Recent zbMATH articles in MSC 70Hhttps://www.zbmath.org/atom/cc/70H2022-05-16T20:40:13.078697ZWerkzeugHamiltonian pitchfork bifurcation in transition across index-1 saddleshttps://www.zbmath.org/1483.370682022-05-16T20:40:13.078697Z"Lyu, Wenyang"https://www.zbmath.org/authors/?q=ai:lyu.wenyang"Naik, Shibabrat"https://www.zbmath.org/authors/?q=ai:naik.shibabrat"Wiggins, Stephen"https://www.zbmath.org/authors/?q=ai:wiggins.stephenSummary: We study the effect of changes in the parameters of a two dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical reactions such as isomerization between two structural conformations or dissociation of a molecule with an intermediate. We present a two degrees of freedom (DOF) quartic Hamiltonian that shows pitchfork bifurcation when the parameters are varied and we derive the bifurcation criteria relating the parameters. Next, we describe the phase space structures -- unstable periodic orbits and its associated invariant manifolds, and phase space dividing surfaces -- for the systems that can show trajectories undergo reaction defined as crossing of a potential energy barrier. Finally, we quantify the reaction dynamics for these systems by obtaining the directional flux and gap time distribution to illustrate the dependence on total energy and coupling strength between the two degrees of freedom.On the Lyapunov instability in Newtonian dynamicshttps://www.zbmath.org/1483.370692022-05-16T20:40:13.078697Z"Burgos, J. M."https://www.zbmath.org/authors/?q=ai:burgos.juan-manuel"Maderna, E."https://www.zbmath.org/authors/?q=ai:maderna.ezequiel"Paternain, M."https://www.zbmath.org/authors/?q=ai:paternain.miguelThe authors consider the classical problem of Lyapunov instability of equilibrium states for a finite-dimensional Newtonian system with a non-strict local minimum of the potential. For the cases when the local minimum of the potential energy is reached on the hypersurface of the configuration space, new results on the instability of equilibrium states are obtained.
Reviewer: Vladimir Sobolev (Samara)Solvable dynamical systems in the plane with polynomial interactionshttps://www.zbmath.org/1483.370732022-05-16T20:40:13.078697Z"Calogero, Francesco"https://www.zbmath.org/authors/?q=ai:calogero.francesco-a"Payandeh, Farrin"https://www.zbmath.org/authors/?q=ai:payandeh.farrinSummary: In this paper we report a few examples of algebraically solvable dynamical systems characterized by \(2\) coupled Ordinary Differential Equations which read as follows:
\[
\dot{x}_n=P^{\left( n\right) }\left( x_1,x_2\right),\quad n=1,2,
\]
with \(P^{(n)}(x_1,x_2)\) specific polynomials of relatively low degree in the \(2\) dependent variables \(x_1\equiv x_1(t)\) and \(x_2\equiv x_2(t)\). These findings are obtained via a new twist of a recent technique to identify dynamical systems solvable by algebraic operations, themselves explicitly identified as corresponding to the time evolutions of the zeros of polynomials the coefficients of which evolve according to algebraically solvable (systems of) evolution equations.
For the entire collection see [Zbl 1456.14003].Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian systemhttps://www.zbmath.org/1483.370802022-05-16T20:40:13.078697Z"Jing, Tianqi"https://www.zbmath.org/authors/?q=ai:jing.tianqi"Si, Wen"https://www.zbmath.org/authors/?q=ai:si.wenThe main result of the paper is about the existence of lower-dimensional tori for a class of degenerate Hamiltonian systems, that are also supposed to be only \(C^\ell\) smooth. This is a generalization of known results for which the degenerate case was considered within the analytic class, or the loss of analyticity was considered in the non-degenerate case.
The proof is ruled out in the framework of KAM theory. The loss of regularity is overcome via the Jackson-Moser-Zehnder analytic approximation, while the degeneracy is treated through normal form theory for quasi-homogeneous polynomial systems and the stability of equilibrium points of odd degree polynomials.
Some applications of the main theorem are given.
