THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT

The concepts of bi-immigration birth and death density matrix in random environment and bi-immigration birth and death process in random environment are introduced. For any bi-immigration birth and death matrix in random environment Q（θ） with birth rate λ 〈 death rate μ, the following results are proved, （1） there is an unique q-process in random environment, P^-（θ＊（0）;t） = （p^-（θ^＊（0）;t,i,j）,i,j ≥ 0）, which is ergodic, that is, lim t→∞（θ^＊（0）;t,i,j） = π^-（θ^＊（0）;j） ≥0 does not depend on i ≥ 0 and ∑j≥0π （θ＊（0）;j） = 1, （2） there is a bi-immigration birth and death process in random enjvironment （X^＊ = {X^＊,t ≥ 0},ε^＊ = {εt,t ∈ （-∞, ∞）}） with random transition matrix P^-（θ^＊ （0）;t） such that X^＊ is a strictly stationary process.

Maternal Age, Low Birth Weight and Early Neonatal Death in Tertiary Hospital in the Volta Region of Ghana

Objectives: Current study sought to determine an association between Low Birth Weight (LBW) and early neonatal mortality at a resource limited country’s referral hospital and to determine relationship between maternal age and birth outcomes. Method: A retrospective study analyzing data on births in the Volta Regional Hospital, Ghana from the period of November 2011 to June 2016. A total of 8279 births were analyzed. Results: Results suggest that teenage mothers (8.60%) are more likely to give birth to pre-term babies than the elderly (6.60%) and the adult mothers (4.61%). LBW is highest among the teenage mothers (12.69%) followed by the elderly mothers (7.87%) and then the least among the adult mothers (6.48%). Extremely Low Birth Weight (ELBW) and Macrosomia births were more observed among the elderly mothers (0.90%;2.17%) than the teenage (0.28%;0.14%) and adult mothers (0.34%;1.61%) respectively. Data suggest that 100% of the ELBW were pre-term birth, 88.28% Very Low Birth Weight (VLBW), 34.56% LBW and only 1.06% of the pre-term birth were with Normal Birth Weight (NBW). Death rate ranges from 50% for ELBW, 33.59% for VLBW, 8.22% for LBW, 5.43% for Macrosomia and 1.5% for NBW. However, death rate distribution among the various age groups was statistically not significant (P 0.106). Conclusions: Our study suggests that early neonatal death, especially deaths among ELBW and VLBW is still high at the VRH of Ghana and therefore there is the need for further studies into interventions to reduce death among neonates born with VLBW and ELBW.

A General Repairable Spare Part Demand Model Based on Quasi Birth and Death Process

This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A general repairable spare part demand model built on quasi birth-and-death process is developed. This model assumes that both the operational time of the unit and the maintenance time of the unit follow the continuous time phase type distributions. The first passage time distribution to be out of spares, the first mean time to be out of spares, and an algorithm to get the minimal amount of spares under certain restrictions are obtained. At the end of this paper, a numerical example is given.

Degree distribution of random birth-and-death network with network size decline

In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network（RBDN） with network size decline.First,by stochastic process rules,the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 〈 p 〈 1/2,then the average degree of network with n nodes is introduced to calculate the degree distributions.Specifically,taking m = 3 for example,we explain the detailed solving process,in which computer simulation is used to verify our degree distribution solutions.In addition,the tail characteristics of the degree distribution are discussed.Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.

The Wartime Bridge Reliability Evaluation Model Based on Birth-and-Death Process

At first, the concept of bridge reliability is given, followed with its mathematic model. Then, based on the analysis about the mechanism of the damage and repair of bridges, and the state diversion of bridge network, the state diversion process is proved to be birth-and-death process. In the end, the state diversion balance equation of bridge network is built, and the evaluation model of wartime bridge reliability is got. The model is used in a certain example, and it is proved to be precise and credible.

An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate

In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.

Kinetics of aggregation growth with competition between catalyzed birth and catalyzed death

An aggregation growth model of three species A, B and C with the competition between catalyzed birth and catalyzed death is proposed. Irreversible aggregation occurs between any two aggregates of the like species with theconstant rate kernels In（n = 1,2, 3）. Meanwhile, a monomer birth of an A species aggregate of size k occurs under the catalysis of a B species aggregate of size j with the catalyzed birth rate kernel K（k, j） = Kkj^v, and a monomer death of an A species aggregate of size k occurs under the catalysis of a C species aggregate of size j with the catalyzed death rate kernel L（k, j） = Lkj^v, whcre v is a parameter reflecting the dependence of the catalysis reaction rates of birth and death on the size of catalyst aggregate. The kinetic evolution behaviours of the three species are investigated by the rate equation approach based on the mean-field theory. The form of the aggregate size distribution of A species ak （t） is found to be dependent crucially on the competition between the catalyzed birth and death of A species, as well as the irreversible aggregation processes of the three species： （i） In the v 〈 0 case, the irreversible aggregation dominates the process, and ak（t） satisfies the conventional scaling form; （2） In the v ≥ 0 casc, the competition between the catalyzed birth and death dominates the process. When the catalyzed birth controls the process, ak（t） takes the conventional or generalized scaling form. While the catalyzed death controls the process, the scaling description of the aggregate size distribution breaks down completely.

