Partial Justification Research Articles

Reinventing Inventory Control

Western notions about inventory control revolve around economic order quantities and buffer stocks that are aimed at avoiding running out of stock but which result in high inventories and long lead times. Our inventory models need to be recast into principles: The lot-size principle is simply to keep cutting it—and cut setup times as partial justification. The buffer-stock principle is also to keep cutting—and solve the exposed quality, equipment, and other problems thereby exposed.

A heuristic approach to steady-state semiconductor filament theory, with applications

We present a heuristic approach for solving the current-voltage characteristic of a semiconductor filament in the steady state excited by a time-independent and space-independent carrier density injected at the front surface. The treatment assumes a model having infinite surface recombination velocity (zero excess carrier density) on the lateral surfaces, a model used by previous workers for both transient and steady-state conditions. For the steady state, we demonstrate that the exact solution for total current crossing the injecting face diverges. Use of partial sums derived from truncating the Fourier or Bessel-function series of the periodic extension in space of the constant carrier density on the injecting face yields closed-form analytic solutions for the current-voltage characteristic. From these solutions, a definition of the effective filament lifetime emerges. Its dependence on lateral dimensions nearly agrees with the dependence of the transient filament lifetime defined by Shockley. The approach advanced here enables treatment of several semiconductor devices containing grain boundaries, including one in which the model employing infinite surface recombination velocity admits use of the superposition principle to build a total solution by summing more elementary solutions. A partial justification for the heuristic approach taken here derives from regarding the partial-sum approximation as a means of moving the model in the direction toward a physically realizable system. Brief discussion appears of electrostatic and thermal analogs of the semiconductor boundary-value problem treated.

Leading large order asymptotics for (?4)2 perturbation theory

We develop a rigorous semiclassical expansion to compute the radius of convergence of the Borel transform for the pressure in (φ4)2 field theory. This result gives a partial justification for the Lipatov method of finding large order perturbation theory asymptotics in quantum field theory.

Two consequences of determinacy consistent with choice

We begin with a ground model satisfying ZF + AD + ACR, and from it construct a generic extension satisfying ZFC + 6? = C2 + nonstationary ideal on coI is Co2-saturated. 0. Introduction. The of determinacy (henceforth AD) implies many interesting propositions about small cardinal numbers, for example c and (O2. It is natural to ask whether these propositions are true or, more realistically, can be true in the full universe V of sets. Our working hypothesis is that in V the axiom of choice is true and all games are determined, so the question becomes whether these propositions are consistent with ZFC together with determinacy. (We shall be vague about definable when we can afford to.) In this paper we shall consider two such consequences of AD, the first being that 2I = W2 and the second that the nonstationary ideal on xl is o2-saturated. We shall show that the theory consisting of ZFC + ADL(R) together with these two propositions is consistent. (ADL(R) is the assertion that all games in L(R), a large class of games, are deterniined.) In consonance with our working hypothesis, we would like to prove our result assuming only the consistency of ZFC + ADL(R), or equivalently, that of ZF + AD + DC (cf. ?1). At present we cannot do this. We instead assume the consistency of ZF + AD + ACR' where ACR is the axiom of choice for families indexed by the reals. Consistency-wise, ZF + AD + ACR is one of the strongest theories known to man; we show in ?1 that it proves the consistency of ZF + AD + DC. The only upper bound we know on the consistency strength of ZF + AD + ACR is that of ZF + ADR + 0 is regular. We offer some partial justification for our use of such a strong hypothesis at the end of the paper. Our consistency proof is by forcing. We start with a ground model M satisfying ZF + AC + ACR. By a two-step iteration we construct a generic extension M[G] onto so that 3h (h: 2 -RM). The forcing will add no new reals and preserve Co2, i.e., RM = RM[G] and (M =1M[G]. We then pass to the inner model N = L(RM, h) and show it has the desired properties. The paper is organized as follows: In ?1 we give some preliminaries and background information. In particular, we set forth those consequences of AD whose Received by the editors February 18, 1980. 1980 Mathematics Subject Classification. Primary 03E35; Secondary 03E60. ?1 982 American Mathematical Society 0002-9947/8 1 /001000/$05.75

A Bayesian Argument in Favor of Randomization

The theory of personal probability must be explored with circumspection and imagination. For example, applying the theory naively one quickly comes to the conclusion that randomization is without value to statistics. This conclusion does not sound right; and it is not right.L. J. Savage (1961, p. 585).Randomization is a generally accepted principle of sound experimental design and common practice among working scientists. But many philosophers and some theoretical statisticians have rejected it. Bayesians have most often stated their opposition to randomization in terms of a decision theoretic argument. Not all Bayesians, however, could go along with that argument, as the above quotation by Leonard Savage testifies.In this paper I will examine the Bayesian decision theoretic argument against randomization and show why it fails. By means of an example I will then give a partial justification of randomization in Bayesian terms.

