Search results for: Asymptotic Theory

Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding

Abstract:

A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, Nonlocal Strain Gradient Theory, velocity gradient

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Authors: Erick Pruchnicki, Nikhil Padhye

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Plates are important engineering structures which have attracted extensive research since the 19th century. The subject of this work is statical analysis of a linearly elastic homogenous plate under small deformations. A 'thin plate' is a three-dimensional structure comprising of a small transverse dimension with respect to a flat mid-surface. The general aim of any plate theory is to deduce a two-dimensional model, in terms of mid-surface quantities, to approximately and accurately describe the plate's deformation in terms of mid-surface quantities. In recent decades, a common starting point for this purpose is to utilize series expansion of a displacement field across the thickness dimension in terms of the thickness parameter (h). These attempts are mathematically consistent in deriving leading-order plate theories based on certain a priori scaling between the thickness and the applied loads; for example, asymptotic methods which are aimed at generating leading-order two-dimensional variational problems by postulating formal asymptotic expansion of the displacement fields. Such methods rigorously generate a hierarchy of two-dimensional models depending on the order of magnitude of the applied load with respect to the plate-thickness. However, in practice, applied loads are external and thus not directly linked or dependent on the geometry/thickness of the plate; thus, rendering any such model (based on a priori scaling) of limited practical utility. In other words, the main limitation of these approaches is that they do not furnish a single plate model for all orders of applied loads. Following analogy of recent efforts of deploying Fourier-series expansion to study convergence of reduced models, we propose two-dimensional model(s) resulting from truncation of the potential energy and rigorously prove the convergence of these two-dimensional plate models to the parent three-dimensional linear elasticity with increasing truncation order of the potential energy.

Keywords: plate theory, Fourier-series expansion, convergence result, Legendre polynomials

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Authors: Muhammad Younis

Abstract:

A ternary 4-point approximating non-stationary subdivision scheme has been introduced that generates the family of $C^2$ limiting curves. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the scheme. The comparison of the proposed scheme has been demonstrated using different examples with the existing 4-point ternary approximating schemes, which shows that the limit curves of the proposed scheme behave more pleasantly and can generate conic sections as well.

Keywords: ternary, non-stationary, approximation subdivision scheme, convergence and smoothness

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

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The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method, wire coating die

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Authors: Arne Fagerstrom, Gary Cunningham, Fredrik Hartwig

Abstract:

In this paper, a theory of sustainable enterprises, sustainable enterprise theory (SET), is developed. The sustainable enterprise theory can only be a valid theory if knowledge about life and nature is complete. Knowledge limitations should not stop enterprises from doing business with a goal of better long-term life on earth. Life demands stewardship of the resources used during one’s lifetime. This paper develops a model influenced by (the classical) enterprise theory and resource theory that includes more than money in the business activities of an enterprise. The sustainable enterprise theory is then used in an analysis of accountability and in discussions about sustainable businesses.

Keywords: sustainable business, sustainability reporting, sustainable values, theory of the firm

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Juan M. Rodriguez-Diaz

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The precision of parameter estimators in the Gaussian linear model is traditionally accounted by the variance-covariance matrix of the asymptotic distribution. However, this measure can underestimate the true variance, specially for small samples. Traditionally, optimal design theory pays attention to this variance through its relationship with the model's information matrix. For this reason it seems convenient, at least in some cases, adapt the optimality criteria in order to get the best designs for the actual variance structure, otherwise the loss in efficiency of the designs obtained with the traditional approach may be very important.

Keywords: correlated observations, information matrix, optimality criteria, variance-covariance matrix

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Authors: Arcady Ponosov., Ramazan Kadiev

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The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: asymptotic stability, delay equations, operator methods, stochastic noise

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Authors: E. M. Hassan, A. L. Kalamkarov

