Basic Limit Research Articles

Analysis of risk in taking measures for radiation and social protection of the public

The necessity of risk analysis for support of radiation and public protection measures and substantiated application of risk analysis for the development of a scientific-methodological and normative-legal base is examined. Recommendations are given for the development and use of risk analysis. For radiation accidents, a priori and postfactum risk assessment and harm must be distinguished (before and after an accident has occurred). In the latter case, detailed risk assessment is needed, especially to establish a link between sickness and the accident as well as for compensation of harm to the health of victims. A collection of risk indicators for different applications is given. A new additional risk indicator is proposed. This indicator is the relative loss of duration of life (lost years of life, referred to the year during which the source of risk acted). It is intended for establishing a universal limit on risk, suitable for any source of risk. The value of this basic limit is proposed and values of dose and risk limits derived from it for ionizing radiation and other sources of risk are presented. Requirements for methods of dose and risk assessment are formulated. 3 figures, 1 table, 16 references.

A Course in Mathematical Statistics

Concepts of Set Theory Some Probabilistic Concepts and Results On Random variables and Their Distributions Distribution Functions, Probability Densities, and their Relationships Moments of Random Variables-Some Moment and Probability Inequalities Characteristic Functions, Moment Generating Functions, and Related Theorems Stochastic Independence with Some Applications Basic Limit Theorems Transformations of Random Variables and Random Vectors Order Statistics and Related Theorems Sufficiency and Related Theorems Point Estimation Testing Hypotheses Sequential Procedures Confidence Regions-Tolerance Intervals The General Linear Hypothesis Analysis of Variance The Multivariate Normal Distribution Quadratic Forms Nonparametric Inference Appendices Table of Selected Discrete and Continuous Distributions and Some of their Characteristics Some Notation and Abbreviations

Calculation of internal from external electrical field strength and its effect on cardiac pacemaker patients

What electric field strength is developed inside a person entering the electric field produced by, e.g., a high-voltage transmission line? This question may be of vital importance for a pacemaker patient. With the aim of finding an answer, known phenomena are combined in such a way that the mean current density within the thorax at the level of the heart can be determined. In this way it can be demonstrated that the internal electric field of a grounded person is twice that of an ungrounded person, that the internal field is 0.72 mV/m per 1 kV/m external field, and that the most sensitive pacemaker can be influenced by 2 kV/m. It is also clear that the field strength limit of 5 kV/m proposed by ICNIRP for the general public cannot be justified by the basic limit of 2 mA/m2.

The Limit Problems for the Equation of Oscillations of a Satellite

We consider the ordinary differential equation of the second order, which describes oscillations of a satellite with respect to its mass center moving along an elliptic orbit with eccentricity e. The equation has two parameters: e and µ. It is regular for 0 ≤ e < 1 and singular when e = 1. For \(e \to \) 1 we obtain three limit problems. Their bounded solution to the first limit problem form a two-dimensional (2D) continuous invariant set with a periodic structure. Solutions to the second limit problem form 2D and 3D manifolds. The µ-depending families of odd bounded solutions are singled out. One of the families is twisted into a self-similar spiral. To obtain the limit families of the periodic solutions to the original problem match together the odd bounded solutions to the first and the second limit problem. The point of conjunction is described by the third (the basic) limit problem. The limit families are very close to prelimit ones computed in earlier studies.

An Introduction to Stochastic Modeling

Stochastic Modeling. Probability Review. The Major Discrete Distributions. @rtant Continuous Distributions. Some Elementary Exercises. Useful Functions, Integrals, and Sums. Conditional Probability and Conditional Expectation: The Discrete Case. The Dice Game Craps. Random Sums. Conditioning on a Continuous Random Variable. Markov Chains: Introduction: Definitions. Transition Probability Matrices of a Markov Chain. Some Markov Chain Models. First Step Analysis. Some Special Markov Chains. Functionals of Random Walks and Success Runs. Another Look at First Step Analysis. The Long Run Behavior of Markov Chains: Regular Transition Probability Matrices. Examples. The Classification of States. The Basic Limit Theorem of Markov Chains. Reducible Markov Chains. Sequential Decisions and Markov Chains. Poisson Processes: The Poisson Distribution and the Poisson Processes. The Law of Rare Events. Distributions Associated with the Poisson Process. The Uniform Distribution and Poisson Processes. Spatial Poisson Processes. Compound and Marked Poisson Processes. Continuous Time Markov Chains: Pure Birth Processes. Ptire Death Processes. Birth and Death Processes. The Limiting Behavior of Birth and Death Processes. Birth and Death Processes with Absorbing States. Finite State Continuous Time Markov Chains. Set Valued Processes. Renewal Phenomena: Definition of a Renewal Process and Related Concepts. Some Examples of Renewal Processes. The Poisson Process Viewed as a Renewal Process. The Asymptotic ]3ehavior as Renewal Process.

