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This research paper investigates the dynamic behaviour of a heterogeneous three-server queuing model with multiple vacation. The model also accounts for the possibility that a disaster could occur during busy periods or on vacation, in which case the restoration process would begin immediately. The time-dependent probabilities of system size are presented in the work with explicit equations computed in terms of modified Bessel functions, employing generating functions. To support the theoretical conclusions, numerical examples are given.

We consider a single server queuing model with three service types, each with three phases. In which the customers arrive according to a Poisson process and the service time of each customer follows Hyper-Erlang distribution. We analyzed the model with interruptions, such as breakdown, repair and single working vacation. The standby server works whenever the main server under breakdown. Using the matrix geometric method, the steady-state probability vector of the model is examined and finally, some numerical examples are presented.

In the presence of a newly created brightener, the zinc metal is coated on steel using the electro deposition process. Experiments using hull cells are used to optimize the settings and components of plating baths. Tafel Polarization and EIS techniques were used to conduct corrosion experiments, which made it possible to investigate the brilliant zinc coating's effective corrosion resistance. SEM and Reflectance spectroscopy both confirm that the bright zinc coating has modified surface morphology. XRD analysis is used to study and validate changes in crystallite orientation and phase structure. Electrochemical methods and theoretical molecular dynamic (MD) simulations were used to examine the interaction between Zn and the metal surface. FTIR spectroscopy has been used in blend investigations which impacts on the physical characteristics of polymer blends. The results of these research showed how novel brighteners can improve zinc deposits' brightness and corrosion resistance when applied to mild steel substrates.

Aims Patients referred to a Personality Disorder (PD) Service are frequently not offered treatment. This has profound implications for patients (who feel dismissed or rejected), referrers (who are perplexed as they have clearly diagnosed a PD) and the PD services themselves (their raison d'etre being to treat PD patients). A systematic search identified no literature on reasons for non-acceptance. This study aimed to describe reasons for not offering therapy in patients, after a specialist assessment. Methods We conducted a case series of 50 patients assessed in a specialist PD service. We collected data from routine service notes, using thematic analysis to identify categories of the reasons identified for treatment unsuitability. Results Reasons for assessing treatment unsuitability (in descending order) were: 1.(20%) – Lack of engagement (e.g. repeated non-attendance of appointments) and motivation to change (e.g. externalising all responsibility, or believing they completely lacked agency in their actions). 2.(18%) – Extremely harmful substance misuse or dependence. 3.(13%) – The underlying diagnosis (e.g. not meeting diagnostic criteria for a personality disorder or a severe psychopathy) and level of severity (e.g. too mild for a specialist service). 4.(11%) – Identified areas of psychological work has very little to no relation to interpersonal difficulties or relationships. 5.(11%) – A comorbid eating disorder (e.g. BMI < 17.5). 6.(9%) – Another service identified as being more appropriate (e.g. another psychological service). 7.(8%) – Risk of aggression to the therapist. 8.(5%) – Comorbid axis I disorder being the primary problem. 9.(5%) – Extreme self-harming behaviours requiring crisis interventions. Conclusion Referrers 1.To accept that many patients with PD will fail to actively engage in psychotherapy. 2.To consider whether severity is of a level requiring specialist PD treatment; or if the patient needs a forensic psychotherapy service rather than a non-forensic PD service. 3.To consider whether the comorbid conditions (e.g. dependent alcohol use) are in fact the primary diagnosis and thus require treatment before the PD service intervention. PD services 1.Need to develop novel interventions to help patients become more active and engaged in the assessment and thus progress onto treatment. 2.Need to inform referrers on their criteria for not offering treatment, allowing referrers the ability to gauge more accurately when to refer the patient.

This study explores a nonautonomous model of prey-predator dynamics, featuring continuous distributed delay and diffusion, with time-dependent parameters. Our model depicts two ecological patches hosting two species: predators remain localized in one patch, while prey can disperse between both. Our analysis concentrates on ensuring the model’s consistent presence and achieving global stability. Additionally, we derive necessary conditions for periodic solutions by developing a pertinent Lyapunov function.

