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Статті в журналах з теми "Jacobi constant"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 28 січня 2023

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1

Andrejic, Vladica. "On Lorentzian spaces of constant sectional curvature." Publications de l'Institut Math?matique (Belgrade) 103, no. 117 (2018): 7–15. http://dx.doi.org/10.2298/pim1817007a.

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Анотація:

We investigate Osserman-like conditions for Lorentzian curvature tensors that imply constant sectional curvature. It is known that Osserman (moreover zwei-stein) Lorentzian manifolds have constant sectional curvature. We prove that some generalizations of the Rakic duality principle (Lorentzian totally Jacobi-dual or four-dimensional Lorentzian Jacobi-dual) imply constant sectional curvature. Moreover, any four-dimensional Jacobi-dual algebraic curvature tensor such that the Jacobi operator for some nonnull vector is diagonalizable, is Osserman. Additionally, any Lorentzian algebraic curvature tensor such that the reduced Jacobi operator for all nonnull vectors has a single eigenvalue has a constant sectional curvature.

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2

Mysen, E., and K. Aksnes. "The Jacobi constant for a cometary orbiter." Astronomy & Astrophysics 443, no. 2 (November 2005): 691–701. http://dx.doi.org/10.1051/0004-6361:20053416.

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3

Álvarez, A. "The p-rank of the reduction mod p of Jacobians and Jacobi sums." International Journal of Number Theory 10, no. 08 (October 29, 2014): 2097–114. http://dx.doi.org/10.1142/s1793042114500705.

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Let YK → XK be a ramified cyclic covering of curves, where K is a cyclotomic field. In this work we study the p-rank of the reduction mod p of a model of the Jacobian of YK. In this way, we obtain counterparts of the Deuring polynomial, defined for elliptic curves, for genus greater than one. We provide a new point of view of this subject in terms of L-functions. To carry out this study we use the relationship between Jacobi sums and L-functions. This is established in [A. Weil, Jacobi sums as "Grössencharaktere", Trans. Amer. Math. Soc. 73 (1952) 487–495] for the case of Fermat curves. We also give a new proof of a result of Deligne concerning the constant terms of these L-functions and Jacobi sums.

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4

Elsner, Carsten, and Yohei Tachiya. "Algebraic results for certain values of the Jacobi theta-constant $\theta_3(\tau)$." MATHEMATICA SCANDINAVICA 123, no. 2 (August 13, 2018): 249–72. http://dx.doi.org/10.7146/math.scand.a-105465.

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In its most elaborate form, the Jacobi theta function is defined for two complex variables $z$ and τ by $\theta (z|\tau ) =\sum _{\nu =-\infty }^{\infty } e^{\pi i\nu ^2\tau + 2\pi i\nu z}$, which converges for all complex number $z$, and τ in the upper half-plane. The special case \[ \theta _3(\tau ):=\theta (0|\tau )= 1+2\sum _{\nu =1}^{\infty } e^{\pi i\nu ^2 \tau } \] is called a Jacobi theta-constant or Thetanullwert of the Jacobi theta function $\theta (z|\tau )$. In this paper, we prove the algebraic independence results for the values of the Jacobi theta-constant $\theta _3(\tau )$. For example, the three values $\theta _3(\tau )$, $\theta _3(n\tau )$, and $D\theta _3(\tau )$ are algebraically independent over $\mathbb{Q} $ for any τ such that $q=e^{\pi i\tau }$ is an algebraic number, where $n\geq 2$ is an integer and $D:=(\pi i)^{-1}{d}/{d\tau }$ is a differential operator. This generalizes a result of the first author, who proved the algebraic independence of the two values $\theta _3(\tau )$ and $\theta _3(2^m\tau )$ for $m\geq 1$. As an application of our main theorem, the algebraic dependence over $\mathbb{Q} $ of the three values $\theta _3(\ell \tau )$, $\theta _3(m\tau )$, and $\theta _3(n\tau )$ for integers $\ell ,m,n\geq 1$ is also presented.

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5

Doha, E. H., A. H. Bhrawy, and R. M. Hafez. "A Jacobi Dual-Petrov-Galerkin Method for Solving Some Odd-Order Ordinary Differential Equations." Abstract and Applied Analysis 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/947230.