Finite family trees of continuous time birth and death processes for evaluating the transmitting speed of information on communication networks

A finite random graph generated by continuous time birth and death processes with exponentially distributed waiting times was investigated, which is similar to a communication network in daily life. The vertices are the living particles, and directed edges go from mothers to daughters. The size of the communication network was studied. Furthermore, the probability of successfully connecting senders with receivers and the transmitting speed of information were obtained.

Kinetics of Infection-Driven Growth Model with Birth and Death

We propose a two-species infection model, in which an infected aggregate can gain one monomer from a healthy one due to infection when they meet together. Moreover, both the healthy and infected aggregates may lose one monomer because of self-death, but a healthy aggregate can spontaneously yield a new monomer. Consider a simple system in which the birth/death rates are directly proportional to the aggregate size, namely, the birth and death rates of the healthy aggregate of size k are J1 k and J2k while the self-death rate of the infected aggregate of size k is J3k. We then investigate the kinetics of such a system by means of rate equation approach. For the J1 〉 J2 case, the aggregate size distribution of either species approaches the generalized scaling form and the typical size of either species increases wavily at large times. For the J1 = J2 case, the size distribution of healthy aggregates approaches the generalized scaling form while that of infected aggregates satisfies the modified scaling form. For the J1 〈 J2 case, the size distribution of healthy aggregates satisfies the modified scaling form, but that of infected aggregates does not scale.

Sudden birth versus sudden death of entanglement for the extended Werner-like state in a dissipative environment

In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits （pure or mixed state）, occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.

Exchange-Driven Growth with Birth Rate Less Than Death

We further study the kinetic behavior of the exchange-driven growth withbirth and death for the case of birth rate kernel being less than that of death based on themean-Geld theory. The symmetric exchange rate kernel is K(k,j) = K′(k,j) = Ikj~v, and the birth anddeath rates are proportional to the aggregate's size. The long time asymptotic behavior of theaggregate size distribution a_k(t) is found to obey a much unusual scaling law with an exponentiallygrowing scaling function Φ(x) = exp(x).

Scaling in Rate-Changeable Birth and Death Processes with Random Removals

We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.

The Effect of Human Immunodeficiency Virus-1 Infection on Low Birth Weight, Mother to Child HIV Transmission and Infants’ Death in African Area

Background: It is yet a controversy subject whether low birth weight and infant death are associated to human immunodeficiency virus-1 infection. Objective: To appreciate association between low birth weights, mother to child HIV transmission and infant mortality in HIV-1 infected pregnant women delivering between 2011 and 2016. Materials: We conducted 6 years cohort study in urban Mali. Outcome included preterm delivery, small for gestational age, infant survival status and HIV transmission. Comparison concerned women clinical WHO stage, mother viro-immunological status, and newborn anthropometric parameters. Results: HIV-1 infected women who delivered low birth weight newborn were 20.9% (111/531) versus 16.5% (1910/11.546) in HIV negative patients (p = 0.016). CD4 T cell counts low than 350 T cells count were strongly associated to LBW (p = 0.000;RR = 3.03;95% CI [1.89 - 3.16]). There is no significant association between ART that was initiated during pregnancy (p = 0.061, RR = 0.02;CI 95% (1.02 - 1.99)) or during delivery (p = 0.571;RR = 1.01;CI 95% (0.10 - 3.02)) and LBW delivery. In multivariate analysis ART regimens containing protease inhibitor (PI) were lone regimens associated with LBW ((p = 0.030;RR = 1.001;95% confidence interval [1.28 - 3.80]). Very low birth weight was statistically associated to women HIV infection (adjusted relative risk, 2.02;p = 0.000;95% confidence interval (2.17 - 4.10)). There is no significant difference between mother to child HIV transmission rate in the two HIV-infected pregnant women (10 infected children in group 2: MTCT rate 4.5%) and 3 infected children in group 1 (MTCT rate: 2.7%) (p = 0.56;RR, 0.59;CI 95% (0.18 - 4.39)). In multivariate analysis, LBW was associated with infant death (p = 0.001;RR = 2.04;CI 95% [1.04 - 5.05]). The median weight of infant at the moment of death in group 1 was 851 g (IQR: 520 - 1833 g). Significant relationship was found between infant death among LBW newborn with mother WHO stage 2 (p = 0.004;adjusted RR = 3.22;CI 95% [2.25 - 6.00]), CD4 T cells count 3 (p = 0.005;RR = 2.81;CI 95% [1.20 - 4.11]), PI regimens (p = 0.030;RR = 1.00;CI 95% [1.28 - 3.80]). Conclusion: We confirm increased risk of low birth weight and mother HIV-1 infection and we identified strongest association between mortality in infant born to HIV-1 infected mother and LBW.

