Narrow Results

We develop the theory of the momentum map for the Maxwell–Lorentz equations for a spinning extended charged particle. The development relies on the Hamilton–Poisson structure of the system. This theory is indispensable for the study of long-time behavior and radiation of the solitons of this system, in particular for the proof of orbital stability of the corresponding solitons moving with constant speed and rotating with constant angular velocity.

We apply the theory to the translation and rotation symmetry groups of the system. The general theory of the momentum map results in formal equations for the corresponding invariants. We solve these equations obtaining expressions for the momentum and the angular momentum.

We check the conservation of these expressions and their coincidence with known classical invariants. For the first time, we specify a general class of finite energy initial states which provide the conservation of angular momentum.

Backpropagation, which is frequently used in Neural Network training, often takes a great deal of time to converge on an acceptable solution. Momentum is a standard technique that is used to speed up convergence and maintain generalization performance. In this paper we present the Windowed Momentum algorithm, which increases speedup over Standard Momentum. Windowed Momentum is designed to use a fixed width history of recent weight updates for each connection in a neural network. By using this additional information, Windowed Momentum gives significant speedup over a set of applications with same or improved accuracy. Windowed Momentum achieved an average speedup of 32% in convergence time on 15 data sets, including a large OCR data set with over 500,000 samples. In addition to this speedup, we present the consequences of sample presentation order. We show that Windowed Momentum is able to overcome these effects that can occur with poor presentation order and still maintain its speedup advantages.

We present a novel simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us to explain both qualitatively and quantitatively important stylized facts observed in the statistics of both microstructure and macrostructure returns, including the short-ranged correlation of returns, the long-ranged correlations of absolute returns, the microstructure noise and Epps effects. According to the microstructure noise effect, volatility is a decreasing function of the time-scale used to estimate it. The Epps effect states that cross correlations between asset returns are increasing functions of the time-scale at which the returns are estimated. The microstructure noise is explained as the result of the negative return correlations inherent in the definition of the bid-ask bounce component (ii). In the presence of a genuine correlation between the returns of two assets, the Epps effect is due to an average statistical overlap of the momentum of the returns of the two assets defined over a finite time-scale in the presence of the long memory process (i).

It is well known that an electron has either spin-up or spin-down state and a photon has two possible polarizations called spin $+1$ or spin $-1$. But when two particles are created, the two particles can have 50% of one state and 50% in the other. This is called the two particles in quantum entanglement. The spooky thing is that an event at one point in the universe can instantaneously affect the event that is arbitrarily far away between these two particles.^a The entanglement of the two particles can be electron or photon. We believe, in order to study this phenomenon we have to study further than the previously established principles of quantum mechanics, that is, to study how an electron creates a photon and how it interacts with the photon emitted.

Quantum entanglement simplified-video results — Quantum entanglement and spooky action at a distance, youtube.com, two years ago.

The effect of the geometry (deviation from the flat space) on the quantum evolution of the momentum and position of a free particle is discussed. It is shown that beginning with a wave-packet of minimum uncertainty (a Gaussian wave), there is a usual increase in the product of the volume uncertainties in the momentum and position space, as seen in the quantum mechanics on a flat spaces. But there is also a contribution from geometry. The leading order of this contribution is calculated.

The first equation in a hierarchy of equations due to Vlasov is studied. The equation can be described as a Schrödinger equation for the probabilistic description of a system. It has applications in other areas as well. A physical meaning can be assigned to the phase of the wavefunction. The approach allows construction of solutions of the Schrödinger equation from known solutions and conversely much like a Bäcklund transformation. Finally, the process of introducing a potential into the Schrödinger equation is generalized to the case of Bohmian mechanics.

In this paper, the energy and momentum operator substitution method derived from the Schrödinger equation is used to list all possible light and matter wave equations, among which the first light wave equation and relativistic approximation equation are proposed for the first time. We expect that we will have some practical application value. The negative sign pairing of energy and momentum operators are important characteristics of this paper. Then the Klein–Gordon equation and Dirac equation are introduced. The process of deriving relativistic energy–momentum relationship by undetermined coefficient method and establishing Dirac equation are mainly introduced. Dirac’s idea of treating negative energy in relativity into positrons is also discussed. Finally, the four-dimensional space-time representation of relativistic wave equation is introduced, which is usually the main representation of quantum electrodynamics and quantum field theory.

