Pyramid scheme in stock market:A kind of financial market simulation

Artificial stock market simulation based on agent is an important means to study financial market. Based on the assumption that the investors are composed of a main fund, small trend and contrarian investors characterized by four parameters, we simulate and research a kind of financial phenomenon with the characteristics of pyramid schemes. Our simulation results and theoretical analysis reveal the relationships between the rate of return of the main fund and the proportion of the trend investors in all small investors, the small investors' parameters of taking profit and stopping loss,the order size of the main fund and the strategies adopted by the main fund. Our work is helpful to explain the financial phenomenon with the characteristics of pyramid schemes in financial markets, design trading rules for regulators and develop trading strategies for investors.     

Conditional Gaussian Fluctuations and Refined Asymptotics of the Spin in the Phase-Coexistence Region

We present four results on the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model. Our first two results refine the main theorem in a previous paper (Ellis et al. in Ann. Appl. Probab. 20:2118?C2161, 2010), in which the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model is given. Our first main result studies the asymptotics of the centered, finite-size magnetization, giving its precise rate of convergence to 0 along parameter sequences lying in the phase-coexistence region and converging sufficiently slowly to either a second-order point or the tricritical point of the model. A simple inequality yields our second main result, which generalizes the main theorem in Ellis et al. (Ann. Appl. Probab. 20:2118?C2161, 2010) by giving an upper bound on the rate of convergence to 0 of the absolute value of the difference between the finite-size magnetization and the thermodynamic magnetization. These first two results have direct relevance to the theory of finite-size scaling. They are consequences of our third main result. This is a new conditional limit theorem for the spin per site, where the conditioning allows us to focus on a neighborhood of the pure states having positive thermodynamic magnetization. Our fourth main result is a conditional central limit theorem showing that the fluctuations of the spin per site are Gaussian in a neighborhood of the pure states having positive thermodynamic magnetization.     

MacNeille Completions of D-Posets and Effect Algebras

Our main result is stating and proving a necessary and sufficient condition forD-poset and effect algebras to have MacNeille completions.     

On Eigenfunction Expansion of Solutions to the Hamilton Equations

We establish a spectral representation for solutions to linear Hamilton equations with positive definite energy in a Hilbert space. Our approach is a special version of M. Krein’s spectral theory of J-selfadjoint operators in the Hilbert spaces with indefinite metric. Our main result is an application to the eigenfunction expansion for the linearized relativistic Ginzburg–Landau equation.     

Stochastic resonance and chaotic resonance in bimodal maps: A case study

We present the results of an extensive numerical study on the phenomenon of stochastic resonance in a bimodal cubic map. Both Gaussian random noise as well as deterministic chaos are used as input to drive the system between the basins. Our main result is that when two identical systems capable of stochastic resonance are coupled, the SNR of either system is enhanced at an optimum coupling strength. Our results may be relevant for the study of stochastic resonance in biological systems.     

Dimensions of Attractors in Pinched Skew Products

We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the pointwise dimension and the information dimension are all equal to one, although the box-counting dimension is known to be two. The assertion concerning the pointwise dimension is deduced from the stronger result that the physical measure is rectifiable. Our findings confirm a conjecture by Ding, Grebogi and Ott from 1989.     

Self-Similarity of Volume Measures for Laplacians¶on P. C. F. Self-Similar Fractals

Our main goal in this paper is to obtain a precise analogue of Weyl's asymptotic formula for the eigenvalue distribution of Laplacians on a certain class of “finitely ramified” (or p.c.f.) self-similar fractals, building, in particular, on the work of [7, 9, 22, 24]. Our main result consists in precisely identifying (for the class of “decimable fractals”) the volume measures constructed by the second author in [24] for general p.c.f. fractals and showing that they are self-similar. From a physical point of view, our results should be relevant to the study of the density of states for diffusions and wave propagation in fractal media. Received: 6 September 1999 / Accepted: 7 October 2000     

New collective mode in the fractional quantum Hall liquid

We apply the methods of continuum mechanics to the study of the collective modes of the fractional quantum Hall liquid. Our main result is that at long-wavelength, there are two distinct modes of oscillations, while previous theories predicted only one. The two modes are shown to arise from the internal dynamics of shear stresses created by the Coulomb interaction in the liquid. Our prediction is supported by recent light scattering experiments, which report the observation of two long-wavelength modes in a quantum Hall liquid.     