Reviewer: Stefano Marò (Pisa)Adaptive Hamiltonian variational integrators and applications to symplectic accelerated optimizationhttps://www.zbmath.org/1483.370992022-05-16T20:40:13.078697Z"Duruisseaux, Valentin"https://www.zbmath.org/authors/?q=ai:duruisseaux.valentin"Schmitt, Jeremy"https://www.zbmath.org/authors/?q=ai:schmitt.jeremy-m"Leok, Melvin"https://www.zbmath.org/authors/?q=ai:leok.melvinSymplectic integrators with a variable stepsize usually do not preserve the energy. Nevertheless, the use of a variable stepsize could be useful in many instances. Motivated by these facts, the authors study the use of variable stepsize for specific classes of variational integrators. This is done by introducing a fictitious time \(\tau\), and defining an augmented Hamiltonian defined in terms of a ``monitor function'' which rules the time-step variation. The considered integrators turn out to be symplectic with constant time-step w.r.t. \(\tau\) and variable time-step w.r.t. the physical time \(t\). Applications to the Kepler problem and to accelerated optimization are presented.
Reviewer: Luigi Brugnano (Firenze)Ergodic decay laws in Newtonian and relativistic chaotic scatteringhttps://www.zbmath.org/1483.371032022-05-16T20:40:13.078697Z"Fernández, Diego S."https://www.zbmath.org/authors/?q=ai:fernandez.diego-s"López, Álvaro G."https://www.zbmath.org/authors/?q=ai:lopez.alvaro-g"Seoane, Jesús M."https://www.zbmath.org/authors/?q=ai:seoane.jesus-m"Sanjuán, Miguel A. F."https://www.zbmath.org/authors/?q=ai:sanjuan.miguel-a-fSummary: In open Hamiltonian systems, the escape from a bounded region of phase space according to an exponential decay law is frequently associated with the existence of hyperbolic dynamics in such a region. Furthermore, exponential decay laws based on the ergodic hypothesis are used to describe escapes in these systems. However, we uncover that the presence of the set that governs the hyperbolic dynamics, commonly known as the chaotic saddle, invalidates the assumption of ergodicity. For the paradigmatic Hénon-Heiles system, we use both theoretical and numerical arguments to show that the escaping dynamics is non-ergodic independently of the existence of KAM tori, since the chaotic saddle, in whose vicinity trajectories are more likely to spend a finite amount of time evolving before escaping forever, is not utterly spread over the energy shell. Taking this into consideration, we provide a clarifying discussion about ergodicity in open Hamiltonian systems and explore the limitations of ergodic decay laws when describing escapes in this kind of systems. Finally, we generalize our claims by deriving a new decay law in the relativistic regime for an inertial and a non-inertial reference frames under the assumption of ergodicity, and suggest another approach to the description of escape laws in open Hamiltonian systems.The entropy of the angenent torus is approximately 1.85122https://www.zbmath.org/1483.531062022-05-16T20:40:13.078697Z"Berchenko-Kogan, Yakov"https://www.zbmath.org/authors/?q=ai:berchenko-kogan.yakovSummary: To study the singularities that appear in mean curvature flow, one must understand \textit{self-shrinkers}, surfaces that shrink by dilations under mean curvature flow. The simplest examples of self-shrinkers are spheres and cylinders. In [Prog. Nonlinear Differ. Equ. Appl. 7, 21--38 (1992; Zbl 0762.53028)], \textit{S. B. Angenent} constructed the first nontrivial example of a self-shrinker, a torus. A key quantity in the study of the formation of singularities is the \textit{entropy}, defined by Colding and Minicozzi based on work of Huisken. The values of the entropy of spheres and cylinders have explicit formulas, but there is no known formula for the entropy of the Angenent torus. In this work, we numerically estimate the entropy of the Angenent torus using the discrete Euler-Lagrange equations.A high order finite difference weighted essentially nonoscillatory schemes with a kernel-based constrained transport method for ideal magnetohydrodynamicshttps://www.zbmath.org/1483.651302022-05-16T20:40:13.078697Z"Cakir, Firat"https://www.zbmath.org/authors/?q=ai:cakir.firat"Christlieb, Andrew"https://www.zbmath.org/authors/?q=ai:christlieb.andrew-j"Jiang, Yan"https://www.zbmath.org/authors/?q=ai:jiang.yanThe ideal magnetohydrodynamics (MHD) equations are considered. While the MHD equations are hyperbolic, standard numerical methods for hyperbolic conservation laws fail to guarantee \(\nabla \cdot B = 0\). In this work, a new high order method to satisfy the involution based on an unstaggered constrained transport (CT) methodology is introduced. The paper is organized as follows. Section 1 is an introduction. In Section 2, the MHD equations, CT method, and the evolution of the magnetic vector equations are briefly reviewed. In Section 3, the novel numerical scheme for 1D Hamilton-Jacobi equations and the multidimensional solver are presented. The resulting 2D and 3D schemes are tested on several numerical problems, in Section 4. In this section, the numerical results are presented to demonstrate the accuracy and efficiency of the constructed algorithm. In Section 5, some conclusions are given. Finally, in Appendix A, all coefficients in weighted essentially nonoscillatory quadrature are shown.
