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Journal articles on the topic 'Generalized Vector Explicit Guidance'
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1
Ohlmeyer, Ernest J., and Craig A. Phillips. "Generalized Vector Explicit Guidance." Journal of Guidance, Control, and Dynamics 29, no. 2 (March 2006): 261–68. http://dx.doi.org/10.2514/1.14956.
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Qi, Zhan Feng, Wen Xia Liu, Li Juan Jia, Yu Feng Qin, and Xiu Jun Sun. "Dynamic Modeling and Motion Simulation for Wave Glider." Applied Mechanics and Materials 397-400 (September 2013): 285–90. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.285.
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Wave gliders as innovative autonomous ocean-going vehicles harvest the abundant marine natural energy for persistent ocean environment monitoring. This paper analyzes wave glider’s operating mechanism and builds the dynamic model of wave glider. By simplifying the model into 3 DOS in longitudinal plane and selecting three generalized velocity, the kinematic equations and the generalized force can be confirmed. Then, based on the equation of Kane vector operation modeling method, the explicit kinetic model of wave glider is presented. According to simulation study of the kinetic model, the relationship between the motion state of wave glider and the wave motion are indicated. The study provides theoretical guidance and reference for wave glider design.
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Kumar, Prem, Prasiddha N. Dwivedi, Abhijit Bhattacharyya, and Radhakant Padhi. "Terminal-Lead-Angle-Constrained Generalized Explicit Guidance." IEEE Transactions on Aerospace and Electronic Systems 53, no. 3 (June 2017): 1250–60. http://dx.doi.org/10.1109/taes.2017.2669598.
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Mondal, Sabyasachi, and Radhakant Padhi. "Generalized explicit guidance with optimal time-to-go and realistic final velocity." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 13 (April 2019): 4926–42. http://dx.doi.org/10.1177/0954410019834780.
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This paper presents an approach to compute the optimal time-to-go and final velocity magnitude in the Generalized Explicit (GENEX) guidance. Time-to-go and final velocity magnitude are two critical input parameters in GENEX guidance implementation. Optimal time-to-go selects that optimal solution which yields less cost compared to the costs yielded by other optimal solutions. In addition to it, the input of realistic final velocity lowers the cost further. These developments relax the existing limitations of GENEX, thereby making this optimal guidance law more optimal, effective and generic.
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Wong, S. K. M., and Wojciech Ziarko. "On Generalized Vector Space Model in Information Retrieval." Fundamenta Informaticae 8, no. 2 (April 1, 1985): 253–67. http://dx.doi.org/10.3233/fi-1985-8207.
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In information retrieval, it is common to model index terms and documents as vectors in a suitably defined vector space. The main difficulty with this approach is that the explicit representation of term vectors is not known a priori. For this reason, the vector space model adopted by Salton for the SMART system treats the terms as a set of orthogonal vectors. In such a model it is often necessary to adopt a separate, corrective procedure to take into account the correlations between terms. In this paper, we propose a systematic method (the generalized vector space model) to compute term correlations directly from automatic indexing scheme. We also demonstrate how such correlations can be included with minimal modification in the existing vector based information retrieval systems.
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El-Zahar, Essam R., José Tenreiro Machado, and Abdelhalim Ebaid. "A New Generalized Taylor-Like Explicit Method for Stiff Ordinary Differential Equations." Mathematics 7, no. 12 (December 1, 2019): 1154. http://dx.doi.org/10.3390/math7121154.
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A new generalised Taylor-like explicit method for stiff ordinary differential equations (ODEs) is proposed. The algorithm is presented in its component and vector forms. The error and stability analysis of the method are developed showing that it has an arbitrary high order of convergence and the L-stability property. Moreover, it is verified that several integration schemes are special cases of the new general form. The method is applied on stiff problems and the numerical solutions are compared with those of the classical Taylor-like integration schemes. The results show that the proposed method is accurate and overcomes the shortcoming of the classical Taylor-like schemes in their component and vector forms.
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Salzo, Saverio, and Johan A. K. Suykens. "Generalized support vector regression: Duality and tensor-kernel representation." Analysis and Applications 18, no. 01 (December 6, 2019): 149–83. http://dx.doi.org/10.1142/s0219530519410069.
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In this paper, we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchel–Rockafellar duality theory, we give an explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving the problem which relies on a tensor-kernel representation. This analysis overcomes the typical difficulties connected to learning in Banach spaces. We finally present a large class of tensor-kernels to which our theory fully applies: power series tensor kernels. This type of kernels describes Banach spaces of analytic functions and includes generalizations of the exponential and polynomial kernels as well as, in the complex case, generalizations of the Szegö and Bergman kernels.
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BAKAS, IOANNIS, and DIDIER A. DEPIREUX. "SELF-DUALITY AND GENERALIZED KdV FLOWS." Modern Physics Letters A 06, no. 05 (February 20, 1991): 399–408. http://dx.doi.org/10.1142/s0217732391000397.
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We obtain the (N+1)-th flow of the generalized (N–1)-KdV hierarchy from self-dual Yang-Mills equations with gauge group SL(N) and space-time signature (2, 2). The dimensional reduction is performed by using a pair of orthogonal Killing vector fields (one time-like and one null) and we generalize previous results by Mason and Sparling to N≥2. We illustrate our method with explicit examples and determine the form of the self-dual solutions for N=2, 3, 4. Applications of this formalism and its possible generalizations are also discussed briefly.
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Адамашвили, Г. Т. "Двухкомпонентный векторный бризер." Письма в журнал технической физики 47, no. 11 (2021): 14. http://dx.doi.org/10.21883/pjtf.2021.11.51000.18511.
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The two-component vector breather solution of the modified Benjamin–Bona–Mahony equation is considered. By means of the generalized perturbation reduction method, the equation is reduced to the coupled nonlinear Schrodinger equations for auxiliary functions. Explicit analytical expressions for the profile and parameters of the two-component vector breather, the components of which oscillating with the sum and difference of the frequencies and wave numbers are obtained.
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Güler, Sinem, and Uday Chand De. "Generalized quasi-Einstein metrics and applications on generalized Robertson–Walker spacetimes." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 083501. http://dx.doi.org/10.1063/5.0086836.
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In this paper, we study generalized quasi-Einstein manifolds ( M n, g, V, λ) satisfying certain geometric conditions on its potential vector field V whenever it is harmonic, conformal, and parallel. First, we construct some integral formulas and obtain some triviality results. Then, we find some necessary conditions to construct a quasi-Einstein structure on ( M n, g, V, λ). Moreover, we prove that for any generalized Ricci soliton [Formula: see text], where [Formula: see text] is a generalized Robertson–Walker spacetime metric and the potential field [Formula: see text] is conformal, [Formula: see text] can be considered as the model of perfect fluids in general relativity. Moreover, the fiber ( M, g) also satisfies the quasi-Einstein metric condition. Therefore, the state equation of [Formula: see text] is presented. We also construct some explicit examples of generalized quasi-Einstein metrics by using a four-dimensional Walker metric.