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Two micromechanical models for 3D smart composite with embedded periodic or nearly periodic network of generally orthotropic reinforcements and actuators are developed and applied to cubic structures with unidirectional orientation of constituents. Analytical formulas for the effective piezothermoelastic coefficients are derived using the Asymptotic Homogenization Method (AHM). Finite Element Analysis (FEA) is subsequently developed and used to examine the aforementioned periodic 3D network reinforced smart structures. The deformation responses from the FE simulations are used to extract effective coefficients. The results from both techniques are compared. This work considers piezoelectric materials that respond linearly to changes in electric field, electric displacement, mechanical stress and strain and thermal effects. This combination of electric fields and thermo-mechanical response in smart composite structures is characterized by piezoelectric and thermal expansion coefficients. The problem is represented by unit-cell and the models are developed using the AHM and the FEA to determine the effective piezoelectric and thermal expansion coefficients. Each unit cell contains a number of orthotropic inclusions in the form of structural reinforcements and actuators. Using matrix representation of the coupled response of the unit cell, the effective piezoelectric and thermal expansion coefficients are calculated and compared with results of the asymptotic homogenization method. A very good agreement is shown between these two approaches.

Keywords: asymptotic homogenization method, finite element analysis, effective piezothermoelastic coefficients, 3D smart network composite structures

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Authors: Eduard Marusic-Paloka

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The Darcy-Weisbach formula is used to compute the pressure drop of the fluid in the pipe, due to the friction against the wall. Because of its simplicity, the Darcy-Weisbach formula became widely accepted by engineers and is used for laminar as well as the turbulent flows through pipes, once the method to compute the mysterious friction coefficient was derived. Particularly in the second half of the 20th century. Formula is empiric, and our goal is to derive it from the basic conservation law, via rigorous asymptotic analysis. We consider the case of the laminar flow but with significant Reynolds number. In case of the perfectly smooth pipe, the situation is trivial, as the Navier-Stokes system can be solved explicitly via the Poiseuille formula leading to the friction coefficient in the form 64/Re. For the rough pipe, the situation is more complicated and some effects of the roughness appear in the friction coefficient. We start from the Navier-Stokes system in the pipe with periodically corrugated wall and derive an asymptotic expansion for the pressure and for the velocity. We use the homogenization techniques and the boundary layer analysis. The approximation derived by formal analysis is then justified by rigorous error estimate in the norm of the appropriate Sobolev space, using the energy formulation and classical a priori estimates for the Navier-Stokes system. Our method leads to the formula for the friction coefficient. The formula involves resolution of the appropriate boundary layer problems, namely the boundary value problems for the Stokes system in an infinite band, that needs to be done numerically. However, theoretical analysis characterising their nature can be done without solving them.

Keywords: Darcy-Weisbach law, pipe flow, rough boundary, Navier law

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Authors: Taehan Bae

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In this paper, a class of length-biased Weibull mixtures is presented to model loss severity data. The proposed model generalizes the Erlang mixtures with the common scale parameter, and it shares many important modelling features, such as flexibility to fit various data distribution shapes and weak-denseness in the class of positive continuous distributions, with the Erlang mixtures. We show that the asymptotic tail estimate of the length-biased Weibull mixture is Weibull-type, which makes the model effective to fit loss severity data with heavy-tailed observations. A method of statistical estimation is discussed with applications on real catastrophic loss data sets.

Keywords: Erlang mixture, length-biased distribution, transformed gamma distribution, asymptotic tail estimate, EM algorithm, expectation-maximization algorithm

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Authors: Pauline E. Ngo-Henha

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Existing turnover intention theories are reviewed in this paper. This review was conducted with the help of the search keyword “turnover intention theories” in Google Scholar during the month of July 2017. These theories include: The Theory of Organizational Equilibrium (TOE), Social Exchange Theory, Job Embeddedness Theory, Herzberg’s Two-Factor Theory, the Resource-Based View, Equity Theory, Human Capital Theory, and the Expectancy Theory. One of the limitations of this review paper is that data were only collected from Google Scholar where many papers were sometimes not freely accessible. However, this paper attempts to contribute to the research in clarifying the distinction between theories and models in the context of turnover intention.