On the nature of singularities inherent, under a given analytic distribution of the external pressure, in solutions of the prandtl equations near the point of separation

A comprehensive analysis of a classical two-dimensional boundary layer is developed with the aim of revealing possible types of singularities related to separation. According to the basic assumption, the limit flow regime with a singular point of vanishing skin friction obeys an analytic solution where the frictional intensity approaches zero according to quadratic law rather than varing linearly with distance. Small deviations from the limit regime are described in terms of eigenfunctions, three of which involve singularities. The flow field for all supercritical regimes is continued into a small region centered about the singular characteristic springing from the point of vanishing skin friction in the undisturbed limit solution. The solvability condition for a key boundary-value problem posed in this region as a result of matching the global-scaled solution upstream gives three different types of singularities of the Prandtl equation. According to the weakest-type singularity the skin friction varies as the square root of the cube of the local distance. The next type includes a sudden change in the wall shear stress derivative with respect to the coordinate along the solid surface, it was ruled out of the basic limit solution. Then the famous Landau-Goldstein singularity with the skin friction being proportional to the square root of the local distance evolves. A still more complicated flow pattern may be composed of the singularity with a sudden change in the wall shear stress derivative superseded by the Landau-Goldstein singularity at some small distance downstream. A qualitative comparison between theoretical predictions and experimental data for a circular cylinder in an incompressible stream is made with the emphasis on conceivable explanations for the nonmonotonic behavior of frictional intensities in the transitional range of Reynolds numbers.

Ion deflection due to sheath field curvature

Plasma sheath electric fields, hence ion motions, deviate near patterned substrate features. This results in a basic directionality limit to ion-assisted processes. Ion deviation is here derived analytically for dc sheaths, and expressed as an ‘‘ion isotropy ratio,’’ the fraction of ions bombarding a trench sidewall instead of its bottom. This ratio is equal to (trench depth/ion acceleration distance) multiplied by a factor of about 0.5. Thus, ion deviation is especially significant for discharges with small sheath heights and yields a fundamental tradeoff between ion directionality, ion energy, and permissible ion current.

Peut-on encore améliorer la protection radiologique dans les mines souterraines ?

Après avoir posé le problème, des résultats et commentaires sont donnés pour illustrer les efforts d'optimisation faits par les exploitants miniers. Dans le cycle du nucléaire, les travailleurs les plus exposés, en routine, sont les mineurs d'uranium (moyenne pour les mines souterraines entre 20 et 30 mSv.an-1). Dans les mines d'uranium, les exploitants font, surtout depuis 10 ans, de gros efforts pour diminuer les doses collectives et pour respecter la réglementation en vigueur basée sur les recommandations de la CIPR (publications 26 et 47). Depuis 1988, chez les mineurs français, aucune dose effective (cumul) ne dépasse la limite fondamentale de 50 mSv.an-1. Il n'en est pas de même dans tous les pays. En 1990, la CIPR a édité de nouvelles recommandations (publications 60 et 61) où la limite fondamentale est telle qu'en moyenne elle ne doit pas dépasser 20 mSv.an-1. Pour respecter cette limite, les exploitants devront prendre un certain nombre de dispositions plus ou moins contraignantes. Les moyens financiers supplémentaires seraient importants dans les mines existantes. De nouveaux concepts d'exploitation minière seraient à rechercher pour les mines nouvelles. Indépendamment des aspects financiers, les dépenses faites pour essayer de réduire un risque déjà très faible (aléatoire et à long terme) ne seraient-elles pas mieux employées pour améliorer les postes de sécurité classique ? On voit, de plus, apparaître toute une série d'effets pervers allant à rencontre du but recherché. En conclusion, l'amélioration de la protection radiologique peut être obtenue plus efficacement par la mise en œuvre du principe de l'optimisation de la dose collective que par un accroissement de la sévérité des limites de dose individuelles.