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Sahu, Uttam K., Prasiddha N. Dwivedi, Abhijit Bhattacharya, and Radhakant Padhi. "Modified Generalized Explicit Guidance for Midcourse with Near-Zero Lateral Acceleration in Terminal Phase." IFAC Proceedings Volumes 47, no. 3 (2014): 3954–59. http://dx.doi.org/10.3182/20140824-6-za-1003.01312.
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Hu, Sen, and Zhi Hu. "On geometry of the (generalized) G2-manifolds." International Journal of Modern Physics A 30, no. 20 (July 19, 2015): 1550112. http://dx.doi.org/10.1142/s0217751x15501122.
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In this paper, we first understand the classical [Formula: see text]-structure and [Formula: see text]-geometry from the viewpoint of spinor, which is a more familiar framework for physicists. Explicit construction of invariant spinor is given via the Dirac gamma matrices. We introduce a notion of multispinor bundle associated with invariant spinor and differential operator on the section of this bundle. Then we study the vector fields satisfy some additional properties on [Formula: see text]-manifold, more precisely, we prove some no-go theorems corresponding to the vector field preserving the associated 4-form on [Formula: see text]-manifold, and we also consider the nowhere-vanishing vector field which induces an integrable complex structure on the vertical direction of tangent bundle. Next we discuss the relation between the variation of metric and that of effective action on the moduli space of integrable [Formula: see text]-structures. In the last section, we deal with the structure operators on generalized [Formula: see text]-manifold after describing the integrability of generalized [Formula: see text]-structure, some identities of structure operators are derived, which are analogues of Kähler-type and Weitzenböck-type identities under the classical case. And finally, we introduce a flow of which a generalized [Formula: see text]-manifold can be realized as the fixed point.
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Lusky, Wolfgang. "Toeplitz operators on generalized Bergman-Hardy spaces." MATHEMATICA SCANDINAVICA 88, no. 1 (March 1, 2001): 96. http://dx.doi.org/10.7146/math.scand.a-14316.
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We study the Toeplitz operators $T_f: H_2 \to H_2$, for $f \in L_\infty$, on a class of spaces $H_2$ which in- cludes, among many other examples, the Hardy and Bergman spaces as well as the Fock space. We investigate the space $X$ of those elements $f \in L_\infty$ with $\lim_j \|T_f-T_{f_j}\|=0$ where $(f_j)$ is a sequence of vector-valued trigonometric polynomials whose coefficients are radial functions. For these $T_f$ we obtain explicit descriptions of their essential spectra. Moreover, we show that $f \in X$, whenever $T_f$ is compact, and characterize these functions in a simple and straightforward way. Finally, we determine those $f \in L_\infty$ where $T_f$ is a Hilbert-Schmidt operator.
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Falcó, Antonio, Lucía Hilario, Nicolás Montés, Marta C. Mora, and Enrique Nadal. "Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD)." Mathematics 9, no. 1 (December 25, 2020): 34. http://dx.doi.org/10.3390/math9010034.
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A novel algorithm called the Proper Generalized Decomposition (PGD) is widely used by the engineering community to compute the solution of high dimensional problems. However, it is well-known that the bottleneck of its practical implementation focuses on the computation of the so-called best rank-one approximation. Motivated by this fact, we are going to discuss some of the geometrical aspects of the best rank-one approximation procedure. More precisely, our main result is to construct explicitly a vector field over a low-dimensional vector space and to prove that we can identify its stationary points with the critical points of the best rank-one optimization problem. To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure.
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Kähne, Bernhard, Markus Clemens, and Sebastian Schöps. "Magnetic field simulations using explicit time integration with higher order schemes." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 41, no. 3 (November 24, 2021): 915–24. http://dx.doi.org/10.1108/compel-03-2021-0090.
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Purpose A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the resulting system of differential algebraic equations is reformulated into a system of ordinary differential equations (ODE). The ODE system is integrated in time by using explicit time integration schemes. The purpose of this paper is to investigate explicit time integration for eddy current problems with respect to the performance of the first-order explicit Euler scheme and the Runge-Kutta-Chebyshev (RKC) method of higher order. Design/methodology/approach The ODE system is integrated in time using the explicit Euler scheme, which is conditionally stable by a maximum time step size. To overcome this limit, an explicit multistage RKC time integration method of higher order is used to enlarge the maximum stable time step size. Both time integration methods are compared regarding the overall computational effort. Findings The numerical simulations show that a finer spatial discretization forces smaller time step sizes. In comparison to the explicit Euler time integration scheme, the multistage RKC method provides larger stable time step sizes to diminish the overall computation time. Originality/value The explicit time integration of the Schur complement vector potential formulation of eddy current problems is accelerated by a multistage RKC method.
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Meissner, Holger, and Josef Paldus. "Analytic Energy Derivatives for the Direct Iterative Approach to the Generalized Bloch Equation." Collection of Czechoslovak Chemical Communications 66, no. 8 (2001): 1164–90. http://dx.doi.org/10.1135/cccc20011164.
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A general formalism for the analytic energy derivatives in the context of the recently developed state-selective version of the direct iterative approach to the generalized Bloch equation is presented. An explicit formalism is developed for both the gradients and the Hessian by exploiting the so-called Z-vector method. A procedure for the development of the corresponding algorithm for higher than the second-order properties is also briefly outlined.
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CHUNG, MYUNG-HOON. "GENERALIZED COULOMB GAS MODELS WITH EXPONENTIAL INTERACTIONS AND A SERIES OF CENTRAL CHARGES." International Journal of Modern Physics A 06, no. 12 (May 20, 1991): 2189–211. http://dx.doi.org/10.1142/s0217751x9100109x.
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The renormalization of the generalized Coulomb gas model with exponential interactions is studied. This model contains a bosonic vector field and several fermionic fields in the presence of a background charge vector. It is shown that the vectors associated with the exponential interactions should satisfy certain conditions for the action to be renormalizable. The conditions require the vectors to form a geometrical figure. In particular, models are considered where the vectors are root systems which form equilateral geometrical figures. Explicit β-functions are obtained for these models. They show several nontrivial fixed points at which the central charges of the system are evaluated. It is found that a renormalization group flow connects the extremal nontrivial fixed points. Some possible applications are indicated.
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Acar, Erdem. "Reliability prediction through guided tail modeling using support vector machines." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 12 (March 11, 2013): 2780–94. http://dx.doi.org/10.1177/0954406213479846.