Keywords: Literature Review, Theory, Turnover, Turnover intention

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Authors: Swati Tyagi, Syed Abbas

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Fractional-order Hopfield neural networks are generally used to model the information processing among the interacting neurons. To show the constancy of the processed information, it is required to analyze the stability of these systems. In this work, we perform Mittag-Leffler stability for the corresponding Caputo fractional-order bidirectional associative memory (BAM) neural networks with various time-delays. We derive sufficient conditions to ensure the existence and uniqueness of the equilibrium point by using the theory of topological degree theory. By applying the fractional Lyapunov method and Mittag-Leffler functions, we derive sufficient conditions for the global Mittag-Leffler stability, which further imply the global asymptotic stability of the network equilibrium. Finally, we present two suitable examples to show the effectiveness of the obtained results.

Keywords: bidirectional associative memory neural network, existence and uniqueness, fractional-order, Lyapunov function, Mittag-Leffler stability

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Authors: Saba Riaz, Syed A. Hussain

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This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

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Authors: Jair Servín-Aguilar, Yu Tang

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We address the problem of robust attitude tracking for agile satellites under unknown bounded torque disturbances using a double-gimbal variable-speed control-moment gyro (DGVSCMG) driven by a cluster of three permanent magnet synchronous motors (PMSMs). Uniform practical asymptotic stability is achieved at the torque control level first. The desired speed of gimbals and the acceleration of the spin wheel to produce the required torque are then calculated by a velocity-based steering law and tracked at the PMSM speed-control level by designing a speed-tracking controller with compensation for the vibration caused by eccentricity and imbalance due to mechanical imperfection in the DGVSCMG. Uniform practical asymptotic stability of the overall system is ensured by loan relying on the analysis of the resulting cascaded system. Numerical simulations are included to show the performance improvement of the proposed controller.

Keywords: agile satellites, vibration compensation, internal model, stability

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Authors: Abdelhafid Zenati, Mohamed Tadjine

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The mathematical formulation of biomedical problems is an important phase to understand and predict the dynamic of the controlled population. In this paper we perform a stability analysis of a coupled model for healthy and cancerous cells dynamics in Acute Myeloid Leukemia, this represents our first aim. Second, we illustrate the effect of the interconnection between healthy and cancer cells. The PDE-based model is transformed to a nonlinear distributed state space model (delay system). For an equilibrium point of interest, necessary and sufficient conditions of global asymptotic stability are given. Thus, we came up to give necessary and sufficient conditions of global asymptotic stability of the origin and the healthy situation and control of the dynamics of normal hematopoietic stem cells and cancerous during myelode Acute leukemia. Simulation studies are given to illustrate the developed results.

Keywords: distributed delay, global stability, modelling, nonlinear models, PDE, state space

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Authors: Mojtaba Hakimi-Moghaddam

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Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Torsten Hermanns, Thoufik Al Khawli, Wolfgang Schulz

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In laser cutting as well as in long pulsed laser drilling of metals, it can be demonstrated that the ablation shape (the shape of cut faces respectively the hole shape) that is formed approaches a so-called asymptotic shape such that it changes only slightly or not at all with further irradiation. These findings are already known from the ultrashort pulse (USP) ablation of dielectric and semiconducting materials. The explanation for the occurrence of an asymptotic shape in laser cutting and long pulse drilling of metals is identified, its underlying mechanism numerically implemented, tested and clearly confirmed by comparison with experimental data. In detail, there now is a model that allows the simulation of the temporal (pulse-resolved) evolution of the hole shape in laser drilling as well as the final (asymptotic) shape of the cut faces in laser cutting. This simulation especially requires much less in the way of resources, such that it can even run on common desktop PCs or laptops. Individual parameters can be adjusted using sliders – the simulation result appears in an adjacent window and changes in real time. This is made possible by an application-specific reduction of the underlying ablation model. Because this reduction dramatically decreases the complexity of calculation, it produces a result much more quickly. This means that the simulation can be carried out directly at the laser machine. Time-intensive experiments can be reduced and set-up processes can be completed much faster. The high speed of simulation also opens up a range of entirely different options, such as metamodeling. Suitable for complex applications with many parameters, metamodeling involves generating high-dimensional data sets with the parameters and several evaluation criteria for process and product quality. These sets can then be used to create individual process maps that show the dependency of individual parameter pairs. This advanced simulation makes it possible to find global and local extreme values through mathematical manipulation. Such simultaneous optimization of multiple parameters is scarcely possible by experimental means. This means that new methods in manufacturing such as self-optimization can be executed much faster. However, the software’s potential does not stop there; time-intensive calculations exist in many areas of industry. In laser welding or laser additive manufacturing, for example, the simulation of thermal induced residual stresses still uses up considerable computing capacity or is even not possible. Transferring the principle of reduced models promises substantial savings there, too.

