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In this paper, we display methods for the computation of convergence and perturbation bounds for Mt/Mt/1 system with balking, catastrophes, server failures and repairs. Based on the logarithmic norm of linear operators, the bounds on the rate of convergence, perturbation bounds, and the main limiting characteristics of the queue-length process are obtained. Finally, we consider the application of all obtained estimates to a specific model.

Introduction: A significant number of patients with moderate asthma remain symptomatic despite treatment with inhaled corticosteroids (ICS). These patients do not yet meet the criteria for oral corticosteroids (OCS) and monoclonal antibodies. The new anti-chemokine oral drug XC8 could represent an alternative treatment option for these patients. The objective of this trial was to evaluate the effect of different doses of the XC8 in patients with partly controlled asthma in a phase 2a clinical trial. Methods: A double-blind, parallel-group, randomized, multicenter, phase 2a trial was conducted at 12 sites in Russia. Patients with asthma were randomized into four groups (n?=?30 each) to receive XC8 at 2 mg, 10 mg, 100 mg or placebo once-daily for 12 weeks in addition to low-dose ICS with or without LABA. Efficacy and safety parameters were evaluated at weeks 0, 2, 6, and 12. Results: No statistically significant difference between the treatment arms in the number of patients with adverse events was observed. The primary endpoint, improvement of forced expiratory volume in 1 s (FEV1) % predicted over 12 weeks compared to placebo, was not statistically significant. The treatment of patients with XC8 (100 mg) resulted in statistically and clinically significant improvements in FEV1compared to baseline (7.40% predicted, p?<?0.001). Patients with elevated peripheral blood eosinophil count (PBEC,?>?300 cells/µl) or serum interferon-? (IFN-?) level (>?100 pg/mL) treated with XC8 (100 mg) achieved a statistically significant improvement in FEV1(11.33% predicted or 8.69% predicted, respectively, p?<?0.05) as compared to the baseline versus the placebo. The strongest effect was observed in patients with both high PBEC and IFN-? level. Pharmacodynamic engagement was demonstrated through the reduction of serum levels of C–C motif ligand 2 (CCL2) and C–X–C motif chemokine 10 (CXCL10). Treatment with XC8 (100 mg) alleviated resistance to maintenance ICS therapy in patients with elevated IFN-? level. Conclusions: Given the high safety, oral route of administration, and efficacy, XC8 may provide a promising treatment option for patients with mild-to-moderate asthma. Trial Registration: 795–30/12/2015 (Ministry of Health Russian Federation), NCT03450434 (ClinicalTrials.gov).

Consideration is given to three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is particularly well suited to describe evolutions of the total number of customers in (in)homogeneous M/M/Squeueing systems with possibly state-dependent arrival and service intensities, batch arrivals and services. One of the methods is based on the logarithmic norm of a linear operator function; the other two rely on Lyapunov functions and differential inequalities, respectively. Less restrictive conditions (compared with those known from the literature) under which the methods are applicable are being formulated. Two numerical examples are given. It is also shown that, for homogeneous birth-death Markov processes defined on a finite state space with all transition rates being positive, all methods yield the same sharp upper bound.

Basic insulation and heating system retrofits of existing homes could achieve annual energy savings of up to $4–5 billion in the USA. However, current US utility energy efficiency (EE) programs are costly and challenging to scale. Customer acquisition occurs primarily through energy bill mailers, mass media, and on-line advertising that lack specificity about particular home retrofit opportunities, expected energy savings, and cost-effectiveness. Specific retrofit opportunities are identified via on-site home energy assessments that can be inconvenient to homeowners, expensive, and of variable accuracy. Our paper discusses using communicating thermostat data to significantly increase the customer uptake of energy conservation measures (ECMs) by identifying homes with the most significant retrofit opportunities, estimating post-retrofit energy savings, and formulating home-specific outreach. We extended our previously developed gray-box building model to identify physical building parameters corresponding to the target retrofit opportunities, i.e., whole-home Rvalue, air leakage characteristics, and heating system efficiency. The estimated Rvalues and air leakage characteristics compare favorably with the ground truth. The validated algorithms can calculate home-specific energy savings estimate for each ECM, and the algorithm outputs can be used by utility EE programs to formulate home-specific retrofit offers.