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Reliability prediction of highly safe mechanical systems can be performed using classical tail modeling. Classical tail modeling is based on performing a relatively small number of limit-state evaluations through a sampling scheme and then fitting a tail model to the tail part of the data. However, the limit-state calculations that do not belong to the tail part are discarded, so majority of limit-state evaluations are wasted. Guided tail modeling, proposed earlier by the author, can provide a remedy through guidance of the limit-state function calculations toward the tail region. In the original guided tail modeling, the guidance is achieved through a procedure based on threshold estimation using univariate dimension reduction and extended generalized lambda distribution and tail region approximation using univariate dimension reduction. This article proposes a new guided tail modeling technique that utilizes support vector machines. In the proposed method, named guided tail modeling with support vector machines (GTM-SVM), the threshold estimation is still performed using univariate dimension reduction and extended generalized lambda distribution, while the tail region approximation is based on support vector machines. The performance of guided tail modeling with support vector machines is tested with mathematical example problems as well as structural mechanics problems with varying number of variables. GTM-SVM is found to be more accurate than both guided tail modeling and classical tail modeling for low-dimensional problems. For high-dimensional problems, on the other hand, the original guided tail modeling is found to be more accurate than guided tail modeling with support vector machines, which is superior to classical tail modeling.
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Song, Yan-Ping, Hui-Feng Hao, Yong-Jian Hu, and Gong-Ning Chen. "Some Propositions on Generalized Nevanlinna Functions of the ClassNk." Advances in Mathematical Physics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/605492.
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Some propositions on the generalized Nevanlinna functions are derived. We indicate mainly that (1) the negative inertia index of a Hermitian generalized Loewner matrix generated by a generalized Nevanlinna function in the classNκdoes not exceedκ. This leads to an equivalent definition of a generalized Nevanlinna function; (2) if a generalized Nevanlinna function in the classNκhas a uniform asymptotic expansion at a real pointαor at infinity, then the negative inertia index of the Hankel matrix constructed with the partial coefficients of that asymptotic expansion does not exceedκ. Also, an explicit formula for the negative index of a real rational function is given by using relations among Loewner, Bézout, and Hankel matrices. These results will provide first tools for the solution of the indefinite truncated moment problems together with the multiple Nevanlinna-Pick interpolation problems in the classNκbased on the so-called Hankel vector approach.
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Cieśliński, Jan L., and Dzianis Zhalukevich. "Explicit Formulas for All Scator Holomorphic Functions in the (1+2)-Dimensional Case." Symmetry 12, no. 9 (September 20, 2020): 1550. http://dx.doi.org/10.3390/sym12091550.
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Scators form a vector space endowed with a non-distributive product, in the hyperbolic case, have physical applications related to some deformations of special relativity (breaking the Lorentz symmetry) while the elliptic case leads to new examples of hypercomplex numbers and related notions of holomorphicity. Until now, only a few particular cases of scator holomorphic functions have been found. In this paper we obtain all solutions of the generalized Cauchy–Riemann system which describes analogues of holomorphic functions in the (1+2)-dimensional scator space.
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KHRENNIKOV, A. YU, V. M. SHELKOVICH, and O. G. SMOLYANOV. "LOCALLY CONVEX SPACES OF VECTOR-VALUED DISTRIBUTIONS WITH MULTIPLICATIVE STRUCTURES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 05, no. 04 (December 2002): 483–502. http://dx.doi.org/10.1142/s0219025702001000.
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We construct an infinite-dimensional linear space [Formula: see text] of vector-valued distributions (generalized functions), or sequences, f*(x)=(fn(x)) finite from the left (i.e. fn(x)=0 for n<n0(f*)) whose components fn(x) belong to the linear span [Formula: see text] generated by the distributions δ(m-1)(x-ck), P((x-ck)-m), xm-1, where m=1, 2, …, ck ∈ ℝ, k = 1, …, s. The space of distributions [Formula: see text] can be realized as a subspace in [Formula: see text] This linear space [Formula: see text] has the structure of an associative and commutative algebra containing a unity element and free of zero divizors. The Schwartz counterexample does not hold in the algebra [Formula: see text]. Unlike the Colombeau algebra, whose elements have no explicit functional interpretation, elements of the algebra [Formula: see text] are infinite-dimensional Schwartz vector-valued distributions. This construction can be considered as a next step and a "model" on the way of constructing a nonlinear theory of distributions similar to that developed by L. Schwartz. The obtained results can be considerably generalized.
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KIM, JINMYONG, HYONJIN KIM, and HAKMYONG MUN. "CONSTRUCTION OF NONLINEAR HIDDEN VARIABLE FRACTAL INTERPOLATION FUNCTIONS AND THEIR STABILITY." Fractals 27, no. 06 (September 2019): 1950103. http://dx.doi.org/10.1142/s0218348x19501032.
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This paper presents a method to construct nonlinear hidden variable fractal interpolation functions (FIFs) and their stability results. We ensure that the projections of attractors of vector-valued nonlinear iterated function systems (IFSs) constructed by Rakotch contractions and function vertical scaling factors are graphs of some continuous functions interpolating the given data. We also give an explicit example illustrating obtained results. Then, we get the stability results of the constructed FIFs in the case of the generalized interpolation data having small perturbations.
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CHUNG, M. Y. "EXPLICIT SOLUTIONS FOR AN ANISOTROPIC PIEZOELECTRIC HALF-SPACE SUBJECT TO LINEARLY-VARYING SURFACE LOADINGS ALONG x3-DIRECTION." International Journal of Applied Mechanics 06, no. 06 (December 2014): 1450074. http://dx.doi.org/10.1142/s1758825114500744.
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Explicit results for a piezoelectric half-space x2 ≥ 0 subject to linearly-varying surface loadings along x3 axis are derived. The extended Stroh formalism is employed to provide three-dimensional solutions with the generalized displacement vector u expressed as a function of (z, x2, x3). A general polynomial solution for u with order of m in x3 is suggested and it provides a particularly efficient solution for half-space problem with loadings on the surface. A simple uniform surface loading is considered first to clarify the derivations. Then explicit solution in case of a linearly-varying surface loading along x3-direction is obtained. In addition, the Green's function for a piezoelectric half-space with a linearly-varying surface line loading along x3-axis is constructed.
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Zhang, Wanqing, Wanchun Chen, and Wenbin Yu. "Impact-Angle and Terminal-Maneuvering-Acceleration Constrained Guidance against Maneuvering Target." Aerospace 9, no. 1 (December 31, 2021): 22. http://dx.doi.org/10.3390/aerospace9010022.
