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AIMS Pharmacokinetic equations, which relate different parameters of a single individual, are often applied to reported mean parameter-values, with the aim of estimating the mean value of an unreported parameter. Due to population heterogeneity this approach generally leads to errors in their estimation. We provide details of this source of error. Our aim is to take into account the effects of population heterogeneity in commonly used pharmacokinetic models. This provides improved estimates and knowledge of the concentration of a drug in the plasma over time. METHODS Inequalities and approximations for corrected mean estimates are derived. These results are then applied to published clinical-trial data to illustrate their accuracy in practical situations. RESULTS By using mean values within the pharmacokinetic equations for a single individual, we show that estimates of mean parameter values, for a variety of dosing regimens, generally have errors. Using published clinical trial data, we show that such estimates can systematically deviate from the exact mean value by up to 19%. We provide analytical results, which amount to inequalities when there are systematic deviations from exact results, along with approximate results that improve the accuracy of estimates. CONCLUSIONS Medical, pharmacy and nursing students should be educated about errors and inequalities that can arise when transforming reported mean values of pharmacokinetic parameters into the mean values of parameters that are required, but not reported. Using approximate results, that correct estimates of mean parameter values so that they more accurately reflect actual average values, may provide a practical solution.

We look at several saturation problems in complete balanced blow-ups of graphs. We let denote the blow-up of H onto parts of size n and refer to a copy of H in as partite if it has one vertex in each part of . We then ask how few edges a subgraph G of can have such that G has no partite copy of H but such that the addition of any new edge from creates a partite H. When H is a triangle this value was determined by Ferrara, Jacobson, Pfender, and Wenger in [5]. Our main result is to calculate this value for when n is large. We also give exact results for paths and stars and show that for 2-connected graphs the answer is linear in n whilst for graphs that are not 2-connected the answer is quadratic in n. We also investigate a similar problem where G is permitted to contain partite copies of H but we require that the addition of any new edge from creates an extra partite copy of H. This problem turns out to be much simpler and we attain exact answers for all cliques and trees.

We summarize life and work on nonideal plasma thermodynamics of the late Fazylkhan Baimbetov. Analyzing Baimbetovs method of pseudo potentials we develop several extensions. First we optimize the parameter choice by comparing with recent exact results for thermodynamics. We compare the result of the pseudopotential method with the available exact results, check the formulae for stability and show generalizations of the pseudo potentials and extensions for higher densities. In particular we demonstrate how the introduction of the full Kelbg potential and the Debye-Kaklyugin methods of suppression of high plasma wave modes allows to include higher orders in density up to Wigner-type lattice-like contributions. We show how a new pseudopotential for the free charges can be combined with HNC integral equations. In conclusion we find that the analytical results obtained by Baimbetovs method are, with some improvements, in good overall agreement with available exact results. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

SUMMARY Many studies in different research fields use lattice models to investigate the mechanical behavior of materials. Full lattice calculations are often performed to determine the influence of localized microscale phenomena on large-scale responses but they are usually computationally expensive. In this study the quasicontinuum (QC) method (Phil. Mag. A 1996; 73:1529–1563) is extended towards lattice models that employ discrete elements, such as trusses and beams. The QC method is a multiscale approach that uses a triangulation to interpolate the lattice model in regions with small fluctuations in the deformation field, while in regions of high interest the exact lattice model is obtained by refining the triangulation to the internal spacing of the lattice. Interpolation ensures that the number of unknowns is reduced while summation ensures that only a selective part of the underlying lattice model must be visited to construct the governing equations. As the QC method has so far only been applied to atomic lattice models, the existing summation procedures have been revisited for structural lattice models containing discrete elements. This has led to a new QC method that makes use of the characteristic structure of the considered truss network. The proposed QC method is, to the best of the authors’ knowledge, the only QC method that does not need any correction at the interface between the interpolated and the fully resolved region and at the same time gives exact results unlike the cluster QC methods. In its present formulation, the proposed QC method can only be used for lattice models containing nearest neighbor interactions, but with some minor adaptations it can also be used for lattices with next-nearest neighbor interactions such as atomic lattices. Copyright 2011 John Wiley & Sons, Ltd.