Use of blood levels to infer carcass levels of contaminants.

Inferences may be made about the carcass levels of a contaminant based on the contaminant level in blood samples. A method is given for comparing such populations that utilizes bivariate normal distributions and their principal axes, thereby avoiding a dilemma arising from the use of regression techniques. Confidence intervals and power calculations are given. Data from captive barn owls provide partial justification for the use of this method.

Brownian approximations to first passage probabilities

By direct probabilistic argument one term of an Edgeworth type asymptotic expansion is obtained for certain first passage distributions for random walks. These results provide partial justification for and extensions of approximations suggested earlier as a heuristic consequence of Laplace transform calculations.

Quasi‐thermal noise in a stable plasma at rest: Theory and observations from ISEE 3

The noise voltage found at the terminals of an electric dipole antenna immersed in a hot plasma is calculated. The plasma is assumed stable and at rest. It is described as made of two maxwellian electron populations. A grid of calculated noise spectra is presented in normalized coordinates, and we give analytical expressions valid for frequencies much lower or larger than the plasma frequency fp or close to the noise peak. The antenna impedance is also calculated; in contrast to the noise spectrum, it is found to be very weakly dependent upon the hot population parameters. From these results one can calculate the response of a receiving system, thus enabling the actual measurement of the plasma parameters from the noise spectrum. Using ISEE 3 SBH experimental data, it is shown that the observations do fit the theoretical predictions over most of the frequency range. Plasma parameters are obtained and found in good agreement with results from the Los Alamos plasma analyzer on the same spacecraft. It appears that the high energy tail of the particle distribution function accounts for the peak noise voltages of several times 10−12 V²Hz−1 found at the terminals of a 45‐m half‐length dipole. The interpretation of these observations does not therefore require an unstable plasma. We discuss these results and show that more work should be done to explain an unpredicted increase of the spectrum below fp and to explain the weak spin modulation. Solving these remaining problems requires the introduction of ions and of the bulk and/or drift velocity into the calculations. Appendix A contains a partial justification of the assumption of a triangular current distribution on the antenna. The calculations are presented in appendix B.

Induction and Enhanced Reactivation of Mammalian Viruses by Light

Publisher Summary The chapter discusses the certain studies that concern the induction and enhanced reactivation of DNA-containing mammalian viruses by light. The chapter also discusses the enhanced reactivation and induction of mammalian viruses because (a) they represent potential mammalian “SOS” functions, (b) they may be associated with mammalian cell oncogenic transformation; and (c) to use viruses as tools to study phenomena related to DNA repair. Response curves were obtained by determining induced SV40 infectivity for different values of light exposure and dye concentration. The induction was clearly a function of both these parameters, which gave partial justification for calling the effect a photodynamic induction. The maximum levels of induction found for each response curve were similar in amount and represented about a thousandfold increase above spontaneous background levels observed with untreated cells. The results suggest that photodynamic treatment also reduces the capacity of the cells to support the growth of induced virus. The ultraviolet-enhanced reactivation of herpes simplex virus in host monkey kidney cells is described.

The Lipatov argument

Lipatov's argument gives a formula for evaluating asymptotically the large order perturbation coefficients for the anharmonic oscillator or (φ4) quantum field models. We give a partial justification of the argument which enables us to prove that the radius of convergence of the Borel transform of the pressure for lattice φ4 models given by $$\exp \left[ {\mathop {\inf }\limits_\phi \left\{ {\tfrac{1}{2}\sum\limits_j {\left[ {(\nabla \phi )^2 (j) + \phi (j)^2 } \right] - \log } \sum {\phi (j)^4 } } \right\} - 2} \right].$$

FLOOD HAZARD MAPS AS PUBLIC INFORMATION: AN ASSESSMENT WITHIN THE CONTEXT OF THE CANADIAN FLOOD DAMAGE REDUCTION PROGRAM

Flood hazard maps are essential for the successful inplementation of a range of flood mitigation measures. However the use of flood maps for public information is often advanced as partial justification for a mapping program. A number of assumptions implicitly underlie such justifications: that the public will read the maps, that they will understand them, and that they will have some effect on people’s attitudes to the flood hazard. A review of the cartographic literature on map perception indicates that no firm statement can be made regarding map comprehension. The results of work by geographers on flood maps as public information suggest that maps have little effect on people’s attitudes to floods, but also reveal difficulties in achieving satisfactory research design.The research reported here examined the flood mapping component of the Canadian Flood Damage Reduction Program. Data was collected on attitudes to floods before and after map distribution. The sampling method used also enabled the effects...