Reviewer: Temur A. Jangveladze (Tbilisi)Optimum dimensional synthesis of planar mechanisms with geometric constraintshttps://www.zbmath.org/1483.700062022-05-16T20:40:13.078697Z"García-Marina, V."https://www.zbmath.org/authors/?q=ai:garcia-marina.v"Fernández de Bustos, I."https://www.zbmath.org/authors/?q=ai:fernandez-de-bustos.i"Urkullu, G."https://www.zbmath.org/authors/?q=ai:urkullu.g"Ansola, R."https://www.zbmath.org/authors/?q=ai:ansola.rubenSummary: The deformed energy method has shown to be a good option for dimensional synthesis of mechanisms. In this paper the introduction of some new features to such approach is proposed. First, constraints fixing dimensions of certain links are introduced in the error function of the synthesis problem. Second, requirements on distances between determinate nodes are included in the error function for the analysis of the deformed position problem. Both the overall synthesis error function and the inner analysis error function are optimized using a Sequential Quadratic Problem (SQP) approach. This also reduces the probability of branch or circuit defects. In the case of the inner function analytical derivatives are used, while in the synthesis optimization approximate derivatives have been introduced. Furthermore, constraints are analyzed under two formulations, the Euclidean distance and an alternative approach that uses the previous raised to the power of two. The latter approach is often used in kinematics, and simplifies the computation of derivatives. Some examples are provided to show the convergence order of the error function and the fulfilment of the constraints in both formulations studied under different topological situations or achieved energy levels.Non-commutative integrability, exact solvability and the Hamilton-Jacobi theoryhttps://www.zbmath.org/1483.700382022-05-16T20:40:13.078697Z"Grillo, Sergio"https://www.zbmath.org/authors/?q=ai:grillo.sergio-danielFor a given Hamiltonian system, the simplest property that ensures the exact solvability of their corresponding equations of motion is given by the commutative-integrability property, which means that a complete system of known independent first integrals Poisson commute. When such a system, of first integrals, do not commute, one have to use the non-commutative integrability property (NCI). This property requires two extra-conditions: \textit{the isotropy condition} regarding the rank of the matrix formed with the Poisson brackets and \textit{the closure condition} with respect to the Poisson brackets. In this paper, the author constructs two methods that allow to integrate the equation of motion for a given Hamiltonian system from a known set of isotropic first integrals, without using the closure condition.