Total Transfer Capability (TTC) should be pre-determined in order to estimate Available Transfer Capability (ATC). Typically, TTC is determined by considering three categories; voltage, stability, and thermal limits. Among these, thermal limits are treated mainly in this paper on the evaluation of TTC due to the relatively short transmission line length of Korea Electric Power Corporation (KEPCO) system. This paper presents a new approach to evaluate the TTC using the Dynamic Line Rating (DLR) for the thermal limit. Since the approach includes not only traditional electrical constraints but also real-time environmental constraints, this paper obtains more cost-effective and exact results. A case study using KEPCO system confirms that the proposed method is useful for real-time operation and the planning of the electricity market. Copyright © 2010 John Wiley & Sons, Ltd.

Much attention has been given to the problem of predicting future observations for some individual within a random coefficient regression (RCR) model, using the previous observations on that individual as well as the information from the rest of the data material. In this paper, the literature on this subject is critically reviewed and new methods of linear prediction are proposed for the general RCR model. Exact results are derived for the mean squared errors of some predictors in a special case, but this is not possible in the general RCR model when its parameters are not known. In this model, the old and new predictors are compared in a simulation study, and further illustrated by prediction in a medical data material.

The problem of determining the optimal warranty period, assumed to coincide with the manufacturer's lower specification limit for the lifetime of the product, is addressed. It is assumed that the quantity sold depends via a Cobb–Douglas-type demand function on the sale price and on the warranty period, and that both the cost incurred for a non-conforming item and the sale price increase with the warranty period. A general solution is derived using Response Modeling Methodology (RMM) and a new approximation for the standard normal cumulative distribution function. The general solution is compared with the exact optimal solutions derived under various distributional scenarios. Relative to the exact optimal solutions, RMM-based solutions are accurate to at least the first three significant digits. Some exact results are derived for the uniform and the exponential distributions. Copyright © 2006 John Wiley & Sons, Ltd.

Aus der Reihe von verschiedenen bepflanzbaren, dauerhaften Sicherungen von Gelandeeinschnitten wird eine neuartige Lamellen-Stutzwand beschrieben. Sie zeichnet sich dadurch aus, das sie aus horizontalen, im Erdreich verankerten Stahlbetongurten besteht, in deren Schutz die endgultige Aushubsohle erreicht wird, und daran spater von unten nach oben fortschreitend, befestigten Fertigteil-Lamellen. Die Verankerungen bestehen vorzugsweise aus schlaffen Nageln Es konnen aber auch Spannanker verwendet werden. Die Vorzuge dieser Bauweise werden hervorgehoben. Ein ausgefuhrtes Beispiel wird mit mehreren Fotos dargestellt und beschrieben. Anschliesend wird auf die Besonderheiten eines vom Verfasser entwickelten Computer-Programms hingewiesen, mit dem nicht nur die beschriebene Konstruktion, sondern auch alle anderen vernagelten Stutzwande, insbesondere die mit Spritzbeton verkleideten, berechnet werden konnen. Dabei werden neue Wege beschritten, die zu schnelleren und genaueren Ergebnissen fuhren. New nailed lamellar retaining wall. A new nailed lamellar retaining wall will be described, which belong in the category of various permanent safeguards designed to prevent the earth behind the sides of an excavation cut from moving, and into which plants can be fitted. They are characterized by horizontal walers made out of reinforced concrete, which are anchored in the earth and support the sides of an excavation so that its final bottom can be reached, and by prefabricated lamellas attached to these walers at some later date starting at the bottom and going up to the top. Preferred means of anchoring are non-prestressed nails. However, prestressed anchors can also be used. Advantages of this construction are highlighted. An example of the mentioned walls that has been put into practice is given and described through various photographs. The particularities of a computer program developed by the author are then briefly presented, which enables not only the described construction but also all other nailed retaining walls to be calculated, notably those walls coated with shotcrete. New approaches are explored here which bring about quicker and more exact results.

The present paper focuses on the evaluation of the shape sensitivities of the limit and bifurcation loads of geometrically non-linear structures. The analytical approach is applied for isoparametric elements, leading to exact results for a given mesh. Since this approach is difficult to apply to other element types, the semi-analytical method has been widely used for shape sensitivity computation. This method combines ease of implementation with computational efficiency, but presents severe accuracy problems. Thus, a general procedure to improve the semi-analytical sensitivities of the non-linear critical loads is presented. The numerical examples show that this procedure leads to sensitivities with sufficient accuracy for shape optimization applications. Copyright © 2002 John Wiley & Sons, Ltd.

