A Probabilistic Symbolic Algorithm to Find the Minimum of a Polynomial Function on a Basic Closed Semialgebraic Set

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

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Exchange rates in India: current account monetarism in a nonlinear context

Studies in Nonlinear Dynamics & Econometrics ◽

10.1515/snde-2019-0072 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Aditi Chaubal

Keyword(s):

Exchange Rate ◽

Current Account ◽

Polynomial Function ◽

Mean Reversion ◽

Smooth Transition ◽

Monetary Model ◽

Forecast Performance ◽

Long Run ◽

Nonlinear Mean Reversion ◽

Long Run Equilibrium

AbstractThe Indian exchange rate system has evolved from a pegged system to the current managed float. The study examines the presence of a long-run equilibrium in the monthly Indian exchange rate (Rs/USD) using a current account monetary model (or flexible price monetary model) while accounting for different nonlinearities over the period January 1993 to January 2014 (pre-inflation targeting period). The nonlinear adjustment to disequilibria is modelled using a nonlinear error correction model (NLECM). The nonlinear current account monetarism (CAM) model includes nonlinear transformations of long-run dynamics in the ECM to account for different nonlinearities: multiple equilibria (cubic polynomial function), nonlinear mean reversion (rational polynomial function), and smooth and gradual regime switches (exponential smooth transition autoregressive (ESTAR) function). The NLECM-ESTAR model outperforms other alternatives based on model and forecast performance measures, implying the existence of nonlinear mean reversion and smooth transition across different periods of overvaluation and undervaluation of the exchange rate. This implies the presence of asymmetric adjustment to the movements from the long-run equilibrium, but the nature of such transitions is smooth and not abrupt. The paper also establishes the uniqueness of the long-run equilibrium. A comparison to the sticky price monetary model could not be made due to stationary exchange rate disequilibrium.

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Multivariate piecewise polynomials

Acta Numerica ◽

10.1017/s0962492900002348 ◽

1993 ◽

Vol 2 ◽

pp. 65-109 ◽

Cited By ~ 20

Author(s):

C. de Boor

Keyword(s):

Approximation Theory ◽

Variational Approach ◽

Polynomial Function ◽

Piecewise Polynomial ◽

Multivariate Splines ◽

Piecewise Polynomial Function ◽

Multivariate Spline ◽

Piecewise Polynomials ◽

The Subject ◽

Function Of Several Arguments

This article was supposed to be on ‘multivariate splines». An informal survey, taken recently by asking various people in Approximation Theory what they consider to be a ‘multivariate spline’, resulted in the answer that a multivariate spline is a possibly smooth piecewise polynomial function of several arguments. In particular the potentially very useful thin-plate spline was thought to belong more to the subject of radial basis funtions than in the present article. This is all the more surprising to me since I am convinced that the variational approach to splines will play a much greater role in multivariate spline theory than it did or should have in the univariate theory. Still, as there is more than enough material for a survey of multivariate piecewise polynomials, this article is restricted to this topic, as is indicated by the (changed) title.

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A transition from a decelerated to an accelerated phase of the universe expansion from the simplest non-trivial polynomial function of T $T$ in the f ( R , T ) $f(R,T)$ formalism

Astrophysics and Space Science ◽

10.1007/s10509-016-2788-y ◽

2016 ◽

Vol 361 (7) ◽

Cited By ~ 33

Author(s):

P. H. R. S. Moraes ◽

G. Ribeiro ◽

R. A. C. Correa

Keyword(s):

Polynomial Function ◽

Universe Expansion ◽

The Universe

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Parallel One-Step Control of Parametrised Boolean Networks

Mathematics ◽

10.3390/math9050560 ◽

2021 ◽

Vol 9 (5) ◽

pp. 560 ◽

Cited By ~ 1

Author(s):

Luboš Brim ◽

Samuel Pastva ◽

David Šafránek ◽

Eva Šmijáková

Keyword(s):