Reviewer: Ioan Bucataru (Iaşi)Lie symmetry and invariants for a generalized Birkhoffian system on time scaleshttps://www.zbmath.org/1483.700392022-05-16T20:40:13.078697Z"Zhang, Yi"https://www.zbmath.org/authors/?q=ai:zhang.yi.2|zhang.yi.12|zhang.yi.14|zhang.yi.5|zhang.yi.8|zhang.yi.3|zhang.yi.10|zhang.yi.4|zhang.yi.1|zhang.yi.6|zhang.yiSummary: The Lie symmetry and invariants for a generalized Birkhoffian system on time scales are studied, which include exact invariants and adiabatic invariants. First, the generalized Pfaff-Birkhoff principle on time scales is established, and by using Dubois-Reymond lemma the generalized Birkhoff's equations on time scale are derived. Secondly, the determining equations of Lie symmetry for the generalized Birkhoffian system on time scales are established. We prove that if the Lie symmetry satisfies the structural equation, it leads to a conserved quantity, which is an exact invariant of the system. Again, the perturbation of Lie symmetry under the action of small disturbance is considered, the determining equations and the structural equations of disturbed system are established, and the adiabatic invariants led by the Lie symmetry perturbation for the generalized Birkhoffian system on time scales are given. Because of the arbitrariness of selecting time scales and the generality of the generalized Birkhoffian system, the results of this paper are of universal significance. The results of this paper contain the corresponding results for Birkhoffian system on time scales and classical generalized Birkhoffian system as its special cases. At the end of the paper, an example is given to illustrate the validity of the method and the results.Entanglement of classical and quantum short-range dynamics in mean-field systemshttps://www.zbmath.org/1483.810272022-05-16T20:40:13.078697Z"Bru, J.-B."https://www.zbmath.org/authors/?q=ai:bru.jean-bernard"de Siqueira Pedra, W."https://www.zbmath.org/authors/?q=ai:pedra.w-de-siqueira|de-siqueira-pedra.walterSummary: The relationship between classical and quantum mechanics is usually understood via the limit \(\hbar\to 0\). This is the underlying idea behind the quantization of classical objects. The apparent incompatibility of general relativity with quantum mechanics and quantum field theory has challenged for many decades this basic idea. We recently showed [the authors, J. Math. Anal. Appl. 493, No. 1, Article ID 124434, 61 p. (2021; Zbl 1451.82023); J. Math. Anal. Appl. 493, No. 1, Article ID 124517, 65 p. (2021; Zbl 1451.82025)] the emergence of classical dynamics for very general quantum lattice systems with mean-field interactions, without (complete) suppression of its quantum features, in the infinite volume limit. This leads to a theoretical framework in which the classical and quantum worlds are entangled. Such an entanglement is noteworthy and is a consequence of the highly non-local character of mean-field interactions. Therefore, this phenomenon should not be restricted to systems with mean-field interactions only, but should also appear in presence of interactions that are sufficiently long-range, yielding effective, classical background fields, in the spirit of the Higgs mechanism of quantum field theory. In order to present the result in a less abstract way than in its original version, here we apply it to a concrete, physically relevant, example and discuss, by this means, various important aspects of our general approach. The model we consider is not exactly solvable and the particular results obtained are new.Shortcut to adiabatic two-qubit state swap in a superconducting circuit QED via effective drivingshttps://www.zbmath.org/1483.810412022-05-16T20:40:13.078697Z"Li, Ming"https://www.zbmath.org/authors/?q=ai:li.ming|li.ming.3|li.ming.1|li.ming.8|li.ming.9|li.ming.2|li.ming.5|li.ming.4|li.ming.6|li.ming.7"Dong, Xin-Ping"https://www.zbmath.org/authors/?q=ai:dong.xin-ping"Yan, Run-Ying"https://www.zbmath.org/authors/?q=ai:yan.run-ying"Lu, Xiao-Jing"https://www.zbmath.org/authors/?q=ai:lu.xiaojing"Zhao, Zheng-Yin"https://www.zbmath.org/authors/?q=ai:zhao.zheng-yin"Feng, Zhi-Bo"https://www.zbmath.org/authors/?q=ai:feng.zhi-boSummary: Optimal two-qubit operation is of significance to quantum information processing. An efficient scheme is proposed for realizing the shortcut to adiabatic two-qubit state swap in a superconducting circuit quantum electrodynamics (QED) via effective drivings. Two superconducting qutrits are coupled to a common cavity field and individual classical drivings. Based on two Gaussian-type