Three-dimensional dynamics and transition to turbulence in the wake of bluff objects

The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast’ transition, from a laminar two-dimensional state at Reynolds number 200 to a turbulent state at Reynolds number 400. The process has been documented in several experimental investigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the Navier—Stokes equations at representative Reynolds numbers, up to 500. A high-order time-accurate, mixed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vortex street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vortex filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vortex filaments.Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance of intermittent phenomena. It is concluded that the wake undergoes transition to turbulence following the period-doubling route.

An Inequality for Multidimensional Characteristic Function

Previous article Next article An Inequality for Multidimensional Characteristic FunctionN. G. GamkrelidzeN. G. Gamkrelidzehttps://doi.org/10.1137/1136071PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] William Feller, An introduction to probability theory and its applications. Vol. II. , Second edition, John Wiley & Sons Inc., New York, 1971xxiv+669 42:5292 0219.60003 Google Scholar[2] J. Lamperti, Probability, Wiley Series in Probability and Statistics: Probability and Statistics, John Wiley & Sons Inc., New York, 1996xii+189 97e:60001 CrossrefGoogle Scholar[3] G. N. Watson, Theory of Bessel Functions, Cambridge Univ. Press, Cambridge, 1922 Google Scholar[4] Milton Abramowitz and , Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, Vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964xiv+1046 29:4914 Google Scholar[5] N. G. Gamkrelidze, A method for proving the central limit theorem, Theory Probab. Appl., 25 (1981), 609–614 10.1137/1125075 0463.60026 LinkGoogle Scholar[6] C. G. Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math., 77 (1945), 1–125 7,312a 0060.28705 CrossrefGoogle Scholar[7] F. W. Olwer, Bessel Functions: Pt. 3, Zeroes and Associated Values, Cambridge Univ. Press, Cambridge, 1960 Google Scholar[8] V. V. Sazonov, Normal approximation—some recent advances, Lecture Notes in Mathematics, Vol. 879, Springer-Verlag, Berlin, 1981vii+105, New York 83g:60035 0462.60006 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Estimate of the Rate of Convergence of Probability Distributions to a Uniform DistributionA. A. Kulikova25 July 2006 | Theory of Probability & Its Applications, Vol. 47, No. 4AbstractPDF (145 KB) Volume 36, Issue 3| 1992Theory of Probability & Its Applications History Submitted:13 February 1989Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136071Article page range:pp. 594-596ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Non-invariant failure probabilities with invariant reliability index

Abstract This paper presents a critical examination of some basic limit state functions that led to development of the invariant code format for reliability analysis. Proper methods of evaluating failure probabilities from these limit state functions are used to check failure probabilities estimated by reliability index methods, and the results show that failure probability for a limit state function that may assume different but seemingly equivalent forms is not always invariant as the invariant format would indicate.

Future independent times and Markov chains

A random timeT is a future independent μ time for a Markov chain (X n ) 0 ∞ ifT is independent of (X T+n ) /∞ =0 and if (X T+n ) /∞ =0 is a Markov chain with initial distribution μ and the same transition probabilities as (X n ) 0 ∞ . This concept is used (with μ the “conditional stationary measure”) to give a new and short proof of the basic limit theorem of Markov chains, improving somewhat the result in the null-recurrent case.

Ultimate limit in low threshold quantum well GaAlAs semiconductor lasers

Gain measurements were performed on buried heterostructure single quantum well lasers to ascertain the transparency current density, which represents a basic limit in the threshold current. By using the optimal design approach, a lowest threshold of 0.55 mA in a 120-μm-long device was achieved. Modulation of the low threshold laser by a pseudorandom digital stream at 1.3 Gbit/s without current bias is demonstrated.

The role of Sphagnum fimbriatum in secondary succession in a road salt impacted bog

Secondary succession of Sphagnum mosses was studied for 7 years along a belt transect in a bog that had been impacted by sodium chloride highway deicing salts. Laboratory studies on Sphagnum fimbriatum Wils., the dominant recolonizing species, were conducted to determine its salt tolerance level and ability to reproduce from spores and fragments across a salt gradient. Vegetative reproduction was also compared with that of four other recolonizing species. Sphagnum fimbriatum represented a high percentage of all recolonizing Sphagnum and generally began growing on low hummocks in quadrats where the salt content of the interstitial peat pore waters had dropped to about 300 mg/L as chloride. This salt concentration was also found to be the basic tolerance limit for mature plants and reproducing spores and fragments. The success of Sphagnum fimbriatum as a pioneer species seems to be associated with its prolific production and probable dispersal of spores, its superior vegetative reproduction, its tolerance of mineralized waters, and its ability to grow on hummocks out of direct contact with mineralized waters.