High-throughput screening has revealed dark chemical matter, a set of drug-like compounds that has never shown bioactivity despite being extensively assayed. If dark molecules are found active at a therapeutic target, their extraordinary selectivity profiles make excellent starting points for drug development. We explored if ligands of therapeutically relevant G-protein-coupled receptors could be discovered by structure-based virtual screening of the dark chemical matter. Molecular docking screens against crystal structures of the A2Aadenosine and the D4dopamine receptors were carried out, and 53 top-ranked molecules were evaluated experimentally. Two ligands of each receptor were discovered, and the most potent had sub-micromolar affinities. Analysis of bioactivity data showed that the ligands lacked activity at hundreds of off-targets, including several that are associated with adverse effects. Our results demonstrate that virtual screening provides an efficient means to mine the dark chemical space, which could contribute to development of drugs with improved safety profiles.

Borderline Personality Disorder (BPD) is a severe psychiatric disorder characterized by behavioral dysregulation, emotion dysregulation, disturbances in self-identity, and social functioning. Despite the existence of evidence-based psychotherapeutic interventions for BPD, these interventions have important limitations (e.g., limited treatment efficacy). Furthermore, little evidence exists for the efficaciousness of pharmacological interventions for BPD. Thus, a strong need for improving current interventions for BPD exists. Although research incorporating psychedelics within interventions for a wide range of psychiatric disorders has shown promise, research has not yet explored the utility of incorporating psychedelics within interventions for BPD. Therefore, this paper reviews the impact of psychedelics on treatment targets in interventions for BPD (i.e., behavioral dysregulation, emotion dysregulation, disturbances in self-identity, and social functioning), as well as purported overlapping mechanisms of change between interventions for BPD and psychedelics (i.e., emotion dysregulation, mindfulness, and self-compassion). Finally, safety concerns, clinical recommendations, and proposed next research steps related to the administration of psychedelics to individuals with BPD are discussed. This paper aims to explore the case for conducting research on, and the potential clinical utility surrounding, incorporating psychedelics within interventions for BPD.

This work examined the influence of trait experiential avoidance (EA) on the relationship between functional versus dysfunctional emotion regulation (ER) strategies and next-day negative emotion. Participants (N = 154) reported levels of EA, and then provided daily measurements of negative emotional intensity and frequency of the use of dysfunctional and functional ER strategies that are focused inwards towards the self (internal) or outwards towards others (external) for six consecutive days. Hierarchical linear modeling indicated that higher internal-dysfunctional ER strategy use predicted higher next-day emotional intensity. Also, trait EA moderated the relationship between external-dysfunctional ER use and next-day negative emotion: lower EA individuals experienced higher, but higher EA individuals experienced lower, negative emotion the day following increased external-dysfunctional strategy use. Findings suggest internal-dysfunctional ER is associated with increased next-day negative emotion. As well, external-dysfunctional strategies are associated with next-day emotion among individuals who are more aware of emotion (i.e., lower EA), and may lead to a blunted response among those higher in EA. A range of explanations for the moderating effect of trait EA on the relationship between external-dysfunctional ER and next day emotion are discussed.

•Pair bonds are biologically prepared and rely on many of the same underlying neural substrates as childhood attachments.•Attachment relationships and pair bonds buffer stress. Paradoxically, the process of establishing attachments can be stressful.•Adults and their children generally profit from stable pair bonds, however, these benefits derive from a myriad of contextual variables.•The degree to which friendships and other close relationships can provide some of the same benefits as pair bonds remains an open question.•Pair bonds develop in stages. The pace of pair bonding is variable and shaped by cultural and individual differences.