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A Jacobi dual-Petrov-Galerkin (JDPG) method is introduced and used for solving fully integrated reformulations of third- and fifth-order ordinary differential equations (ODEs) with constant coefficients. The reformulated equation for theJth order ODE involvesn-fold indefinite integrals forn=1,…,J. Extension of the JDPG for ODEs with polynomial coefficients is treated using the Jacobi-Gauss-Lobatto quadrature. Numerical results with comparisons are given to confirm the reliability of the proposed method for some constant and polynomial coefficients ODEs.

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6

Reisinger, C., and P. A. Forsyth. "Piecewise constant policy approximations to Hamilton–Jacobi–Bellman equations." Applied Numerical Mathematics 103 (May 2016): 27–47. http://dx.doi.org/10.1016/j.apnum.2016.01.001.

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7

Zagirov, N. Sh, and T. U. Gadzhieva. "Estimates of Markov constant in the Jacobi weight space." Herald of Dagestan State University 33, no. 3 (2018): 54–61. http://dx.doi.org/10.21779/2542-0321-2018-33-3-54-61.

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8

Arias-Marco, Teresa, and Antonio M. Naveira. "Constant Jacobi osculating rank of a g.o. space. A method to obtain explicitly the Jacobi operator." Publicationes Mathematicae Debrecen 74, no. 1-2 (January 1, 2009): 135–57. http://dx.doi.org/10.5486/pmd.2009.4334.

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9

Wang, Fa Xing, and Ying Zheng. "Alternative Method of Progressive Eigenvalue of the Unbounded Jacobi Matrix." Applied Mechanics and Materials 543-547 (March 2014): 846–49. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.846.

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This article introduces the alternative principle of progressive characteristic of unbounded Jacobi matrix into the process of automatic control of circuit which makes the feedback signal of control circuit has two different delay characteristics using unbounded Jacobi matrix. It also adds the weight of transconductance unit. The voltage signal can output smoothly which reduces the oscillation of the circuit and improves the accuracy of the circuits automatic control. This paper studies the control role of unbounded Jacobi matrix on the circuit using experimental method and gets the I / V curve. From the curve, we can concludes that the I / V of the circuit is not constant. The boundaries of linear region and the saturation region correspond with unbounded Jacobi matrix theory. Linear and saturation regions have no obviously transition boundary which applies unbounded Jacobi matrix to the automatic process of circuits successfully.

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10

Koufogiorgos, T., M. Markellos, and C. Tsichlias. "Tangent sphere bundles with constant trace of the Jacobi operator." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 53, no. 2 (June 14, 2011): 551–68. http://dx.doi.org/10.1007/s13366-011-0057-3.

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11

Dombrowski, Joanne, and Steen Pedersen. "Absolute Continuity for Unbounded Jacobi Matrices with Constant Row Sums." Journal of Mathematical Analysis and Applications 267, no. 2 (March 2002): 695–713. http://dx.doi.org/10.1006/jmaa.2001.7808.

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12

Romik, Dan. "The Taylor coefficients of the Jacobi theta constant $$\theta _3$$." Ramanujan Journal 52, no. 2 (March 15, 2019): 275–90. http://dx.doi.org/10.1007/s11139-018-0109-5.

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13

San-Juan, Juan F., Luis M. López, and Martin Lara. "On Bounded Satellite Motion under Constant Radial Propulsive Acceleration." Mathematical Problems in Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/680394.

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The Hamiltonian formulation of the constant radial propulsive acceleration problem in nondimensional units reveals that the problem does not depend on any physical parameter. The qualitative description of the integrable flow is given in terms of the energy and the angular momentum, showing that the different regimes are the result of a bifurcation phenomenon. The solution via the Hamilton-Jacobi equation demonstrates that the elliptic integrals of the three kinds are intrinsic to the problem.

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14

BARNICH, G., M. HENNEAUX, and R. TATAR. "CONSISTENT INTERACTIONS BETWEEN GAUGE FIELDS AND LOCAL BRST COHOMOLOGY: THE EXAMPLE OF YANG-MILLS MODELS." International Journal of Modern Physics D 03, no. 01 (March 1994): 139–44. http://dx.doi.org/10.1142/s0218271894000149.

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Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the Yang-Mills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincaré invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the Yang-Mills coupling is therefore rederived through cohomological arguments.

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15

Gilkey, P., G. Stanilov, and V. Videv. "Pseudo Riemannian manifolds whose generalized Jacobi operator has constant characteristic polynomial." Journal of Geometry 62, no. 1-2 (July 1998): 144–53. http://dx.doi.org/10.1007/bf01237606.