This article attempts to elucidate the underlying mathematical connection between the well-known exact solutions for the deep water capillary wave problem [G.D. CRAPPER, J. Fluid Mech., 2:532-540 (1957)] and the recent discovery of a very special polar decomposition of solutions for a steadily translating bubble with surface tension [S. TANVEER, Proc. Roy, Soc. A, 452:1397-1410 (1996)]. This is achieved by describing a new and unified mathematical approach to the two separate physical problems. Using the new approach, Crapper's capillary wave solutions are retrieved in a novel and simplified fashion, while additional analytical insight into the nature of solutions for a steadily-translating bubble is obtained. The new approach is quite general and can also be used to obtain new exact results to other related free surface problems.

A method is suggested for handling multiple comparisons in repeated measurement situations with completely random missing values. Exact results are obtained for the situation with normally distributed observations in the case of compound symmetry. The method uses grouping with respect to the positions of the missing values. It is most efficient and best suited when there are not too many measurement occasions in the longitudinal investigation.

The average density of states that determines the thermodynamic properties is calculated analytically and numerically for two random versions of the one-dimensional spin-1/2 XY model. The exact results obtained are compared with the results derived within some well-known approximate approaches that permits to understand the region of their validity.

A new local density functional approach for the calculation of correlation energies of many-electron atomic systems is proposed by using the exact results for the correlation energy of a two-electron system bound by a harmonic oscillator external potential. This is motivated by the fact that the correlation energy is a universal functional of the electron density, and the form of this functional is independent of the external potential. The calculated numerical results for the correlation energies show very good agreement with the standard values reported in the literature. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 461–465, 1997

Part I: Fluctuation relations Fluctuation relations: A pedagogical overview Fluctuation Relations and the foundations of statistical thermodynamics: A deterministic approach and numerical demonstration Fluctuation relations in small systems: Exact results from the deterministic approach Measuring out of equilibrium fluctuations Recent progress in fluctuation theorems and free energy recovery Information thermodynamics: Maxwell's demon in nonequilibrium dynamics Time-reversal symmetry relations for currents in nonequilibrium stochastic and quantum systems Anomalous fluctuation relations Part II: Beyond fluctuation relations Out-of-equilibrium generalized fluctuation-disspation relations Anomalous thermal transport in nanostructures Large deviation approach to nonequilibrium systems Lyapunov modes in extended systems Study of single molecule dynamics in mesoporous systems, glasses and living cells

Exciton absorptison lines are calculated for weakly disordered tight-binding systems, using the coherent-potential approximation (CPA). The scaled lineshapes depend only on the dimension of the system. The CPA results are compared with known exact results for chains, and numerical results for finite two-and three-dimensional systems. Exciton-Absorptionslinien werden fur schwach ungeordnete, stark gebundene Systeme in der Kohaent-Potential-Approximation (CPA) berechnet. Die skalierten Linienformen hangen nur von der Dimension des Systems ab. Die CPA-Ergebnisse werden mit bekannten exakten Resultaten fur Ketten und numerischen Resultaten fur endliche zwei- und dreidimensionale Systeme verglichen.

SUMMARY A stochastic simulation procedure is proposed in this papa for obtaining median unbiased (Mu) estimates in macroeconometric models. MU estimates are computed for lagged dependent variable (LDV) coefficients in 18 equations of a macroeconometric model. The 2SLS bias for a coefficient, defined as the difference between the 2SLS estimate and the MU estimate, is on average smaller in absolute value than would be expected from Andrew’ exact results for an equation with only a constant term, time trend, and LDV. The results also show that in a practical sense the estimated biases are not very large because they have little effect on the overall predictive accuracy of the model and on its multiplier properties.

Die Iodbestimmung nach Brit. 1993 bzw. USP 1990 entspricht den Originalangaben von Schoniger2,3) und ist einfacher und schneller durchfuhrbar als die Iodbestimmung nach Ph.Eur.2/DAB 10. Es wird gezeigt, das durch den Ameisensaureuberschus sowohl Iod als auch in Gegenwart von Br Iodat partiell reduziert werden. Beide Reaktionen sind lichtkatalysiert. Daher konnen nach Schoniger2,3) richtige Werte nur bei kurzen Wartezeiten erhalten werden. Nur unter den Bedingungen der Ph.Eur. ist eine Ermittlung von Blindwerten moglich. Comparison of Iodine Determination According to Ph.Eur.2/DAB. 10 and Brit. 1993 The iodine determination according to Brit, 1993, resp. USP 1990, which corresponds to the original publications of Schoniger is less time consuming and simpler in handling than the Ph.Eur 2/DAB 10 procedure. It is shown, that the excess of formic acid reduces not only iodine but also iodate in the presence of Br, Both reactions are accelerated by light. Therefore, according to Schoniger exact results can only be found after short waiting times. Blank values can only be determined under the conditions of Ph.Eur.

