Nonlinear Math Research Articles

Application of ACP Nonlinear Math in Analyzing Toxicokinetic and Pharmacokinetic Data (Application 5 and 6)

Analyses of toxicokinetic and pharmacokinetic are demonstrated using the ACP (asymptotic curve based and proportionality oriented) Alpha Beta (αβ) Nonlinear Math. In the new nonlinear concepts, various skewed-bell elementary “y” data are collected, followed by analyzing the asymptotic cumulative Y curves. In using the concise data, the asymptotic cumulativenumbers are emphasized and shun the use of unrelated elementary-numbers. The kinetic results are expressed as equations and straight lines in the proportionality graphs, where the change of the response β (Y, Yu, Yb) is proportional to the change of the time or dose α(X, Xu, Xb) and assuming the mathematical form dα = Kdβ. The K is the proportionality constant or the kinetic constant. The baseline asymptote Yb is mostly a nonlinear zero thus no need of calculation, but the upper asymptote Yu can be resolved through guided estimation using the coefficient of determination (COD) and graphical resolution

Application of ACP Nonlinear Math in Analyzing Arithmetic and Radiation Transmission Data (Application 1 & 2) [4-21-2024, 820P] (V)

Application of ACP Nonlinear Math in Analyzing Arithmetic and Radiation Transmission Data (Application 1 & 2) [4-21-2024, 820P] (V)

Effect of unsaturated soil water transport function linearization for mulched drip irrigation

Effect of unsaturated soil water transport function linearization for mulched drip irrigation

Implementation in Direct Digital Synthesizers (DDS) Based on CORDIC Algorithm

The universality of computerized signal handling (DSP) has made expanding request to create territory effective and precise structures in completing numerous nonlinear math tasks. One such design is CORDIC unit which has numerous applications in the field of DSP including actualizing changes dependent on Fourier premise. This paper offers structure of CORDIC, inserted with a pipelined unit that has exclusively negligible scope of adders and shifters. It tends to be applied in pivot mode as appropriately as vectoring mode. The reason for the arrangement is to get a pipelined CORDIC unit keeping up the format of valid calculation. Preparing and discussion structures work CORDIC in round organize contraption and in both of pivot or vectoring modes.

Dynamics of the FitzHugh–Nagumo system having invariant algebraic surfaces

In this paper, we study the dynamics of the FitzHugh–Nagumo system $$\dot{x}=z,\;\dot{y}=b\left( x-dy\right) ,\;\dot{z}=x\left( x-1\right) \left( x-a\right) +y+cz$$ having invariant algebraic surfaces. This system has four different types of invariant algebraic surfaces. The dynamics of the FitzHugh–Nagumo system having two of these classes of invariant algebraic surfaces have been characterized in Valls (J Nonlinear Math Phys 26:569–578, 2019). Using the quasi-homogeneous directional blow-up and the Poincaré compactification, we describe the dynamics of the FitzHugh–Nagumo system having the two remaining classes of invariant algebraic surfaces. Moreover, for these FitzHugh–Nagumo systems we prove that they do not have limit cycles.

Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs

We investigate the relation between pluri-Lagrangian hierarchies of 2-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings in Petrera and Suris (Nonlinear Math. Phys. 24(suppl. 1):121–145, 2017) for ordinary differential equations. We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural (1,{+},1)-dimensional space-time interpretation) and show that if the flow of each PDE is a variational symmetry of all others, then there exists a pluri-Lagrangian 2-form for the hierarchy. The corresponding multi-time Euler–Lagrange equations coincide with the original system supplied with commuting evolutionary flows induced by the variational symmetries.