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16

Prince, G. E., J. E. Aldridge, S. E. Godfrey, and G. B. Byrnes. "The separation of the Hamilton-Jacobi equation for the Kerr metric." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 41, no. 2 (October 1999): 248–59. http://dx.doi.org/10.1017/s033427000001119x.

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AbstractWe discuss the separability of the Hamilton-Jacobi equation for the Kerr metric. We use a recent theorem which says that a completely integrable geodesic equation has a fully separable Hamilton-Jacobi equation if and only if the Lagrangian is a composite of the involutive first integrals. We also discuss the physical significance of Carter's fourth constant in terms of the symplectic reduction of the Schwarzschild metric via SO(3), showing that the Killing tensor quantity is the remnant of the square of angular momentum.

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17

Osetrin, Konstantin, and Evgeny Osetrin. "Shapovalov Wave-Like Spacetimes." Symmetry 12, no. 8 (August 18, 2020): 1372. http://dx.doi.org/10.3390/sym12081372.

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Анотація:

A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles.

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18

Duangpan, Ampol, Ratinan Boonklurb, Kittisak Chumpong, and Phiraphat Sutthimat. "Analytical Formulas for Conditional Mixed Moments of Generalized Stochastic Correlation Process." Symmetry 14, no. 5 (April 27, 2022): 897. http://dx.doi.org/10.3390/sym14050897.

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This paper proposes a simple and novel approach based on solving a partial differential equation (PDE) to establish the concise analytical formulas for a conditional moment and mixed moment of the Jacobi process with constant parameters, accomplished by including random fluctuations with an asymmetric Wiener process and without any knowledge of the transition probability density function. Our idea involves a system with a recurrence differential equation which leads to the PDE by involving an asymmetric matrix. Then, by using Itô’s lemma, all formulas for the Jacobi process with constant parameters as well as time-dependent parameters are extended to the generalized stochastic correlation processes. In addition, their statistical properties are provided in closed forms. Finally, to illustrate applications of the proposed formulas in practice, estimations of parametric methods based on the moments are mentioned, particularly in the method of moments estimators.

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19

RAMAKRISHNAN, B., and BRUNDABAN SAHU. "RANKIN’S METHOD AND JACOBI FORMS OF SEVERAL VARIABLES." Journal of the Australian Mathematical Society 88, no. 1 (January 26, 2010): 131–43. http://dx.doi.org/10.1017/s1446788709000330.

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AbstractFollowing R. A. Rankin’s method, D. Zagier computed the nth Rankin–Cohen bracket of a modular form g of weight k1 with the Eisenstein series of weight k2, computed the inner product of this Rankin–Cohen bracket with a cusp form f of weight k=k1+k2+2n and showed that this inner product gives, up to a constant, the special value of the Rankin–Selberg convolution of f and g. This result was generalized to Jacobi forms of degree 1 by Y. Choie and W. Kohnen. In this paper, we generalize this result to Jacobi forms defined over ℋ×ℂ(g,1).

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20

Chao, Ding-Qun, Shu-Zheng Yang, and Zhong-Wen Feng. "Tunneling radiation of fermions with 1/2 and 3/2 spins from a charged axisymmetric nonstationary black hole." Modern Physics Letters A 34, no. 29 (September 21, 2019): 1950242. http://dx.doi.org/10.1142/s0217732319502420.

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In this paper, we derived Hamilton–Jacobi equation for spin 1/2 and 3/2 fermions from Dirac equation and Rarita–Schwinger equation. Then, by using the Hamilton–Jacobi equation and general tortoise coordinate transformation, the tunneling rate and Hawking temperatures of a nonstationary axisymmetric symmetry black hole are investigated. The result shows that the tunneling rate, temperature and surface gravity are all related to the properties of horizons of the black hole, the cosmological constant [Formula: see text], the charge [Formula: see text], mass of black hole [Formula: see text] and the Eddington time [Formula: see text].

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21

Wang, Bo, and Guiqin Jin. "Solving a Class of Nonlinear Evolution Equations Using Jacobi Elliptic Functions." Journal of Physics: Conference Series 2381, no. 1 (December 1, 2022): 012038. http://dx.doi.org/10.1088/1742-6596/2381/1/012038.

