Optimum Profile of Thin Fins With Volumetric Heat Generation: A Unified Approach

2005 ◽  
Vol 127 (8) ◽  
pp. 945-948 ◽  
Author(s):  
B. Kundu ◽  
P. K. Das
Keyword(s):  
Closed Form ◽  
Heat Generation ◽  
Variational Calculus ◽  
Optimality Criteria ◽  
Closed Form Expression ◽  
Pin Fins ◽  
Fin Thickness ◽  
Optimum Profile ◽  
Special Case ◽  
Volumetric Heat Generation

In this paper, a generalized methodology for the optimum design of thin fins with uniform volumetric heat generation is described. Using variational calculus, the optimum profiles of longitudinal, annular, and pin fins are determined from the basic fin equation under the constraint of specified fin volume. From a common optimality criteria, a generalized closed form expression for the fin thickness is obtained for the above three types of fins. Closed-form expressions are also obtained for the optimum profiles of longitudinal and pin fins. As a special case, both the temperature profile and the shape of optimum fins without heat generation are determined.

scholarly journals Recombination and sterility in inversion homo- and heterokaryotypes under a general counting model of chiasma interference

2020 ◽  
Author(s):  
Øystein Kapperud
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Poisson Model ◽  
Closed Form Expression ◽  
Form Expression ◽  
Special Case ◽  
Counting Model ◽  
Chiasma Interference

AbstractIt has long been known that chiasmata are not independently generated along the chromosome, a phenomenon known as chiasma interference. In this paper, I suggest a model of chiasma interference that generalizes the Poisson model, the counting model, the Poisson-skip model and the two-pathway counting model into a single framework, and use it to derive infinite series expressions for the sterility and recombination pattern probabilities in inversion homo- and heterokaryotypes, and a closed-form expression for the special case of the two-pathway counting model in homokaryotypes.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

Simple Closed-Form Expression to Estimate the Ring Ratio of 16-APSK to Compensate for Distortion in Nonlinear Systems

2017 ◽  
Author(s):  
M.J. Cañavate-Sánchez ◽  
A. Segneri ◽  
S. Godi ◽  
A. Georgiadis ◽  
S. Kosmopoulos ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression ◽  
Ring Ratio

Approximate closed-form expression for the ergodic capacity of polarisation-diversity MIMO systems

2004 ◽  
Vol 40 (19) ◽  
pp. 1192 ◽  
Author(s):  
J. Pérez ◽  
J. Ibáñez ◽  
L. Vielva ◽  
I. Santamaría
Keyword(s):  
Closed Form ◽  
Mimo Systems ◽  
Ergodic Capacity ◽  
Closed Form Expression ◽  
Form Expression
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