Group delay equalisation of discrete Butterworth tan filters in the continuous domain

ABSTRACTA new optimisation method for equalising the group delay frequency response of the discrete transfer function of recursive digital filters, so-called tan filters, is presented in this paper. The method is based on an algorithm that is used for a stable all-pass filter approximation. Allpass filter acts as a group delay equaliser, with the purpose of equalising group delay of the discrete tan filter in a maximal flat sense. The algorithm relies on a set of simultaneous nonlinear equations. These set equations are derived directly from the flatness conditions of the equalised group delay response at the origin in the analogue -domain, in order to obtain the unknown coefficient values of the discrete allpass filter. The iterative method most widely used for solving set nonlinear equations and Symbolic Math Toolbox for Matlab features for finding numerical solutions are presented in detail.In the given examples, firstly a discrete Butterworth tan filter was designed by using transfer function poles in closed form. Secondly, the Butterworth tan filter was augmented with cascade connection of non-minimum phase all-pass discrete filter, in order for the group delay response of the whole filter to be equalised in a maximally flat sense.

Reconstructing a Lattice Equation: a Non-Autonomous Approach to the Hietarinta Equation

In this paper we construct a non-autonomous version of the Hietarinta equation [Hietarinta J., J. Phys. A: Math. Gen. 37 (2004), L67-L73] and study its integrability properties. We show that this equation possess linear growth of the degrees of iterates, generalized symmetries depending on arbitrary functions, and that it is Darboux integrable. We use the first integrals to provide a general solution of this equation. In particular we show that this equation is a sub-case of the non-autonomous $Q_{\rm V}$ equation, and we provide a non-autonomous M\"obius transformation to another equation found in [Hietarinta J., J. Nonlinear Math. Phys. 12 (2005), suppl. 2, 223-230] and appearing also in Boll's classification [Boll R., Ph.D. Thesis, Technische Universit\"at Berlin, 2012].

Intelligent control of a grain drying system using a GA-SVM-IMPC controller

ABSTRACTThe grain drying is difficult to control because of its characteristics of long delay, strong nonlinearity, and uncertainty parameters. The aim of the paper is to design a suitable controller for a newly designed grain dryer. First, a nonlinear math model of the wheat mixed flow drying was established and analyzed based on the fundamental laws of simultaneous heat and mass transfer. The simulations for the batch circulating drying process and the continuous grain drying process have been made and the simulation results show that it fits well with the actual drying process. Second, an internal model proportional integral derivative (PID) controller (IMPC) based on the support vector machine (SVM) algorithm and the genetic algorithm (GA-SVM-IMPC) was proposed from the view of the energy loss and the dried grain quality. The structure of the GA-SVM-IMPC controller consists of a SVM prediction model, a SVM inverse model controller, a PID controller and a genetic optimization algorithm. Finally, the effectiveness of this controller was demonstrated by computer simulations, and the comparative study with the other controllers further confirmed the superiority of the proposed dryer controller.

Darboux integrability of trapezoidal H4 and H4 families of lattice equations I: first integrals

In this paper we prove that the trapezoidal and the families of quad-equations are Darboux integrable by constructing their first integrals. This result explains why the rate of growth of the degrees of the iterates of these equations is linear (Gubbiotti et al 2016 J. Nonlinear Math. Phys. 23 507–43), which according to the algebraic entropy conjecture implies linearizability. We conclude by showing how first integrals can be used to obtain general solutions.

Semi-Analytic Probability Density Function for System Uncertainty

In general, the behavior of science and engineering is predicted based on nonlinear math models. Imprecise knowledge of the model parameters alters the system response from the assumed nominal model data. One proposes an algorithm for generating insights into the range of variability that can be expected due to model uncertainty. An automatic differentiation tool builds the exact partial derivative models required to develop a state transition tensor series (STTS)-based solution for nonlinearly mapping initial uncertainty models into instantaneous uncertainty models. The fully nonlinear statistical system properties are recovered via series approximations. The governing nonlinear probability distribution function is approximated by developing an inverse mapping algorithm for the forward series model. Numerical examples are presented, which demonstrate the effectiveness of the proposed methodology.