Rabi drivings, two-qubit state swap can be adiabatically implemented within a reduced three-state system. To speed up the operation, these two original Rabi drivings are modified in the framework of shortcuts to adiabaticity, instead of adding an extra counterdiabatic driving. Moreover, owing to a shorter duration time, the decoherence effects on the accelerated quantum operation can be mitigated significantly. The strategy could offer an optimized method to construct fast and robust quantum operations on superconducting qubits experimentally.Reformulation of gauge theories in terms of gauge invariant fieldshttps://www.zbmath.org/1483.811012022-05-16T20:40:13.078697Z"Fontana, Pierpaolo"https://www.zbmath.org/authors/?q=ai:fontana.pierpaolo"Pinto Barros, Joao C."https://www.zbmath.org/authors/?q=ai:pinto-barros.joao-c"Trombettoni, Andrea"https://www.zbmath.org/authors/?q=ai:trombettoni.andreaSummary: We present a reformulation of gauge theories in terms of gauge invariant fields. Focusing on abelian theories, we show that the gauge and matter covariant fields can be recombined to introduce new gauge invariant degrees of freedom. Starting from the \((1+1)\) dimensional case on the lattice, with both periodic and open boundary conditions, we then generalize to higher dimensions and to the continuum limit. To show explicit and physically relevant examples of the reformulation, we apply it to the Hamiltonian of a single particle in a (static) magnetic field, to pure abelian lattice gauge theories, to the Lagrangian of quantum electrodynamics in \((3+1)\) dimensions and to the Hamiltonian of the \(2d\) and the \(3d\) Hofstadter model. In the latter, we show that the particular construction used to eliminate the gauge covariant fields enters the definition of the magnetic Brillouin zone. Finally, we briefly comment on relevance of the presented reformulation to the study of interacting gauge theories.Modeling of compact stars: an anisotropic approachhttps://www.zbmath.org/1483.830042022-05-16T20:40:13.078697Z"Das, Shyam"https://www.zbmath.org/authors/?q=ai:das.shyam"Singh, Ksh. Newton"https://www.zbmath.org/authors/?q=ai:singh.ksh-newton"Baskey, Lipi"https://www.zbmath.org/authors/?q=ai:baskey.lipi"Rahaman, Farook"https://www.zbmath.org/authors/?q=ai:rahaman.farook"Aria, Anil K."https://www.zbmath.org/authors/?q=ai:aria.anil-kSummary: We present here a new class of singularity free interior solutions relevant for the description of realistic anisotropic compact stellar objects with spherically symmetric matter distribution. In this geometric approach, specific choices of one of the metric functions and a selective anisotropic profile allow us to develop a stellar model by solving Einstein Field equations. The interior solutions thus obtained are matched with the Schwarzschild exterior metric over the bounding surface of a compact star. These matching conditions together with the condition that the radial pressure vanishes at the boundary are used to fix the model parameters. The different physical features for the developed model explicitly studied from the aspect of the pulsar 4U \(1820-30\) with its current estimated data (mass \(=1.46\pm 0.21~M\odot\) and radius \(=11.1\pm 1.8\) km [\textit{F. Özel} et al., ``The dense matter equation of state from neutron star radius and mass measurements'', Astrophys. J. 820, No. 1, Paper No. 28, 25 p. (2016)]. Analysis has shown that all the physical aspects are acceptable demanded for a physically admissible star and satisfy all the required physical conditions. The stability of the model is also explored in the context of causality conditions, adiabatic index, generalized Tolman-Oppenheimer-Volkov (TOV) equation, Buchdahl Condition and Herrera Cracking Method. To show that the developed model is compatible with a wide range of recently observed pulsars, various relevant physical variables are also highlighted in tabular form. The data studied here are in agreement with the observation of gravitational waves from the first binary merger event. Assuming a particular surface density \((7.5\times 10^{14}\text{ gm cm}^{-3})\), the mass-radius \((M-b)\) relationship and the radius-central density relationship \((b-\rho(0))\) of the compact stellar object are analyzed for this model. Additionally, comparing the results with a slow rotating configuration, we have also discussed moment of inertia and the time period using Bejger-Haensel idea.Particle motion in a space-time of a 3D Einstein gravity with