Enhancement Factors in Ozone Absorption Based on the Surface Renewal Model and its Application

Based on the Danckwerts surface renewal model, a simple explicit expression of the enhancement factor in ozone absorption with a first order ozone self-decomposition and parallel second order ozonation reactions has been derived. The results are compared with our previous work based on the film theory. The 2,4-dichlorophenol destruction rate by ozonation is predicted using the enhancement factor model in this paper.

Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models

This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.

A Local Asymptotic Behavior for Ruin Probability in the Renewal Risk Model

Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.

Asymptotics of discounted aggregate claims for renewal risk model with risky investment

Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.

A Revised CFB Wall-to-suspension Heat Transfer Model

Based on the Cluster Renewal Model of the particle motion in a CFB riser, a revised heat transfer model is developed, which introduces the latest research results of the hydrodynamics of the suspension flow in CFB. This model divides the heat transfer into two parts, which are due to the transient heat conduction by the covered clusters and the convection between the uncovered wall and the dispersed phase. Radiation at high temperature is regarded as being additive. The fraction of the covered wall by clusters is revised by a new formula, which is a function of the operating condition and the particle properties. The radiation between the dispersed phase and the uncovered wall includes not only the direct radiation to the uncovered wall, but also the radiation to the clusters and then reflected to the uncovered wall. Calculation was carried out for the CFB heat transfer model. The results were compared with the published typical experimental data of other researchers and showed a good agreement between them.

A Joint Density Function in the Renewal Risk Model

In this paper, we consider a general expression for Ф（u, x, y）, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is O. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for Ф（u, x, y）. Finally, we give a numerical example to illustrate the application of these results.

Synthesized Poisson and renewal model and its application in seismic hazard analysis

In this paper, the 'memory' characteristics of large earthquakes is described by renewal process and the 'memoryless' characteristics of small earthquakes by Poisson process. At the same time, the change of earthquake distribution caused by using model with 'memory' characteristics is considered, so that drawback in the current research which assumes that time and magnitude distributions are independent is overcomed. Also in the paper, effect on the seismic hazard reaults caused by magnitude distribution' s change with time is calculated by a practical example. The results obtained in the paper has some application in the present research on the model with 'memory' characteristics.

A Stochastic Model for Optimizing the Patching Time of Software Bugs

New bugs and vulnerabilities are discovered and reported from time to time even after software products are released. One of the common ways to handle these bugs is to patch the software. In this paper, the authors propose a stochastic model for optimizing the patching time for software bugs and vulnerabilities. The optimal patching time can be computed in the patching script development and operational costs in fix. The authors present two case studies using the Nimda worm vulnerability in Microsoft Internet Information Services web server and the bug report of the Debian project. These studies indicate that the patch applications are later than their optimal fix time.

A SOLVABLE ONE-DIMENSIONAL ALLOCATION DECISION MODEL OF RENEWABLE RESOURCES

In the paper, the determinate atlecation decision model and the probabilistic allocation decision model of a kind of renewable resource are separatly studied by means of dynamic programming, and the optimal allocation policy is given under some special conditions.

Economic Assessment of Standby Diesel Generator for Peak Reduction in Commercial and Industrial Buildings:A Case Study in Malaysia

This paper outlines the barriers and potential benefits of using standby diesel generators in mitigating the peak demands for commercial and industrial customers. The feasibility of utilizing the standby diesel generators to reduce the electricity bills for customers is carried out by using the hybrid optimization model for electric renewable(HOMER)software. The size of the standby diesel generator and its operational duration are determined based on the lowest cost of electricity obtained from the evaluations. The economic assessments demonstrate that there is potential to reduce the electricity bills for commercial and industrial customers under the existing fuel price and tariffs. The commercial customers under the tariff C2 have the highest potential to save their electricity bills with the use of standby diesel generators for peak reduction. This study demonstrates the potential of the standby diesel generators in peak reduction.

Ruin probability of the renewal model with risky investment and large claims

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin probability.As a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.

Uniform tail asymptotics for the aggregate claims with stochastic discount in the renewal risk models

Considering an insurer who is allowed to make risk-free and risky investments, as in Tang et al.(2010), the price process of the investment portfolio is described as a geometric L′evy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of extended regular variation, we obtain an asymptotically equivalent formula which holds uniformly for all time horizons, and furthermore, the same asymptotic formula holds for the finite-time ruin probabilities. The results extend the works of Tang et al.(2010).

Asymptotic Estimates of Gerber-Shiu Functions in the Renewal Risk Model with Exponential Claims

This paper continues to study the asymptotic behavior of Gerber-Shiu expected discounted penalty functions in the renewal risk model as the initial capital becomes large. Under the assumption that the claim-size distribution is exponential, we establish an explicit asymptotic formula. Some straightforward consequences of this formula match existing results in the field.

Extension of Some Classical Results on Ruin Probability to Delayed Renewal Model

Embrechts and Veraverbeke investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities (?)(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model.

A contribution to large deviations for heavy-tailed random sums

In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.

The Asymptotic Behavior of the Ruin Probability within a Random Horizon

Subject to the assumption that the common distribution of claim sizes belongs to the extendedregular variation class,the present work obtains a simple asymptotic formula for the ruin probability within arandom or nonrandom horizon in the renewal model.

RUIN PROBABILITIES WITH PAIRWISE QUASI-ASYMPTOTICALLY INDEPENDENT AND DOMINATEDLY-VARYING TAILED CLAIMS

This paper considers the nonstandard renewal risk model in which a part of surplus is invested into a Black-Scholes market whose price process is modelled by a geometric Brownian motion, claim sizes form a sequence of not necessarily identically distributed and pairwise quasi-asymptotically independent random variables with dominatedly-varying tails.The authors obtain a weakly asymptotic formula for the finite-time and infinite-time ruin probabilities.In particular,if the claims are identically distributed and consistently-varying tailed,then an asymptotic formula is presented.

A Class of Delayed Renewal Risk Processes with a Threshold Dividend Strategy

This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.

Impact of Renewable Energy Sources on Steady-state Stability of Weak AC/DC Systems

In recent years,the penetration of renewable resources into AC power systems has increased tremendously,creating a significantly impact on the latter’s operations and stability.In this respect,it is also important to gain a basic analytical understanding of such impact on the steady-state stability of power systems with electrically weak AC/DC interconnections,but such works are not very evident in the literature.Therefore,a classical analytic model of the single and multi-infeed HVDC system which now incorporates renewable resources is proposed.Then the well-established concept of voltage sensitivity of the AC/DC interconnection is applied to analyze the impact of the renewable resources on the steady-state stability of these composite system models,as well as on the influence of system conditions and parameters.This impact is also compared with that arising from other types of shunt devices alternatively connected at the same AC/DC interconnection,therefore their relative beneficial or negative impacts will also be benchmarked.