Modulation of multiple biological targets with a single drug can lead to synergistic therapeutic effects and has been demonstrated to be essential for efficient treatment of CNS disorders. However, rational design of compounds that interact with several targets is very challenging. Here, we demonstrate that structure-based virtual screening can guide the discovery of multi-target ligands of unrelated proteins relevant for Parkinson’s disease. A library with 5.4 million molecules was docked to crystal structures of the A2Aadenosine receptor (A2AAR) and monoamine oxidase B (MAO-B). Twenty-four compounds that were among the highest ranked for both binding sites were evaluated experimentally, resulting in the discovery of four dual-target ligands. The most potent compound was an A2AAR antagonist with nanomolar affinity (Ki= 19 nM) and inhibited MAO-B with an IC50of 100 nM. Optimization guided by the predicted binding modes led to the identification of a second potent dual-target scaffold. The two discovered scaffolds were shown to counteract 6-hydroxydopamine-induced neurotoxicity in dopaminergic neuronal-like SH-SY5Y cells. Structure-based screening can hence be used to identify ligands with specific polypharmacological profiles, providing new avenues for drug development against complex diseases.

In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.

Functionally selective ligands stabilize conformations of G protein-coupled receptors (GPCRs) that induce a preference for signaling viaa subset of the intracellular pathways activated by the endogenous agonists. The possibility to fine-tune the functional activity of a receptor provides opportunities to develop drugs that selectively signal viapathways associated with a therapeutic effect and avoid those causing side effects. Animal studies have indicated that ligands displaying functional selectivity at the D2dopamine receptor (D2R) could be safer and more efficacious drugs against neuropsychiatric diseases. In this work, computational design of functionally selective D2R ligands was explored using structure-based virtual screening. Molecular docking of known functionally selective ligands to a D2R homology model indicated that such compounds were anchored by interactions with the orthosteric site and extended into a common secondary pocket. A tailored virtual library with close to 13 000 compounds bearing 2,3-dichlorophenylpiperazine, a privileged orthosteric scaffold, connected to diverse chemical moieties viaa linker was docked to the D2R model. Eighteen top-ranked compounds that occupied both the orthosteric and allosteric site were synthesized, leading to the discovery of 16 partial agonists. A majority of the ligands had comparable maximum effects in the G protein and β-arrestin recruitment assays, but a subset displayed preference for a single pathway. In particular, compound 4stimulated β-arrestin recruitment (EC50= 320 nM, Emax= 16%) but had no detectable G protein signaling. The use of structure-based screening and virtual libraries to discover GPCR ligands with tailored functional properties will be discussed.

•Crying can provide evidence about an infant’s metabolic and neurological condition.•Excessive crying can trigger feeding problems, parental depression and infant abuse.•Specific parental vulnerabilities make adverse outcomes more likely.•The mechanisms underlying adult responses are starting to be uncovered.•Support programmes join paediatric with adult mental health services.

Service life of many real-life systems cannot be considered infinite, and thus the systems will be eventually stopped or will break down. Some of them may be re-launched after possible maintenance under likely new initial conditions. In such systems, which are often modelled by birth and death processes, the assumption of stationarity may be too strong and performance characteristics obtained under this assumption may not make much sense. In such circumstances, time-dependent analysis is more meaningful. In this paper, transient analysis of one class of Markov processes defined on non-negative integers, specifically, inhomogeneous birth and death processes allowing special transitions from and to the origin, is carried out. Whenever the process is at the origin, transition can occur to any state, not necessarily a neighbouring one. Being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend (except for transition to the origin) on the process state. To the best of our knowledge, first ergodicity and perturbation bounds for this class of processes are obtained. Extensive numerical results are also provided.

