ANALYTICAL APPROACH TO THE PENNE’S BIOHEAT EQUATION FOR THE EVALUATION OF TEMPERATURE FOR DEEP SEATED TISSUES

In clinical practice, body temperature is an acclaimed indicator for diagnosis and treatments amongst other follow - ups. This work studied the temperature distribution in deep-seated tissues using Penne’s bio-heat equation (PBE). The analytical solution of the PBE was formulated using the separation of variable technique. The resulting solution gives an expression for tissue temperature in organs that are located inside the body. This revealed that the tissue temperature is subject to changes in tissue thickness, the distance of tissue from the skin surface and other thermal properties of tissues under consideration.

Positive solutions for (p, q)-equations with convection and a sign-changing reaction

We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a reaction which is dependent on the gradient. We look for positive solutions and we do not assume that the reaction is nonnegative. Using a mixture of variational and topological methods (the "frozen variable" technique), we prove the existence of a positive smooth solution.

Does Local Environmental Governance Improve Tourism Companies’ Performance? Evidence from Vietnam

Institutions (rules of law) are important to tourism activities. However, national institutions cannot become effective when the execution of rules of law is inconsistent at the local levels. This study thus examines the role of local governance arrangements on the performance of tourism companies, focusing on environmental governance quality. Utilizing institutional theory, we propose a U-shaped relationship between tourism performance and environmental governance. When environmental governance arrangements are initially implemented, the performance of local tourism companies may be negatively affected due to institutional conflicts. However, as new environmentally responsible values are gradually institutionalized, the performance of the local tourism sector will improve. Analyzing more than three thousand tourism companies in Vietnam in 2018 using instrumental variable technique to control for endogeneity, we find some evidence to support the U-shaped function. Also, it is found that the U-shaped effect is stronger on foreign inbound tourists than on domestic tourists.

Performance assessment of the complex repairable system with n-identical units under (k-out-of-n: G) scheme and copula linguistic repair approach

PurposeThis paper analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The computed results are more supportable for repairable system performability analysis.Design/methodology/approachIn this paper, the authors have analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The supplementary variable technique has employed for analyzing the performance of the system.FindingsReliability measures have been computed for different types of configuration. It generalized the results for purely series and purely parallel configurations.Research limitations/implicationsThis research may be beneficial for industrial system performances whereas a k-out-of-n-type configuration exists.Practical implicationsNot sure as it is a theoretical assessment.Social implicationsThis research may not have social implications.Originality/valueThis work is the sole work of authors that have not been communicated to any other journal before.

Stochastic Behavior of a Two-Unit Parallel System with Dissimilar Units and Optional Vacations under Poisson Shocks

This article examines the impact of some system parameters on an industrial system composed of two dissimilar parallel units with one repairman. The active unit may fail due to essential factors like aging or deteriorating, or exterior phenomena such as Poisson shocks that occur at various time periods. Whenever the value of a shock is larger than the specified threshold of the active unit, the active unit will fail. The article assumes that the repairman has the right to take any of two decisions at the beginning of the system operation: either a takes a vacation if the two units work in a normal way, or stay in the system to monitor the system until the first system failure. In case of having a failure in any of the two units during the absence of the repairman, the failing unit will have to wait until the repairman is called back to work. We suppose that the value of every shock is assumed to be i.i.d. with some known distribution. The length of the repairman’s vacation, repair time, and recall time are arbitrary distributions. Various reliability measures have been calculated by the supplementary variable technique and the Markov’s vector process theory. At last, numerical computation and graphical analysis have been given for a particular case to validate the derived indices.

Synchronized abandonment in discrete-time renewal input queues with vacations

<p style='text-indent:20px;'>We consider a discrete-time infinite buffer renewal input queue with multiple vacations and synchronized abandonment. Waiting customers get impatient during the server's vacation and decide whether to take service or abandon simultaneously at the vacation completion instants. Using the supplementary variable technique and difference operator method, we obtain an explicit expression to find the steady-state system-length distributions at pre-arrival, random, and outside observer's observation epochs. We provide the stochastic decomposition structure for the number of customers and discuss the various performance measures. With the help of numerical experiments, we show that the method formulated in this work is analytically elegant and computationally tractable. The results are appropriate for light-tailed inter-arrival distributions and can also be leveraged to find heavy-tailed inter-arrival distributions.</p>

Reliability and Availability analysis of a cloud computing transition system under multiple failures

PurposeTo analyze the performance of multistate cloud computing transition system through the various reliability measures is the purpose of this paper.Design/methodology/approachIn this article, a mathematical model for a multistate cloud computing transition system with various types of failures has been analyzed by using the Markov process, supplementary variable technique and Laplace transformation.FindingsVarious reliability measures such that reliability, availability, mean time to failure (MTTF), mean time to repair and cost analysis have also been analyzed. This article presents some geographic illustrations for the practical utility of the model.Originality/valueThe authors developed a mathematical model to analyze the reliability of the cloud computing transition system by considering the possible failures.

Non – Markovian Queue with Multi vacation Policies

This article characterizes a lining framework wherein the administration is given in a solitary stage. Clients show up in bunches follows the FCFS discipline. Customers appearance follows a Poisson dispersion. Administration follows a general conveyance. After the culmination of the administration, if there are no clients in the framework, server goes for a long get-away with a likelihood p in any case server remains in the framework with likelihood 1-p.Here long excursion is given in two phases. After the fulfillment of the long excursion of stage2, it gets into a discretionary short get-away. Next, administration proceeds once more. This covering issue is analyzed through a birth passing system of Queuing speculation and it's clarified by one among the coating issue procedure known to be gainful variable technique. The model is all around explained very well by techniques for sensible application. The model is all around supported by methods for numerical depiction and graphical technique

Transient Analysis of M[X1],M[X2]/G1,G2/1 retrial queueing system with priority services, working breakdown, start up/close down time, Bernoulli vacation, reneging and balking

This paper considers M[X1],M[X2]/G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the pre-emptive priority rule subject to working breakdown, startup/closedown time and Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there are no priority customers present in the system the server may go for a vacation or close down the system. On completion of the close down, the server needs some time to set up the system. The priority customers who find the server busy are queued in the system. A low-priority customer who find the server busy are routed to a retrial (orbit) queue that attempts to get the service. The system may breakdown at any point of time when it is in operation. However, when the system fails, instead of stopping service completely, the service is continued only to the high priority customers at a slower rate. We consider balking to occur to the low priority customer while the server is busy or idle, and reneging to occur at the high priority customers during server’s vacation, start up/close down time. Using the supplementary variable technique, we derive the joint distribution of the server state and the number of customers in the system. Finally, some performance measures and numerical examples are presented.