Simple model for the quasiparticle interactions inHe3. I. The superfluid transition temperatures

Taking as a basis both the $s\ensuremath{-}p$ and paramagnon approximations, we explore the consequences of a phenomenological model for the low-frequency effective interaction (vertex function) in $^{3}\mathrm{He}$ of the form (unsymmetrized) ${\ensuremath{\Gamma}}^{k}\ensuremath{\sim}\ensuremath{-}J(q)\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}+V(q)$. Here $q$ represents the magnitudes of the momentum and energy transfer and $S=\frac{1}{2}$. Using the known Landau scattering amplitudes, we demonstrate that within this ansatz it is possible to (i) understand the magnitude and pressure dependence of the superfluid transition temperature ${T}_{c}$, (ii) give a partial justification for the validity of the $s\ensuremath{-}p$ approximation as applied to transport properties, and (iii) understand qualitatively the stabilization of the superfluid $A$ phase within a more general framework than the paramagnon model. The present ansatz yields the same expression for the scattering amplitudes $A(\ensuremath{\theta},\ensuremath{\varphi})$, as does the $s\ensuremath{-}p$ approximation at $\ensuremath{\theta}=\ensuremath{\pi}$, which limit is most significant for transport properties. We find that the values of the Landau scattering amplitudes, (i) and (iii) are consistent with the picture that $J(q)$ is peaked around $q=0$ and that $J(0)$ is larger than the potential term, $V$. This description is similar to that used in spin-fluctuation theories. Choosing the parameters in ${\ensuremath{\Gamma}}^{k}$ to yield reasonable fits to the measured ${{A}_{l}^{s,a}}$, we find by numerical solution of the Eliashberg equations that ${T}_{c}\ensuremath{\sim}0.1{T}_{F}{e}^{\ensuremath{-}\frac{9}{{A}_{1}^{s}}}$. This expression which is in good agreement with experiment at all pressures provides confirmation of the importance of spin fluctuations in ${T}_{c}$. Numerical examples of the pressure dependent ${{A}_{l}^{s,a}}$ and ${T}_{c}$ are given for a number of different models for the functions $J$ and $V$.

The Distribution of Public Expenditure: The Case of Health Care

In contrast to the amount of attention paid recently to the distribution of income and wealth, very little work has been done in Britain on the distribution of public expenditure. The gap is particularly wide in the case of the distribution of expenditure conferring such as that on the public provision of education or health care. There are a number of North American studies, particularly on education (see, for example, Gillespie, 1965; Hansen and Weisbrod, 1969; Pechman, 1970; and Judy, 1970). However the only recent British work is the annual estimates of tax and services produced by the Central Statistical Office (see Harris, 1977); and these do not pretend to be an elaborate study of the distribution of expenditure on benefits-in-kind, the distribution being simply assumed to be equal for individuals of the same age and sex. This omission is a serious one. Since expenditure on benefits-in-kind is an important part of the so-called social wage, and since the latter has become a focus of political attention (being used, for example, as a partial justification for the holding down of private wages), it seems important to establish exactly how such expenditure is distributed between different groups in the population. This paper is an attempt to do so for one element of the wage: the distribution of public expenditure on the National Health Service (NHS). The paper relates public expenditure on the Health Service to the incidence of illness by socioeconomic group, in order to see whether the position in society where an individual is placed affects the amount of medical treatment he receives when he is ill. It is divided into five parts. In Section I the distribution of morbidity (or ill health) among different groups in the population is discussed. In Section II an attempt is made to estimate the costs of the health service facilities used by different groups, and to relate this to the morbidity of the groups. The calculations are very tentative, and should not be regarded as in any way definitive. In Section III some possible explanations for the results are discussed. In Section IV some of the implications of the results are explored, and the conclusions are briefly summarized in Section V. The paper is a substantially revised version of evidence submitted to the Royal Commission on the Health Service (Le Grand, 1976). Access to more data has permitted the use of a method of calculation superior to that used in the Royal Commission evidence. Reassuringly, the change in the methods of calculation has not greatly changed the results. For reasons described below the basic source for the data used in the calculations is the health section of the General Household Survey undertaken by the Office of Population Censuses and Surveys (henceforth OPCS),

