Auxiliary Mapping Research Articles

Dispersive solitary wave solutions of nonlinear further modified Korteweg–de Vries dynamical equation in an unmagnetized dusty plasma

In this work, we consider the propagation of one-dimensional nonlinear unmagnetized dusty plasma, by using the reductive perturbation technique to formulate the nonlinear mathematical model which is further modified Korteweg–de Vries (fmKdV) dynamical equation. We use the extend form of two methods, auxiliary equation mapping and direct algebraic methods, to investigate the families of dust and ion solitary wave solutions of one-dimensional nonlinear fmKdV. These new exact and solitary wave solutions, which represent the electrostatic potential and pressure for fmKdV, and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica.

More general families of exact solitary wave solutions of the nonlinear Schrödinger equation with their applications in nonlinear optics

In this article we analytically studied the complex nonlinear Schrodinger equation with Kerr law nonlinearity using the auxiliary equation mapping method, as a result, we found a series of more general and new families of exact solutions, which are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies, nonlinear optics and many other fields. The calculations demonstrate that this method is more reliable, straightforward and effective to analytically study other nonlinear complicated physical problems modeled by complex nonlinear partial differential equations arising in mathematical physics, hydrodynamics, fluid mechanics, mathematical biology, plasma physics, engineering disciplines, chemistry and many other natural sciences. We have also expressed our solutions graphically with the help of Mathematica 10.4 to physically understand the behavior of different shapes of solutions including kink-type, anti-kink-type, half-bright and dark solitons.

Mathematical methods via construction of traveling and solitary wave solutions of three coupled system of nonlinear partial differential equations and their applications

Abstract In this research work, we applying the modification form of extended auxiliary equation mapping method on three couple system of nonlinear ovulation equations which have odd and even partial derivatives. We investigated the new exact traveling and solitary wave solutions of coupled Whitham-Broer-Kaup, (2 + 1)-dimensional Broer-Kaup-Kupershmit and Drinfel’d-Sokolow-Wilson equations. We applied successfully this new method and obtained the new form of exact traveling and solitary wave solutions. As a results, obtained new solutions in the form of solitons, bright and dark solitons, kink and anti-kink type solitons, traveling wave, periodic solitary wave,trigonometric functions and elliptic functions solutions. These new different type of solutions are show the effectiveness and power of this new method and also show two and three dimensional graphically with the help of computer software Mathematica. These new solutions have many applications in the field of physics and other branches of applied science. We can also be solved other couple system of partial differential equations by this new technique.

Comparação entre as análises integrada e paramétrica na suscetibilidade a escorregamentos no entorno de dutos: faixa de dutos Orbel, Estado do Rio de Janeiro

Este trabalho teve como objetivo comparar a Abordagem Paramétrica, realizada por meio da sobreposição com ponderação de mapas, com a Integrada/Fisiográfica, ancorada na fotointerpretação de produtos de sensoriamento remoto, na obtenção da suscetibilidade a escorregamentos com a utilização de imagens de alta resolução. A área de estudo possui 108,6 km² e corresponde a um trecho da faixa de dutos ORBEL, Estado do Rio de Janeiro. As etapas de trabalho envolveram: levantamento bibliográfico; confecção de mapas auxiliares através do MDE; o Mapa de Inventário a Escorregamentos, onde foram identificadas 165 cicatrizes; elaboração do Mapa de Suscetibilidade a Escorregamento - Compartimentação Fisiográfica a partir da fotointerpretação das imagens orbitais, e do Mapa de Suscetibilidade a Escorregamento – Método AHP (Processo de Análise Hierárquico) pelo cruzamento com ponderação dos mapas correspondentes aos fatores condicionantes do processo. A comparação dos mapas de suscetibilidade, ambos com 4 classes, foi realizada por tabulação cruzada e também de forma descritiva. Concluiu-se que a Abordagem Paramétrica mostrou-se mais detalhada e consistente, com maior número de cicatrizes nas classes de Muito Alta e Alta suscetibilidade. A análise integrada, embora mais geral, foi suficiente para a produção do mapa de suscetibilidade e pode se constituir numa alternativa para obras lineares de grande extensão, por não requerer mapas em escalas compatíveis, o que se configura como uma dificuldade no país. As duas abordagens podem ser complementares, com a Abordagem Paramétrica somente em trechos onde o detalhamento seja necessário.

