scholarly journals Logarithmic Generalization of the Lambert W Function and Its Applications to Adiabatic Thermostatistics of the Three-Parameter Entropy

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Cristina B. Corcino ◽  
Roberto B. Corcino
Keyword(s):  
Taylor Series ◽  
Ideal Gas ◽  
Lambert W Function ◽  
Approximation Formula ◽  
Lambert Function ◽  
Specific Heats ◽  
Taylor Series Approximation ◽  
Series Approximation

A generalization of the Lambert W function called the logarithmic Lambert function is introduced and is found to be a solution to the thermostatistics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula, and branches of the function are obtained. The heat functions and specific heats are computed using the “unphysical” temperature and expressed in terms of the logarithmic Lambert function.

Conservation Law of Energy Using Fractional Taylor Series

2016 ◽  
Vol 841 ◽  
pp. 105-109
Author(s):  
Ali Soroush ◽  
Farzam Farahmand
Keyword(s):  
Taylor Series ◽  
Conservation Law ◽  
Control Volume ◽  
Fractional Differentiation ◽  
Linear Flow ◽  
First Order ◽  
Taylor Series Approximation ◽  
Series Approximation ◽  
Non Linear ◽  
Flow Power

Customary conservation law of energy is commonly derived using first-order Taylor series, which is only valid for situation of linear changes in the flow of energy in control volume. It is shown that using high-order Taylor series will approximate non-linear changes in the flow of energy but in fact some error remains. We used fractional Taylor series which exactly represent non-linear flow of energy in control volume. By replacing the customary integer-order Taylor series approximation with the fractional-order Taylor series approximation, limitation of the linear flow of energy in the control volume and the restriction that the control volume must be infinitesimal is omitted. The innovation of this paper is we show that as long as the order of fractional differentiation is equal with flow power-law, the fractional conservation law of energy will be exact and it can be used for fluid in a porous medium.

scholarly journals Squaring Technique using Vedic Mathematics

2021 ◽  
Author(s):  
Jasmine Bajaj ◽  
Babita Jajodia
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Number System ◽  
Approximation Technique ◽  
Approximation Techniques ◽  
Vedic Mathematics ◽  
Decimal Number ◽  
Taylor Series Approximation ◽  
Series Approximation ◽  
Interesting Approach

Vedic Mathematics provides an interesting approach to modern computing applications by offering an edge of time and space complexities over conventional techniques. Vedic Mathematics consists of sixteen sutras and thirteen sub-sutras, to calculate problems revolving around arithmetic, algebra, geometry, calculus and conics. These sutras are specific to the decimal number system, but this can be easily applied to binary computations. This paper presented an optimised squaring technique using Karatsuba-Ofman Algorithm, and without the use of Duplex property for reduced algorithmic complexity. This work also attempts Taylor Series approximation of basic trigonometric and inverse trigonometric series. The advantage of this proposed power series approximation technique is that it provides a lower absolute mean error difference in comparison to previously existing approximation techniques.

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