Control Problem ◽

Boolean Networks ◽

Actual State ◽

Worst Case ◽

Symbolic Data ◽

One Step ◽

The One ◽

Step Control ◽

Symbolic Algorithm ◽

Naive Approach

Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as this model allows leaving some update functions unspecified. In our work, we attack the control problem for ParBNs with asynchronous semantics. While there is an extensive work on controlling BNs without parameters, the problem of control for ParBNs has not been in fact addressed yet. The goal of control is to ensure the stabilisation of a system in a given state using as few interventions as possible. There are many ways to control BN dynamics. Here, we consider the one-step approach in which the system is instantaneously perturbed out of its actual state. A naïve approach to handle control of ParBNs is using parameter scan and solve the control problem for each parameter valuation separately using known techniques for non-parametrised BNs. This approach is however highly inefficient as the parameter space of ParBNs grows doubly exponentially in the worst case. We propose a novel semi-symbolic algorithm for the one-step control problem of ParBNs, that builds on symbolic data structures to avoid scanning individual parameters. We evaluate the performance of our approach on real biological models.

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Polynomial Moving Fitting Method for Edge Identification

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.308-310.2560 ◽

2011 ◽

Vol 308-310 ◽

pp. 2560-2564 ◽

Cited By ~ 2

Author(s):

Xiang Rong Yuan

Keyword(s):

Edge Detection ◽

Curve Fitting ◽

Polynomial Function ◽

High Order ◽

Polynomial Fitting ◽

Fitting Method ◽

Order Polynomial ◽

Better Than ◽

Low Order

A moving fitting method for edge detection is proposed in this work. Polynomial function is used for the curve fitting of the column of pixels near the edge. Proposed method is compared with polynomial fitting method without sub-segment. The comparison shows that even with low order polynomial, the effects of moving fitting are significantly better than that with high order polynomial fitting without sub-segment.

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Soft Impact in a Biomechanical System With Shape Memory Element

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4036614 ◽

2017 ◽

Vol 12 (6) ◽

Cited By ~ 4

Author(s):

R. Rusinek ◽

M. Szymanski ◽

J. Warminski

Keyword(s):

Shape Memory ◽

Middle Ear ◽

Polynomial Function ◽

Ossicular Chain ◽

Excitation Amplitude ◽

Patient Needs ◽

Memory Element ◽

The Impact ◽

Irregular Behavior ◽

Two Degree Of Freedom

The analysis of the shape memory prosthesis (SMP) of the middle ear is presented in this paper. The shape memory prosthesis permits the adjustment of its length to individual patient needs, but sometimes the prosthesis cannot be properly fixed to the stapes. In this case, the impact between the prosthesis and stapes is important. Therefore, the reconstructed middle ear is modeled as a two degree-of-freedom system with a nonlinear shape memory element and soft impact to represent its behavior when the prosthesis is not properly placed or fixed. The properties of the shape memory prosthesis, in the form of a helical spring, are represented by a polynomial function. The system exhibits advisable periodic and undesirable aperiodic and irregular behavior depending on the excitation amplitude, the frequency, and the prosthesis length. The prosthesis length can change, resulting in a modification of the distance between the prosthesis and the stapes. The results of this study provide an answer in terms of how the prosthesis length, which produces the ossicular chain tension, influences the system dynamics and its implication in medical practice.

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2-D gravity modeling with analytically defined geometry and quadratic polynomial density functions

Geophysics ◽

10.1190/1.1444677 ◽

1999 ◽

Vol 64 (6) ◽

pp. 1730-1734 ◽

Cited By ~ 34

Author(s):

Beatriz Martín‐Atienza ◽

Juan García‐Abdeslem

Keyword(s):

Numerical Methods ◽

Polynomial Function ◽

Continuous Functions ◽

Model Solution ◽

Gravity Modeling ◽

Density Functions ◽

Gravity Effect ◽

New Methods ◽

Order Polynomial ◽

Broad Variety

New methods for 2-D modeling of gravity anomaly data are developed following an approach that uses both analytic and numerical methods of integration. The forward‐model solution developed here is suitable to calculate the gravity effect caused by a 2-D source body bounded either laterally or vertically by continuous functions. In our models, the density contrast is defined by a second‐order polynomial function of depth and distance along the profile. We present several examples to show that our models are capable of accommodating a broad variety of geologic structures.

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