Classification of solutions to Toda systems of types C and B with singular sources

In this paper, the classification in Lin et al. (Invent. Math. 190(1):169–207, 2012) of solutions to Toda systems of type A with singular sources is generalized to Toda systems of types C and B. Like in the A case, the solution space is shown to be parametrized by the abelian subgroup and a subgroup of the nilpotent subgroup in the Iwasawa decomposition of the corresponding complex simple Lie group. The method is by studying the Toda systems of types C and B as reductions of Toda systems of type A with symmetries. The theories of Toda systems as integrable systems as developed in Leznov (Teoret. Mat. Fiz. 42(3):343–349, 1980), Leznov and Saveliev (Group-theoretical methods for integration of nonlinear dynamical systems, Progress in Physics, vol. 15. Birkhauser, Verlag, 1992), Nie (J. Geom. Phys. 62(12):2424–2442, 2012), Nie (J. Nonlinear Math. Phys. 21(1):120–131, 2014), in particular the W-symmetries and the iterated integral solutions, play essential roles in this work, together with certain characterizing properties of minors of symplectic and orthogonal matrices.

HETLAS를 활용한 헬리콥터 비행제어 법칙 Rapid Prototyping 프로세스 설계

항공기 비행제어시스템의 개발기간, 비용 및 위험도를 최소화시키기 위해서는 비행제어 법칙의 적용 및 시험을 효율적으로 수행할 수 있는 통합개발 도구와 Rapid Prototyping 프로세스가 요구된다. 본 논문에서는 Matlab/Simulink 환경을 통해 생성한 제어법칙 자동코드와 비행동역학 해석프로그램(HETLAS: HElicopter Trim, Linearization and Simulation)과의 연동 절차를 개발하여 시뮬레이션 평가를 효율적으로 수행할 수 있는 환경의 구축에 대해 기술하였다. 또한, 본 연구를 통해 제어법칙의 다양한 모드의 조종사 시뮬레이션 평가를 위해 HETLAS를 이용한 데스크탑 시뮬레이션 환경을 개발하고 조종성 시뮬레이터 및 HILS(Hardware In the Loop Simulation) 시험 환경과 효율적으로 연동하여 시험할 수 있는 절차를 개발하였다. 비행제어법칙 개발과정에서 HETLAS를 중심으로 한 해석/시험 환경을 개발함으로써 반복적인 제어법칙의 설계/해석 및 시험 절차를 효율적으로 수행할 수 있도록 하였다. The rapid prototyping process and development tool which enable the control law evaluation efficiently are needed to minimize the development cycle, cost and risk of aircraft flight control system. This paper describes a development process that integrates the designed control law into HETLAS to evaluate simulation effectively using nonlinear mathematical models. The desktop engineering simulator was developed using HETLAS for the piloted simulation evaluation of a various control modes and the procedure was developed, which quickly integrates the HETLAS into HQS(Handling Quality Simulator) and HILS(Hardware In the Loop Simulation) environments. This paper presents a rapid prototyping process using HETLAS that significantly shortens the integration process of the control law into the nonlinear math model, HETLAS, and allows the control law designs to be quickly tested in the piloted simulation and HILS environments.

On the Stochastic Strichartz Estimates and the Stochastic Nonlinear Schrödinger Equation on a Compact Riemannian Manifold

We prove the existence and the uniqueness of a solution to the stochastic NSLE on a two-dimensional compact riemannian manifold. Thus we generalize a recent work by Burq, G\'erard and Tzvetkov in the deterministic setting, and a series of papers by de Bouard and Debussche, who have examined similar questions in the case of the flat euclidean space with random perturbation. We prove the existence and the uniqueness of a local maximal solution to stochastic nonlinear Schr\"odinger equations with multiplicative noise on a compact d-dimensional riemannian manifold. Under more regularity on the noise, we prove that the solution is global when the nonlinearity is of defocusing or of focusing type, d=2 and the initial data belongs to the finite energy space. Our proof is based on improved stochastic Strichartz inequalities.

