scholarly journals Analysis of Polynomial Nonlinearity Based on Measures of Nonlinearity Algorithms

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3426
Author(s):  
Mahendra Mallick ◽  
Xiaoqing Tian
Keyword(s):  
Extrinsic Curvature ◽  
Two Dimensions ◽  
Affine Function ◽  
Linear Filtering ◽  
Polynomial Nonlinearity ◽  
Polynomial Curve ◽  
Non Linear ◽  
Curvature Measures ◽  
Independent Variable ◽  
The Mean

We consider measures of nonlinearity (MoNs) of a polynomial curve in two-dimensions (2D), as previously studied in our Fusion 2010 and 2019 ICCAIS papers. Our previous work calculated curvature measures of nonlinearity (MoNs) using (i) extrinsic curvature, (ii) Bates and Watts parameter-effects curvature, and (iii) direct parameter-effects curvature. In this paper, we have introduced the computation and analysis of a number of new MoNs, including Beale’s MoN, Linssen’s MoN, Li’s MoN, and the MoN of Straka, Duník, and S̆imandl. Our results show that all of the MoNs studied follow the same type of variation as a function of the independent variable and the power of the polynomial. Secondly, theoretical analysis and numerical results show that the logarithm of the mean square error (MSE) is an affine function of the logarithm of the MoN for each type of MoN. This implies that, when the MoN increases, the MSE increases. We have presented an up-to-date review of various MoNs in the context of non-linear parameter estimation and non-linear filtering. The MoNs studied here can be used to compute MoN in non-linear filtering problems.

The laminar boundary-layer equations II. Integration of non-linear ordinary differential equations

1948 ◽  
Vol 192 (1031) ◽  
pp. 567-575 ◽  
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Differential Equations ◽  
Two Dimensions ◽  
Boundary Layer Problem ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Non Linear ◽  
Independent Variable ◽  
Linear Differential

The aim of this paper is to find particular integrals of non-linear differential equations which satisfy certain boundary conditions and tend exponentially to zero at infinity. The equations arise in connexion with the problem of integration of the equations of laminar flow in two dimensions. The paper consists of two parts. In the first part the equation / " '+ / / ' = A ( 1 - /'2) is discussed, where A is generally a known parameter, and the primes denote deviations with respect to the independent variable, x. This is the well-known Falkner & Skan’s (1930) equation. It was derived in connexion with the solution of the boundary-layer problem for a particular distribution of the velocity outside the boundary layer. It appears, however, that this equation is of far more fundamental importance in the problem of laminar flow, although, of course, A has a different meaning in the general case than it has in Falkner & Skan’s treatment.

POTRET PERILAKU RELIGIUS MAHASISWA UIN SAYARIF HIDAYATULLAH JAKARTA

Al-Risalah ◽  
2018 ◽  
Vol 8 (2) ◽  
pp. 126-148
Author(s):  
Ay Maryani
Keyword(s):  
Religious Behavior ◽  
Male And Female ◽  
Mean Values ◽  
Significance Level ◽  
Average Value ◽  
Environment Variable ◽  
Independent Variable ◽  
The Mean ◽  
Gender Factor ◽  
Level 2

This study describes the religious behavior of UIN Syarif Hidayatullah Jakarta students. The variables used are internal and external environment as independent variable and religious behavior as dependent variable. The internal environment variable consists of gender factor, (male and female). The external environmental variables comprise the faculty environment, the present resident and the place to grow. The present resident consist of dormitories, boarding houses and parents' homes and the place to grow consist of urban and rural environment. Religious behavior variables consist of habluminallah behavior and habluminannas behavior. Habluminallah's behavior measured by (1) knowledge of faith and worship, (2) attitudes toward faith and worship, and (3) practice of faith and worship. The habluminannas variable measured by (1) Islamic behavior for them self, like honest, discipline and good work / studyethics, trust and concern on legality, (2) Islamic behavior with others, like generous, cooperation, caring, respect to the people's rights and tolerance and (3) Islamic behavior for the natural surroundings, like love of nature and nature conservation efforts. The methodology used was (1) Statistical descriptive, (2) MANOVA (Multivariate Analysis of Variance) and (3) Independent sample t-test. The results showed the religious behavior UIN Syarif Hidayatullah Jakarta students has a very good category. This is indicated by the mean values for the behavior of haluminallah and habluminannas of 158.85 and 178.76,  espectively. The average value of habluminallah behaviour in the range of values "145-180" with the category of "very good" and habluminannas behavior in the range value "165-205" with the category "very good. Habluminallah and habluminannas behavior are different for each faculty. This is indicated by the significance level of Pillai Trace, Wilk Lambda, Hotelling Trace, Roy's Largest Root of 0.00 (<0.05). Habluminallah and habluminannas behavior are the same for respondents who live in dormitories, boarding houses, and parents' homes. This is indicated by the value of F test and significance at Wilk's Lambda respectively for 2.055 and 0.085 (>0.05). Habluminallah and habluminannas behaviors are similar for urban and rural respondents. This is known from the sig level. (2-tailed) for habluminallah and habluminannas behavior of 0.317 and 0.245 (> 0.05), respectively. Habluminallah and habluminannas behaviors are similar for male and female. This is known from the sig level. (2-tailed) for habluminallah and habluminannas behavior of 0.950 and 0.307 (> 0.05),respectively. The results of this study are expected to be used to develop university policies that can enhance the Islamic values of UIN Syarif Hidayatullah Jakarta.