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Abstract Nonlinear evolution equations play a crucial role in many applied scientific disciplines. Finding the exact solutions to such equations can contribute to a wide variety of applied disciplines. To be able to calculate exact periodic solutions of nonlinear evolution equations, this paper discusses the expansion of the Jacobi elliptic function and finds the proper expansion of the function. Additionally, by analyzing the applicable conditions of the function according to its specific properties, we find the exact periodic solutions to nonlinear evolution equations with constant coefficients and variable coefficients that satisfy the applicable conditions of the Jacobi elliptic function.

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22

Cao, Limei, Didong Li, Erchuan Zhang, Zhenning Zhang, and Huafei Sun. "A Statistical Cohomogeneity One Metric on the Upper Plane with Constant Negative Curvature." Advances in Mathematical Physics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/832683.

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we analyze the geometrical structures of statistical manifoldSconsisting of all the wrapped Cauchy distributions. We prove thatSis a simply connected manifold with constant negative curvatureK=-2. However, it is not isometric to the hyperbolic space becauseSis noncomplete. In fact,Sis approved to be a cohomogeneity one manifold. Finally, we use several tricks to get the geodesics and explore the divergence performance of them by investigating the Jacobi vector field.

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23

Ito, S., M. Keane, and M. Ohtsuki. "Almost everywhere exponential convergence of the modified Jacobi—Perron algorithm." Ergodic Theory and Dynamical Systems 13, no. 2 (June 1993): 319–34. http://dx.doi.org/10.1017/s0143385700007380.

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AbstractWe prove that there exists a constant δ > 0 such that for almost every pair of numbers α and β there exists n0= n0(α,β) such that for any n ≥ n0where the integers pn,qn, rn are provided by the modified Jacobi-Perron algorithm.

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24

Li, Haizhong, and Xianfeng Wang. "Second eigenvalue of a Jacobi operator of hypersurfaces with constant scalar curvature." Proceedings of the American Mathematical Society 140, no. 1 (May 6, 2011): 291–307. http://dx.doi.org/10.1090/s0002-9939-2011-10892-x.

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25

Chirkunov, Yu A. "Nonlinear mappings whose Jacobi matrix commutes with constant matrices of a ring." Journal of Mathematical Sciences 186, no. 3 (September 16, 2012): 379–86. http://dx.doi.org/10.1007/s10958-012-0992-z.

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26

Leech, C. M., and B. Tabarrok. "Nonseparable Solutions to the Hamilton-Jacobi Equation." Journal of Applied Mechanics 64, no. 3 (September 1, 1997): 636–41. http://dx.doi.org/10.1115/1.2788940.

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Анотація:

The Hamilton-Jacobi partial differential equation is solved for potential energy functionals of constant, linear, and quadratic form using a class of nonseparable solutions; these solutions give a geometric property to the generating solution, embedding it into the class of conics. These solutions have two basic components, that designated as a kernel component which belongs to the system regardless of the specific dynamics of the system and the primary and secondary system functions that are dependent on the specific initial conditions. Solutions are obtained for the linear oscillator, a rheonomic oscillator and a two-degree-of-freedom system, the latter suggesting an approach for general multidegree-of-freedom systems.

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27

Mazzuca, G. "On the mean density of states of some matrices related to the beta ensembles and an application to the Toda lattice." Journal of Mathematical Physics 63, no. 4 (April 1, 2022): 043501. http://dx.doi.org/10.1063/5.0076539.

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In this paper, we study tridiagonal random matrix models related to the classical β-ensembles (Gaussian, Laguerre, and Jacobi) in the high-temperature regime, i.e., when the size N of the matrix tends to infinity with the constraint that βN = 2 α constant, α > 0. We call these ensembles the Gaussian, Laguerre, and Jacobi α-ensembles, and we prove the convergence of their empirical spectral distributions to their mean densities of states, and we compute them explicitly. As an application, we explicitly compute the mean density of states of the Lax matrix of the Toda lattice with periodic boundary conditions with respect to the Gibbs ensemble.

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28

Ho, Choon-Lin, and Ryu Sasaki. "Zeros of the Exceptional Laguerre and Jacobi Polynomials." ISRN Mathematical Physics 2012 (September 11, 2012): 1–27. http://dx.doi.org/10.5402/2012/920475.