Chemical diffusion through boundaries involving two charged diffusing species (e.g., O 2 and 2e in an oxide) is modeled taking into account Poisson's equation, restricted to dilute systems and small driving forces. The results are compared with conventional treatments on a single crystal. Grain boundary effects are exemplified for (i) a bicrystal containing a grain boundary with adjacent space-charge layers and (ii) a polycrystal involving space-charge-free amorphous grain boundaries. Numerical results (i) are analyzed in the context of recent experiments on a SrTiO 3 bicrystal. Transmissionline approximations for chemical diffusion in polycrystals are proposed and briefly compared with exact results.

The one-dimensional Blume-Capel model with an arbitrary spin S is studied by the use of a recently developed effective-field theory. The internal energy, susceptibility, specific heat, and all the two-spin correlations are obtained analytically and for spin-1/2 the exact results are reproduced. Das eindimensionale Blume-Capel-Modell mit beliebigem Spin S wird mit einer kurzlich entwickelten Effektivfeld-Theorie untersucht. Die innere Energie, die Suszeptibilitat, die spezifische Warme und die Zwei-Spin-Korrelationen werden analytisch abgeleitet und fur S = 1/2 werden exakte Ergebnisse erhalten.

Perturbation expansion for the ground-state energy in the strongly correlated limit of cyclic polyenes, as described by the Pariser–Parr-Pople (PPP) and Hubbard Hamiltonians, is examined. Focus is placed on the first- and second-order contributions in terms of the resonance integral, and the performance of the approximate coupled pair theory corrected for the connected quadruple excitations (ACPQ), as well as ACPTQ and ACPQ + T(ACPQ) methods, which are two different versions of ACPQ approximately accounting for the triexcited clusters, is studied. The second-order contribution obtained with the ACPQ, ACPTQ, and ACPQ + T(ACPQ) approaches is then compared with the exact result for the fully correlated limit as provided by the diagonalization of the nearest-neighbor Heisenberg Hamiltonian. It is shown that all three coupled pair theories yield vanishing first-order contribution, in agreement with the exact result. The best result for the second-order contribution for the cyclic polyenes considered in this article is provided by the ACPQ + T(ACPQ) method. In this respect, all three coupled pair theories seem to deteriorate as the polyene size approaches infinity, in spite of yielding excellent energies. Comparison is also made with the results of alternant molecular orbital method.

An important aspect of earthquake loads exerted on extended structures, or structures founded on several foundations, is the spatial variability of the seismic motion. Hence, a rigorous earthquake resistant design of lifeline structures should account for the spatial character of the seismic input, at least in an approximate way. A procedure is proposed which enables addressing the problem of multiply supported structures, subjected to imperfectly correlated seismic excitations, by means of an extension to the response spectrum method. A modified response spectrum model is developed for the design of extended facilities subjected to single and multicomponent ground motion. The modification procedure is based on adjusting each spectral value of the given design response spectrum by means of a correction factor, which depends on the structural properties and on the characteristics of the wave propagation phenomenon. Finally, the theoretical model is validated through digital simulation of seismic ground motion, whereby model predictions are found to be in good agreement with exact results.

Proposed concepts on the nature language and the intuition of meaning are presented here using existential and mathematical primitives. Topologically exact results are given for the structure of human memory, for the inner nature of a meaning, and for some of the psychic principles which give rise to language. These results follow from a linguistic model which so defines a verb that all other linguistic elements become special cases of it. Both the topological and clinical results on the emergence of language and the perception of meaning support this position. Some results are also given on the structure and formation of non-verbal meaning.

Approximate expressions for the conditional reaction time variances in general random walk models based on Wald's (1947) approximation are first derived, and then the corresponding exact results for a model assuming a Laplacean density of step sizes are derived. The results are applied to auditory choice reaction time data obtained by Green et al. (1983), and approximate and exact results are compared. The paper concludes with a discussion of whether the predictions, which are the first relevant results on conditional first passage time variances, increase the identifiability and the power of tests of the general random walk model.