Cascading failures, such as the Northeast outage of 2003, can keep millions of people without power for extended periods of time. A combination of simultaneous occurrence of rare events in the physical grid, the human inability to apprehend and act on the real circumstances, and failures in the IT infrastructure result- ing in poor situation awareness may lead to power outages. The formation and propagation of cascading events is nonlinear. There is a precursor phase, in which some system recovery is possible and human oper- ators are able to act and recover failed lines, followed by an escalation phase, in which the number of failed lines increases rapidly, and by a cascading phase that corresponds to the blackout. Although stochastic power grid simulation is an appropriate tool to study cascading events, human intervention, which is mostly ignored in simulation, can nonetheless influence the recovery and the extension of the blackouts. In this pa- per we model the probability of human failure by applying a human reliability modeling approach, the, Standardized Plant Analysis Risk-Human Reliability Analysis (SPAR-H), to the analysis of failure scenari- os narrated by grid operators with different levels of expertise. The SPAR-H methodology is a simplified approach to human error quantification that accounts for individual performance-shaping factors that affect perception, processing and response to events in complex environments. To implement this approach, we started by interviewing system operators from New England and the South East, and took note of the narra- tives of the emergencies that happened during their shift. Next, we applied the SPAR-H methodology to each task and calculated dependency between the cognitive and action-based tasks. We then calculated the final failure probability and compared the empirical evaluation of error probability with what actually oc- curred. Using Monte Carlo methods and the SPAR-H equations, we finally estimated the HEP that can be readily integrated into the stochastic simulation of a physical power grid. With the intention to calculate the HEP specific to each cascading phase, we propose to increase the number of narrated events and classify each, according to a phase (precursor and escalation). We will then improve the model by calculating the frequency associated with each level of severity for each factor, and by creating a probability distribution for each factor, conditional to a specific phase.

Abstract Hypoxic pulmonary vasoconstriction (HPV) is a compensatory physiological mechanism in the lung that optimizes the matching of ventilation to perfusion and thereby maximizes gas exchange. Historically, HPV has been primarily studied in isolated perfused/ventilated lungs; however, the results of these studies have varied greatly due to different experimental conditions and species. Therefore, in the present study, we utilized the mouse isolated perfused/ventilated lung model for investigation of the role of extracellular Ca2+ and caveolin-1 and endothelial nitric oxide synthase expression on HPV. We also compared HPV using different perfusate solutions: Physiological salt solution (PSS) with albumin, Ficoll, rat blood, fetal bovine serum (FBS), or Dulbecco’s Modified Eagle Medium (DMEM). After stabilization of the pulmonary arterial pressure (PAP), hypoxic (1% O2) and normoxic (21% O2) gases were applied via a ventilator in five-minute intervals to measure HPV. The addition of albumin or Ficoll with PSS did not induce persistent and strong HPV with or without a pretone agent. DMEM with the inclusion of FBS in the perfusate induced strong HPV in the first hypoxic challenge, but the HPV was neither persistent nor repetitive. PSS with rat blood only induced a small increase in HPV amplitude. Persistent and repetitive HPV occurred with PSS with 20% FBS as perfusate. HPV was significantly decreased by the removal of extracellular Ca2+ along with addition of 1 mM EGTA to chelate residual Ca2+ and voltage-dependent Ca2+ channel blocker (nifedipine 1 μM). PAP was also reactive to contractile stimulation by high K+ depolarization and U46619 (a stable analogue of thromboxane A2). In summary, optimal conditions for measuring HPV were established in the isolated perfused/ventilated mouse lung. Using this method, we further confirmed that HPV is dependent on Ca2+ influx.

Hypoxic pulmonary vasoconstriction (HPV) is a compensatory physiological mechanism in the lung that optimizes the matching of ventilation to perfusion and thereby maximizes gas exchange. Historically, HPV has been primarily studied in isolated perfused/ventilated lungs; however, the results of these studies have varied greatly due to different experimental conditions and species. Therefore, in the present study, we utilized the mouse isolated perfused/ventilated lung model for investigation of the role of extracellular Ca2+and caveolin-1 and endothelial nitric oxide synthase expression on HPV. We also compared HPV using different perfusate solutions: Physiological salt solution (PSS) with albumin, Ficoll, rat blood, fetal bovine serum (FBS), or Dulbecco's Modified Eagle Medium (DMEM). After stabilization of the pulmonary arterial pressure (PAP), hypoxic (1% O2) and normoxic (21% O2) gases were applied via a ventilator in five-minute intervals to measure HPV. The addition of albumin or Ficoll with PSS did not induce persistent and strong HPV with or without a pretone agent. DMEM with the inclusion of FBS in the perfusate induced strong HPV in the first hypoxic challenge, but the HPV was neither persistent nor repetitive. PSS with rat blood only induced a small increase in HPV amplitude. Persistent and repetitive HPV occurred with PSS with 20% FBS as perfusate. HPV was significantly decreased by the removal of extracellular Ca2+along with addition of 1 mM EGTA to chelate residual Ca2+and voltage-dependent Ca2+channel blocker (nifedipine 1 μM). PAP was also reactive to contractile stimulation by high K+depolarization and U46619 (a stable analogue of thromboxane A2). In summary, optimal conditions for measuring HPV were established in the isolated perfused/ventilated mouse lung. Using this method, we further confirmed that HPV is dependent on Ca2+influx.