Saul and Selected Poems by Charles Heavysege

502 usually hung on bits of quotation jostle each other from one end of the book to the other. Apart from major texts, there are well over one hundred authors cited, and nearly one hundred and twenty titles - novels, plays, the scriptures, poems, autobiographies, letters, criticism, philosophy, psychology, and social commentary. There is a comparable hospitality to patent irrelevancies, as in a partial justification of the ending of Howard's End, and in the judgement that it is a fine novel, neither of which has even a glancing relevance to the thesis of the book. More obvious is an irrelevant page of defense of Freud against Gide and Sartre. "It would be interesting," the author concludes, "to pursue this comparison further, but to do so would carry us quite beyond the scope of the present inquiry into the realms of comparative psycho-biography." Surely there can be no argument against full documentation. And surely one wishes here to put the best possible construction on extensive referential procedure, even though it seems hardly necessary or useful to the stated objective. But one reference, in calling attention to itself, may create unhappy uncertainties as to others. "Consider again," Professor Mendel writes, "W hit­ man's popular poem, 'Animals.' " The lines quoted are the first eight of Section 32 of a well-known, if not a popular poem, "Song of Myself." They are not very carefully transcribed, as though they might have come from a carelessly edited intermediary source. Too, the title for the 'poem' reminds one of sentimental popular anthologies whose ancestors were the Friendship's Offerings of the nineteenth century. It is not that we have, as Horace says, "dignus vindice nodus," but in the words of some unknown German critic, "die Saiten hoch spannen." To borrow a phrase from Goethe, "entbehren sollst du! Sollst entbehren." It is regrettable to have to record the inescapable conclusion that what might have been a rewarding reconsideration of basic values in human experience had there been care in reading and restraint in writing - turns out to be a cluttered, derivative, inexact, and pretentious book. P.J. ALDUS Charles Heavysege, Saul and Selected Poems, Introduction by Sandra Djwa (Toronto: University of Toronto Press, 1976). lxvii, 373. $7.95 For the past several years, whenever a new volume of the University of Toronto "Literature of Canada, Poetry and Prose in Reprint" series has appeared, much negative criticism has arisen. First, the anti-academic critic (and Canada has a large number of parti-pris poet-critics) decries the resurrection of earlier writ­ ers. Then, the academic criticizes the series for not supplying a definitive text with scholarly editing. And finally we hear rumblings from the insides of the University of Toronto Press, when the volumes fail to sell well. At the moment 503 it is rumoured that the series is rapidly coming to an end, and that several of the proposed texts, some of which were almost completed in m s , may never see the light of day. This would be a shame: while the series has definite drawbacks, it also serves a useful purpose, bringing back into print many central texts at a time when the study of Canadian literature has expanded so rapidly that the discipline is being taught by thousands of teachers working, shorthanded and lefthanded, from a few anthologies. Although plans for definitive texts have been set in motion, these take years to complete, and in the interim we need reliable reading texts. The reader of Canadian literature owes a considerable debt to Douglas Lochhead for undertaking a series which proves our literary heritage begins prior to the twentieth century. The latest volume in the series is Charles Heavysege's Saul and Selected Poems, which includes all of Saul, excerpts from Jephthah's Daughter, all of the narrative poem Jezebel, four sonnets, and an introduction by Professor Sandra Djwa of Simon Fraser University. In the past it has sometimes appeared that the scholar introducing the reprint had little actual knowledge of his text's history, because frequently little or no comment was offered on the choice of copy text. In part, this may have been the Press's fault in simply hiring a...