Weeds pose a significant challenge to environmental sustainability and agricultural productivity, contributing to land degradation and reduced forest health. Reliance on chemical herbicides for weed control has raised serious concerns for food safety and public health, and has necessitated the development of sustainable weed management strategies. To identify viable weed-eradication techniques, this study introduces a novel hybrid fuzzy multi-criteria decision-making (F-MCDM) approach. Numerical illustration of the proposed framework is shown through a case study to demonstrate strong practical applicability. A total of eight contradictory criteria are used to evaluate the sustainability of the alternatives. To effectively balance subjective expert opinions and objective data, the significance of each criterion is thoroughly assessed using the integration of factor relationship analysis (FARE) and criterion impact loss assessment (CILOS). With a weight of 0.2507, weed density was shown to be the most significant factor, outweighing factors like cost and time consumption. The designed fusion model applied the trace to median index method to rank alternatives (RATMI), with precision weed control emerging as the optimal solution in a t-spherical probabilistic hesitant fuzzy (t-SPHF) environment. By targeting only the specific areas where weeds are present, precision techniques which includes smart machines and autonomous robots decrease chemical runoff and the risk of harming beneficial plants and organisms, ultimately leading to healthier ecosystems. The model’s reliance on criterion weights was supported by sensitivity analysis, and comparative analysis demonstrated the t-SPHF set-based method’s resilience in managing intricate, multi-criteria scenarios. This framework for hybrid decision-making is a dependable resource for directing decisions on sustainable weed control, with possible consequences for agricultural policy and practice. Future research may delve deeper into its utilization in various environmental scenarios.

We consider a single server queueing model in which the customers arrive according to a Markovian Arrival Process (MAP). We modeled this queueing system with many kinds of service where the customers can choose any kind from the server. Each kind of service follows Phase-type (PH) distribution. We analyzed the model with breakdown, repair, single working vacation and standby server. A standby server works only when the main server is breakdown while serving the customer during a busy or vacation period. Using the matrix-geometric approach, we examined the model. A few real-world examples have been given, and several graphical and numerical examples have also been provided.

This study quantifies the performance of an international cohort of cornea specialists in image-based differentiation of bacterial and fungal keratitis, identifying significant regional variation and establishing a reference standard for comparison against machine learning models.

Abstract The probabilistic hesitant elements (PHFEs) are a beneficial augmentation to the hesitant fuzzy element (HFE), which is intended to give decision-makers more flexibility in expressing their biases while using hesitant fuzzy information. To extrapolate a more accurate interpretation of the decision documentation, it is sufficient to standardize the organization of the elements in PHFEs without introducing fictional elements. Several processes for unifying and arranging components in PHFEs have been proposed so far, but most of them result in various disadvantages that are critically explored in this paper. The primary objective of this research is to recommend a PHFE unification procedure that avoids the deficiencies of operational practices while maintaining the inherent properties of PHFE probabilities. The prevailing study advances the hypothesis of permutation on PHFEs by suggesting a new sort of PHFS division and subtraction compared with the existing unification procedure. Eventually, the proposed PHFE-unification process will be used in this study, an innovative PHFEs based on the Weighted Aggregated Sum Product Assessment Method–Analytic Hierarchy Process (WASPAS–AHP) perspective for selecting flexible packaging bags after the prohibition on single-use plastics. As a result, we have included the PHFEs-WASPAS in our selection of the most effective fuzzy environment for bio-plastic bags. The ranking results for the suggested PHFEs-MCDM techniques surpassed the existing AHP methods in the research study by providing the best solution. Our solutions offer the best bio-plastic bag alternative strategy for mitigating environmental impacts.

Background: Alzheimer’s disease (AD) is a severe, varied, and complex brain condition that gradually impairs memory and cognitive function. Epidemiological studies have shown that patients who have a history of long-term NSAID use have a decreased risk of developing AD. The objective of this study is to conduct the structural analysis of a novel ibuprofen prodrug and test its anti-Alzheimer’s properties. Methods: Computational and docking studies were conducted using AMBER 18 package. The in-vivo studies were performed using aluminum chloride-induced experimental AD in rats. Adult Wistar rats of either sex were used and treated with aluminum chloride (32.5 mg/kg, p.o) and ibuprofen prodrug (50 mg/kg, p.o) daily for 30 days. The hole-board test and elevated plus maze were conducted on 10th, 20th and 30th day. Further, on 31st day, animals were euthanized and the brain tissue was used for histopathology. The results obtained were subjected to statistical analysis by one-way ANOVA and Dunnet’s test, p

Optically good quality morpholine p-nitrophenol (MPN) crystal was effectively grown from a slow evaporation technique. Unit cell parameters of MPN were estimated by single crystal X-ray diffraction and it crystallizes in the P21/c space group. The existence of several functional groups in MPN is established by FTIR analysis. UV–vis-NIR spectroscopy inspected the lower cut-off wavelength and band gap energy of MPN. A fluorescence spectral analysis of MPN was carried out. Experimental and computational calculations of nonlinear optical activity have been studied. The second harmonic generation of MPN is 1.9 times greater than the reference KDP material. Using the Z-scan approach, the grown crystal's third-order NLO susceptibility (χ3) was determined. The laser damage threshold of MPN crystal is studied and it is estimated as 5.12 GW/cm2. The highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO) and molecular tying-up explorations were executed. Ground state enhanced geometry and molecular electrostatic potential (MEP) were analysed.