torsionhttps://www.zbmath.org/1483.830052022-05-16T20:40:13.078697Z"Kaya, R."https://www.zbmath.org/authors/?q=ai:kaya.rustem"Özçelik, H. T."https://www.zbmath.org/authors/?q=ai:ozcelik.hasan-tuncaySummary: We analyze the motion of both massive and massless particles in a model with space-time of 3D Einstein gravity with torsion. We consider the spinor field and the massless scalar field as the source of torsion respectively. Following the Hamilton-Jacobi formalism, we investigate the effective potential of radial motion for test particles in a homogeneous and isotropic space-time with torsion. We show that there are no stable circular orbits for massive and massless particles in the Einstein gravity with torsion induced by the spinor field, in a space-time with two spatial and one time dimensions. In the case of massive particles, we show that stable orbits exist in 3D Einstein gravity with torsion induced by the scalar field.Loop quantum gravity and cosmological constanthttps://www.zbmath.org/1483.830252022-05-16T20:40:13.078697Z"Zhang, Xiangdong"https://www.zbmath.org/authors/?q=ai:zhang.xiangdong"Long, Gaoping"https://www.zbmath.org/authors/?q=ai:long.gaoping"Ma, Yongge"https://www.zbmath.org/authors/?q=ai:ma.yonggeSummary: A one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as special cases. The quantum bounce nature is tenable in the generalized cases. For positive value of the regularization parameter, the effective Hamiltonian leads to an asymptotic de-Sitter branch of the Universe connecting to the standard Friedmann branch by the quantum bounce. Remarkably, by suitably choosing the value of the regularization parameter, the observational cosmological constant can emerge at large volume limit from the effect of quantum gravity, and the effective Newtonian constant satisfies the experimental restrictions in the meantime.Corrections to Hawking radiation and Bekenstein-Hawking entropy of novel four-dimensional black holes in Gauss-Bonnet gravityhttps://www.zbmath.org/1483.830532022-05-16T20:40:13.078697Z"Li, Gu-Qiang"https://www.zbmath.org/authors/?q=ai:li.guqiang"Mo, Jie-Xiong"https://www.zbmath.org/authors/?q=ai:mo.jie-xiong"Zhuang, Yi-Wen"https://www.zbmath.org/authors/?q=ai:zhuang.yi-wenSummary: We make use of the Hamilton-Jacobi and Parikh-Wilczek methods to investigate the Hawking radiation from the event horizon of a new charged anti-de Sitter black hole in four-dimensional Gauss-Bonnet gravity space-time. Both the tunneling rate of charged particles and the Bekenstein-Hawking entropy are evaluated. The emission spectrum is an impure thermal one and consistent with an underlying unitary theory. There is no difference between the emission rate of massive particle and that of massless one. The entropy is modified by a logarithmic term so that the area law of the black hole entropy is violated. It satisfies the first law of black hole thermodynamics and has the same expression as that calculated by Loop Quantum Gravity and String Theory. When the Gauss-Bonnet coupling coefficient is equal to zero, the logarithmic correction vanishes and the Bekenstein-Hawking relation in general relativity is recovered. So our results show the effects of the Gauss-Bonnet modified gravity on the Bekenstein-Hawking entropy and Hawking radiation.Covariant Hamiltonian formalism for \(F(R)\)-gravityhttps://www.zbmath.org/1483.830702022-05-16T20:40:13.078697Z"Klusoň, J."https://www.zbmath.org/authors/?q=ai:kluson.josef"Matouš, B."https://www.zbmath.org/authors/?q=ai:matous.bSummary: In this short note we apply Weyl-De Donder formalism, also known as covariant Hamiltonian formalism, for \(F(R)\)-gravity. We derive covariant Hamiltonian and derive corresponding equations of motion.Straightforward Hamiltonian analysis of \textit{BF} gravity in \(n\) dimensionshttps://www.zbmath.org/1483.830772022-05-16T20:40:13.078697Z"Montesinos, Merced"https://www.zbmath.org/authors/?q=ai:montesinos.merced"Escobedo, Ricardo"https://www.zbmath.org/authors/?q=ai:escobedo.ricardo"Celada, Mariano"https://www.zbmath.org/authors/?q=ai:celada.marianoSummary: We perform, in a manifestly \(\mathrm{SO}(n-1,1) [\mathrm{SO}(n)]\) covariant fashion, the Hamiltonian analysis of general relativity in \(n\) dimensions written as a constrained \textit{BF} theory. We solve the constraint on the \(B\) field in a way naturally adapted to the foliation of the spacetime that avoids explicitly the introduction of the vielbein. This leads to a form of the action involving a presymplectic structure, which is reduced by doing a suitable parametrization of the connection and then, after