Search

In this paper, we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a non-homogeneous Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally, numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.

We study an M/G/1-type queueing model with the following additional feature. The server works continuously, at fixed speed, even if there are no service requirements. In the latter case, it is building up inventory, which can be interpreted as negative workload. At random times, with an intensity ω(x) when the inventory is at level x>0, the present inventory is removed, instantaneously reducing the inventory to 0. We study the steady-state distribution of the (positive and negative) workload levels for the cases ω(x) is constant and ω(x) = ax. The key tool is the Wiener–Hopf factorization technique. When ω(x) is constant, no specific assumptions will be made on the service requirement distribution. However, in the linear case, we need some algebraic hypotheses concerning the Laplace–Stieltjes transform of the service requirement distribution. Throughout the paper, we also study a closely related model arising from insurance risk theory.

Patients with paranoia have always been a group of exiting but daunting patients for mental health professionals. Indeed, the risk of a violent acting out with important aggressive discharges confers to these patients an elevated dangerosity potential. If various criminological aspects of violence in paranoia have been described, their link to functional prognosis of patients have been seldom addressed.AimTo determine if criminological details of violence acts in paranoia patients predict their functional prognosis.MethodsA retrospective, descriptive and analytic study have been conducted, based on a chart consult. Twenty-three patients with paranoia (i.e. Chronic delusional disorder type jealousy or erotomania in DSM IV) patients have been included. These patients have been hospitalized in the forensic psychiatry department of Razi hospital of Tunis (Tunisia), between 1995 and 2015, after not being held by reason of insanity, according to article 38 of the Tunisian Criminal Code.ResultsDelusional disorder types were: jealousy (17), persecution (4), erotomania (1) and claim (1). The majority were married (18), undereducated (17), with irregular work (13). Forensic acts were uxoricide (15), attempted murder (5), violence against people (2) and destruction of public properties (1). Patients used bladed weapon in most of the cases (13), in the victim's residence (19), with premeditation in (17) of the crimes. Only 5 patients worked regularly after discharge.ConclusionIf our results expose further data concerning potential dangerosity of patients with delusional disorders, they also highlight the marginalized situation of these patients when released back into society.Disclosure of interestThe authors have not supplied their declaration of competing interest.

The structure of chromosomal inversions mediated by hobo transposable elements in the Uc-1 X chromosome was investigated using cytogenetic and molecular methods. Uc-1 contains a phenotypically silent hobo element inserted in an intron of the Notch locus. Cytological screening identified six independent Notch mutations resulting from chromosomal inversions with one breakpoint at cytological position 3C7, the location of Notch. In situ hybridization to salivary gland polytene chromosomes determined that both ends of each inversion contained hobo and Notch sequences. Southern blot analyses showed that both breakpoints in each inversion had hobo-Notch junction fragments indistinguishable in structure from those present in the Uc-1 X chromosome prior to the rearrangements. Polymerase chain reaction amplification of the 12 hobo-Notch junction fragments in the six inversions, followed by DNA sequence analysis, determined that each was identical to one of the two hobo-Notch junctions present in Uc-1. These results are consistent with a model in which hobo-mediated inversions result from homologous pairing and recombination between a pair of hobo elements in reverse orientation.