Keywords: asymptotic ablation shape, interactive process simulation, laser drilling, laser cutting, metamodeling, reduced modeling

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Authors: Mohammad Ahmadi

Abstract:

Argumentative writing is a highly opinion-based form of discourse that necessitates the ability to address commonly held opinions (endoxa). To enhance the development of persuasive, argumentative essays, the incorporation of classical rhetorical theory, with a specific focus on topics related to the canon of Invention (inventio), can be advantageous. This research investigates the practical application of rhetorical theory in teaching students how to construct compelling argumentative essays. The fundamental premise of this study is the limited familiarity of rhetoric and composition students with rhetorical theory. Consequently, this paper presents an effective pedagogical approach to introduce rhetorical theory to students, beginning from a foundational level. It delineates the procedures and progression that educators should adopt to elucidate and facilitate students' comprehension of rhetorical theory while demonstrating its utilization in the writing of an argumentative essay.

Keywords: argumentative essay, rhetorical theory, pedagogy, invention

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Authors: M. Shoukath Ali, Rajendra Prasad Singh

Abstract:

Game Theory approaches and their application in improving the performance of Wireless Sensor Networks (WSNs) are discussed in this paper. The mathematical modeling and analysis of WSNs may have low success rate due to the complexity of topology, modeling, link quality, etc. However, Game Theory is a field, which can efficiently use to analyze the WSNs. Game Theory is related to applied mathematics that describes and analyzes interactive decision situations. Game theory has the ability to model independent, individual decision makers whose actions affect the surrounding decision makers. The outcome of complex interactions among rational entities can be predicted by a set of analytical tools. However, the rationality demands a stringent observance to a strategy based on measured of perceived results. Researchers are adopting game theory approaches to model and analyze leading wireless communication networking issues, which includes QoS, power control, resource sharing, etc.

Keywords: wireless sensor network, game theory, cooperative game theory, non-cooperative game theory

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

Abstract:

In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Soheib Fergani

Abstract:

This paper concerns with the formal asymptotic stability guarantees, analysis and evaluation of a nonlinear controlled unmanned aerial vehicles (uav) for trajectory tracking purpose. As the system has been recognised as an under-actuated non linear system, the control strategy has been oriented towards a hierarchical control. The dynamics of the system and the mission purpose make it mandatory to provide an absolute proof of the vehicle stability during the maneuvers. For this sake, this work establishes the complete theoretical proof for an implementable control oriented strategy that asymptotically stabilizes (GAS and LISS) the system and has never been provided in previous works. The considered model is reorganized into two partly decoupled sub-systems. The concidered control strategy is presented into two stages: the first sub-system is controlled by a nonlinear backstepping controller that generates the desired control inputs to stabilize the second sub-system. This methodology is then applied to a harware in the loop uav simulator (SiMoDrones) that reproduces the realistic behaviour of the uav in an indoor environment has been performed to show the efficiency of the proposed strategy.

Keywords: UAV application, trajectory tracking, backstepping, sliding mode control, input to state stability, stability evaluation

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Authors: Amir Deljoo

Abstract:

The endeavor to comprehend the existence have been the center of thought for human in form of different disciplines and now basically in physics as the theory of everything. Here, after a brief review of the basic frameworks of thought, and a history of thought since ancient up to present, a logical methodology is presented based on a core axiom after which a function, a proto-field and then a coordinates are explained. Afterwards a generalization to Standard Model is proposed as General Standard Model which is believed to be the base of the Unified Theory of Everything.