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A new, highly constrained guidance law is proposed against a maneuvering target while satisfying both impact angle and terminal acceleration constraints. Here, the impact angle constraint is addressed by solving an optimal guidance problem in which the target’s maneuvering acceleration is time-varying. To deal with the terminal acceleration constraint, the closed-form solutions of the new guidance are needed. Thus, a novel engagement system based on the guidance considering the target maneuvers is put forward by choosing two angles associated with the relative velocity vector and line of sight (LOS) as the state variables, and then the system is linearized using small angle assumptions, which yields a special linear time-varying (LTV) system that can be solved analytically by the spectral-decomposition-based method. For the general case where the closing speed, which is the speed of approach of the missile and target, is allowed to change with time arbitrarily, the solutions obtained are semi-analytical. In particular, when the closing speed changes linearly with time, the completely closed-form solutions are derived successfully. By analyzing the generalized solutions, the stability domain of the guidance coefficients is obtained, in which the maneuvering acceleration of the missile can converge to zero finally. Here, the key to investigating the stability domain is to find the limits of some complicated integral terms of the generalized solutions by skillfully using the squeeze theorem. The advantages of the proposed guidance are demonstrated by conducting trajectory simulations.
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Greiner, Peter, and Yutian Li. "A fundamental solution for a nonelliptic partial differential operator, II." Analysis and Applications 16, no. 03 (May 2018): 407–33. http://dx.doi.org/10.1142/s0219530516500196.
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Let [Formula: see text] denote the holomorphic tangential vector field to the generalized upper-half plane [Formula: see text]. In our terminology, [Formula: see text]. Consider the [Formula: see text] operator on the boundary of [Formula: see text], [Formula: see text]; note that [Formula: see text] is nowhere elliptic, but it is subelliptic with step three. The principal result of this paper is the derivation of an explicit fundamental solution [Formula: see text] to [Formula: see text]. Our approach is based on special functions and their properties.
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Lee, Ji-Eun. "Slant Curves in Contact Lorentzian Manifolds with CR Structures." Mathematics 8, no. 1 (January 1, 2020): 46. http://dx.doi.org/10.3390/math8010046.
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In this paper, we first find the properties of the generalized Tanaka–Webster connection in a contact Lorentzian manifold. Next, we find that a necessary and sufficient condition for the ∇ ^ -geodesic is a magnetic curve (for ∇) along slant curves. Finally, we prove that when c ≤ 0 , there does not exist a non-geodesic slant Frenet curve satisfying the ∇ ^ -Jacobi equations for the ∇ ^ -geodesic vector fields in M. Thus, we construct the explicit parametric equations of pseudo-Hermitian pseudo-helices in Lorentzian space forms M 1 3 ( H ^ ) for H ^ = 2 c > 0 .
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Dutiné, Jennifer Susanne, Markus Clemens, and Sebastian Schöps. "Explicit time integration of eddy current problems using a selective matrix update strategy." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 5 (September 4, 2017): 1364–71. http://dx.doi.org/10.1108/compel-02-2017-0100.
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Purpose Discretizing the magnetic vector potential formulation of eddy current problems in space results in an infinitely stiff differential algebraic equation system that is integrated in time using implicit time integration methods. Applying a generalized Schur complement to the differential algebraic equation system yields an ordinary differential equation (ODE) system. This ODE system can be integrated in time using explicit time integration schemes by which the solution of high-dimensional nonlinear algebraic systems of equations is avoided. The purpose of this paper is to further investigate the explicit time integration of eddy current problems. Design/methodology/approach The resulting magnetoquasistatic Schur complement ODE system is integrated in time using the explicit Euler method taking into account the Courant–Friedrich–Levy (CFL) stability criterion. The maximum stable CFL time step can be rather small for magnetoquasistatic field problems owing to its proportionality to the smallest edge length in the mesh. Ferromagnetic materials require updating the reluctivity matrix in nonlinear material in every time step. Because of the small time-step size, it is proposed to only selectively update the reluctivity matrix, keeping it constant for as many time steps as possible. Findings Numerical simulations of the TEAM 10 benchmark problem show that the proposed selective update strategy decreases computation time while maintaining good accuracy for different dynamics of the source current excitation. Originality/value The explicit time integration of the Schur complement vector potential formulation of the eddy current problem is accelerated by updating the reluctivity matrix selectively. A strategy for this is proposed and investigated.
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Khulief, Y. A., and A. A. Shabana. "Dynamic Analysis of Constrained System of Rigid and Flexible Bodies With Intermittent Motion." Journal of Mechanisms, Transmissions, and Automation in Design 108, no. 1 (March 1, 1986): 38–45. http://dx.doi.org/10.1115/1.3260781.
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A method for dynamic analysis of large-scale constrained system of mixed rigid and flexible bodies with intermittent motion is presented. The system equations of motion are written in the Lagrangian formulation using a finite set of coupled reference position and local elastic generalized coordinates. Equations of motion are computer generated and integrated forward in time using an explicit-implicit integration algorithm. Points in time at which sudden events of the intermittent behavior occur are monitored by an event predictor which controls the integration algorithm and forces a solution for the system impulse-momentum relation at those points. Solutions of impulse-momentum relations define the jump discontinuities in the composite velocity vector as well as the generalized impulses of the reaction forces at different joints of the mechanical system.
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CHAVARRIGA, J., I. A. GARCÍA, and J. GINÉ. "ON INTEGRABILITY OF DIFFERENTIAL EQUATIONS DEFINED BY THE SUM OF HOMOGENEOUS VECTOR FIELDS WITH DEGENERATE INFINITY." International Journal of Bifurcation and Chaos 11, no. 03 (March 2001): 711–22. http://dx.doi.org/10.1142/s0218127401002390.
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The paper deals with polynomials systems with degenerate infinity from different points of view. We show the utility of the projective techniques for such systems, and a more detailed study in the quadratic and cubic cases is carried out. On the other hand, some results on Darboux integrability in the affine plane for a class of systems are given. In short we show the explicit form of generalized Darboux inverse integrating factors for the above kind of systems. Finally, a short proof of the center cases for arbitrary degree homogeneous systems with degenerate infinity is given, and moreover we solve the center problem for quartic systems with degenerate infinity and constant angular speed.
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Jenkovszky, László. "Spin and Polarization in High-Energy Hadron-Hadron and Lepton-Hadron Scattering." Symmetry 12, no. 11 (October 28, 2020): 1784. http://dx.doi.org/10.3390/sym12111784.
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The role of spin degrees of freedom in high-energy hadron-hadron and lepton-hadron scattering is reviewed with emphasis on the dominant role of soft, diffractive, non-perturbative effects. Explicit models based on analyticity and Regge-pole theory, including the pomeron trajectory (gluon exchange in the t channel) are discussed. We argue that there is a single, universal pomeron in Nature, manifest as relatively “soft” or “hard”, depending on the kinematics considered. Both the pomeron and the non-leading (secondary) Regge trajectories, made of quarks are non-linear, complex functions. They are populated by a finite number of resonances: known baryons and mesons in case of the reggeons and hypothetical glueballs in case of the pomeron (“oddballs” on the odderon trajectory). Explicit models and fits are presented that may be used in recovering generalized parton distributions from deeply virtual Compton scattering and electoproduction of vector mesons.