The role of dissipation with respect to a microscopic superposition of quantum states is investigated by means of master equations. This has implications for the study of the emergence of classicality from the quantum level. In particular, it illustrates why it is difficult to observe a macroscopic quantum state. The role of the environment is assumed by the measuring apparatus. A pure state is reduced to a mixture in the pointer basis of the system by means of the interaction with the apparatus. It is the intention that this type of analysis will have applications to experiments which are designed to better understand the environmental-assisted invariance formulation of quantum mechanics.

Recently, Ahn et al. created dumbbell-shaped silica nanoparticles, then optically levitated in vacuum, capable of spinning at 300 billion revolutions per minute, driven only by the force and torque of laser. This is by far the fastest spinning object in the world. We show that in this system, there is an additional change in momentum (or extra force) that is proportional to the change in the angular momentum of the particle (or torque). We suggest that this effect also applies to microscopic particles. In the experiment of Ahn et al., although the angular momentum of the particle itself L is large, the rate of change of the angular momentum $\dot{\mathit{L}}$ may not be large. Therefore, experimentally, the physical effects associated with changes in angular momentum can be verified either by applying very strong force and torque to the particle, or by allowing the axis of rotation of the particle to find a way to change very quickly.

In the 21st century, understanding the mechanism of high-temperature superconductivity has emerged as a pinnacle achievement in condensed matter physics, capturing the lifelong interest of numerous physicists. This paper endeavors to offer a theoretical elucidation for this mechanism, advancing the broader field of physics. Recognizing that high-temperature superconductivity is an aspect of condensed matter physics — underpinned by Maxwell’s classical electromagnetic theory — we turn to theoretical mechanics and field theory, which are foundational perspectives in the contemporary scientific era. By framing Maxwell’s classical electromagnetic theory within the context of theoretical mechanics and field theory, this paper not only sheds light on the mechanism of high-temperature superconductivity but also recasts Maxwell’s theory within a purer theoretical mechanics and field theory domain. This represents a paradigmatic shift and cognitive transformation in physics. Furthermore, leveraging this theoretical mechanics and field theory interpretation of electromagnetic phenomena, we discern that electromagnetic phenomena can be more aptly explained without resorting to the concepts of charges and electric fields, leading to a reinterpretation of Coulomb’s law. We propose that protons and electrons might exist as entities devoid of charge-specific attributes and negate the possibility of a strongly correlated particle system within them.

Traditional derivations of general relativity (GR) from the graviton degrees of freedom assume spacetime Lorentz covariance as an axiom. In this paper, we survey recent evidence that GR is the unique spatially-covariant effective field theory of the transverse, traceless graviton degrees of freedom. The Lorentz covariance of GR, having not been assumed in our analysis, is thus plausibly interpreted as an accidental or emergent symmetry of the gravitational sector. From this point of view, Lorentz covariance is a necessary feature of low-energy graviton dynamics, not a property of spacetime. This result has revolutionary implications for fundamental physics.

Temperature is an important and commonly used parameter among others to study properties of matter created during high energy collisions of nuclei. Experimental data from JINR and UrQMD (version 3.3p2) model simulations have been used to estimate temperature and other properties of positive pions in collisions of deuteron with carbon nuclei at incident momentum of 4.2GeV/$c$ in this paper. Transverse mass and transverse momentum spectra have been used to get inverse slope parameter/temperature of said particles, with the help of some fitting equations. These equations are referred as Hagedorn Thermodynamic and Boltzmann Distribution functions. Such functions or equations are used to describe particles spectra. Temperature of positive pions has been found to be equal to $104\pm 2$ and $112\pm 2$MeV in experimental and model, respectively, using Hagedorn function. Results from both experimental and model calculations have also been compared with each other and thus most reliable fitting function has been suggested. It is found that Hagedorn Thermodynamic function is the most reliable function to get pions’ temperature in said collision system at given momentum. Similarly, results obtained in this paper have been compared with results from other experiments in the world and worthy conclusions have been reached and reported.

The main purpose of this paper is to explore a high-frequency tactical asset allocation strategy. In particular, we investigate the profitability of momentum trading and contrarian investment strategies for equities listed on the Australian Stock Exchange (ASX). In these two strategies we take into consideration the short-selling restrictions imposed by the ASX on the stocks used. Within our sample portfolios we look at the relationship between stock returns and past trading volume for these equities. This research also investigates the seasonal aspects of contrarian portfolios and observes weekly, monthly and yearly effects. We report significant contrarian profits for the period investigated (from 2001 to 2006) and show that contrarian profit is a persistent feature for the strategies examined. We also document that contrarian portfolios earn returns as high as 6.54% per day for portfolios with no short-selling restrictions, and 4.71% in the restricted model. The results also support the view that volume traded affects stock returns, and show that market imperfections such as short-selling restrictions affect investors' returns.

