scholarly journals On determinantal recurrence relations of banded matrices

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Zhibin Du ◽  
◽  
Carlos M. da Fonseca ◽  
António Pereira ◽  
◽  
...  
Keyword(s):  
Recurrence Relations ◽  
Banded Matrices ◽  
Simple Alternative

We provide an algorithm based on a less-known result about recurrence relations for the determinants of banded matrices. As a consequence, we prove recent conjectures on the determinants of particular classes of pentadiagonal matrices and simple alternative proofs for other results.

Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials

2018 ◽  
Vol 11 (3) ◽  
pp. 29-39
Author(s):  
E. I. Jafarov ◽  
A. M. Jafarova ◽  
S. M. Nagiyev
Keyword(s):  
Recurrence Relations ◽  
Pollaczek Polynomials

COMMUNICATION OF COMMON AND MARGINAL CHARACTERISTICS OF CONDITIONS IN A TWO-CHANNEL SYSTEM WITH SIMPLE STREAMLINES OF APPLICATIONS

2017 ◽  
pp. 7-19 ◽  
Author(s):  
Georgiy Aleksandrovich Popov
Keyword(s):  
Operating Systems ◽  
Queue Length ◽  
Recurrence Relations ◽  
Queuing Systems ◽  
Channel System ◽  
Current Period ◽  
Multichannel Systems ◽  
Incoming Call ◽  
Marginal Values ◽  
Time Required

The article deals with a two-channel queuing system with a Poisson incoming call flow, in which the application processing time on each of the devices is different. Such models are used, in particular, when describing the operation of the system for selecting service requests in a number of operating systems. A complex system characteristic was introduced at the time of service endings on at least one of the devices, including the queue length, the remaining service time on the occupied device, and the time since the beginning of the current period of employment. This characteristic determines the state of the system at any time. Recurrence relations are obtained that connect this characteristic with its marginal values when there is no queue in the system. The method of introducing additional events was chosen as one of the main methods for analyzing the model. The relationships presented in this article can be used for analysis of the average characteristics of this system, as well as in the process of its simulation. Summarizing the results of work on multichannel systems with an arbitrary number of servicing devices will significantly reduce the time required for simulating complex systems described by sets of multichannel queuing systems.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

Optimizing preventive maintenance over a finite planning horizon in a semi-Markov framework

2020 ◽  
Author(s):  
Antonio Sánchez Herguedas ◽  
Adolfo Crespo Márquez ◽  
Francisco Rodrigo Muñoz
Keyword(s):  
Preventive Maintenance ◽  
Recurrence Relations ◽  
Direct Calculation ◽  
Planning Horizon ◽  
Practical Implementation ◽  
Practical Application ◽  
Mathematical Solution ◽  
Accumulated Reward ◽  
Finite Planning Horizon

Abstract This paper describes the optimization of preventive maintenance (PM) over a finite planning horizon in a semi-Markov framework. In this framework, the asset may be operating, and providing income for the asset owner, or not operating and undergoing PM, or not operating and undergoing corrective maintenance following failure. PM is triggered when the asset has been operating for τ time units. A number m of transitions specifies the finite horizon. This system is described with a set of recurrence relations, and their z-transform is used to determine the value of τ that maximizes the average accumulated reward over the horizon. We study under what conditions a solution can be found, and for those specific cases the solution τ* is calculated. Despite the complexity of the mathematical solution, the result obtained allows the analyst to provide a quick and easy-to-use tool for practical application in many real-world cases. To demonstrate this, the method has been implemented for a case study, and its accuracy and practical implementation were tested using Monte Carlo simulation and direct calculation.

scholarly journals Personalized medicine for reconstruction of critical-size bone defects – a translational approach with customizable vascularized bone tissue

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Annika Kengelbach-Weigand ◽  
Carolina Thielen ◽  
Tobias Bäuerle ◽  
Rebekka Götzl ◽  
Thomas Gerber ◽  
...  
Keyword(s):  
Personalized Medicine ◽  
Large Scale ◽  
Critical Size ◽  
Therapeutic Option ◽  
Living Organism ◽  
Bone Defects ◽  
Sheep Model ◽  
Simple Alternative ◽  
Translational Approach ◽  
Near Future

AbstractTissue engineering principles allow the generation of functional tissues for biomedical applications. Reconstruction of large-scale bone defects with tissue-engineered bone has still not entered the clinical routine. In the present study, a bone substitute in combination with mesenchymal stem cells (MSC) and endothelial progenitor cells (EPC) with or without growth factors BMP-2 and VEGF-A was prevascularized by an arteriovenous (AV) loop and transplanted into a critical-size tibia defect in the sheep model. With 3D imaging and immunohistochemistry, we could show that this approach is a feasible and simple alternative to the current clinical therapeutic option. This study serves as proof of concept for using large-scale transplantable, vascularized, and customizable bone, generated in a living organism for the reconstruction of load-bearing bone defects, individually tailored to the patient’s needs. With this approach in personalized medicine for the reconstruction of critical-size bone defects, regeneration of parts of the human body will become possible in the near future.

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