Percolation clusters as partial justification of classical nucleation theory : By D. Stauffer; Institut für Theoretische Physik, Universität, 5000 Köln 41, W. Germany

Percolation clusters as partial justification of classical nucleation theory : By D. Stauffer; Institut für Theoretische Physik, Universität, 5000 Köln 41, W. Germany

Partial justification of the Borda count

Partial justification of the Borda count

Some Results from a Simplified Three-Dimensional Numerical Model of Atmospheric Turbulence

Abstract A simplified set of subgrid-scale transport equations is used to compute the stresses in a three-dimensional model of thermal convection in the atmosphere. Terms appearing in the full transport equations thought not to be essential to the large-scale dynamics are discarded, leaving prognostic equations to be solved for the subgrid-scale energy and the virtual potential temperature variance only. Equations for the Reynolds stresses and the subgrid-scale temperature-velocity correlations are considerably simplified and can be solved algebraically. A scale analysis of the full transport equations is offered as partial justification for the present approach in the case of nearly isotropic turbulence. The problem studied is that of a well-mixed layer bounded above by a region of strong stable stratification. The present model gives a significant improvement in the representation of the large-scale variables as compared with the more conventional eddy viscosity approach. In three experiments testing di...

Electron-positron annihilation cross section near the new threshold

Heavy-quark models of the new narrow resonances are presented. The relative heaviness of the assumed new quarks suggests applying the adiabatic approximation familiar from molecular physics here. This approach provides partial justification for the use of potential models to describe the new resonances. Vacuum polarization plays an important role in determining the shape of the adiabatic potential. Model calculations of the psi''(4.1) are presented. Agreement with experiment is good. A coupled-channel formulation of the narrow resonances and the new threshold is presented. The resulting coupled-channel Schrodinger equations can be solved iteratively. The lowest-order approximation reproduces the adiabatic picture, and higher-order corrections are calculable. Several coupled-channel models are analyzed numerically and qualitatively. Although detailed numerical results are model-dependent, certain trends occur. We estimate that the radiative decays of the psi'(3.7) should be less important than is indicated by naive-pure-quark-model calculations. In addition, the psi'(3.7) is not a simple two-quark state but has considerable charm--anticharm meson content. The leptonic widths of the psi(3.1) and psi'(3.7) are computed and good agreement with experiment is found. Corrections to the adiabatic- potential-model approximation to R(Q$sup 2$) = sigma(e$sup +$e$sup -$ $Yields$ hadrons)/ sigma(e$sup +$e$sup -$ $Yields$ $mu$$sup +$$mu$$sup -$) above threshold are computed. If the coupled-channel model uses the SU(4) charm scheme, then D*'s are expected to outnumber D's by a wide margin above threshold. The potential-model calculations of R(Q$sup 2$) which accept the conventional SU(4) scheme are systematically below the data for E/sub c.m./ greater than or approx. = 4.6--4.8 GeV. By adding the contribution of a heavy lepton with mass 2.3--2.4 GeV to the four-quark prediction, a curve of R vs E/sub c.m./ which is in good agreement with the data over the entire energy range occurs. (AIP)

Nearly hamiltonian systems in two degrees of freedom

Perturbed systems of differential equations are studied which are close to Hamiltonian systems of the type for which small divisor problems arise. If the non-Hamiltonian terms involve both damping and self-excitation, behavior characteristic of Hamiltonian systems can occur but is confined to small regions of space in which these opposite effects are in balance. The results provide a partial justification for truncating the Fourier series occurring in these problems. The principle method is local averaging, which is used to obtain global results by compactness arguments.

Spin Fluctuations in Heisenberg Paramagnets. II. Kinetic Theory and Approximate High-Temperature Solutions

A set of kinetic equations describing the time evolution of the two-spin correlation functions $〈{S}^{\ensuremath{-}}({q}_{1},t){S}^{+}({q}_{2},t)〉$ and $〈{S}^{z}({q}_{1},t){S}^{z}({q}_{2},t)〉$ is derived. The derivation is based upon a cluster expansion of the equations of motion and an intuitively plausible renormalization. The resultant equations may be interpreted graphically, and the derivation of the kinetic equations taken to be a partial justification of the summation of a particular set of graphs in the moment expansion for the spectral density. The kinetic equations have the property that they conserve the total spin $\ensuremath{\Sigma}〈\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},t)\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}(\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},t)〉$ and the total energy $\ensuremath{\Sigma}{q}^{}V(q)〈\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},t)\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}(\ensuremath{-}\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}},t)〉$. The second and fourth moments of the spectral density for fluctuations in the magnetization predicted by these equations are correct to lowest order in $\frac{1}{c}$, where $c$ is the number of spins in the range of the interaction. Numerical calculations of the spectral density, based upon an approximate solution of the kinetic equations that is valid outside of the critical region, are compared with the neutron-scattering data for a wide range of temperatures and wave vectors and found to be in good agreement. The temperature dependence of the diffusion coefficient in the high-temperature region is calculated and compared with experiment.