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Ansari, Uzair, and Abdulrahman H. Bajodah. "Launch vehicle ascent flight attitude control using direct adaptive generalized dynamic inversion." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 11 (November 28, 2018): 4141–53. http://dx.doi.org/10.1177/0954410018814135.
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This paper presents the attitude control design of satellite launch vehicle based on the direct adaptive generalized dynamic inversion approach. The proposed adaptive generalized dynamic inversion approach encompasses the equivalent and the adaptive control elements. The equivalent (continuous) control part of adaptive generalized dynamic inversion is based on the conventional generalized dynamic inversion approach that comprises two noninterfering control actions, i.e. the particular part and the auxiliary part. In the particular part, dynamical constraint is prescribed in the form of time differential equation, which is evaluated along the vehicle attitude trajectories that encapsulates the control objectives and is inverted by utilizing Moore Penrose Generalized Inverse (MPGI). The singularity problem is solved by augmenting a dynamic scaling factor in the involved MPGI. In the auxiliary part, the null control vector is designed using the proportionality gain matrix, constructed by employing the Lyapunov function that guarantees global closed-loop asymptotic stability of the angular body rate dynamics. The adaptive (discontinuous) control part of adaptive generalized dynamic inversion is based on the sliding mode control with adaptive modulation gain, that provides robustness against tracking performance deterioration due to generalized scaling, system nonlinearities, and uncertainties, such that semi-global practically stable attitude tracking is guaranteed. External guidance loop based on the trajectory following method is designed, which reshapes the predefined pitch and yaw attitude profiles based on the respective normal and lateral positional errors, for acquiring the desired orbital parameters such as height, injection angle, orbital velocity, etc. To analyze the ascent flight trajectory, a detailed six-degrees-of-freedom simulator of a four-stage satellite launch vehicle is developed. The intensive numerical simulations are performed, which demonstrate the stability, robustness and the tracking capability of the proposed control and guidance methods in the presence of parametric uncertainties and external disturbances.
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Dubnitskiy, Valeriy, Anatolii Kobylin, Oleg Kobylin, Yuri Kushneruk, and Alexander Khodyrev. "Calculation of harrington function (desirability function) values under interval determination of its arguments." Advanced Information Systems 7, no. 1 (March 13, 2023): 71–81. http://dx.doi.org/10.20998/2522-9052.2023.1.12.
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Purpose of work. Development of proposals for desirability function calculation by interval arithmetic method. Obtained results. A connection was shown between multiple-criterial (vector) optimization problem and calculation of Harrington function (desirability function) values. Generalized desirability function was shown to be treated as a multiplicative convolution of partial desirabilities. Using golden section properties, a connection was discerned between hierarchy analysis methods and calculation of desirability function values. In this case the distribution of probable desirability function values among intervals determined in accordance with golden mean rule does coincide with values obtained by expert method. Application of golden proportion enables increasing the number of intervals; thus, it may prove convenient in improvement of Harrington function sensitivity. Conclusions. For partial desirability function in its explicit form such geometric characteristics were determined as values of tangent, curvature of curve and center of curvature coordinates. For a necessary averaged desirability system obtaining process control, such characteristics were determined in general and explicit form as partial desirability elasticity, generalized desirability elasticity relative to partial desirability, generalized desirability elasticity relative to a variable that has physical sense and respective dimension depending on particular subject area and affects partial desirability value. To determine the boundary value of one partial desirability being substituted for another partial desirability, the rate of substitution function and boundary rate of substitution elasticity function were established. Due to errors emerging in determination of desirability function values application of interval analysis methods was proposed. Application of interval numbers as presented in hyperbolic form was shown for calcutaion of partial and generalized desirability, A partial power series sum was determined relative to a variable presented in hyperbolic form. Suggestions. The method of calculation of Harrington function (desirability function) values at interval determination of arguments was shown to be eventually used in development of specifications and preliminary design of complicated engineering аnd organizational systems.
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GRAVVANIS, G. A., C. K. FILELIS-PAPADOPOULOS, K. M. GIANNOUTAKIS, and E. A. LIPITAKIS. "A NOTE ON PARALLEL FINITE DIFFERENCE APPROXIMATE INVERSE PRECONDITIONING ON MULTICORE SYSTEMS USING POSIX THREADS." International Journal of Computational Methods 10, no. 05 (May 2013): 1350032. http://dx.doi.org/10.1142/s0219876213500321.
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New parallel computational techniques are introduced for the parallelization of explicit finite difference (FD) approximate inverse matrix methods, based on Portable Operating System Interface for UniX (POSIX) threads, for multicore systems. Parallelization of the Optimized Banded Generalized Approximate Inverse Matrix (OBGAIM) algorithm is achieved based on the concept of the "fish bone" approach with the use of a thread pool pattern. Theoretical estimates on speedups and efficiency are also presented. Additionally, new parallel computational techniques are proposed for the parallelization of explicit preconditioned biconjugate conjugate gradient type methods, based on POSIX threads, for multicore systems. For parallelization purposes a replication of the parallel explicit preconditioned biconjugate conjugate gradient-STAB (PEPBICG-STAB) method was assigned on each created thread, with different index bands and with proper synchronization points on inner products and matrix-vector multiplications. Theoretical estimates on speedups and efficiency are also presented. Finally, numerical results for the performance of the Parallel Fish Bone OBGAIM (PaFiBo-OBGAIM) algorithm and the PEPBICG-STAB method for solving classical two-dimensional boundary value problems on multicore computer systems are presented, which are favorably compared to corresponding results from multiprocessor systems. The implementation issues of the proposed method are also discussed using POSIX threads on multicore systems.
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de Rham, Claudia, Sebastian Garcia-Saenz, Lavinia Heisenberg, and Victor Pozsgay. "Cosmology of Extended Proca-Nuevo." Journal of Cosmology and Astroparticle Physics 2022, no. 03 (March 1, 2022): 053. http://dx.doi.org/10.1088/1475-7516/2022/03/053.
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Abstract Proca-Nuevo is a non-linear theory of a massive spin-1 field which enjoys a non-linearly realized constraint that distinguishes it among other generalized vector models. We show that the theory may be extended by the addition of operators of the Generalized Proca class without spoiling the primary constraint that is necessary for consistency, allowing to interpolate between Generalized Proca operators and Proca-Nuevo ones. The constraint is maintained on flat spacetime and on any fixed curved background. Upon mixing extended Proca-Nuevo dynamically with gravity, we show that the constraint gets broken in a Planck scale suppressed way. We further prove that the theory may be covariantized in models that allow for consistent and ghost-free cosmological solutions. We study the models in the presence of perfect fluid matter, and show that they describe the correct number of dynamical variables and derive their dispersion relations and stability criteria. We also exhibit, in a specific set-up, explicit hot Big Bang solutions featuring a late-time self-accelerating epoch, and which are such that all the stability and subluminality conditions are satisfied and where gravitational waves behave precisely as in General Relativity.