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Анотація:

An interesting discovery in the last two years in the field of mathematical physics has been the exceptional Xℓ Laguerre and Jacobi polynomials. Unlike the well-known classical orthogonal polynomials which start with constant terms, these new polynomials have the lowest degree ℓ=1,2,…, and yet they form complete sets with respect to some positive-definite measure. In this paper, we study one important aspect of these new polynomials, namely, the behaviors of their zeros as some parameters of the Hamiltonians change. Most results are of heuristic character derived by numerical analysis.

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29

D’Ambroise, Jennie, and Floyd L. Williams. "Elliptic Function Solutions in Jackiw-Teitelboim Dilaton Gravity." Advances in Mathematical Physics 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/2154784.

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We present a new family of solutions for the Jackiw-Teitelboim model of two-dimensional gravity with a negative cosmological constant. Here, a metric of constant Ricci scalar curvature is constructed, and explicit linearly independent solutions of the corresponding dilaton field equations are determined. The metric is transformed to a black hole metric, and the dilaton solutions are expressed in terms of Jacobi elliptic functions. Using these solutions, we compute, for example, Killing vectors for the metric.

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30

Zapata-Carratalá, Carlos. "Jacobi geometry and Hamiltonian mechanics: The unit-free approach." International Journal of Geometric Methods in Modern Physics 17, no. 12 (September 24, 2020): 2030005. http://dx.doi.org/10.1142/s0219887820300056.

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We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalize the ordinary categories of smooth manifolds and vector bundles to account for a lack of choice of a preferred unit, which in standard differential geometry is always given by the global constant function [Formula: see text]. This is what we call the “unit-free” approach. After giving a characterization of local Lie brackets via their symbol maps, we apply our novel categorical language to review Jacobi manifolds and related notions such as Lichnerowicz brackets and Jacobi algebroids. The main advantage of our approach is that Jacobi geometry is recovered as the direct unit-free generalization of Poisson geometry, with all the familiar notions translating in a straightforward manner. We then apply this formalism to the question of whether there is a unit-free generalization of Hamiltonian mechanics. We identify the basic categorical structure of ordinary Hamiltonian mechanics to argue that it is indeed possible to find a unit-free analogue. This paper serves as a prelude to the investigation of dimensioned structures, an attempt at a general mathematical framework for the formal treatment of physical quantities and dimensional analysis.

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31

Wang, Zhuande, Chuansheng Yang, and Yubo Yuan. "Convergence Results on Iteration Algorithms to Linear Systems." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/273873.

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Анотація:

In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.

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32

Bhrawy, A. H., and M. A. Alghamdi. "Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations." Abstract and Applied Analysis 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/364360.

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Анотація:

A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. The key to the efficiency of these algorithms is to construct appropriate base functions, which lead to systems with specially structured matrices that can be efficiently inverted. A quadrature Galerkin method is introduced for the numerical solution of these problems with variable coefficients. A new shifted Jacobi collocation method based on basis functions satisfying the initial conditions is presented for solving nonlinear initial value problems. Through several numerical examples, we evaluate the accuracy and performance of the proposed algorithms. The algorithms are easy to implement and yield very accurate results.

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33

Marrocco, Michele. "“A call to action”: Schrödinger's representation of quantum mechanics via Hamilton's principle." American Journal of Physics 91, no. 2 (February 2023): 110–15. http://dx.doi.org/10.1119/5.0083015.

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Анотація:

A few years ago, one of the former Editors of this journal launched “a call to action” (E. F. Taylor, Am. J. Phys. 71, 423–425 (2003)) for a revision of teaching methods in physics in order to emphasize the importance of the principle of least action. In response, we suggest the use of Hamilton's principle of stationary action to introduce the Schrödinger equation. When considering the geometric interpretation of the Hamilton–Jacobi theory, the real part of the action [Formula: see text] defines the phase of the wave function [Formula: see text], and requiring the Hamilton–Jacobi wave function to obey wave-front propagation (i.e., [Formula: see text] is a constant of the motion) yields the Schrödinger equation.

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34

Schmidt, Benjamin, Krishnan Shankar, and Ralf Spatzier. "Almost isotropic Kähler manifolds." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 767 (October 1, 2020): 1–16. http://dx.doi.org/10.1515/crelle-2019-0030.