integrating out some auxiliary fields, the Hamiltonian form involving only first-class constraints is obtained.Noether symmetry in Newtonian dynamics and cosmologyhttps://www.zbmath.org/1483.830852022-05-16T20:40:13.078697Z"Guendelman, E. I."https://www.zbmath.org/authors/?q=ai:guendelman.eduardo-i"Zamlung, E."https://www.zbmath.org/authors/?q=ai:zamlung.e"Benisty, D."https://www.zbmath.org/authors/?q=ai:benisty.davidSummary: A new symmetry for Newtonian Dynamics is analyzed, this corresponds to going to an accelerated frame, which introduces a constant gravitational field into the system and subsequently. We consider the addition of a linear contribution to the gravitational potential \(\phi\) which can be used to cancel the gravitational field induced by going to the accelerated from, the combination of these two operations produces then a symmetry. This symmetry leads then to a Noether current which is conserved. The conserved charges are analyzed in special cases. The charges may not be conserved if the Noether current produces flux at infinity, but such flux can be eliminated by going to the CM (center of mass) system in the case of an isolated system. In the CM frame the Noether charge vanishes, Then we study connection between the Cosmological Principle and the Newtonian Dynamics which was formulated via a symmetry \textit{D. Benisty} and \textit{E. I. Guendelman} [Mod. Phys. Lett. A 35, No. 16, Article ID 2050131, 7 p. (2020; Zbl 1435.85006)] of this type, but without an action formulation. Homogeneous behavior for the coordinate system relevant to cosmology leads to a zero Noether current and the requirement of the Newtonian potential to be invariant under the symmetry in this case yields the Friedmann equations, which appear as a consistency condition for the symmetry.Galactic clustering under power-law modified Newtonian potentialhttps://www.zbmath.org/1483.850062022-05-16T20:40:13.078697Z"Khanday, Abdul W."https://www.zbmath.org/authors/?q=ai:khanday.abdul-w"Upadhyay, Sudhaker"https://www.zbmath.org/authors/?q=ai:upadhyay.sudhaker"Ganai, Prince A."https://www.zbmath.org/authors/?q=ai:ganai.prince-ahmadSummary: We estimate galaxy clustering under a modified gravitational potential. In particular, the modifications in gravitational potential energy occur due to a power-law and cosmological constant terms. We derive a canonical partition function for the system of galaxies interacting under such a modified gravitational potential. Moreover, we compute various thermodynamical equation of states for the system. We do comparative analysis in order to emphasize the effect of corrections on thermodynamics of the system. Interestingly, the modifications in thermodynamical quantities are embedded in clustering parameter only.Research on early warning algorithm for economic management based on Lagrangian fractional calculushttps://www.zbmath.org/1483.910602022-05-16T20:40:13.078697Z"Su, Xin"https://www.zbmath.org/authors/?q=ai:su.xin"Yu, Keshu"https://www.zbmath.org/authors/?q=ai:yu.keshu"Yu, Miao"https://www.zbmath.org/authors/?q=ai:yu.miaoSummary: The occurrence of economic management crisis has seriously affected the production and operation of enterprises, the stability of capital markets and even the economic security of the entire country and the world. The use of higher mathematics in economic management is very beneficial to the economic restructuring. For example, in the Lagrangian method for solving the constraint optimization problem, the correlation function can be listed in the Lagrangian fractional calculus equation for the economic management early warning problem with many independent variables. Then take one of the factors as the dependent variable and other factors as fixed constants, and bring them into the Lagrangian fractional calculus equation, you can find the variable solution and get the extreme value of the economic management early warning algorithm. Therefore, this paper combines normative research and empirical research to study the algorithm design, theoretical analysis and numerical experiments of Lagrangian-based methods for solving constrained optimization problems. The Lagrangian fractional calculus method is used to evaluate the early warning algorithm of economic management, improve the prediction accuracy and practicability of the model, and conduct empirical research. It is expected to find a way to effectively determine whether a listed company is caught in an economic management crisis and provide early warning for the listed company's own management.