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Tansri, Kanjanaporn, and Pattrawut Chansangiam. "General Solutions for Descriptor Systems of Coupled Generalized Sylvester Matrix Fractional Differential Equations via Canonical Forms." Symmetry 12, no. 2 (February 14, 2020): 283. http://dx.doi.org/10.3390/sym12020283.
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We investigate a descriptor system of coupled generalized Sylvester matrix fractional differential equations in both non-homogeneous and homogeneous cases. All fractional derivatives considered here are taken in Caputo’s sense. We explain a 4-step procedure to solve the descriptor system, consisting of vectorization, a matrix canonical form concerning ranks, and matrix partitioning. The procedure aims to reduce the descriptor system to a descriptor system of fractional differential equations. We also impose a condition on coefficient matrices, related to the symmetry of the solution for descriptor systems. It follows that an explicit form of its general solution is given in terms of matrix power series concerning Mittag–Leffler functions. The main system includes certain systems of coupled matrix/vector differential equations, and single matrix differential equations as special cases. In particular, we obtain an alternative procedure to solve linear continuous-time descriptor systems via a matrix canonical form.
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Santana, Tiago V. F., Edwin M. M. Ortega, Gauss M. Cordeiro, and Adriano K. Suzuki. "Generalized Exponentiated Weibull Linear Model in the Presence of Covariates." International Journal of Statistics and Probability 6, no. 3 (May 14, 2017): 75. http://dx.doi.org/10.5539/ijsp.v6n3p75.
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A new regression model based on the exponentiated Weibull with the structure distribution and the structure of the generalized linear model, called the generalized exponentiated Weibull linear model (GEWLM), is proposed. The GEWLM is composed by three important structural parts: the random component, characterized by the distribution of the response variable; the systematic component, which includes the explanatory variables in the model by means of a linear structure; and a link function, which connects the systematic and random parts of the model. Explicit expressions for the logarithm of the likelihood function, score vector and observed and expected information matrices are presented. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. To detect influential observations in the new model, we use diagnostic measures based on the local influence and Bayesian case influence diagnostics. Also, we show that the estimates of the GEWLM are robust to deal with the presence of outliers in the data. Additionally, to check whether the model supports its assumptions, to detect atypical observations and to verify the goodness-of-fit of the regression model, we define residuals based on the quantile function, and perform a Monte Carlo simulation study to construct confidence bands from the generated envelopes. We apply the new model to a dataset from the insurance area.
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Peled, Irit, and Yoram Halevi. "Continuous Modeling of a Multi-Link Flexible Transmission." Shock and Vibration 15, no. 2 (2008): 163–77. http://dx.doi.org/10.1155/2008/565068.
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The problem of dynamic, infinite dimension, modeling of a transmission is considered. An accurate Laplace transfer function matrix of the system that consists of flexible shafts connected by gears that are either rigid or flexible is found. The first step is deriving a set of single input, infinite dimension, transfer functions for a single uniform link. The building blocks of those transfer functions are time delays, representing the wave motion, and low order rational expressions, representing the boundary phenomena. The next step is combining these individual transfer functions into an overall model of the transmission, by means of the link reaction approach that makes use of the geometric relationships and reaction moments between neighboring links. The outcome is a generalized dynamic model with the moments in the gear pairs as the generalized state vector. The explicit and highly structured form of the transfer functions allows physical insight into the system, exact calculation of natural frequencies and the construction of exact simulation schemes built from standard blocks that are available in multi-purpose simulation software.
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Lazar, Markus, and Eleni Agiasofitou. "Eshelbian mechanics of novel materials: Quasicrystals." Journal of Micromechanics and Molecular Physics 01, no. 03n04 (October 2016): 1640008. http://dx.doi.org/10.1142/s2424913016400087.
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In this work, the so-called Eshelbian or configurational mechanics of quasicrystals is presented. Quasicrystals are considered as a prototype of novel materials. Material balance laws for quasicrystalline materials with dislocations are derived in the framework of generalized incompatible elasticity theory of quasicrystals. Translations, scaling transformations as well as rotations are examined; the latter presents particular interest due to the quasicrystalline structure. This derivation provides important quantities of the Eshelbian mechanics, as the Eshelby stress tensor, the scaling flux vector, the angular momentum tensor, the configurational forces (Peach–Koehler force, Cherepanov force, inhomogeneity force or Eshelby force), the configurational work, and the configurational vector moments for dislocations in quasicrystals. The corresponding [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-integrals for dislocation loops and straight dislocations in quasicrystals are derived and discussed. Moreover, the explicit formulas of the [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-integrals for parallel screw dislocations in one-dimensional hexagonal quasicrystals are obtained. Through this derivation, the physical interpretation of the [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-integrals for dislocations in quasicrystals is revealed and their connection to the Peach–Koehler force, the interaction energy and the rotational vector moment (torque) of dislocations in quasicrystals is established.
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Su, Ren-He. "Eisenstein series in the Kohnen plus space for Hilbert modular forms." International Journal of Number Theory 12, no. 03 (March 23, 2016): 691–723. http://dx.doi.org/10.1142/s1793042116500469.
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In 1975, Cohen constructed a kind of one-variable modular forms of half-integral weight, say [Formula: see text], whose [Formula: see text]th Fourier coefficient only occurs when [Formula: see text] is congruent to 0 or 1 modulo 4. The space of modular forms whose Fourier coefficients have the above property is called Kohnen plus space, initially introduced by Kohnen in 1980. Recently, Hiraga and Ikeda generalized the plus space to the spaces for half-integral weight Hilbert modular forms with respect to general totally real number fields. The [Formula: see text]th Fourier coefficients [Formula: see text] of a Hilbert modular form of parallel weight [Formula: see text] lying in the generalized Kohnen plus space does not vanish only if [Formula: see text] is congruent to a square modulo 4. In this paper, we use an adelic way to construct Eisenstein series of parallel half-integral weight belonging to the generalized Kohnen plus spaces and give an explicit form for their Fourier coefficients. These series give a generalization of the one introduced by Cohen. Moreover, we show that the Kohnen plus space is generated by the cusp forms and the Eisenstein series we constructed as a vector space over [Formula: see text].
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Deng, Qi. "A generalized VECM/VAR-DCC/ADCC framework and its application in the Black-Litterman model." China Finance Review International 8, no. 4 (November 19, 2018): 453–67. http://dx.doi.org/10.1108/cfri-07-2016-0095.