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Анотація:

AbstractLet M be a complete Riemannian manifold and suppose {p\in M}. For each unit vector {v\in T_{p}M}, the Jacobi operator, {\mathcal{J}_{v}:v^{\perp}\rightarrow v^{\perp}} is the symmetric endomorphism, {\mathcal{J}_{v}(w)=R(w,v)v}. Then p is an isotropic point if there exists a constant {\kappa_{p}\in{\mathbb{R}}} such that {\mathcal{J}_{v}=\kappa_{p}\operatorname{Id}_{v^{\perp}}} for each unit vector {v\in T_{p}M}. If all points are isotropic, then M is said to be isotropic; it is a classical result of Schur that isotropic manifolds of dimension at least 3 have constant sectional curvatures. In this paper we consider almost isotropic manifolds, i.e. manifolds having the property that for each {p\in M}, there exists a constant {\kappa_{p}\in\mathbb{R}} such that the Jacobi operators {\mathcal{J}_{v}} satisfy {\operatorname{rank}({\mathcal{J}_{v}-\kappa_{p}\operatorname{Id}_{v^{\perp}}}% )\leq 1} for each unit vector {v\in T_{p}M}. Our main theorem classifies the almost isotropic simply connected Kähler manifolds, proving that those of dimension {d=2n\geqslant 4} are either isometric to complex projective space or complex hyperbolic space or are totally geodesically foliated by leaves isometric to {{\mathbb{C}}^{n-1}}.

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35

Cheng, Qing-Ming. "First eigenvalue of a Jacobi operator of hypersurfaces with a constant scalar curvature." Proceedings of the American Mathematical Society 136, no. 09 (May 5, 2008): 3309–18. http://dx.doi.org/10.1090/s0002-9939-08-09304-0.

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36

Fujita, T., S. Ito, M. Keane, and M. Ohtsuki. "On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof." Ergodic Theory and Dynamical Systems 16, no. 6 (December 1996): 1345–52. http://dx.doi.org/10.1017/s0143385700010063.

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The following theorem was published in [2].Theorem. There exists a constant δ > 0 such that for Lebesgue almost every (α, β) ∈ X = [0, 1] × [0, 1], there exists no = no(α, β) such that for any n > nowhere the integers pn, qn, rn are provided by the modified Jacobi-Perron algorithm.

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37

Hounkonnou, Mahouton Norbert, Mahougnon Justin Landalidji, and Melanija Mitrović. "Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds." Universe 8, no. 4 (April 17, 2022): 247. http://dx.doi.org/10.3390/universe8040247.

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Анотація:

We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides, using the Hamiltonian–Jacobi separability, we construct recursion operators for Hamiltonian vector fields in conformable Poisson–Schwarzschild and Friedmann–Lemaître–Robertson–Walker (FLRW) manifolds, and derive the related constants of motion, Christoffel symbols, components of Riemann and Ricci tensors, Ricci constant and components of Einstein tensor. We highlight the existence of a hierarchy of bi-Hamiltonian structures in both the manifolds, and compute a family of recursion operators and master symmetries generating the constants of motion.

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38

Zhang, Li-Chun, and Ren Zhao. "The universal Ehrenfest scheme on black holes." Modern Physics Letters A 30, no. 36 (November 3, 2015): 1550187. http://dx.doi.org/10.1142/s0217732315501874.

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Анотація:

By use of the Jacobi determinant, we verify that, for a thermodynamic system which satisfies the first law of thermodynamics, if only there is second-order phase transition in the system, the Prigogine–Defay ratio is the constant 1. This conclusion is universal and independent of the concrete forms of the thermodynamic functions and also apply to black holes.

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39

Bracken, Paul. "Delaunay surfaces expressed in terms of a Cartan moving frame." Journal of Applied Analysis 26, no. 1 (June 1, 2020): 153–60. http://dx.doi.org/10.1515/jaa-2020-2012.

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AbstractDelaunay surfaces are investigated by using a moving frame approach. These surfaces correspond to surfaces of revolution in the Euclidean three-space. A set of basic one-forms is defined. Moving frame equations can be formulated and studied. Related differential equations which depend on variables relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case in which the mean curvature is constant, these functions can be expressed in terms of Jacobi elliptic functions.

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40

Cherif, Ahmed Mohammed. "Some results on harmonic and bi-harmonic maps." International Journal of Geometric Methods in Modern Physics 14, no. 07 (March 7, 2017): 1750098. http://dx.doi.org/10.1142/s0219887817500980.

