scholarly journals Modeling of pressure–volume controlled artificial respiration with local derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bahar Acay ◽  
Mustafa Inc ◽  
Yu-Ming Chu ◽  
Bandar Almohsen
Keyword(s):  
Efficient Solution ◽  
Clinical Medicine ◽  
Artificial Respiration ◽  
Pd Controller ◽  
Governing Equations ◽  
Conformable Derivative ◽  
Solution Methods ◽  
Conformable Derivatives ◽  
Derivatives Of ◽  
Volume Controlled

AbstractWe attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated M-derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations.

scholarly journals Generalized Conformable Mean Value Theorems with Applications to Multivariable Calculus

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Francisco Martínez ◽  
Inmaculada Martínez ◽  
Mohammed K. A. Kaabar ◽  
Silvestre Paredes
Keyword(s):  
Research Work ◽  
Mean Value ◽  
Higher Order ◽  
Conformable Derivative ◽  
Mean Value Theorems ◽  
Classical Calculus ◽  
Multivariable Calculus ◽  
Conformable Derivatives ◽  
The Mean ◽  
Derivatives Of

The conformable derivative and its properties have been recently introduced. In this research work, we propose and prove some new results on the conformable calculus. By using the definitions and results on conformable derivatives of higher order, we generalize the theorems of the mean value which follow the same argument as in the classical calculus. The value of conformable Taylor remainder is obtained through the generalized conformable theorem of the mean value. Finally, we introduce the conformable version of two interesting results of classical multivariable calculus via the conformable formula of finite increments.

scholarly journals Measuring Strain Response Mode Shapes with a Continuous-Scan LDV

2002 ◽  
Vol 9 (1-2) ◽  
pp. 19-27 ◽  
Author(s):  
Anthony B. Stanbridge ◽  
Milena Martarelli ◽  
David J. Ewins
Keyword(s):  
Mode Shape ◽  
Response Mode ◽  
Mode Shapes ◽  
Stress And Strain ◽  
Governing Equations ◽  
Convenient Means ◽  
Straight Line ◽  
Polynomial Series ◽  
Spatial Derivatives ◽  
Derivatives Of

A continuous-scan LDV is a convenient means for measuring the response mode shape (ODS) of a vibrating surface, particularly in view of the fact that the ODS is automatically derived as a spatial polynomial series. Second spatial derivatives of the deflection equations are therefore easily derived, and these should, in principle, give curvature equations from which, for a beam or plate of known cross-section, stresses and strains can be obtained directly. Unfortunately, the stress and strain distributions depend critically on higher terms in the original ODS series, which are not accurately measured. This problem can be avoided by a method described here, which enables accurate stress and strain distributions to be derived, from a straight-line LDV scan along a uniform beam, using only five terms in the mode-shape polynomial series. A similar technique could be applied to uniform plates but the analysis and the governing equations are rather more complicated.

scholarly journals Ursolic Acid-Based Derivatives as Potential Anti-Cancer Agents: An Update

2020 ◽  
Vol 21 (16) ◽  
pp. 5920 ◽  
Author(s):  
Vuyolwethu Khwaza ◽  
Opeoluwa O. Oyedeji ◽  
Blessing A. Aderibigbe
Keyword(s):  
Ursolic Acid ◽  
Clinical Medicine ◽  
Biological Activities ◽  
Therapeutic Effects ◽  
Pharmacological Activities ◽  
Pentacyclic Triterpenoid ◽  
Anti Cancer ◽  
Pharmacologically Active ◽  
Derivatives Of ◽  
Cell Signaling Pathways

Ursolic acid is a pharmacologically active pentacyclic triterpenoid derived from medicinal plants, fruit, and vegetables. The pharmacological activities of ursolic acid have been extensively studied over the past few years and various reports have revealed that ursolic acid has multiple biological activities, which include anti-inflammatory, antioxidant, anti-cancer, etc. In terms of cancer treatment, ursolic acid interacts with a number of molecular targets that play an essential role in many cell signaling pathways. It suppresses transformation, inhibits proliferation, and induces apoptosis of tumor cells. Although ursolic acid has many benefits, its therapeutic applications in clinical medicine are limited by its poor bioavailability and absorption. To overcome such disadvantages, researchers around the globe have designed and developed synthetic ursolic acid derivatives with enhanced therapeutic effects by structurally modifying the parent skeleton of ursolic acid. These structurally modified compounds display enhanced therapeutic effects when compared to ursolic acid. This present review summarizes various synthesized derivatives of ursolic acid with anti-cancer activity which were reported from 2015 to date.

Entry Flow in Straight and Curved Channels With Slender Channel Approximations

1977 ◽  
Vol 99 (4) ◽  
pp. 666-673 ◽  
Author(s):  
F. G. Blottner
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Streamwise Velocity ◽  
Governing Equations ◽  
Core Flow ◽  
The Core ◽  
Curved Channels ◽  
Box Scheme ◽  
Dependent Variables ◽  
Derivatives Of

The slender channel equations for laminar flow are solved downstream of the entrance of curved channels of variable height. The singularities at the entrance are removed with coordinate transformations which stretch the boundary layer and shrink the core flow. Initial conditions at the entrance are obtained from the governing equations with only the streamwise velocity specified. A modified box scheme is used to develop a finite-difference method which allows the derivatives of the dependent variables across the channel to be discontinuous at the interface between the boundary layer and core flow. Numerical results are presented for several channel geometries and entry conditions.

scholarly journals On fractional KdV-burgers and potential KdV equations: Existence and uniqueness results

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2107-2117
Author(s):  
Mir Hashemi ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Exact Solutions ◽  
Invariant Subspace ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Subspace Method ◽  
Conformable Derivative ◽  
Existence And Uniqueness Results ◽  
Kdv Equations ◽  
Uniqueness Results ◽  
Conformable Derivatives

Recently a new kind of derivatives, namely the conformable derivative is introduced which have not many drawbacks of other fractional derivatives. Two types of KdV equations with conformable derivative are investigated in this paper. Ex-istence and uniqueness of two different equations of KdV class with conformable derivatives are investigated. It is also shown that the invariant subspace method can be extended to find the exact solutions of these equations.

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