The properties of linearly steep, tapered cut-off waveguide filters are analyzed by the eigenmode expanding method. Coupling from higher modes to the fundamental mode and coupling between higher modes have been taken into account in order to get exact results. The numerical results of the reflectional loss are in good agreement with the experimental results over a wide range from one-wavelength tapered waveguides to a step-connected waveguide. The effect of higher modes is marked in asymmetric waveguides and very steep waveguides, and is shown by the down shifting of the first resonant frequency.

By means of an analytic method the exact value of torsional rigidity for a beam with frame-type profile and asymptotics for stress intensity factor for a beam with crack have been obtained.

Subradiant states — as a special kind of entangled states of severel two-level atoms — have recently gained wide attention because these states are exceptional in the sense that they dissipate energy much slower then other collective states. This property implies also that their decoherence is slow, and henceforth they are promising candidates for registers of a quantum computer. Here we propose a scheme which can be used to prepare subradiant states in a cavity. We present perturbative and also exact results showing that after a certain time the evolution of a multiatomic system in a detuned cavity leads to an appropriate entangled state. At this time instant it is sufficient to apply subsequent laser pulses on a control atom in order prepare a state in the subradiant, i.e., a decoherence free subspace.

… the acquirement of knowledge was interesting and attractive but it could only give clear and exact results in proportion to its inapplicability to the question of life. The less it had to do with these questions, the clearer and more exact it was; the more it took the character of a solution of these questions, the obscurer and less attractive they became….(Tolstoy, 1887, p. 41)

The localized bond model of Malrieu, Diner, and Claverie is extended to fourth order in perturbation theory. Single, double, triple, and quadruple replacements from the doubly occupied bonding reference function are included utilizing a symmetric form of diagrammatic perturbation theory. The fourth order theory derived executes on a computer as quickly as does the third order theory. Results are examined utilizing the Pariser–Parr–Pople and CNDO/2 model Hamiltonians, and are compared with third order results and with either exact results where they are known, or with a configuration interaction of all singles and doubles. The influence of the initial hybridization, localization, and bond polarization is discussed. In general, the fourth order corrections are of comparable size to third order. Improvement in results appears to be marginal in the Nesbet–Epstein scheme in passing to fourth order because of the oscillating nature of the series; for Moller–Plesset theory errors are approximately halved. The relative energies as a function of modest geometry change about minima is about the same at third order as it is at fourth for most cases examined.

In a preceding paper the diffraction theory on this subject has been worked out by using far less approximations than those which had been involved in earlier tratments, arriving at more general and exact results. The approach used to obtain the expressions for the variance and integral breadth of reflections differs from another one which sometimes had been used in the literature. It is shown fthe equivalence of both approaches by genralizing that of Wilson. The connetion betwen diferent probilistic concepts and order parameters used in those treatments is elucidated as well. It is also shown the equivalence with some diffraction theories on layer structures with mistakes. The expression for the variance, as well as their relation with the integral breadths, are obtained in detail in order to facilite the selection between two probable domain size distributions in crystals. [Russian Text Ignored].

The dynamics of the spin 1/2 one-dimensional XY-model in a transverse field is considered. The short-time behaviour of the auto-correlation function 〈S(t) S(0)〉 for the closed chain is obtained numerically by considering the exact results known for the open chain which are given in terms of Pfaffians. The bulk auto-correlation is identified with the correlation 〈S(t) S(0)〉 for the open chain, and this identification is shown to be valid up to a characteristic time Jt ≅ 20. It is also shown, as expected, that the boundary effects are more pronounced for fields smaller than the exchange constant (h < |J|) and in the low temperature limit. The results are obtained for different temperatures and field strengths, and the numerical convergence is discussed in each case. Es wird die Dynamik eines eindimensionalen XY-Modells mit Spin 1/2 im transversalen Feld untersucht. Das Kurzzeitverhalten der Autokorrelationsfunktion 〈S(t) S(0)〉 fur die abgeschlos-sene Kette wird numerisch unter Berucksichtigung der bekannten exakten Ergebnisse fur die offene Kette, die durch Pfaff-Funktionen gegeben sind, erhalten. Die Volumen-Autokorrelation wird mit der Korrelation 〈S(t) S(0)〉 fur die offene Kette identifiziert, und es wird gezeigt, das diese Identifikation bis zu einer charakteristischen Zeit Jta < 20 gultig ist. Es wird ebenfalls gezeigt, das, wie erwartet, die Randeffekte fur Felder, die kleiner als die Austauschkonstante (h < |J|) sind, und im Grenzfall niedriger Temperatur, ausgepragter sind. Die Ergebnisse werden fur verschiedene Temperaturen und Feldstarken erhalten, und fur jeden Fall wird die numerische Konvergenz diskutiert.