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In this paper, we prove that any bi-harmonic map from a compact orientable Riemannian manifold without boundary [Formula: see text] to Riemannian manifold [Formula: see text] is necessarily constant with [Formula: see text] admitting a strongly convex function [Formula: see text] such that [Formula: see text] is a Jacobi-type vector field (or [Formula: see text] admitting a proper homothetic vector field). We also prove that every harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a proper homothetic vector field, satisfying some condition, is constant. We present an open problem.

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41

Oizumi, Ryo, and Hisashi Inaba. "Evolution of heterogeneity under constant and variable environments." PLOS ONE 16, no. 9 (September 13, 2021): e0257377. http://dx.doi.org/10.1371/journal.pone.0257377.

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Various definitions of fitness are essentially based on the number of descendants of an allele or a phenotype after a sufficiently long time. However, these different definitions do not explicate the continuous evolution of life histories. Herein, we focus on the eigenfunction of an age-structured population model as fitness. The function generates an equation, called the Hamilton–Jacobi–Bellman equation, that achieves adaptive control of life history in terms of both the presence and absence of the density effect. Further, we introduce a perturbation method that applies the solution of this equation to the long-term logarithmic growth rate of a stochastic structured population model. We adopt this method to realize the adaptive control of heterogeneity for an optimal foraging problem in a variable environment as the analyzable example. The result indicates that the eigenfunction is involved in adaptive strategies under all the environments listed herein. Thus, we aim to systematize adaptive life histories in the presence of density effects and variable environments using the proposed objective function as a universal fitness candidate.

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42

Chang, Hao, Xi-min Rong, Hui Zhao, and Chu-bing Zhang. "Optimal Investment and Consumption Decisions under the Constant Elasticity of Variance Model." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/974098.

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We consider an investment and consumption problem under the constant elasticity of variance (CEV) model, which is an extension of the original Merton’s problem. In the proposed model, stock price dynamics is assumed to follow a CEV model and our goal is to maximize the expected discounted utility of consumption and terminal wealth. Firstly, we apply dynamic programming principle to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function. Secondly, we choose power utility and logarithm utility for our analysis and apply variable change technique to obtain the closed-form solutions to the optimal investment and consumption strategies. Finally, we provide a numerical example to illustrate the effect of market parameters on the optimal investment and consumption strategies.

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43

Oliveros, A., and Hernán E. Noriega. "Constant-roll inflation driven by a scalar field with nonminimal derivative coupling." International Journal of Modern Physics D 28, no. 12 (September 2019): 1950159. http://dx.doi.org/10.1142/s0218271819501591.

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Анотація:

In this work, we study constant-roll inflation driven by a scalar field with nonminimal derivative coupling to gravity, via the Einstein tensor. This model contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling and a parameter [Formula: see text] which characterizes the constant-roll condition. In this scenario, using the Hamilton–Jacobi-like formalism, an ansatz for the Hubble parameter (as a function of the scalar field) and some restrictions on the model parameters, we found new exact solutions for the inflaton potential which include power-law, de Sitter, quadratic hilltop and natural inflation, among others. Additionally, a phase-space analysis was performed and it is shown that the exact solutions associated to natural inflation and a “cosh-type” potential, are attractors.

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44

CHO, JONG TAEK, and JI-EUN LEE. "SLANT CURVES IN CONTACT PSEUDO-HERMITIAN 3-MANIFOLDS." Bulletin of the Australian Mathematical Society 78, no. 3 (December 2008): 383–96. http://dx.doi.org/10.1017/s0004972708000737.

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AbstractBy using the pseudo-Hermitian connection (or Tanaka–Webster connection) $\widehat \nabla $, we construct the parametric equations of Legendre pseudo-Hermitian circles (whose $\widehat \nabla $-geodesic curvature $\widehat \kappa $ is constant and $\widehat \nabla $-geodesic torsion $\widehat \tau $ is zero) in S3. In fact, it is realized as a Legendre curve satisfying the $\widehat \nabla $-Jacobi equation for the $\widehat \nabla $-geodesic vector field along it.

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45

Timoshkova, E. I. "The Possible Orbital Evolution of the Near-Earth Asteroids." Symposium - International Astronomical Union 152 (1992): 175–78. http://dx.doi.org/10.1017/s0074180900091105.

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The subject of this paper is a study of a possible orbital evolution for near-Earth asteroids. The investigation is fulfilled in the frame of the restricted circular three body problem. It is based on the calculations of the Jacobi constant. The osculating elements of some real Apollo-Amor-Aten asteroids are used as the starting parameters. The comparison with the results of other authors is given.