The ST-Transformation Approach to Analytic Solutions of Quantum Systems. I: General Formulations and Basic Limit Theorems

The ST-Transformation Approach to Analytic Solutions of Quantum Systems. I: General Formulations and Basic Limit Theorems

The Markov branching-castastrophe process

This paper considers a Markov branching process modified to allow decrements which occur randomly at a rate proportional to the population size. The problems considered are (i) Conditions for eventual extinction, (ii) Asymptotic behaviour of the probability of extinction and the mean time to extinction; and (iii) Behaviour of the population size. Special consideration is given to the case where the decrement distribution is geometric. In this case limit theorems for the population size are obtained which are analogues of the basic limit theorems for the Markov branching process.

Tracking a temporal gap in band-limited noise: frequency and level effects.

Temporal gap resolution in band-limited noise signals was examined with a B6k6sy procedure in which listeners tracked the minimum signal intensity needed to resolve a periodic temporal gap of fixed duration. Gaps from 25 msec to the smallest detectable value were tested to derive performance functions that described intensity threshold as a function of gap duration. Each of four octaveband signals, centered at .5, 1.0, 2.0, and 4.0 kHz, was presented with a complementary filtered noise masker to restrict the listening band and avoid extraneous spectral cues. Performance functions were also derived in different levels of a white-noise background that was added to shift the subject’s audibility thresholds to greater sound-pressure levels. Results show that gap resolution improves to a basic limit as signal level is increased from audibility threshold; the rate of improvement, however, increases progressively as audibility threshold is elevated. This observation suggests that shifts in audibility criteria for gap resolution are correhted with loudness changes. The smallest detectable gap for each signal was largely independent of sound-pressure level in a 35-40-dB range, but decreased systematically as a function of signal frequency. The frequency dependency is consistent with the hypothesis that temporal resolution is limited in part by spectral filtering in the auditory periphery.

On the formula for the upper limit of photovoltaic solar energy conversion efficiency

The formula for the maximum efficiency of photovoltaic energy conversion in tandem solar cells is discussed. This formula is obtained by the use of a thermodynamically founded diode I-V characteristic, and is compared to a previously published formula which was based on the classical diode I-V characteristic within the framework of the theory of Shockley and Queisser (1961). Series expansions of the complicated efficiency formula are presented. They enable an easy and accurate computation of the maximum efficiency and provide more insight in the basic limit of the photovoltaic effect.

Structural Stochastic Stability of a Simple Auto-Oscillatory Climatic Feedback System

Based on a more detailed model developed previously, governing possible feedbacks between sea ice extent (η), deep-ocean temperature (θ), and atmospheric carbon dioxide, we have constructed a simple, deterministic, dynamical system for η and θ that yields a stable limit cycle as a solution. To make the system more realistic we add random (white noise) forcing and explore the new response as a function of the amplitude of this stochastic forcing. Included in the analysis are examples of sample time series, sample phase trajectories, variance spectra, and “residence density” in the phase space. The results show that physically reasonable values of the stochastic amplitude do not completely obscure the basic limit cycle, but they do convert an intransitive, deterministic system to an almost-intransitive one that tends to reside longer in two distinct regions of the phase space, with relatively fast transitions between thorn. The solutions also show how stochastic forcing of one component of the climatic feed-back system (i.e., η) can lead to a damped response in another unforced component (θ).

Weak moment conditions for time coordinates in first-passage percolation models

A generalization of first-passage percolation theory proves that the fundamental convergence theorems hold provided only that the time coordinate distribution has a finite moment of a positive order. The existence of a time constant is proved by considering first-passage times between intervals of sites, rather than the usual point-to-point and point-to-line first-passage times. The basic limit theorems for the related stochastic processes follow easily by previous techniques. The time constant is evaluated as 0 when the atom at 0 of the time-coordinate distribution exceeds½.