We present a BAYEsian theory for testing model adequacy which provides exact results whether the model is linear or nonlinear in the parameters. We consider two cases: (a) replicated data exists, and (b) no replicated data exists but an external estimate of the variance is available. Furthermore, we derive a useful approximation for testing model adequacy when the model is nonlinear in the parameters.

A graph G has property A(m, n, k) if for any sequence of m + n distinct points of G, there are at least k other points, each of which is adjacent to the first m points of the sequence but not adjacent to any of the latter n points. the minimum order among all graphs with property A(m, n, k) is denoted a(m, n, k). Bounds are given on the numbers a(m, n, k) and some exact results are indicated.

Scattering and momentum-relaxation rates are calculated for a semiconductor quantum well (QW) considering electron scattering by confined LO phonons. Electron coupling with confined LO phonons is treated on the basis of an interaction Hamiltonian deduced in a previous work, while both electrons and LO phonons are assumed to be completely confined to the QW active layer. Besides the exact results, results are reported in the so-called momentum-conservation approximation (MCA) and the fractional error implied in the MCA is calculated. Detailed comparison with previous works (in the non-confined phonon case) is made. Streu- und Impuls-Relaxationsraten werden fur ein Halbleiterquantenwell (QW) unter Berucksichtigung von Elektronenstreuung durch begrenzte LO-Phononen berechnet. Elektronenkopplung mit begrenzten LO-Phononen wird auf der Grundlage eines Wechselwirkungs-Hamiltonians behandelt, der in einer fruheren Arbeit abgeleitet wurde, wahrend sowohl Elektronen als auch LO-Phononen als vollstandig in der aktiven QW-Schicht begrenzt angenommen werden. Neben den exakten Ergebnissen werden auch Ergebnisse in der sogenannten Impulserhaltungsnaherung (MCA) mitgeteilt und der Anteilfehler, der in der MCA enthalten ist, berechnet. Ein ausfuhrlicher Vergleich mit fruheren Arbeiten (fur den Fall nicht-begrenzter Phononen) wird durchgefuhrt.

A formula for the ferromagnetic resonance (FMR) linewidth is presented for the case of isotropic bulk ferromagnetic metals in the parallel configuration, free surface magnetization motion being assumed. The numerical evaluation of the formula agrees with the relative accuracy −0.5 × 10−2 to +1.5 × 10−2 with exact results based on macroscopic FMR theory. The influence of surface magnetization pinning on the linewidth value is also discussed.

In this study a method for obtaining the derivatives of eigenvectors of a locally modified structure with respect to a design variable is presented. Eigensolution to the locally modified structure is expressed by equations consisting of the condensed matrices only which refer to the modified part. The analysis presented herein is developed in conjunction with eigensolution to the modified structure, and the derived fundamental equations are also represented by the same type of condensed matrices only. So, advantages are realized both in computational effort and in computer storage, if the modified part is small compared with the unmodified part. To find exact results, complete eigensolution to the unmodified structure needs to be given. Approximate results are obtained from a few lower eigenvectors and eigenvalues. A pin-jointed truss is solved as a numerical example.

A simplified procedure for the analysis of single-storey base-isolated structures on a viscoelastic halfspace is extended to multistorey structures. Results of displacements and base shear obtained by this procedure compare favourably to exact results obtained by a computer program that has been developed.

SUMMARY Two problem areas are discussed. The first concerns the distribution of sojourn, or response times in networks which allow overtaking. Exact results for a few special cases are presented. The second problem area has to do with determining the average response times in local area networks under particular communication protocols. Models which do not lend themselves to exact solution are studied approximately.