A new approach to curvature measures in linear shell theories

2020 ◽  
pp. 108128652097275
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Strain Tensor ◽  
Middle Surface ◽  
Surface Strain ◽  
Affine Function ◽  
Shear Deformations ◽  
Strain Measure ◽  
Bending Strain ◽  
Curvature Measures ◽  
Tensor Formula ◽  
Strain Measures

The paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of a 3D shell-like body and then linearizes E in two smallness parameters: the displacement and the distance of a point from the middle surface. The linearized expression is an affine function of the signed distance from the middle surface: the absolute term is the surface strain measure and the coefficient of the linear term is the bending strain measure. The main result of the paper determines these two tensors explicitly for general shear deformations and for the subcase of Kirchhoff-Love deformations. The derived surface strain measures are the classical ones: Naghdi’s surface strain measure generally and its well-known particular case for the Kirchhoff-Love deformations. With the bending strain measures comes a surprise: they are different from the traditional ones. For shear deformations our analysis provides a new tensor [Formula: see text], which is different from the widely used Naghdi’s bending strain tensor [Formula: see text]. In the particular case of Kirchhoff–Love deformations, the tensor [Formula: see text] reduces to a tensor [Formula: see text] introduced earlier by Anicic and Léger (Formulation bidimensionnelle exacte du modéle de coque 3D de Kirchhoff–Love. C R Acad Sci Paris I 1999; 329: 741–746). Again, [Formula: see text] is different from Koiter’s bending strain tensor [Formula: see text] (frequently used in this context). AMS 2010 classification: 74B99

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

2021 ◽  
pp. 014233122110196
Author(s):  
Ravish H. Hirpara ◽  
Shambhu N. Sharma
Keyword(s):  
State Vector ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Linear Filtering ◽  
Homogeneous Markov Process ◽  
Non Linear ◽  
Backward Equation ◽  
Noise Correction ◽  
Ito Process ◽  
Correction Terms

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

Non-linear dynamics, chaos, complexity and enclaves in granitoid magmas

1996 ◽  
Vol 87 (1-2) ◽  
pp. 217-223 ◽  
Author(s):  
James Flinders ◽  
John D. Clemens
Keyword(s):  
Deterministic Chaos ◽  
Interfacial Area ◽  
Two Dimensions ◽  
Mixing Processes ◽  
Nd Isotope ◽  
Natural Systems ◽  
Non Linear ◽  
The Difference ◽  
Magma System ◽  
Isotope Systematics

ABSTRACT:Most natural systems display non-linear dynamic behaviour. This should be true for magma mingling and mixing processes, which may be chaotic. The equations that most nearly represent how a chaotic natural system behaves are insoluble, so modelling involves linearisation. The difference between the solution of the linearised and ‘true’ equation is assumed to be small because the discarded terms are assumed to be unimportant. This may be very misleading because the importance of such terms is both unknown and unknowable. Linearised equations are generally poor descriptors of nature and are incapable of either predicting or retrodicting the evolution of most natural systems. Viewed in two dimensions, the mixing of two or more visually contrasting fluids produces patterns by folding and stretching. This increases the interfacial area and reduces striation thickness. This provides visual analogues of the deterministic chaos within a dynamic magma system, in which an enclave magma is mingling and mixing with a host magma. Here, two initially adjacent enclave blobs may be driven arbitrarily and exponentially far apart, while undergoing independent (and possibly dissimilar) changes in their composition. Examples are given of the wildly different morphologies, chemical characteristics and Nd isotope systematics of microgranitoid enclaves within individual felsic magmas, and it is concluded that these contrasts represent different stages in the temporal evolution of a complex magma system driven by nonlinear dynamics. If this is true, there are major implications for the interpretation of the parts played by enclaves in the genesis and evolution of granitoid magmas.

Non-linear filtering with discontinuous observations and applications to life sciences

1983 ◽  
Vol 45 (4) ◽  
pp. 571-577 ◽  
Author(s):  
Giovanni B. Di Masi ◽  
Wolfgang J. Runggaldier
Keyword(s):  
Life Sciences ◽  
Linear Filtering ◽  
Non Linear
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