The vibration of thermoelastic silicon nitride Nanobeam based on green-naghdi theorem type-II subjected to mechanical damage and ramp-type heat

2021 ◽  
pp. 030932472110582
Author(s):  
Hamdy M Youssef ◽  
Hamzah Alharthi ◽  
Mohamed Kurdi
Keyword(s):  
Silicon Nitride ◽  
Laplace Transform ◽  
Damage Mechanics ◽  
Mechanical Damage ◽  
Theory Model ◽  
Type Ii ◽  
The Laplace Transform ◽  
Heat Parameter ◽  
Beam Thickness

In this work, an analysis for thermoelastic homogeneous isotropic nanobeams under damage mechanics consideration was built. Under easily supported boundary conditions with fixed side ratios, the Green-Naghdi model type-II, an extended thermoelasticity theory model, has been utilized. For the governing differential equations, the Laplace transforms technique was used on the time variable. The answers were found in the domain of the Laplace transform. Tzou’s approximation approach based on an iteration formula was used to calculate the Laplace transform inversions numerically. The numerical findings for a rectangular silicon nitride thermoelastic nanobeam have been obtained and validated. As a case study, we assumed that the beam is thermally loaded with ramp-type heat and that its two edges are simply supported. Figures representing different scenarios have been used to display the numerical results. Mechanical damage value, ramp-time heat parameter and beam thickness are all reported to have a substantial influence on all of the examined functions.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

Management of Prameha with Mustadi Kwatha - A Case Study

2018 ◽  
Vol 3 (4) ◽  
Author(s):  
Dr. Akshay H. Malshikare ◽  
Dr. Sharada Chikurte
Keyword(s):  
Type Ii Diabetes ◽  
Single Case ◽  
Type Ii Diabetes Mellitus ◽  
Ayurvedic Medicine ◽  
Type Ii ◽  
Single Case Study ◽  
Major Health Problem ◽  
Major Health ◽  
Uncontrolled Diabetes

Diabetes is a major health problem in whole world. In spite of many drugs available, uncontrolled diabetes remains a challenge. Moreover, some anti-diabetic drugs are on the verge of withdrawal due to its adverse effects. So, there is an acute need for a new effective and safe drug. So in this case study we used Ayurvedic medicine ‘Mustadi Kwatha’ mentioned in Bhaishajya Ratnawali in Prameha Chikitsa. A single case study was done on use of Mustadi Kwatha on Type II Diabetes Mellitus. Significant reduction was seen in blood sugar level fasting and post-prandial.

SARS-CoV-2 and The Case for Empirical Treatment (Preprint)

2020 ◽  
Author(s):  
Richard P Bartlett ◽  
Alexandria Watkins
Keyword(s):  
Diabetes Mellitus ◽  
Type Ii Diabetes ◽  
The United States ◽  
Type Ii Diabetes Mellitus ◽  
Outpatient Setting ◽  
Empirical Treatment ◽  
Residual Effects ◽  
Type Ii ◽  
West Texas

UNSTRUCTURED Background: This is an outpatient case study that examines two patients in the United States with unique cases that involve oncology, hypertension, Type II Diabetes Mellitus, and Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2), also known as COVID-19. This case study involves two patients in the outpatient setting - treated via telemedicine, with laboratory-confirmed SARS-CoV-2 infection in the West Texas region between March 29th, 2020, and May 14th, 2020. Case Report: The first patient is a 63-year-old female, non-smoker, who is diagnosed with Waldenstrom’s Macroglobulinemia (2012) and Primary Cutaneous Marginal Zone Lymphoma (2020) and the second patient is a 38-year-old male, non-smoker, who has the following comorbidities: Type II Diabetes Mellitus (DM), hypertension, and gout. Both patients were empirically started on budesonide 0.5mg nebulizer twice daily, clarithromycin (Biaxin) 500mg tab twice daily for ten days, Zinc 50mg tab twice daily, and aspirin 81mg tab daily. Both patients have fully recovered with no residual effects. Conclusion: The goal is to call attention to the success of proactive, early empirical treatment, combining a classic corticosteroid (budesonide) administered via a nebulizer and an oral macrolide antibiotic known as clarithromycin (Biaxin).

scholarly journals Algebraic inversion of the Laplace transform

2005 ◽  
Vol 50 (1-2) ◽  
pp. 179-185 ◽  
Author(s):  
P.G. Massouros ◽  
G.M. Genin
Keyword(s):  
Laplace Transform ◽  
The Laplace Transform

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

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