By using the relationship between high sentiment and momentum, the main purpose of this paper is to investigate if psychological biases of investors have an influence on behavioral biases. We find that in the China stock market, high sentiment of loser groups is correlated with contributors of momentum profits, while high sentiment of winner groups is correlated with contributors of contrarian returns. Further analysis indicates that, the higher the investor psychological bias is, the greater the momentum return will become. Winners/losers that are most sensitive to sentiment and having the longest duration of being kept under the situation will result in higher returns.

This paper provides an analysis of the effectiveness of certain return predictors in Taiwan Stock Exchange (TWSE) from January 1990 to December 2011 by employing both portfolio method and cross-sectional regressions. While we found no statistically significant predictive power of beta, total volatility, and idiosyncratic volatility the two cheapness variables, book-to-market (BKMT) and cash-flow-to-price (FPR) ratios showed strong consistent economically and statistically significant predictive powers. In addition, our multiple regressions found predictive power in total volatility, short-term reversal (STREV), and market capitalization in the set of small stocks, while our all stock set showed predictive power only in total volatility and STREV.

This paper examines relative performance of alternative asset pricing models using individual security returns. The standard multivariate test used in studies comparing the performance of asset pricing models requires the number of stocks to be less than the number of time series observations, which requires grouping stocks into portfolios. This results in a loss of disaggregate stock information. We apply a different statistical test to overcome this problem and to investigate relative performance of alternative asset pricing models using individual security returns instead of portfolio returns. Our findings suggest that a parsimonious six-factor model that includes the momentum and orthogonal value factors outperforms all other models based on a number of measures as well as the average $F$-test. Unlike the standard multivariate test, we find that the average $F$-test has superior power to discriminate among competing models and does not reject all tested models.

Very small time steps are usually needed in numerical computation as conventional time integration methods are used to compute the response of a structure subjected to a dynamic loading with rapid changes or load discontinuity. To overcome this drawback, this study proposed a fast, fourth-order accurate step-by-step time integration (FASSTI) algorithm that is unconditionally stable and allows larger time steps for linear dynamic problems. From the stability and accuracy analysis, it is shown that the FASSTI algorithm retains the features of unconditional stability, accuracy, and fast convergence than the Newmark method. As a first test, a closed-form solution of an excited single degree of freedom (SDOF) system is derived and used to verify the reliability of the present algorithm in solving linear dynamic problems. In the numerical examples, the accuracy and efficiency of the proposed method is demonstrated in the solution of the dynamic response of an SDOF system under a series of impulse-type forces.

An efficient time-integration algorithm for nonlinear dynamic analysis of structures is presented. By adopting the temporal discretization for time finite element approximation, very large time steps can be used by the algorithm. With an accuracy of fourth order, this technique requires only displacements and velocities to be made available at the start of the current time step for integration in state space. Using the weighted momentum principle, the problem of discontinuity caused by impulsive loads is resolved after time-integration of the applied load in external momentum. Since no knowledge is required of acceleration at the current time step, the errors caused by estimation of acceleration by previous finite-difference methods are circumvented. Moreover, an iterative procedure is included for each time step, involving the three phases of predictor, corrector, and error-checking. The effectiveness and robustness of the proposed algorithm in solving nonlinear dynamic problems is demonstrated in the numerical examples.

This paper presents a momentum-based control framework for floating-base robots and its application to the humanoid robot “Atlas”. At the heart of the control framework lies a quadratic program that reconciles motion tasks expressed as constraints on the joint acceleration vector with the limitations due to unilateral ground contact and force-limited grasping. We elaborate on necessary adaptations required to move from simulation to real hardware and present results for walking across rough terrain, basic manipulation, and multi-contact balancing on sloped surfaces (the latter in simulation only). The presented control framework was used to secure second place in both the DARPA Robotics Challenge Trials in December 2013 and the Finals in June 2015.

A number of behavioral finance theories posit that investors adhere to prior beliefs in spite of new information. This paper reports the results of an investment experiment which shows that subjects' inferences are biased by their prior beliefs in a manner that depends on investment outcomes. Specifically, survey responses and investment behavior indicate that subjects' perception of new information was more positively biased for their previously favored assets when incurring losses than gains. This asymmetric bias may help explain empirical patterns such as loser momentum and suggests modifications to models of belief persistence in markets.