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Purpose The existing literature on the Black-Litterman (BL) model does not offer adequate guidance on how to generate investors’ views in an objective manner. Therefore, the purpose of this paper is to establish a generalized multivariate Vector Error Correction Model (VECM)/Vector Auto-Regressive (VAR)-Dynamic Conditional Correlation (DCC)/Asymmetric DCC (ADCC) framework, and applies it to generate objective views to improve the practicality of the BL model. Design/methodology/approach This paper establishes a generalized VECM/VAR-DCC/ADCC framework that can be utilized to model multivariate financial time series in general, and produce objective views as inputs to the BL model in particular. To test the VECM/VAR-DCC/ADCC preconditioned BL model’s practical utility, it is applied to a six-asset China portfolio (including one risk-free asset). Findings With dynamically optimized view confidence parameters, the VECM/VAR-DCC/ADCC preconditioned BL model offers clear advantage over the standard mean-variance method, and provides an automated portfolio optimization alternative to the classic BL approach. Originality/value The VECM/VAR-DCC/ADCC framework and its application in the BL model proposed by this paper provide an alternative approach to the classic BL method. Since all the view parameters, including estimated mean return vectors, conditional covariance matrices and pick matrices, are generated in the VECM/VAR and DCC/ADCC preconditioning stage, the model improves the objectiveness of the inputs to the BL stage. In conclusion, the proposed model offers a practical choice for automated portfolio balancing and optimization in a China context.
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Min, Moonsik, and Tae-Kyoung Kim. "Spherical-Cap Approximation of Vector Quantization for Quantization-Based Combining in MIMO Broadcast Channels with Limited Feedback." Sensors 22, no. 14 (July 8, 2022): 5146. http://dx.doi.org/10.3390/s22145146.
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The spherical-cap approximation of vector quantization (SCVQ) is an analytical model used for the mathematical analysis of multiple-input multiple-output (MIMO) systems with limited feedback. SCVQ closely emulates the distribution of the quantization error induced by the finite-rate quantization of a channel using a simple and analytically tractable approach. However, the conventional SCVQ model is not applicable when antenna-combining schemes such as quantization-based combining (QBC) are considered. Because QBC is an effective antenna-combining method that minimizes channel quantization errors, it can be adopted for various practical MIMO broadcast systems. Nevertheless, evaluating the performance of QBC-based MIMO systems with an explicit codebook can be extremely difficult, depending on the system complexity. To resolve this, this study generalizes the conventional SCVQ to be compatible with the QBC. The proposed generalized version of the SCVQ effectively emulates the quantization error obtained using QBC, while enabling a simple simulation independent of the number of feedback bits and mathematically tractable analysis. We validate the effectiveness of the proposed model by presenting a wireless communication application based on a dense cellular network.
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KALADZE, T. D., D. J. WU, O. A. POKHOTELOV, R. Z. SAGDEEV, L. STENFLO, and P. K. SHUKLA. "Rossby-wave driven zonal flows in the ionospheric E-layer." Journal of Plasma Physics 73, no. 1 (February 2007): 131–40. http://dx.doi.org/10.1017/s0022377806004351.
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Abstract.A novel mechanism for the generation of large-scale zonal flows by small-scale Rossby waves in the Earth's ionospheric E-layer is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude magnetized Rossby waves. To describe this process a generalized Charney equation containing both vector and scalar (Korteweg–de Vries type) nonlinearities is used. The magnetized Rossby waves are supposed to have arbitrary wavelengths (as compared with the Rossby radius). A set of coupled equations describing the nonlinear interaction of magnetized Rossby waves and zonal flows is obtained. The generation of zonal flows is due to the Reynolds stresses produced by finite amplitude magnetized Rossby waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the magnetized Rossby pump wave. Explicit expression for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with existing results is carried out. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere.
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Felker, Emily, Mirjam Broersma, and Mirjam Ernestus. "The role of corrective feedback and lexical guidance in perceptual learning of a novel L2 accent in dialogue." Applied Psycholinguistics 42, no. 4 (June 15, 2021): 1029–55. http://dx.doi.org/10.1017/s0142716421000205.
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AbstractPerceptual learning of novel accents is a critical skill for second-language speech perception, but little is known about the mechanisms that facilitate perceptual learning in communicative contexts. To study perceptual learning in an interactive dialogue setting while maintaining experimental control of the phonetic input, we employed an innovative experimental method incorporating prerecorded speech into a naturalistic conversation. Using both computer-based and face-to-face dialogue settings, we investigated the effect of two types of learning mechanisms in interaction: explicit corrective feedback and implicit lexical guidance. Dutch participants played an information-gap game featuring minimal pairs with an accented English speaker whose /ε/ pronunciations were shifted to /ɪ/. Evidence for the vowel shift came either from corrective feedback about participants’ perceptual mistakes or from onscreen lexical information that constrained their interpretation of the interlocutor’s words. Corrective feedback explicitly contrasting the minimal pairs was more effective than generic feedback. Additionally, both receiving lexical guidance and exhibiting more uptake for the vowel shift improved listeners’ subsequent online processing of accented words. Comparable learning effects were found in both the computer-based and face-to-face interactions, showing that our results can be generalized to a more naturalistic learning context than traditional computer-based perception training programs.
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Wu, Jiulin, Lizhan Zeng, Bin Han, Xin Luo, Xuedong Chen, and Wei Jiang. "Inverse Eigenvalue Theory-Based Rigid Multibody Modeling Method of Complex Flexible Structures in Large-Scale Mechanical Systems." Mathematical Problems in Engineering 2020 (January 28, 2020): 1–18. http://dx.doi.org/10.1155/2020/8329395.
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Increasing attention is paid to modeling flexibility of individual components in the multibody simulation of large-scale mechanical systems. Nevertheless, the high model order of common methods such as FEA restricts efficient explorations, especially in dynamic design and iterative optimization. In this paper, a rigid multibody modeling strategy (RMMS) with low DOFs and explicit physical meaning is proposed, which directly discretizes a continuous structure into a number of rigid finite elements (RFEs) connected by spring-damping elements (SDEs). In the RMMS, a new identification method from the perspective of the inverse vibration problem is particularly put forward to resolve the parameters of SDEs, which is crucial to the implementation of RMMS in complex flexible structures. With decoupling and linearization, this nonlinear problem is transformed into solving the incompatible linear equations in Rn2 vector space based on vectorization operator and Kronecker product, and optimal parameters are obtained by calculating the Moore–Penrose generalized inverse. Finally, the comparison of the experimental results with the simulated ones by the RMMS strongly validates the feasibility and correctness of the RMMS in predicting the dynamic behaviors while with few DOFs and explicit physical meaning; the application in a lithography system exhibits the applicability of the RMMS for dynamic modeling of large-scale mechanical systems.
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Song, Yuwei, and Guimei Zheng. "Height Measurement for Meter Wave Polarimetric MIMO Radar with Electrically Long Dipole under Complex Terrain." Remote Sensing 15, no. 5 (February 24, 2023): 1265. http://dx.doi.org/10.3390/rs15051265.