Regularization and convergence for singular perturbations

We present an abstract result on removing regularization for singular perturbations in the operator theory. Our main result concerns singular perturbations which are not (formally) semibounded from below.     

Lottery and Auction on Quantum Blockchain

This paper proposes a protocol for lottery and a protocol for auction on quantum Blockchain. Our protocol of lottery satisfies randomness, unpredictability, unforgeability, verifiability, decentralization and unconditional security. Our protocol of auction satisfies bid privacy, posterior privacy, bids’ binding, decentralization and unconditional security. Except quantum Blockchain, the main technique involved in both protocols is quantum bit commitment.     

Charge distributions of many particle final states and the energy dependence of forward charge exchange

We will describe a possible dynamical origin of the energy dependence of charge exchange cross sections. Our main assumption is local compensation of charge in a certain class of many particle final states.     

Nonleptonic weak decays of bottom mesons

Based on the Kobayashi-Maskawa weak current model we investigate the properties of weak hadronic decays of the anticipated bottom mesons. Our main results concern twobody and quasitwobody decays of bottom mesons into pseudoscalar and vector mesons.     

Quasiperiodic Solutions of the Heisenberg Ferromagnet Hierarchy

We present quasi-periodic solutions in terms of Riemann theta functions of the Heisenberg ferromagnet hierarchy by using algebro-geometric method. Our main tools include algebraic curve and Riemann surface, polynomial recursive formulation and a special meromorphic function.     

Nonsequential double ionization as a completely classical photoelectric effect

We introduce a unified and simplified theory of atomic double ionization. Our results show that at high laser intensities (I>/=10(14) W/cm(2)) purely classical correlation is strong enough to account for all of the main features observed in experiments to date.     

Analysis on DFB laser diode with main and multiple side modes injection-locked

One distributed feedback (DFB) laser diode with main and multiple side modes injection-locked is proposed and demonstrated. DFB laser diode can be successfully injection-locked not only in the main mode but also in the side modes. The side mode suppression ratio (SMSR) value of each injection-locked mode is enhanced, thereby, it can be a promising candidate for the use of multiple optical sources. Our proposed scheme has the potential to be used as optical sources for radio-on-wavelength division multiplexing (WDM) transport systems to provide multiple services.     

Disorder,local order and asymptotic freedom in spin and lattice gauge theories

We examine some aspects of the confinement problem from the point of view of simple molecular field and spin wave concepts applied to lattice gauge theory. Our main endeavour is to discover the reasons for the absence of a deconfining phase transition in 4 dimensions. The essential point we make is that the mechanism responsible for eliminating the transition is deeply related to, not to say implied by, asymptotic freedom, which is the principal characteristic of the system at low temperatures and short wavelenghts. Our analysis is built on the analogy of lattice gauge theories with 2-dimensional spin systems.     

Localization of Non-Relativistic Particles

This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2) to show that the rigged Hilbert space incorporates particle localization in a natural manner.     

There are no scalar Lie fields in three or more dimensional space-time

We show that a Lie field structure is incompatible with a scalar relativistic quantum field theory if the dimension of space-time is greater than two. Our main argument is based on the Jacobi identity and the spectrum condition.     

Drift and diffusion of a confined semiflexible chain

We study the transverse and longitudinal linear response function of rigid chains subjected to an external force. Our main concern are stiff polymers confined in narrow pores with diameter less than their persistence length. We explicitly consider confinement in a transverse harmonic potential and generalize results by scaling arguments. Our results describe the drift of the filament under an external force, time evolution of the filament shape, and filament diffusion. Diffusion of a confined filament resembles the celebrated reptation process for flexible chains, albeit with distinct kinetic exponents. The limiting case of stiff free filaments is also mentioned.