The Bekenstein-Hawking Entropy of Higher-Dimensional Rotating Black Holes

A black hole can be regarded as a thermodynamic system described by a grand canonical ensemble. In this paper, we study the Bekenstein-Hawking entropy of higher-dimensional rotating black holes using the Euclidean path-integral method of Gibbons and Hawking. We give a general proof demonstrating that ignoring quantum corrections, the Bekenstein-Hawking entropy is equal to one-fourth of its horizon area for general higher-dimensional rotating black holes.Comment: 9 pages, Latex, v2: arxiv-id for the references supplemented, v3: accepted for publication by Progress of Theoretical Physic

Hegel's Eurocentric Triads of Dialectics and its Transformation to Kelly's Planetary Paradigm

This article introduces Hegel's Eurocentric philosophy of dialectics in the 19th century and its transformation to Kelly’s planetary paradigm at the turn of the 20th-21st century. The new theory develops Hegel’s thesis—antitheses—synthesis to identity—difference—new-identity which is applicable for the entire human history, including the planetary era. The new triad generalizes Hegel’s mechanic view of nature by suggesting a dominant worldview which is featured by a series of tightening and converging dynamic fractal cycles

Color Realism: True or Not?

Color realism refers to that things are colored, or colors are real. Although the view goes in a minority opinion, Byrne & Hilbert defend it based on the physical properties of color and the peculiarly assumed hue-magnitudes. However, hues are mind-dependent and cannot be used as a measure of the physical properties of things. As a result, the defense fails to justify the proposition of color realism

Plasma Brain Dynamics (PBD): A Mechanism for EEG Waves Under Human Consciousness

EEG signals are records of nonlinear solitary waves in human brains. The waves have several types (e.g., α, β, γ, θ, δ) in response to different levels of consciousness. They are classified into two groups: Group-1 consists of complex storm-like waves (α, β, and γ); Group-2 is composed of simple quasilinear waves (θ and δ). In order to elucidate the mechanism of EEG wave formation and propagation, this paper extends the Vlasov-Maxwell equations of Plasma Brain Dynamics (PBD) to a set of two-fluid, self-similar, nonlinear solitary wave equations. Numerical simulations are performed for different EEG signals. Main results include: (1) The excitation and propagation of the EEG wave packets are dependent of electric and magnetic fields, brain aqua-ions, electron and ion temperatures, masses, and their initial fluid speeds; (2) Group-1 complex waves contain three ingredients: the high-frequency ion-acoustic (IA) mode, the intermediate-frequency lower-hybrid (LH) mode, and, the low-frequency ion-cyclotron (IC) mode; (3) Group-2 simple waves fall within the IA band, featured by one or a combination of the three envelopes: sinusoidal, sawtooth, and spiky/bipolar. The study proposes an alternative model to Quantum Brain Dynamics (QBD) by suggesting that the formation and propagation of the nonlinear solitary EEG waves in the brain have the same mechanism as that of the waves in space plasmas

Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Robust H∞ control of time-varying systems with stochastic non-linearities: the finite-horizon case

The official published version can be obtained from the link below.This paper is concerned with the robust H∞ control problem for the class of uncertain non-linear discrete time-varying stochastic systems with a covariance constraint. All the system parameters are time-varying and the uncertainties enter into the state matrix. The non-linearities under consideration are described by statistical means and they cover several classes of well-studied non-linearities. The purpose of the addressed problem is to design a dynamic output-feedback controller such that, the H∞ disturbance rejection attenuation level is achieved in the finite-horizon case while the state covariance is not more than an individual upper bound at each time point. An algorithm is developed to deal with the addressed problem by means of recursive linear matrix inequalities (RLMIs). It is shown that the robust H∞ control problem is solvable if the series of RLMIs is feasible. An illustrative simulation example is given to show the applicability and effectiveness of the proposed algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Trickster-Like Teachings in Tibetan Buddhism: Shortcuts towards Destroying Illusions

Trickster-like Dharma teachings in Tibetan Buddhism behave as a kind of shortcuts in the approach to leading people along the path of enlightenment. This essay collects three such teachings of different levels towards destroying illusions, i.e., Buddha’s silence, Guru’s paradox, and Ego’s kleshas. They are necessary as “an ace up the sleeve” for Buddha to destruct disciples’ metaphysical quagmire, for Guru to lead community toward perfect transcendence, and for individuals to attain self-consciousness

Robust variance-constrained filtering for a class of nonlinear stochastic systems with missing measurements

The official published version of the article can be found at the link below.This paper is concerned with the robust filtering problem for a class of nonlinear stochastic systems with missing measurements and parameter uncertainties. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution, and the nonlinearities are expressed by the statistical means. The purpose of the filtering problem is to design a filter such that, for all admissible uncertainties and possible measurements missing, the dynamics of the filtering error is exponentially mean-square stable, and the individual steady-state error variance is not more than prescribed upper bound. A sufficient condition for the exponential mean-square stability of the filtering error system is first derived and an upper bound of the state estimation error variance is then obtained. In terms of certain linear matrix inequalities (LMIs), the solvability of the addressed problem is discussed and the explicit expression of the desired filters is also parameterized. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK and the Alexander von Humboldt Foundation of Germany

Review: The Powers of the Universe by Brian Swimme

This essay presents a review on Brian Swimme’s 3-DVD set of lecture series in the interdisciplinary field of philosophy, cosmology and consciousness. In the eleven 45-minute episodes of a systematic 9-hour immersive program, a set of 12 intercorrelated cosmological powers is proposed on the basis of modern scientific theory. A positive and life-affirming vision of human potential is attained together with a new level of ecological responsibility and relatedness. The interwoven cosmological paradigm compromises with two ancient eastern wisdoms

Partonic State and Single Transverse Spin Asymmetry in Drell-Yan Process

Single transverse-spin asymmetries have been studied intensively both in experiment and theory. Theoretically, two factorization approaches have been proposed. One is by using transverse-momentum-dependent factorization and the asymmetry comes from the so called Sivers function. Another is by using collinear factorization where the nonperturbative effect is parameterized by a twist-3 hadronic matrix element. However, the factorized formulas for the asymmetries in the two approaches are derived at hadron level formally by diagram expansion, where one works with various parton density matrices of hadrons. If the two factorizations hold, they should also hold at parton level. We examine this for Drell-Yan processes by replacing hadrons with partons. By calculating the asymmetry, Sivers function and the twist-3 matrix element at nontrivial leading order of $\alpha_s$, we find that we can reproduce the result of the transverse-momentum-dependent factorization. But we can only verify the result of the collinear factorization partly. Two formally derived relations between Sivers function and the twist-3 matrix element are also examined with negative results.Comment: 15 pages, 6 figure