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Height measurement of meter wave radar is a difficult and important problem. This paper studies the height measurement of meter wave polarimetric (MWP)-MIMO array radar under complex terrain. The traditional electrically short dipole has low radiation efficiency, and the collocated dipole vector antenna has strong mutual coupling. This paper proposes to use electrically long dipoles and separated vector antennae to solve the problems of low radiation efficiency and strong mutual coupling. In addition, different from the traditional flat terrain, the research of this paper is based on the conditions of complex undulating terrain. First, the height measurement signal model of the MWP-MIMO radar with separated electrically long dipole under the complex terrain is derived. Then, a preprocessing method of block orthogonal matching pursuit is proposed to obtain the coarse estimation of the target’s elevation. Then, under the guidance of the coarse estimation, the generalized MUSIC algorithm is used to obtain the high-precision elevation estimation of the target, and then the height measurement of the target is obtained according to the geometric relationship. Finally, the effectiveness of the proposed algorithm is proved by computer simulations.
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Wang, Zhong Chang. "Application of Stereographic Projection in the Search of Key Block of Surrounding Rock Mass for Underground Powerhouse." Applied Mechanics and Materials 44-47 (December 2010): 1189–92. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.1189.
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The rose diagram of joint is generalized by grouping the attitude of disclosed discontinuous faces in detecting cavern and measuring point coordinate. The search of movable and key blocks of surrounding rock mass for underground powerhouse is implemented, the combinations of discontinuous faces and sliding faces, the location and the parameter of stability of movable and key blocks are obtained by used of the method of stereographic projection and vector analysis of the block theory. It is shown that the numbers of movable and key blocks in the location of downriver right side wall and vault are larger than those in other location owing to numerous discontinuous faces, and the faults of F34 and F33 play a main role in the stability of movable and key blocks. The guidance for excavation and reinforce of underground caverns is provided.
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GATES, DAVID J. "SYMMETRIC SOLUTIONS FOR TWO-BODY DYNAMICS IN A COLLISION PREVENTION MODEL." ANZIAM Journal 52, no. 3 (January 2011): 263–88. http://dx.doi.org/10.1017/s1446181111000691.
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AbstractThis paper presents the first analytical solutions for the three-dimensional motion of two idealized mobiles controlled by a particular guidance law designed to avoid a collision with minimal path deviation. The mobiles can be regarded as particles, and guidance can be interpreted as complex forces of interaction between the particles. The motion is then a generalized form of two-body Newtonian dynamics. If the mobiles have equal speeds, the relative motion is determined through various transformations of the differential equations. Solvability relies on congruence and symmetries of the paths, which is exploited to reduce the original twelve first-order differential equations to three first-order equations for the relative motion. The resulting state space is partitioned into five invariant subsets, with various symmetries and stabilities. One of these sets describes planar motion, where simple explicit solutions are given. In nonplanar motion, the solution is formally reduced to quadrature. A numerical calculation gives the separation at the closest point of approach, which provides control over minimum separation. The results should be of interest because of their application, which includes, most importantly, the prevention of midair collisions between aircraft, but also potential application to land, water and space vehicles. The solutions should be of interest to mathematical specialists in dynamical systems, because of some novel constants of the motion, novel symmetries, and the associated reducibility of the equations.
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Rong, Dalun, Junhai Fan, C. W. Lim, Xinsheng Xu, and Zhenhuan Zhou. "A New Analytical Approach for Free Vibration, Buckling and Forced Vibration of Rectangular Nanoplates Based on Nonlocal Elasticity Theory." International Journal of Structural Stability and Dynamics 18, no. 04 (March 28, 2018): 1850055. http://dx.doi.org/10.1142/s0219455418500554.
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In this paper, an analytical Hamiltonian-based model for the dynamic analysis of rectangular nanoplates is proposed using the Kirchhoff plate theory and Eringen’s nonlocal theory. In a symplectic space, the dynamic problem is reduced to solving a unified Hamiltonian dual equation formed by a total unknown vector consisting of displacements, rotation angles, bending moments and generalized shear forces. The exact solutions for free vibration, buckling and steady state forced vibration are established by the eigenvalue analysis and expansion of eigenfunction without any trial functions. In addition, the explicit expressions of the characteristic equations, mode functions and steady state response of the nanoplate with two opposite edges that are simply supported or guided supported are obtained. To verify the accuracy and reliability of the present method, numerical results are compared with published solutions and excellent agreement is obtained. Comprehensive benchmark results that consider the nonlocal effect on the dynamic behaviors of rectangular nanoplates are also presented in dimensionless tabular and graphical forms.
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Hunt, Barry. "Knowledge-Based Nonlinear Boundary Integral Models of Compressible Viscous Flows Over Arbitrary Bodies: Taking CFD Back to Basics." Applied Mechanics Reviews 44, no. 11S (November 1, 1991): S130—S142. http://dx.doi.org/10.1115/1.3121345.
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The paper starts with a discussion of a knowledge-based CFD methodology. A new incompressible formulation known as SAVER is first introduced, employing a novel relaxation approach. This is then generalized through a modification of the boundary conditions to the GENESIS methodology, for analysis or design in compressible, rotational flow. A discussion is presented of how the basic causal nature of integral methods offers new insights into certain flow phenomena, such as shocks and separations, and facilitates aerodynamic sensitivity analysis. The paper presents a new class of vector fields approximating the Euler equations for transonic flows, and shows how GENESIS can be used to construct first an exact solution of these approximate fields, then a numerical solution of the residual error fields. The explicit representation of a shock discontinuity on the body boundary exploits its causal link with conditions at the sonic point to suppress, non-dissipatively, the mathematically-valid but physically-impossible formation of an expansion shock.
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QUESNE, C., and N. VANSTEENKISTE. "PSEUDOSUPERSYMMETRIC QUANTUM MECHANICS: GENERAL CASE, ORTHOSUPERSYMMETRIES, REDUCIBILITY, AND BOSONIZATION." International Journal of Modern Physics A 18, no. 02 (January 20, 2003): 271–92. http://dx.doi.org/10.1142/s0217751x03012199.
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Pseudosupersymmetric quantum mechanics (PsSSQM), based upon the use of pseudofermions, was introduced in the context of a new Kemmer equation describing charged vector mesons interacting with an external constant magnetic field. Here we construct the complete explicit solution for its realization in terms of two superpotentials, both equal or unequal. We prove that any orthosupersymmetric quantum mechanical system has a pseudosupersymmetry and give conditions under which a pseudosupersymmetric one may be described by orthosupersymmetries of order two. We propose two new matrix realizations of PsSSQM in terms of the generators of a generalized deformed oscillator algebra (GDOA) and relate them to the cases of equal or unequal superpotentials, respectively. We demonstrate that these matrix realizations are fully reducible and that their irreducible components provide two distinct sets of bosonized operators realizing PsSSQM and corresponding to nonlinear spectra. We relate such results to some previous ones obtained for a GDOA connected with a C3-extended oscillator algebra (where C3 = ℤ3) in the case of linear spectra.