Construction of solitary wave solutions to the nonlinear modified Kortewege-de Vries dynamical equation in unmagnetized plasma via mathematical methods

In this research, we consider the propagation of one-dimensional nonlinear behavior in a unmagnetized plasma. By using the reductive perturbation technique to formulate the nonlinear mathematic model which is modified Kortewege-de Vries (mKdV), we apply the extended form of two methods, which are extended auxiliary equation mapping and extended direct algebraic methods, to investigate the new families of electron-acoustic solitary wave solutions of mKdV. These new exact traveling and solitary wave solutions which represent the electrostatic potential for mKdV and also the graphical representation of electrostatic potential are shown with the aid of Mathematica.

Existence and continuity of solution trajectories of generalized equations with application in electronics

We consider a special form of parametric generalized equations arising from electronic circuits with AC sources and study the effect of perturbing the input signal on solution trajectories. Using methods of variational analysis and strong metric regularity property of an auxiliary map, we are able to prove the regularity properties of the solution trajectories inherited by the input signal. Furthermore, we establish the existence of continuous solution trajectories for the perturbed problem. This can be achieved via a result of uniform strong metric regularity for the auxiliary map.

Small-objectness sensitive detection based on shifted single shot detector

We present a small object sensitive method for object detection. Our method is built based on SSD (Single Shot MultiBox Detector (Liu et al. 2016)), a simple but effective deep neural network for image object detection. The discrete nature of anchor mechanism used in SSD, however, may cause misdetection for the small objects located at gaps between the anchor boxes. SSD performs better for small object detection after circular shifts of the input image. Therefore, auxiliary feature maps are generated by conducting circular shifts over lower extra feature maps in SSD for small-object detection, which is equivalent to shifting the objects in order to fit the locations of anchor boxes. We call our proposed system Shifted SSD. Moreover, pinpoint accuracy of localization is of vital importance to small objects detection. Hence, two novel methods called Smooth NMS and IoU-Prediction module are proposed to obtain more precise locations. Then for video sequences, we generate trajectory hypothesis to obtain predicted locations in a new frame for further improved performance. Experiments conducted on PASCAL VOC 2007, along with MS COCO, KITTI and our small object video datasets, validate that both mAP and recall are improved with different degrees and the speed is almost the same as SSD.

TEC Regional Modeling and prediction using ANN method and single frequency receiver over IRAN

In order to study in the field of the dynamics and continuous variations in the ionosphere, the ionospheric measurement tools such as ionosondes, incoherent scatter radars, satellites, and Global Positioning System (GPS) networks should be used. Total Electron Content (TEC) is a key parameter in the investigation and identification of ionosphere layer. From observations of dual frequency GPS receivers, the ionospheric TEC can be extracted. Global Ionospheric Maps (GIM) are auxiliary Maps for a study on ionosphere layer in around the world. It is necessary to produce the regional TEC map for precise studying of the ionospheric TEC. Bernese software is used to extract TEC by dual frequency GPS receivers. Regional modeling of ionospheric TEC by Artificial Neural Network (ANN) is a significant domain for prediction TEC at both single and double frequency GPS receivers. Five locations in Iran during the period of 2006-2010 were identified and used in the development of an input space and ANN architecture for the TEC modeling. The input space included the day number (seasonal variation), hour (diurnal variation), sunspot number (a measure of the solar activity) and magnetic index (a measure of magnetic activity). Based on the results, the ANN have capability and flexibility to model and to predict TEC. TEC predicted by ANN A (NN TEC) and TEC obtained from the IRI2007 version of the International Reference Ionosphere (IRI TEC) are compared during equinoxes and solstices. Results show that ANN predicts GPS TEC more accurately than the IRI over Iran. The IRI-2007 model is not a suitable method to produce TEC over IRAN.

Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems

The displacement discontinuity method (DDM) is a kind of boundary element method aiming at modeling two-dimensional linear elastic crack problems. The singularity around the crack tip prevents the DDM from optimally converging when the basis functions are polynomials of first order or higher. To overcome this issue, enlightened by the mapped finite element method (FEM) proposed in Ref. [13], we present an optimally convergent mapped DDM in this work, called the mapped DDM (MDDM). It is essentially based on approximating a much smoother function obtained by reformulating the problem with an appropriate auxiliary map. Two numerical examples of crack problems are presented in comparison with the conventional DDM. The results show that the proposed method improves the accuracy of the DDM; moreover, it yields an optimal convergence rate for quadratic interpolating polynomials.