Slow rotational degrees of freedom in ligands can make alchemical FEP simulations unreliable due to inadequate sampling. We addressed this problem by introducing a FEP-based protocol of ligand conformer focusing in explicit solvent. Our method involves FEP transformations between conformers using equilibrium dihedral angle as a reaction coordinate and provides the cost of “focusing” on one specific conformational state that binds to a protein. The calculated conformer focusing term made a considerable difference of 5–10 kJ/mol in computed relative binding free energies of studied Syk inhibitors and significantly improved the resulting accuracy of predictions.

Fenfluramine is prescribed either alone or in combination with phentermine as part of Fen-Phen, an anti-obesity medication. Fenfluramine was withdrawn from the US market in 1997 due to reports of heart valvular disease, pulmonary arterial hypertension, and cardiac fibrosis. Particularly, idiopathic pulmonary arterial hypertension (IPAH), previously referred to as primary pulmonary hypertension (PPH), was found to be associated with the use of Fen-Phen, fenfluramine, and fenfluramine derivatives. The underlying mechanism of fenfluramine-associated pulmonary hypertension is still largely unknown. We reasoned that investigating drug-induced gene dysregulation would enhance our understanding of the fenfluramine-associated pathogenic mechanism of IPAH. Whole-genome gene expression profiles in fenfluramine-treated human pulmonary artery smooth muscle (PASMC) and endothelial (PAEC) cells (isolated from normal subjects) were compared with baseline expression in untreated cells. Fenfluramine treatment caused dysregulation in a substantial number of genes involved in a variety of pathways and biological processes. In addition to several common pathways and biological processes such as “MAPK signaling pathway,” “inflammation response,” and “calcium signaling pathway” shared between both cell types, pathways and biological processes such as “blood circulation,” “muscle system process,” and “immune response” were enriched among the dysregulated genes in PASMC. Pathways and biological processes such as those related to cell cycle, however, were enriched among the dysregulated genes in PAEC, indicating that fenfluramine could affect unique pathways (or differentially) in different types of pulmonary artery cells. While awaiting validation in a larger cohort, these results strongly suggested that fenfluramine could induce significant dysregulation of genes in multiple biological processes and pathways critical for normal pulmonary vascular functions and structure. The transcriptional and posttranscriptional changes in these genes may, therefore, contribute to the pathogenesis of fenfluramine-associated IPAH.

Abstract Fenfluramine is prescribed either alone or in combination with phentermine as part of Fen-Phen, an anti-obesity medication. Fenfluramine was withdrawn from the US market in 1997 due to reports of heart valvular disease, pulmonary arterial hypertension, and cardiac fibrosis. Particularly, idiopathic pulmonary arterial hypertension (IPAH), previously referred to as primary pulmonary hypertension (PPH), was found to be associated with the use of Fen-Phen, fenfluramine, and fenfluramine derivatives. The underlying mechanism of fenfluramine-associated pulmonary hypertension is still largely unknown. We reasoned that investigating drug-induced gene dysregulation would enhance our understanding of the fenfluramine-associated pathogenic mechanism of IPAH. Whole-genome gene expression profiles in fenfluramine-treated human pulmonary artery smooth muscle (PASMC) and endothelial (PAEC) cells (isolated from normal subjects) were compared with baseline expression in untreated cells. Fenfluramine treatment caused dysregulation in a substantial number of genes involved in a variety of pathways and biological processes. In addition to several common pathways and biological processes such as “MAPK signaling pathway,” “infl0ammation response,” and “calcium signaling pathway” shared between both cell types, pathways and biological processes such as “blood circulation,” “muscle system process,” and “immune response” were enriched among the dysregulated genes in PASMC. Pathways and biological processes such as those related to cell cycle, however, were enriched among the dysregulated genes in PAEC, indicating that fenfluramine could affect unique pathways (or differentially) in different types of pulmonary artery cells. While awaiting validation in a larger cohort, these results strongly suggested that fenfluramine could induce significant dysregulation of genes in multiple biological processes and pathways critical for normal pulmonary vascular functions and structure. The transcriptional and posttranscriptional changes in these genes may, therefore, contribute to the pathogenesis of fenfluramine-associated IPAH.