Supertransvectants, cohomology, and deformations

Over the (1, N)-dimensional real superspace, N = 2, 3, we classify \documentclass[12pt]{minimal}\begin{document}$\mathfrak {osp}(N|2)$\end{document}osp(N|2)-invariant binary differential operators acting on the superspaces of weighted densities, where \documentclass[12pt]{minimal}\begin{document}$\mathfrak {osp}(N|2)$\end{document}osp(N|2) is the orthosymplectic Lie superalgebra. This result allows us to compute the first differential \documentclass[12pt]{minimal}\begin{document}$\mathfrak {osp}(N|2)$\end{document}osp(N|2)-relative cohomology of the Lie superalgebra \documentclass[12pt]{minimal}\begin{document}$\mathcal {K}(N)$\end{document}K(N) of contact vector fields with coefficients in the superspace of linear differential operators acting on the superspaces of weighted densities. We classify generic formal \documentclass[12pt]{minimal}\begin{document}$\mathfrak {osp}(3|2)$\end{document}osp(3|2)-trivial deformations of the \documentclass[12pt]{minimal}\begin{document}$\mathcal {K}(3)$\end{document}K(3)-module structure on the superspaces of symbols of differential operators. We prove that any generic formal \documentclass[12pt]{minimal}\begin{document}$\mathfrak {osp}(3|2)$\end{document}osp(3|2)-trivial deformation of this \documentclass[12pt]{minimal}\begin{document}$\mathcal {K}(3)$\end{document}K(3)-module is equivalent to its infinitesimal part. This work is the simplest generalization of a result by the first author et al. [Basdouri, I., Ben Ammar, M., Ben Fraj, N., Boujelbene, M., and Kammoun, K., “Cohomology of the Lie superalgebra of contact vector fields on \documentclass[12pt]{minimal}\begin{document}$\mathbb {K}^{1|1}$\end{document}K1|1 and deformations of the superspace of symbols,” J. Nonlinear Math. Phys. 16, 373 (2009)10.1142/S1402925109000431].

Life: Test decodes dolphins' sonar skill: Nonlinear math may explain ability to ‘see’ through bubbles

Science NewsVolume 182, Issue 4 p. 12-12 In The News Life: Test decodes dolphins' sonar skill: Nonlinear math may explain ability to ‘see’ through bubbles Meghan Rosen, Meghan RosenSearch for more papers by this author Meghan Rosen, Meghan RosenSearch for more papers by this author First published: 14 August 2012 https://doi.org/10.1002/scin.5591820411Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume182, Issue425 August 2012Pages 12-12 RelatedInformation

Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space \({\mathbb{R}^3}\) with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

SCHRÖDINGER–LICHNEROWICZ LIKE FORMULA ON KÄHLER–NORDEN MANIFOLDS

A new kind of spinors and Dirac operator are introduced on Kähler–Norden manifolds in [Spinors on Kähler–Norden manifolds, J. Nonlinear Math. Phys.17(1) (2010) 27–34]. In this work the square D2 of the Dirac operator D is computed and a kind of Schrödinger–Lichnerowicz formula is obtained.

A q-analogue of the exponential integral

A q-analogue of the Tricomi expansion is derived and proved in terms of q-analogue of the incomplete gamma function by Mansour (J. Nonlinear Math. Phys. 16:141–150, 2009). In this paper, q-analogue of the exponential integral is presented as expansion in series of incomplete q-gamma functions and shown to be a limiting case of q-Tricomi expansion. Companion results for the complementary incomplete q-gamma function are presented and can be applied to yield expansions of q-exponential integral.

On the nonlocal symmetries of certain nonlinear oscillators and their general solution

Abstract In this Letter we establish the integrability of two nonlinear oscillators through group theoretical method. We utilize the algorithm given in [M.L. Gandarias, M.S. Bruzon, J. Nonlinear Math. Phys. 18 (2011) 123] and construct nonlocal symmetries for these two oscillators. From the knowledge of the latter we derive first integral and general solution for these two nonlinear nonpolynomial oscillator equations.