Limitations of Robust Stability of a Linear Delayed Feedback Control

In this paper we consider the issue of robust stability of a linear delayed feedback control (DFC) mechanism. In particular we consider a DFC for stabilizing fixed points of a smooth function $f: \mathbb{R}^m \rightarrow \mathbb{R}^m$ of the form $x(k+1) = f(x(k)) + u(k),$ where $u(k)$ is given by the formula $u(k) = - \sum_{j=1}^{N-1}\epsilon_j(x(k - j) - x(k - j + 1)).$ We associate with each fixed point of $f$ an explicit polynomial whose Schur stability corresponds to the local asymptotic stability of the DFC at that fixed point. This polynomial is the characteristic polynomial of the Jacobian matrix of an auxiliary map from $\mathbb{R}^{mN}$ to $\mathbb{R}^{mN}$ and may be given in terms of the eigenvalues of the Jacobian of $f$ at the fixed point. This enables us to evaluate the robustness of the control by considering over what possible sets of eigenvalues of the Jacobian of $f$ the associated characteristic polynomials are Schur stable. We will show that, for a given control of the above form, sta...

Spatial hidden Markov models and species distributions

ABSTRACTA spatial hidden Markov model (SHMM) is introduced to analyse the distribution of a species on an atlas, taking into account that false observations and false non-detections of the species can occur during the survey, blurring the true map of presence and absence of the species. The reconstruction of the true map is tackled as the restoration of a degraded pixel image, where the true map is an autologistic model, hidden behind the observed map, whose normalizing constant is efficiently computed by simulating an auxiliary map. The distribution of the species is explained under the Bayesian paradigm and Markov chain Monte Carlo (MCMC) algorithms are developed. We are interested in the spatial distribution of the bird species Greywing Francolin in the south of Africa. Many climatic and land-use explanatory variables are also available: they are included in the SHMM and a subset of them is selected by the mutation operators within the MCMC algorithm.

Sensitivity Analysis of Multiobjective Optimization Problems with Parameterized Quasi-Variational Inequalities

ABSTRACTThis paper mainly establishes the sensitivity analysis of a multiobjective optimization problem with parameterized quasi-variational inequalities (QVIs). Using the (regular) coderivative of the associated epigraphical multifunction, the (regular) subdifferentials of the efficient frontier maps are estimated, which involve the (regular) coderivatives of the solution mapping to the parameterized QVIs. Under the linear independent constraint qualification, the defined auxiliary set-valued mappings in the parameterized QVIs are clam. The detailed formulae of subdifferentials of the efficient frontier maps are obtained and examples are simultaneously provided for analyzing and illustrating the obtained results.

New conformal mapping for adaptive resolving of the complex singularities of Stokes wave.

A new highly efficient method is developed for computation of travelling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. The efficiency of that conformal mapping is demonstrated for the Stokes wave approaching the limiting Stokes wave (the wave of the greatest height) which significantly expands the family of numerically accessible solutions. It allows us to provide a detailed study of the oscillatory approach of these solutions to the limiting wave. Generalizations of the conformal mapping to resolve multiple singularities are also introduced.

Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma

We consider the propagation of three-dimensional nonlinear magnetized two-ion-temperature dusty plasma. The problem formulation of this mathematical model leads to nonlinear extended Zakharov–Kuznetsov (EZK) dynamical equation in three-dimensional by applying the reductive perturbation theory. We found the families of dust and ion solitary wave solutions of the three-dimensional nonlinear EZK dynamical equation using the auxiliary equation mapping method and direct algebraic mapping method.

New Implicit and explicit approximation methods for solutions of integral equations of Hammerstein type

Let H be a real Hilbert spae and F,K:H→H be mappings such that D(K)=D(F)=H. Suppose that Hammerstein equation of the type u+KFu=0 has a solution in H, then we studied in this paper methods that contain an auxiliary mapping (defined on an appropriate real Hilbert space in terms of the mappings K and F) which is pseudocontractive whenever K and F are monotone; and approximation of a fixed point of this pseudocontractive mapping induces approximation of a solution of the equation u+KFu=0. Moreover, the mappings K and F need not be defined on compact subset of H or angle bounded on H. Furthermore, our methods which do not involve K-1 provide an implicit algorithm for approximation of solutions of the equation u+KFu=0 whenever K and F are assumed to be bounded and continuous; if K and F are assumed to be Lipschitz continuous, then an explicit iterative algorithm for computation of solutions of the equation u+KFu=0 is provided, still without involving K-1.

