Algebraic solution for geometry from dimensional constraints

1991 ◽  
Author(s):  
J. C. Owen
Keyword(s):  
Algebraic Solution

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.

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.

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

Thermal Effectiveness of Multiple Shell and Tube Pass TEMA E Heat Exchangers

1988 ◽  
Vol 110 (1) ◽  
pp. 54-59 ◽  
Author(s):  
A. Pignotti ◽  
P. I. Tamborenea
Keyword(s):  
Heat Transfer ◽  
Heat Capacity ◽  
Heat Transfer Coefficient ◽  
Heat Exchangers ◽  
Rate Ratio ◽  
Algebraic Solution ◽  
Tube Heat Exchanger ◽  
Transverse Mixing ◽  
Shell And Tube ◽  
The Heat Transfer Coefficient

The thermal effectiveness of a TEMA E shell-and-tube heat exchanger, with one shell pass and an arbitrary number of tube passes, is determined under the usual symplifying assumptions of perfect transverse mixing of the shell fluid, no phase change, and temperature independence of the heat capacity rates and the heat transfer coefficient. A purely algebraic solution is obtained for the effectiveness as a function of the heat capacity rate ratio and the number of heat transfer units. The case with M shell passes and N tube passes is easily expressed in terms of the single-shell-pass case.

scholarly journals An algebraic solution for the relativistic hydrogen atom

2005 ◽  
Vol 339 (3-5) ◽  
pp. 259-268 ◽  
Author(s):  
R.P. Martínez-y-Romero ◽  
H.N. Núñez-Yépez ◽  
A.L. Salas-Brito
Keyword(s):  
Hydrogen Atom ◽  
Algebraic Solution ◽  
Relativistic Hydrogen ◽  
Relativistic Hydrogen Atom

Algebraic solutions in determining the coordinates of the radiator by the results of multi-position measurements of field strength

2021 ◽  
Author(s):  
V.A. Ufaev
Keyword(s):  
Maximum Likelihood ◽  
Field Strength ◽  
Reference Point ◽  
Linear Equations ◽  
Type System ◽  
Energy Parameter ◽  
Likelihood Estimation ◽  
Likelihood Method ◽  
Algebraic Solution ◽  
Algebraic Solutions

On the basis of the hypothesis of equality of the measured and true values of the amplitude of the field strength, an algebraic solution for estimating the unknown coordinates and the energy parameter of the radiator is obtained. Initially, by compiling and solving a redefined system of linear equations by pseudo-rotation of matrices, the coordinates of the emitter are determined under the assumption of independence of the distance to the reference point from the coordinates of the emitter. Then make and solve the square equation concerning distance to a reference point with the subsequent estimation of coordinates and an energy parameter. The ambiguity of the algebraic solution is resolved by comparing the maximum likelihood functional and choosing the parameters at which its maximum is reached. According to the simulation of a cellular-type system in multiplicative noise, the results of algebraic solutions by the maximum likelihood method and the calculated ones are close, except for a special zone where anomalous changes occur due to the limitations of the coordinate determination method. Algebraic solutions for maximum likelihood estimation provide an increase in the calculation speed of about 500 times. The proposed principle can be used in solving the ambiguity of algebraic solutions in systems of difference-rangefinder type and in the inverse problem of self-positioning of the receiving point by the amplitude of the electromagnetic field of beacons with a known location. The article contains 4 figures, a list of references from 9 sources.

scholarly journals Carotid and aortic baroreflexes of the rat: II. Open-loop frequency response and the blood pressure spectrum

2000 ◽  
Vol 279 (5) ◽  
pp. R1922-R1933 ◽  
Author(s):  
Barry R. Dworkin ◽  
Xiaorui Tang ◽  
Alan J. Snyder ◽  
Susan Dworkin
Keyword(s):  
Blood Pressure ◽  
Venous Pressure ◽  
Low Frequency ◽  
Noise Spectrum ◽  
Open Loop ◽  
Step Response ◽  
Algebraic Solution ◽  
Noise Power ◽  
Vascular Conductance ◽  
Aortic Depressor Nerve

To determine the relationship between blood pressure (BP) variability and the open-loop frequency domain transfer function (TF) of the baroreflexes, we measured the pre- and postsinoaortic denervation (SAD) spectra and the effects of periodic and step inputs to the aortic depressor nerve and isolated carotid sinus of central nervous system-intact, neuromuscular-blocked (NMB) rats. Similar to previous results in freely moving rats, SAD greatly increased very low frequency (VLF) (0.01–0.2 Hz) systolic blood pressure (SBP) noise power. Step response-frequency measurements for SBP; interbeat interval (IBI); venous pressure; mesenteric, femoral, and skin blood flow; and direct modulation analyses of SBP showed that only VLF variability could be substantially attenuated by an intact baroreflex. The −3-dB frequency for SBP is 0.035–0.056 Hz; femoral vascular conductance is similar to SBP, but mesenteric vascular conductance has a reliably lower and IBI has a reliably higher −3-dB point. The overall open-loop transportation lag, of which ≤0.1 s is neural, is ≈1.07 s. Constrained algebraic solution, over a range of frequencies, of the pre- and postSAD endogenous noise spectra and the independently determined relative frequency and absolute lag measurements was used to calculate the absolute gain for the open-loop TF. The average gain at 0.02 Hz, the frequency of maximum sensitivity, was 1.47 (95% confidence interval = ±0.48), which agrees well with estimates for the dog reversible sinus. We found that, in the NMB rat, the effects of SAD on the BP noise spectrum were accounted for by the open-loop properties of the baroreflex.

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