed at determining the familiarity with, and usage of, OR techniques, background of OR personnel, degree of computer usage, application areas, implementation and contributions of OR, problems attendant in using OR techniques, and future prospects for OR usage.     

Minimax risk overl p -balls forl p -error

Summary Consider estimating the mean vector from dataN _n (, ² I) withl _q norm loss,q1, when is known to lie in ann-dimensionall _p ball,p(0, ). For largen, the ratio of minimaxlinear risk to minimax risk can bearbitrarily large ifp. Obvious exceptions aside, the limiting ratio equals 1 only ifp=q=2. Our arguments are mostly indirect, involving a reduction to a univariate Bayes minimax problem. Whenp, simple non-linear co-ordinatewise threshold rules are asymptotically minimax at small signal-to-noise ratios, and within a bounded factor of asymptotic minimaxity in general. We also give asymptotic evaluations of the minimax linear risk. Our results are basic to a theory of estimation in Besov spaces using wavelet bases (to appear elsewhere).     

Strong converse inequality for Kantorovich polynomials

For the Kantorovich polynomial approximationK _n (f, t), 1<p≤∞, we prove that, for somem, This equivalence includes a strong converse inequality of type B.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

The invertibility of the product of unbounded Toeplitz operators

In this note I give necessary and sufficient conditions on outer functionsf andg for the operator to be bounded and invertible on H². I also discuss the relationship of this question to two open questions in operator theory and weighted norm inequalities.