Subcritical Randomly Indexed Branching Processes

2000 Mathematics Subject Classification: 60J80, 62P05.The paper continues the study of the randomly indexed branching processes in the subcritical case. The asymptotic behavior of the moments and the probability for non-extinction is investigated. Conditional limiting distributions are obtained.The first author wish to thank the Organizing Committee of the ISCPS, SDA, and WBPA 2010 for the financial support which allows him to participate in the conference

An Estimate of the Probability Pr(X<Y)

2000 Mathematics Subject Classification: 33C90, 62E99In the area of stress-strength models there has been a large amount of work as regards estimation of the probability R = Pr(X<Y) when X and Y are independent random variables belonging to the same univariate family of distributions. In this paper we propose an estimate of this quantity based on a simple property of the uniform distribution. We illustrate the use of the estimate with bootstrap confidence intervals for four commonly known distributions (normal, exponential, gamma and beta).The third author is supported by by NFSI-Bulgaria, Grant No. MM-1101/2001

Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.It is well known that under linear normalization the maxima of iid random variables converges in distribution to one of the three types of max-stable laws: Frechet, Gumbel and Weibull. During the last two decades the first author and her collaborators worked out a limit theory for extremes and extremal processes under non-linear but monotone normalizing mappings. In this model there is only one type of max-stable distributions and all continuous and strictly increasing df's belong to it. In a recent paper on General max-stable laws, Sreehari points out two "confusing" results in Pancheva (1984). They concern the explicit form of a max-stable df with respect to a continuous one-parameter group of max-automorphisms, and domain of attraction conditions. In the present paper the first claim is answered by a detailed explanation of the explicit form, while for the second we give a revised proof. The rate of convergence is also discussed

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05We consider subcritical Bellman-Harris branching processes with two types of immigration - one appears whenever the process hits zero state and an other one is in accordance of an independent renewal process. The law of large numbers (LLN) for the total progeny of these processes and Anscombe's type central limit theorem (CLT) for the total number of particles in the cycles completely finished by the moment t are obtained.The paper is supported by NFSI-Bulgaria, Grant No. MM-1101/2001

EPIDEMIOLOGICAL, CLINICA.L AND VIROLOGICAL STUDIES ON INFLUENZA MORBIDITY RATES FOR ТНЕ PERIOD APRIL 1962 – МАY 1963 IN ТНЕ СIТУ OF VARNA

Тhe epidemic process of influenza acquires vaгious forms in its couгse: pandemics, epidemics аnd sporadic morbidity inbetween epidemics. Wе dispose of mоrе precise data оn its course in Bulgaria since 1952. Мorе scanty аrе the data which characteгize influenza epidemics in the city of Vагnа up to 1955 which is seen on Diagr. 1. From the latter it becomes evident that influenza morbidity rates in the city of Vагnа run parallel to morbidity rates in the whole country, being occasionally morе intensive - 1959, 1962. Тlie diаgrаm reveals high level for influenza morbldity rates fог the countгy and the city of Vаrnа in 1956 and аn epidemic peak in 1957, 1959 аnd 1962. Тhe epidemic peak in 1962 is due to аn influenza outbreak caused bу virus А2 which started at the end of January and continued till Магсh, the same уеаr.After the epidemics а period was established, characteгized bу а low level of influenza morbldity rates in the city of Varna. Stress should bе laid оn the fact that determination of actual levels of influenza morbidity rates inbetween epidemics is particularly difficult owing to the imperfect diagnosis and the diversity of clinical forms of influenza

NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels

This is a second paper in our ongoing calculation of the next-to-next-to-leading order (NNLO) QCD correction to the total inclusive top-pair production cross-section at hadron colliders. In this paper we calculate the reaction $q\bar q \to t\bar t + q\bar q$ which was not considered in our previous work on $q\bar q \to t\bar t +X$ due to its phenomenologically negligible size. We also calculate all remaining fermion-pair-initiated partonic channels $qq', q\bar q'$ and $qq$ that contribute to top-pair production starting from NNLO. The contributions of these reactions to the total cross-section for top-pair production at the Tevatron and LHC are small, at the permil level. The most interesting feature of these reactions is their characteristic logarithmic rise in the high energy limit. We compute the constant term in the leading power behavior in this limit, and achieve precision that is an order of magnitude better than the precision of a recent theoretical prediction for this constant. All four partonic reactions computed in this paper are included in our numerical program Top++. The calculation of the NNLO corrections to the two remaining partonic reactions, $qg\to t\bar t+X$ and $gg\to t\bar t+X$, is ongoing.Comment: 1+16 pages; 3 figure

Loop amplitudes in gauge theories: modern analytic approaches

This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop amplitudes in massless theories such as Yang-Mills theory, QCD, and QED.Comment: 34 pages. Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories." v2: typesetting macro error fixe