Intracellular Ca2+plays a fundamental role in regulating cell functions in pulmonary arterial smooth muscle cells (PASMCs). A rise in cytosolic Ca2+concentration ([Ca2+]cyt) triggers pulmonary vasoconstriction and stimulates PASMC proliferation. [Ca2+]cytis increased mainly by Ca2+release from intracellular stores and Ca2+influx through plasmalemmal Ca2+-permeable channels. Given the high concentration of intracellular Cl−in PASMCs, Ca2+-activated Cl−(ClCa) channels play an important role in regulating membrane potential and cell excitability of PASMCs. In this study, we examined whether activity of ClCachannels was involved in regulating [Ca2+]cytin human PASMCs via regulating receptor- (ROCE) and store- (SOCE) operated Ca2+entry. The data demonstrated that an angiotensin II (100 nM)-mediated increase in [Ca2+]cytvia ROCE was markedly attenuated by the ClCachannel inhibitors, niflumic acid (100 µM), flufenamic acid (100 µM), and 4,4′-diisothiocyanatostilbene-2,2′-disulfonic acid (100 µM). The inhibition of ClCachannels by niflumic acid and flufenamic acid significantly reduced both transient and plateau phases of SOCE that was induced by passive depletion of Ca2+from the sarcoplasmic reticulum by 10 µM cyclopiazonic acid. In addition, ROCE and SOCE were abolished by SKF-96365 (50 µM) and 2-aminoethyl diphenylborinate (100 µM), and were slightly decreased in the presence of diltiazem (10 µM). The electrophysiological and immunocytochemical data indicate that ClCacurrents were present and TMEM16A was functionally expressed in human PASMCs. The results from this study suggest that the function of ClCachannels, potentially formed by TMEM16A proteins, contributes to regulating [Ca2+]cytby affecting ROCE and SOCE in human PASMCs.

Abstract Intracellular Ca2+ plays a fundamental role in regulating cell functions in pulmonary arterial smooth muscle cells (PASMCs). A rise in cytosolic Ca2+ concentration ([Ca2+]cyt) triggers pulmonary vasoconstriction and stimulates PASMC proliferation. [Ca2+]cyt is increased mainly by Ca2+ release from intracellular stores and Ca2+ influx through plasmalemmal Ca2+-permeable channels. Given the high concentration of intracellular Cl- in PASMCs, Ca2+-activated Cl- (ClCa) channels play an important role in regulating membrane potential and cell excitability of PASMCs. In this study, we examined whether activity of ClCa channels was involved in regulating [Ca2+]cyt in human PASMCs via regulating receptor- (ROCE) and store- (SOCE) operated Ca2+ entry. The data demonstrated that an angiotensin II (100 nM)-mediated increase in [Ca2+]cyt via ROCE was markedly attenuated by the ClCa channel inhibitors, niflumic acid (100 µM), flufenamic acid (100 µM), and 4,4′-diisothiocyanatostilbene-2,2′-disulfonic acid (100 µM). The inhibition of ClCa channels by niflumic acid and flufenamic acid significantly reduced both transient and plateau phases of SOCE that was induced by passive depletion of Ca2+ from the sarcoplasmic reticulum by 10 µM cyclopiazonic acid. In addition, ROCE and SOCE were abolished by SKF-96365 (50 µM) and 2-aminoethyl diphenylborinate (100 µM), and were slightly decreased in the presence of diltiazem (10 µM). The electrophysiological and immunocytochemical data indicate that ClCa currents were present and TMEM16A was functionally expressed in human PASMCs. The results from this study suggest that the function of ClCa channels, potentially formed by TMEM16A proteins, contributes to regulating [Ca2+]cyt by affecting ROCE and SOCE in human PASMCs.