An verschiedenen Beispielen aus Praxis und Forschung wird die Einsatzmoglichkeit des Rasterelektronenmikroskopes (REM) fur die Aufdeckung von Schadensursachen gezeigt. Es versteht sich von selbst, das dies ohne Kenntnis der Betriebs- bzw. Beanspruchungsbedingungen nur in Sonderfallen moglich ist. Failure Analysis with the Scanning Electron Microscope. Examples of practice and research will show the possibility to use the scanning electron microscopy for studying the various crack mechanisms. It is necessary, of course, to know most of parameters like material, stress, temperature, pressure, corrosive agent to get exact results.

Die Berechnung der Weltfunktion in Riemannscher Raum-Zeit - das ist im wesentlichen das Quadrat des geodatischen Abstands zweier Ereignisse -, die durch ein System nichtlinearer Differentialgleichungen bestimmt ist, wird im statischen kugelsymmetrischen Fall auf ein Quadratur- und Eliminationsproblem reduziert. Danach folgt die symmetrieangepaste Konstruktion weiterer Invarianten der Raum-Zeit, die sich aus Ableitungen der Weltfunktion zusammensetzen. Anwendung der gewonnenen Fundamentalgleichungen auf spezielle Scharen von Modell-Metriken, die als Einsteinsche Gravitationspotentiale interpretiert werden, gibt explizite strenge Resultate fur die betrachteten Zweipunkt-Skalare. On the Calculation of the Geodetic Distance and Associated Invariants in Relativistic Gravitational Fields In the static spherically symmetric case, the calculation of the world function of Riemannian space-time, i. e., essentially, the square of the geodetic distance of two events, which is determined by a system of nonlinear differential equations, is reduced to quadrature and elimination problems. Then the symmetry-adapted construction of further invariants of space-time built up by derivatives of the world function is given. By applying the derived basic scheme to special families of model metrics, which are interpreted as Einstein gravitational potentials, explicit exact results for the considered two-point scalars are obtained.

The cochromatic number of a graph G, denoted by z(G), is the minimum number of subsets into which the vertex set of G can be partitioned so that each sbuset induces an empty or a complete subgraph of G. In this paper we introduce the problem of determining for a surface S, z(S), which is the maximum cochromatic number among all graphs G that embed in S. Some general bounds are obtained; for example, it is shown that if S is orientable of genus at least one, or if S is nonorientable of genus at least four, then z(S) is nonorientable of genus at least four, then z(S)≤χ(S). Here χ(S) denotes the chromatic number S. Exact results are obtained for the sphere, the Klein bottle, and for S. It is conjectured that z(S) is equal to the maximum n for which the graph Gn = K1 ∪ K2 ∪ … ∪ Kn embeds in S.

The standard problem in sampling inspection is to consider plans with and without curtailment. Curtailment causes difficulty and authors rarely give exact results (i.e., exact OC and ASN functions) for curtailed procedures. In this article we regard curtailment as an inverse sampling procedure and use Dirichlet integrals to obtain exact formulas for the OC, the ASN, and also the variance of the number of observations required under three types of plans: no curtailment, semicurtailment (for rejection only) and two-sided curtailment. Different sections of the article deal with the single sample, the two-stage, and the multiple-stage sampling problems. New tables for carrying out the single-sample procedure are included in the article. The authors feel that this article presents new directions and new ways of dealing with problems associated with quality control.

A self-consistent approximation scheme for the spectral densities of the one-dimensional spinless fermion model is developed, where the one-particle spectral density fulfils the first four moments. At T = 0 the one-particle excitation spectrum is calculated in dependence on the Coulomb and band energy parameters. The exact results for the atomic and band limits and the gas—liquid like phase transition are reproduced. Es wird ein selbstkonsistentes Approximationsschema fur die Spektraldichten des eindimensionalen spinlosen Fermionenmodells entwickelt, wobei die Einteilchen-Spektraldichte die ersten vier Momente erfullt. Bei T = 0 wird das Einteilchen-Anregungsspektrum in Abhangigkeit von den Coulomb- und Bandenergieparametern berechnet. Die exakten Ergebnisse fur den atomaren und Bandgrenzfall sowie fur den Phasenubergang vom Typ Dampf—Flussigkeit werden reproduziert.

