Algebraic Solution in theV−θSector of the Lee Model

1968 ◽  
Vol 166 (5) ◽  
pp. 1760-1767 ◽  
Author(s):  
M. Bolsterli
Keyword(s):  
Algebraic Solution ◽  
Lee Model

Algebraische Lösung des Eigenwertproblems im N ΘΘ -Sektor des Lee-Modells / An Algebraic Solution of the Eigenvalue Problem in the N ΘΘ-Sector of the Lee-Model

1972 ◽  
Vol 27 (8-9) ◽  
pp. 1172-1176
Author(s):  
K. Helmers ◽  
H. Dewitz
Keyword(s):  
Scattering Amplitudes ◽  
Eigenvalue Problem ◽  
Algebraic Solution ◽  
Lee Model

Abstract An Trying to write the NΘ-eigenstates of the Lee-model in a more compact way, we define operators containing the NΘ-scattering-amplitudes. With these operators, the structure of the Hamiltonian can be strongly simplified. - It is now possible to solve the eigenvalue-problem in the NΘΘ-sector with few simple, pure algebraic, calculations.

Algebraic Solution of the Horton-Izzard Turbulent Overland Flow Model of the Rising Hydrograph

1977 ◽  
Vol 8 (4) ◽  
pp. 249-256 ◽  
Author(s):  
Mohammad Akram Gill
Keyword(s):  
Differential Equation ◽  
Turbulent Flow ◽  
Flow Model ◽  
Overland Flow ◽  
Flow Equation ◽  
Algebraic Solution ◽  
Mixed Flow ◽  
Overland Flow Model

In the differential equation of the overland turbulent flow which was first postulated by Horton, Eq.(6), the value of c equals 5/3. For this value of c, the flow equation could not be integrated algebraically. Horton solved the equation for c = 2 and believed that his solution was valid for mixed flow. The flow equation with c = 5/3 is solved algebraically herein. It is shown elsewhere (Gill 1976) that the flow equation can indeed be integrated for any rational value of c.

scholarly journals Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 303
Author(s):  
Nikolai Krivulin
Keyword(s):  
Decision Problem ◽  
Optimization Problem ◽  
Pareto Frontier ◽  
Sufficient Conditions ◽  
Approximation Error ◽  
Optimal Solution ◽  
Algebraic Solution ◽  
Pairwise Comparisons ◽  
Logarithmic Scale ◽  
Idempotent Algebra

We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective optimization problem of constrained matrix approximation in the Chebyshev sense in logarithmic scale. The problem is to approximate the pairwise comparison matrices for each criterion simultaneously by a common consistent matrix of unit rank, which determines the vector of ratings. We represent and solve the optimization problem in the framework of tropical (idempotent) algebra, which deals with the theory and applications of idempotent semirings and semifields. The solution involves the introduction of two parameters that represent the minimum values of approximation error for each matrix and thereby describe the Pareto frontier for the bi-objective problem. The optimization problem then reduces to a parametrized vector inequality. The necessary and sufficient conditions for solutions of the inequality serve to derive the Pareto frontier for the problem. All solutions of the inequality, which correspond to the Pareto frontier, are taken as a complete Pareto-optimal solution to the problem. We apply these results to the decision problem of interest and present illustrative examples.

scholarly journals Swarm-Inspired Algorithms to Optimize a Nonlinear Gaussian Adaptive PID Controller

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3385
Author(s):  
Erickson Puchta ◽  
Priscilla Bassetto ◽  
Lucas Biuk ◽  
Marco Itaborahy Filho ◽  
Attilio Converti ◽  
...  
Keyword(s):  
Pid Controller ◽  
Optimization Algorithms ◽  
Optimization Methods ◽  
Buck Converter ◽  
Algebraic Solution ◽  
Nonlinear Load ◽  
Bee Colony ◽  
Arduous Task ◽  
Whale Optimization

This work deals with metaheuristic optimization algorithms to derive the best parameters for the Gaussian Adaptive PID controller. This controller represents a multimodal problem, where several distinct solutions can achieve similar best performances, and metaheuristics optimization algorithms can behave differently during the optimization process. Finding the correct proportionality between the parameters is an arduous task that often does not have an algebraic solution. The Gaussian functions of each control action have three parameters, resulting in a total of nine parameters to be defined. In this work, we investigate three bio-inspired optimization methods dealing with this problem: Particle Swarm Optimization (PSO), the Artificial Bee Colony (ABC) algorithm, and the Whale Optimization Algorithm (WOA). The computational results considering the Buck converter with a resistive and a nonlinear load as a case study demonstrated that the methods were capable of solving the task. The results are presented and compared, and PSO achieved the best results.

Diagonal structure of the S-matrix in the lee model

1973 ◽  
Vol 79 (1) ◽  
pp. 146-170 ◽  
Author(s):  
O.W Greenberg ◽  
H Yabuki
Keyword(s):  
Lee Model ◽  
S Matrix

Asymptotic Fields of the Lee Model

1969 ◽  
Vol 10 (8) ◽  
pp. 1326-1339
Author(s):  
Stanley Jernow ◽  
Emil Kazes
Keyword(s):  
Lee Model ◽  
Asymptotic Fields

A completeness theorem for higher order logics

2000 ◽  
Vol 65 (2) ◽  
pp. 857-884 ◽  
Author(s):  
Gábor Sági
Keyword(s):  
Set Theory ◽  
Representation Theorem ◽  
Completeness Theorem ◽  
Higher Order ◽  
Algebraic Solution ◽  
Algebraic Proof ◽  
Relation Algebras ◽  
Cylindric Algebras ◽  
Strong Representation ◽  
Algebraic Counterpart

AbstractHere we investigate the classes of representable directed cylindric algebras of dimension α introduced by Németi [12]. can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, “purely cylindric algebraic” proof for the following theorems of Németi: (i) is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain a strong representation theorem for if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories.

A ghostless lee model

1970 ◽  
Vol 29 (4) ◽  
pp. 373-378 ◽  
Author(s):  
J. Cunningham
Keyword(s):  
Lee Model
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