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46

Krylov, N. V., G. V. Nosovskii, and M. V. Safonov. "Degeneracy domain of a nonlinearity in the Hamilton-Jacobi-Bellman equation with constant coefficients." Mathematical Notes of the Academy of Sciences of the USSR 42, no. 5 (November 1987): 877–80. http://dx.doi.org/10.1007/bf01137432.

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47

Li, Zonghai, Yujie Duan, and Junji Jia. "Deflection of charged massive particles by a four-dimensional charged Einstein–Gauss–Bonnet black hole." Classical and Quantum Gravity 39, no. 1 (December 6, 2021): 015002. http://dx.doi.org/10.1088/1361-6382/ac38d0.

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Abstract Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel four-dimensional charged Einstein–Gauss–Bonnet black hole. We focus on the weak field approximation and consider the deflection angle with finite distance effects. To this end, we use a geometric and topological method, which is to apply the Gauss–Bonnet theorem to the Jacobi space to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution δ g, a pure electrostatic δ c and a gravitational–electrostatic coupling term δ gc. We find that the deflection angle increases (decreases) if the Gauss–Bonnet coupling constant α is negative (positive). Furthermore, the effects of the BH charge, the particle charge-to-mass ratio and the particle velocity on the deflection angle are analyzed.

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48

TENG, LONG, MATTHIAS EHRHARDT, and MICHAEL GÜNTHER. "QUANTO PRICING IN STOCHASTIC CORRELATION MODELS." International Journal of Theoretical and Applied Finance 21, no. 05 (August 2018): 1850038. http://dx.doi.org/10.1142/s0219024918500383.

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Correlation plays an important role in pricing multi-asset options. In this work we incorporate stochastic correlation into pricing quanto options which is one special and important type of multi-asset option. Motivated by the market observations that the correlations between financial quantities behave like a stochastic process, instead of using a constant correlation, we allow the asset price process and the exchange rate process to be stochastically correlated with a parameter which is driven either by an Ornstein–Uhlenbeck process or a bounded Jacobi process. We derive an exact quanto option pricing formula in the stochastic correlation model of the Ornstein–Uhlenbeck process and a highly accurate approximated pricing formula in the stochastic correlation model of the bounded Jacobi process, where correlation risk has been hedged. The comparison between prices using our pricing formula and the Monte-Carlo method are provided.

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49

Yang, Sung-Jin, Min-Ku Lee, and Jeong-Hoon Kim. "Portfolio optimization under the stochastic elasticity of variance." Stochastics and Dynamics 14, no. 03 (May 29, 2014): 1350024. http://dx.doi.org/10.1142/s021949371350024x.

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Based on the observation that the elasticity of variance of risky assets is randomly varying around a constant, we take an underlying asset model in which the averaged constant elasticity of variance is perturbed by a small fast fluctuating process and study the Merton type portfolio optimization problem using dynamic programming as well as asymptotic expansions. The Hamilton–Jacobi–Bellman equation for each of the power and exponential utility functions leads to an optimal trading strategy as a perturbation around the well known one. We reveal the impact of both the constant elasticity of variance upon the Merton investment optimal control under the Black–Scholes model and the stochastic elasticity of variance upon the investment optimal control under the constant elasticity of variance model. The concavity of the investment policy with respect to the excess return is characteristic of a market economy with the constant or stochastic elasticity of variance.

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50

Kurochkin, Yu A., D. V. Shoukavy, and I. P. Boyarina. "Center mass theorem in three dimensional spaces with constant curvature." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 3 (October 18, 2020): 328–34. http://dx.doi.org/10.29235/1561-2430-2020-56-3-328-334.

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In this paper, based on the definition of the center of mass given in [1, 2], its immobility is postulated in spaces with a constant curvature, and the problem of two particles with an internal interaction, described by a potential depending on the distance between points on a three-dimensional sphere, is considered. This approach, justified by the absence of a principle similar to the Galileo principle on the one hand and the property of isotropy of space on the other, allows us to consider the problem in the map system for the center of mass. It automatically ensures dependence only on the relative variables of the considered points. The Hamilton – Jacobi equation of the problem is formulated, its solutions and the equations of trajectories are found. It is shown that the reduced mass of the system depends on the relative distance. Given this circumstance, a modified system metric is written out.

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