A priori mapping of historical water-supply galleries based on archive records and sparse material remains. An application to the Amaniel qanat (Madrid, Spain)

Engineering heritage refers to a broad variety of items of social, economic, aesthetic or historic relevance, including roads, dams, buildings and supply networks. Due to their utilitarian nature, their heritage value is often overlooked. This occurs even with those infrastructures that have played an essential role in underpinning the daily existence of entire civilizations. Underground water-supply networks provide an excellent example. Although there are exceptions, water networks tend to be functional in design, rather than monumental. Moreover, they present intricate linear layouts that often span several kilometres. This means they are costly to maintain once their operational life is over, and that they are prone to abandonment and destruction. Devising a priori protection strategies is important to preserve these valuable cultural assets. The following pages present a method to map linear structures based on archive records and sparse material remains. The method is illustrated through its application to the Amaniel qanat, a water-supply gallery built in Madrid, Spain, in the early 17th Century. An appraisal of the known remains was carried out first, leading to an inventory of galleries, shafts, shaft caps and deposits. This was followed by a thorough survey of over one thousand handwritten manuscripts, including physical descriptions of the aqueduct, budget accounts or water metering campaigns, among other documents. Known remains and written evidence were matched against original and auxiliary maps to reconstruct the itinerary of the aqueduct. This led to the identification of sectors where it is still possible to find remains in good condition. Thus, a priori mapping is advocated a valuable technique to locate and preserve these remains, as well as to devise non-invasive surveys and establish heritage protection zones.

Slowly oscillating wavefronts of the KPP-Fisher delayed equation

This paper concerns the semi-wavefronts (i.e. bounded solutions $u=\phi(x \nu +ct) >0,$ $ |\nu|=1, $ satisfying $\phi(-\infty)=0$) to the delayed KPP-Fisher equation $$u_t(t,x) = \Delta u(t,x) + u(t,x)(1-u(t-\tau,x)), \ u \geq 0,\ x \in \R^m. \eqno(*)$$ First, we show that each semi-wavefront should be either monotone or slowly oscillating. Then a complete solution to the problem of existence of semi-wavefronts is provided. We prove next that the semi-wavefronts are in fact wavefronts (i.e. additionally $\phi(+\infty)=1$) if $c \geq 2$ and $\tau \leq 1$; our proof uses dynamical properties of some auxiliary one-dimensional map with the negative Schwarzian. The analysis of the fronts' asymptotic expansions at infinity is another key ingredient of our approach. It allows to indicate the maximal domain ${\mathcal D}_n$ of $(\tau,c)$ where the existence of non-monotone wavefronts can be expected. Here we show that the problem of wavefront's existence is closely related to the Wright's global stability conjecture.

On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems

Our aim is introduce a new class of procedures, the Uniformly Asymptotically Regular-class of procedures (UAR-precedures). Then by a UAR-procedure we prove the convergence of two explicit iterative methods to the unique solution of a variational inequality problem on the set of common fixed points of a family of mappings, in the setting of Hilbert spaces.

Fixed point theorems for generalized contractions on GP-metric spaces

Abstract In this paper, we present two fixed point theorems on mappings, defined on GP-complete GP-metric spaces, which satisfy a generalized contraction property determined by certain upper semi-continuous functions. Furthermore, we illustrate applications of our theorems with a number of examples. Inspired by the work of Jachymski, we also establish equivalences of certain auxiliary maps in the context of GP-complete GP-metric spaces. MSC:47H10, 54H25.

Weak and Strong Convergence Theorems for Strictly Pseudononspreading Mappings and Equilibrium Problem in Hilbert Spaces

The purpose of this paper is to propose an iterative algorithm for equilibrium problem and a class of strictly pseudononspreading mappings which is more general than the class of nonspreading mappings studied recently in Kurokawa and Takahashi (2010). We explored an auxiliary mapping in our theorems and proofs and under suitable conditions, some weak and strong convergence theorems are proved. The results presented in the paper extend and improve some recent results announced by some authors.