The character of equilibrium of an incompressible visco-elastic fluid of variable density stratified in the vertical direction has been investigated. It is demonstrated that the solution is characterized by a variational principle. Use has been made of this principle to obtain approximate solution for an Oldroyd fluid of exponentially varying density confined between two horizontal boundaries. It is shown that the rate at which the system departs from equilibrium increases with the stress relaxation time and decreases as the strain retardation time increases. For a configuration in which gravity effects are ignored, it is found that the waves can be excited for some disturbances for which no oscillatory motion is possible in a newtonian fluid. The effects of rotation are also considered. Finally the usefulness of variational principle is checked by comparing some exact results with approximate ones. Es wird der Charakter des Gleichgewichtes einer inkompressiblen viskoelastischen Flussigkeit mit veranderlicher Dichte in der vertikalen Richtung untersucht. Wie gezeigt wird, ist die Losung durch ein Variationsproblem bestimmt. Von diesem Prinzip wird Gebrauch gemacht, um Naherungslosungen fur eine Oldroyd-Flussigkeit mit exponentiell veranderlicher Dichte zu erhalten, die durch zwei horizontale Rander begrenzt wird. Es wird gezeigt, das die Rate, mit der sich das System vom Gleichgewichtszustand entfernt, mit der Spannungs-Relaxationszeit anwachst und fallt, wenn die Dehnungs-Verzogerungszeit steigt. Es wird gefunden, das bei einer Konfiguration, wo Gravitationseffekte zu vernachlassigen sind, Wellen durch gewisse Storungen erregt werden konnen, bei denen in einer Newtonschen Flussigkeit keine Oszillationen moglich sind. Die Rotationseffekte werden ebenfalls behandelt. Schlieslich, wird die Brauchbarkeit des Variationsprinzips durch Vergleich einiger exakter Ergebnisse mit den Naherungslosungen uberpruft.

A seasonal random walk is an ARIMA process such that the first difference of order s (s ≥ 1) is a white noise. Given a series of observations from a particular linear transformation of a seasonal random walk, we study the autocovariances c'(k) based on uncentered data and the autocovariances c(k) based on centered data. In both cases, we provide exact, explicit formulae for the mean, variance, and covariance of the sample autocovariances. It is seen that the moments of the c(k)'s are different from those of the c'(k)'s, even asymptotically. Several analytical results presented in the paper were derived by using a symbolic manipulation program. Une promenade aleatoire saisonniere est un processus ARIMA pour lequel une premiere difference d'ordre s (s ≥ 1) produit un bruit blanc. Dans le contexte ou les donnees proviennent d'une transformation lineaire particuliere d'une promenade aleatoire saisonniere, nous etudions les autocovariances c'(k), basees sur des donnees non centrees, de měme que les autocovariances c(k), basees sur des donnees centrees. Dans les deux cas, nous fournissons des formules exactes et explicites pour la moyenne et la variance des autocovariances echantillonnales de měme que la covariance entre deux autocovariances dont les delais sont des multiples de la periode. Nous constatons que les moments de c(k) different de ceux de c'(k), et ce, měme asymptotiquement. Plusieurs resultats analytiques ont ete obtenus a l'aide d'un programme de manipulation symbolique.

In the local density approximation (LDA) the density of a many-electron system is expressed as a function of the spatially varying potential. Here a modified LDA is derived applicable for a potential with a high step at some plane which is e.g. a model for the band edges in an inversion layer at the semiconductor—insulator interface. The local density of states shows oscillations and decreases to zero at the interface as a consequence of quantum mechanical reflection. Simple expressions for the density are obtained for the strongly degenerate and for the non-degenerate system. The comparison with exact results for a model system (triangular potential) shows that the modified LDA yields good results for a wide range of parameters corresponding to real inversion layers.

The robustness of the standardized selection difference is investigated for the family of central chi-squared-distributions. The results are compared with those for the uniform, a family of triangular distributions and the exponential distribution. Beside these exact results and some simulation results are considered.

In X-ray fluorescence analysis the concept of radiometric diameter, d, is often introduced in considerations of the fluorescent intensity from a particulate sample. It represents the mean geometric path of the X-rays through one particle and is usually simply taken to be equal to the volume-to-area ratio of the particle. The effective radiometric path is, however, itself dependent on geometry and absorption effects. Rigorous calculations of the fluorescent intensity from a particle in the π and π/2 geometries were carried out to evaluate the errors involved. It appears that, for π geometry, the discrepancy between these exact results and the intensity calculated via the use of d does not exceed 5.2%. For the π/2 geometry, the errors are much larger and can amount to 50% in realistic cases of X-ray fluorescence analysis. These conclusions are also applicable to monolayers. The effective radiometric diameter approaches d only when absorption effects become negligible, but is smaller in other cases.