Keywords: general relativity, grand unified theory, quantum mechanics, standard model, theory of everything

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

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Authors: Damir Latypov

Abstract:

A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: I. M. L. Nadeesha Jayaweera, Adao Alex Trindade

Abstract:

In choosing a candidate model in likelihood-based modeling via an information criterion, the practitioner is often faced with the difficult task of deciding just how far up the ranked list to look. Motivated by this pragmatic necessity, we construct an uncertainty band for a generalized (model selection) information criterion (GIC), defined as a criterion for which the limit in probability is identical to that of the normalized log-likelihood. This includes common special cases such as AIC & BIC. The method starts from the asymptotic normality of the GIC for the joint distribution of the candidate models in an independent and identically distributed (IID) data framework and proceeds by deriving the (asymptotically) exact distribution of the minimum. The calculation of an upper quantile for its distribution then involves the computation of multivariate Gaussian integrals, which is amenable to efficient implementation via the R package "mvtnorm". The performance of the methodology is tested on simulated data by checking the coverage probability of nominal upper quantiles and compared to the bootstrap. Both methods give coverages close to nominal for large samples, but the bootstrap is two orders of magnitude slower. The methodology is subsequently extended to two other commonly used model structures: regression and time series. In the regression case, we derive the corresponding asymptotically exact distribution of the minimum GIC invoking Lindeberg-Feller type conditions for triangular arrays and are thus able to similarly calculate upper quantiles for its distribution via multivariate Gaussian integration. The bootstrap once again provides a default competing procedure, and we find that similar comparison performance metrics hold as for the IID case. The time series case is complicated by far more intricate asymptotic regime for the joint distribution of the model GIC statistics. Under a Gaussian likelihood, the default in most packages, one needs to derive the limiting distribution of a normalized quadratic form for a realization from a stationary series. Under conditions on the process satisfied by ARMA models, a multivariate normal limit is once again achieved. The bootstrap can, however, be employed for its computation, whence we are once again in the multivariate Gaussian integration paradigm for upper quantile evaluation. Comparisons of this bootstrap-aided semi-exact method with the full-blown bootstrap once again reveal a similar performance but faster computation speeds. One of the most difficult problems in contemporary statistical methodological research is to be able to account for the extra variability introduced by model selection uncertainty, the so-called post-model selection inference (PMSI). We explore ways in which the GIC uncertainty band can be inverted to make inferences on the parameters. This is being attempted in the IID case by pivoting the CDF of the asymptotically exact distribution of the minimum GIC. For inference one parameter at a time and a small number of candidate models, this works well, whence the attained PMSI confidence intervals are wider than the MLE-based Wald, as expected.

Keywords: model selection inference, generalized information criteria, post model selection, Asymptotic Theory

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

Abstract:

In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: Li-Ching Chen

Abstract:

The case-control design has been widely applied in clinical and epidemiological studies to investigate the association between risk factors and a given disease. The retrospective design can be easily implemented and is more economical over prospective studies. To adjust effects for confounding factors, methods such as stratification at the design stage and may be adopted. When some major confounding factors are difficult to be quantified, a matching design provides an opportunity for researchers to control the confounding effects. The matching effects can be parameterized by the intercepts of logistic models and the conditional logistic regression analysis is then adopted. This study demonstrates an information-matrix-based goodness-of-fit statistic to test the validity of the logistic regression model for matched case-control data. The asymptotic null distribution of this proposed test statistic is inferred. It needs neither to employ a simulation to evaluate its critical values nor to partition covariate space. The asymptotic power of this test statistic is also derived. The performance of the proposed method is assessed through simulation studies. An example of the real data set is applied to illustrate the implementation of the proposed method as well.

Keywords: conditional logistic model, goodness-of-fit, information matrix, matched case-control studies

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Authors: Bok Check Meng, Goh Ying Soon

Abstract:

Giving additional learning materials such as Chinese fantasy novel to non-native learners can be strenuous. Instructors have to understand the underpinning theories about cognitive theory for new word instruction. This paper discusses the underpinning theories. Relevant literature reviews are given. There are basically five major areas of cognitive related theories mentioned in this article. These include motivational learning theory, Affective theory of learning, Cognitive psychology theory, Vocabulary acquisition theory and Bloom’s cognitive levels theory. A theoretical framework has been constructed. Thus, this will give a hand in ensuring non-native learners might gain positive outcomes in the instruction process. Instructors who are interested in teaching new word from Chinese fantasy novel in specific to support additional learning might be able to get insights from this article.

Keywords: Chinese fantasy novel, new word teaching, non-native learners, cognitive theory, bloom

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