Risk factors of clinical birth asphyxia and subsequent newborn death following nuchal cord in a low-resource setting

Introduction: Our aim was to identify the risk factors of clinical birth asphyxia and subsequent newborn death in the presence of nuchal cord in a sub-Saharan Africa setting. Methodology: It was a six-months’ case-control study involving 117 parturients whose babies presented with a nuchal cord at delivery. The study was carried out at the Yaoundé Gyneco-Obstetric and Pediatric Hospital, Cameroon, from January 1st to June 30th 2013. Results: The risk factors of clinical birth asphyxia identified were: first delivery, absence of obstetrical ultrasound during pregnancy, nuchal cord with more than one loop, duration of second stage of labor more than 30 minutes during vaginal delivery. The risk factors for newborn death from clinical birth asphyxia in the presence of nuchal cord were: maternal age Conclusion: We recommend a systematic obstetrical ultrasound before labor, so as to detect the presence of a nuchal cord, its tightness and the number of loops. Also, cesarean section should be considered when a nuchal cord is associated with first delivery, tightness or multiple looping.

A Stochastic SIVS Epidemic Model Based on Birth and Death Process

A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.

Logarithmic Sobolev Inequalities for Two-Sided Birth-Death Processes

In this paper, we study the logarithmic Sobolev inequalities for two-sided birth-death processes. An estimate of the logarithmic Sobolev constant α for a two-sided birth-death process is obtained by the Hardy-type inequality and a criteria for a is also presented.

A Linear Immigration-Birth-Death Model and Its Statistical Inference

formula of simulation proccss by In this paper, we employ monmnt generating function to obtain some exact transition probability of inlmigration-birth-death（IBD） model and discuss the of sample path and statistical inference with complete observations of the IBD the exact transition density formula.

Inferring Multi-Type Birth-Death Parameters for a Structured Host Population with Application to HIV Epidemic in Africa

Human Immunodeficiency Virus (HIV) dynamics in Africa are purely characterised by sparse sampling of DNA sequences for individuals who are infected. There are some sub-groups that are more at risk than the general population. These sub-groups have higher infectivity rates. We came up with a likelihood inference model of multi-type birth-death process that can be used to make inference for HIV epidemic in an African setting. We employ a likelihood inference that incorporates a probability of removal from infectious pool in the model. We have simulated trees and made parameter inference on the simulated trees as well as investigating whether the model distinguishes between heterogeneous and homogeneous dynamics. The model makes fairly good parameter inference. It distinguishes between heterogeneous and homogeneous dynamics well. Parameter estimation was also performed under sparse sampling scenario. We investigated whether trees obtained from a structured population are more balanced than those from a non-structured host population using tree statistics that measure tree balance and imbalance. Trees from non-structured population were more balanced basing on Colless and Sackin indices.

一类二次矩阵方程的牛顿迭代法及其收敛性

二次矩阵方程是科学与工程计算中一类重要的方程,探讨有效的数值方法是一项有意义的工作,拟生灭过程在股价模拟、库存控制、排队论等很多领域都有着重要的应用,对一类来源于拟生灭过程的特殊的二次矩阵方程进行了研究。在最小非负解存在且唯一的假设条件下,提出了牛顿迭代法并证明其收敛性。当初始矩阵取零矩阵时,牛顿迭代法产生的矩阵列收敛到方程的唯一最小非负解。最后通过数值例子验证算法的有效性与可行性。

清代诗人生卒年丛考——以湖北梅钺、李中黄等七位诗人为中心

中国古典诗歌按照加速度的原理发展,至清代而达到极度繁荣。迄今仍有作品传世的清代诗人,少说也在十万人以上,超过此前历代诗人总和的若干倍。但他们的生卒年,目前能够现成查到的,仅仅只有很少的一部分。日后像编纂《全清诗》以及其他诸多诗歌文献,这都会成为一个棘手的问题。因此,在学术界既有的相关工具书之外,从各种原始资料不断补充考察清代诗人生卒年,的确很有必要。这里就湖北梅钺、李中黄,浙江张懋忠、钟氏(海宁徐濬妻),河南郜献珂,山东刘士聪,云南李凤彩,以及江苏易震吉等诗人,对他们的生卒年做些探讨。