In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are studied, which are helpful to describe a nonhomogeneous BDP X = X(t), t≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration of the BDP). We find conditions of existence of the means and determine bounds for their values, involving also the truncated BDP XN. Finally we present some examples where these bounds are used in order to approximate the double mean.

We study birth-death processes on the nonnegative integers, where {1, 2,…} is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 may occur from any state. We give a condition for absorption (extinction) to be certain and obtain the eventual absorption probabilities when absorption is not certain. We also study the rate of convergence, as t? 8, of the probability of absorption at time t, and relate it to the common rate of convergence of the transition probabilities that do not involve state 0. Finally, we derive upper and lower bounds for the probability of absorption at time tby applying a technique that involves the logarithmic norm of an appropriately defined operator.

The paper is devoted to the estimation of the rate of of exponential convergence of nonhomogeneous queues exhibiting different types of ergodicity. The main tool of our study is the method, which was proposed by the second author in the late 1980s and was subsequently extended and developed in different directions in a series of joint papers by the authors of the present paper. The method originated from the idea of Gnedenko and Makarov to employ the logarithmic norm of a matrix to the study of the problem of stability of nonhomogeneous Markov chains. In the present paper we apply the method to a class of Markov queues with a special form of nonhomogenuity that is common in applications.

Abstract: For a class of Markov queues, we estimate the decay function in different types of exponential convergence.

1.A new method is proposed for the synthesis of perfluoro-tert-alkylamines by the azo coupling of fluorocarbanions with arenediazonium fluoroborates followed by reduction of the arylazoperfluoroalkanes with zinc in trifluoroacetic acid.2.Ethyl a-aminohexafluoroisobutyrate and phenyl 2-aminohexafluoroisopropyl ketone were obtained for the first time by the acid hydrolysis of substituted 3 3-bis(trifluoromethyl) azirines.

1.The reaction of vicinal dihalopolyfluoroalkanes and related compounds with sodium azide causes replacement of halogen by an azide group, probably by an ionic cleavageaddition chain mechanism.2.Nucleophilic azidobromination of fluoroolefins has been carried out by the action of sodium azide and bromine.3.These reactions were used to synthesize new ß-halopolyfluoroalkyl azides.

1.N-Acylimidoyl fluorides of fluorine-containing carboxylic acids were synthesized for the first time.2.Perfluoropropionic acid N-perfluoropivaloylimidoyl fluoride enters 1,4-cycloaddition reactions with nitriles and carbonyl compounds, and by the successive action of CsF and boron trifluoride etherate, converts into the isomeric perfluoro-a-tert-butylpropyl isocyanate.

Conclusions In vicinal dihalopolyfluoroalkanes and related compounds, an exchange of the halogen for fluorine takes place by the action of CsF, according to an ionic elimination—addition chain mechanism.

1.The reaction of fluoromethyldimethylamine with polyfluoroketones leads to N,N-dimethylmethylenimmonium polyfluoroalcoholates which are capable of adding to perfluoroolefins to form polyfluoro-substituted alkoxyalkyldimethylamines.2.Alkali metal perfluoroalcoholates add reversibly to perfluoroolefins to give ß-perfluoroalkoxy carbanions which may be trapped by reaction with electrophilic reagents.3.These results indicate that the perfluoroalkoxyhalogenation of higher perfluoroolefins proceeds by a nucleophilic mechanism.

A CsF-catalyzed condensation of octafluoroisobutylene with tetrafluoroethylene leads to perfluoro-2,6,6-trimethyl-2-heptene as a result of a combined addition of perfluoro-tert-butyl anion and octafluoroisobutylene to the multiple bond of tetrafluoroethylene.