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Bing Li

Publications and source records attributed to Bing Li.

At least 487 records · Page 27Linked to original sources
arXiv2016

On the escape rate of unique beta-expansions

Let $1<β\leq 2$. It is well-known that the set of points in $% [0,1/(β-1)]$ having unique $β$-expansion, in other words, those points whose orbits under greedy $β$-transformation escape a hole depending on $β$, is of zero Lebesgue measure. The corresponding escape rate is investigated in this paper. A formula which links the Hausdorff dimension of univoque set and escape rate is established in this study. Then we also proved that such rate forms a devil's staircase function with respect to $β$.

math.DS↗
arXiv2016

Intensity Distribution Function and Statistical Properties of Fast Radio Bursts

Fast Radio Bursts (FRBs) are intense radio flashes from the sky that are characterized by millisecond durations and Jansky-level flux densities. We carried out a statistical analysis on FRBs discovered. Their mean dispersion measure, after subtracting the contribution from the interstellar medium of our Galaxy, is found to be $\sim 660\,\rm pc\,cm^{-3}$, supporting their being from cosmological origin. Their energy released in radio band spans about two orders of magnitude, with a mean value of $\sim 10^{39}$ ergs. More interestingly, although the FRB study is still in a very early phase, the published collection of FRBs enables us to derive a useful intensity distribution function. For the 16 non-repeating FRBs detected by Parkes telescope and the Green Bank Telescope, the intensity distribution can be described as $dN/dF_{\rm obs} = (4.1 \pm 1.3) \times 10^3 \, F_{\rm obs}^{-1.1\pm0.2} \; \rm sky^{-1}\,day^{-1}$, where $F_{\rm obs}$ is the observed radio fluence in units of Jy~ms. Here the power-law index is significantly flatter than the expected value of 2.5 for standard candles distributed homogeneously in a flat Euclidean space. Based on this intensity distribution function, the Five-hundred-meter Aperture Spherical radio Telescope (FAST) will be able to detect about 5 FRBs for every 1000 hours of observation time.

astro-ph.HE↗
arXiv2016

The denominators of convergents for continued fractions

For any real number $x \in [0,1)$, we denote by $q_n(x)$ the denominator of the $n$-th convergent of the continued fraction expansion of $x$ $(n \in \mathbb{N})$. It is well-known that the Lebesgue measure of the set of points $x \in [0,1)$ for which $\log q_n(x)/n$ deviates away from $π^2/(12\log2)$ decays to zero as $n$ tends to infinity. In this paper, we study the rate of this decay by giving an upper bound and a lower bound. What is interesting is that the upper bound is closely related to the Hausdorff dimensions of the level sets for $\log q_n(x)/n$. As a consequence, we obtain a large deviation type result for $\log q_n(x)/n$, which indicates that the rate of this decay is exponential.

math.NT↗
arXiv2016

Approximation orders of real numbers by $β$-expansions

We prove that almost all real numbers (with respect to Lebesgue measure) are approximated by the convergents of their $β$-expansions with the exponential order $β^{-n}$. Moreover, the Hausdorff dimensions of sets of the real numbers which are approximated by all other orders, are determined. These results are also applied to investigate the orbits of real numbers under $β$-transformation, the shrinking target type problem, the Diophantine approximation and the run-length function of $β$-expansions.

math.NT↗
arXiv2016

Hitting probabilities of random covering sets in tori and metric spaces

We provide sharp lower and upper bounds for the Hausdorff dimension of the intersection of a typical random covering set with a fixed analytic set both in Ahlfors regular metric spaces and in the $d$-dimensional torus. In metric spaces, we consider covering sets generated by balls and, in the torus, we deal with general analytic generating sets.

math.PR↗
arXiv2016

Zero-one law of Hausdorff dimensions of the recurrent sets

Let $(Σ, σ)$ be the one-sided shift space with $m$ symbols and $R_n(x)$ be the first return time of $x\inΣ$ to the $n$-th cylinder containing $x$. Denote $$E^φ_{α,β}=\left\{x\inΣ: \liminf_{n\to\infty}\frac{\log R_n(x)}{φ(n)}=α,\ \limsup_{n\to\infty}\frac{\log R_n(x)}{φ(n)}=β\right\},$$ where $φ: \mathbb{N}\to \mathbb{R}^+$ is a monotonically increasing function and $0\leqα\leqβ\leq +\infty$. We show that the Hausdorff dimension of the set $E^φ_{α,β}$ admits a dichotomy: it is either zero or one depending on $φ, α$ and $β$.

math.DS↗
arXiv2016

JADE for Tensor-Valued Observations

Independent component analysis is a standard tool in modern data analysis and numerous different techniques for applying it exist. The standard methods however quickly lose their effectiveness when the data are made up of structures of higher order than vectors, namely matrices or tensors (for example, images or videos), being unable to handle the high amounts of noise. Recently, an extension of the classic fourth order blind identification (FOBI) specifically suited for tensor-valued observations was proposed and showed to outperform its vector version for tensor data. In this paper we extend another popular independent component analysis method, the joint approximate diagonalization of eigen-matrices (JADE), for tensor observations. In addition to the theoretical background we also provide the asymptotic properties of the proposed estimator and use both simulations and real data to show its usefulness and superiority over its competitors.

math.ST↗
arXiv2016

Beta-expansion and continued fraction expansion of real numbers

Let $β> 1$ be a real number and $x \in [0,1)$ be an irrational number. We denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $β$-expansion of $x$ ($n \in \mathbb{N}$). It is known that $k_n(x)/n$ converges to $(6\log2\logβ)/π^2$ almost everywhere in the sense of Lebesgue measure. In this paper, we improve this result by proving that the Lebesgue measure of the set of $x \in [0,1)$ for which $k_n(x)/n$ deviates away from $(6\log2\logβ)/π^2$ decays to 0 exponentially as $n$ tends to $\infty$, which generalizes the result of Faivre \cite{lesFai97} from $β= 10$ to any $β>1$. Moreover, we also discuss which of the $β$-expansion and continued fraction expansion yields the better approximations of real numbers.

math.NT↗
arXiv2016

CP-odd component of the lightest neutral Higgs boson in the MSSM

The Higgs sector of the Minimal Supersymmetric Extension of the Standard Model may be described with a two Higgs doublet model with properties that depend on the soft supersymmetry breaking parameters. For instance, flavor independent CP-violating phases associated with the gaugino masses, the squark trilinear mass parameters and the Higgsino mass parameter $μ$ may lead to sizable CP-violation in the Higgs sector. For these CP-violating effects to affect the properties of the recently observed SM-like Higgs resonance, the non-standard charged and neutral Higgs bosons masses must be of the order of the weak scale, and both $μ$ as well as the trilinear stop mass parameter $A_t$ must be of the order or larger than the stop mass parameters. Constraints on this possibility come from direct searches for non-standard Higgs bosons, precision measurements on the lightest neutral Higgs properties, including its mass, and electric dipole moments. In this article, we discuss these constraints within the MSSM, trying to evaluate the possible size of the CP-odd component of the lightest neutral Higgs boson, and the possible experimental tests of this CP-violating effect at the LHC.

hep-ph↗
arXiv2016

Limit theorems related to beta-expansion and continued fraction expansion

Let $β> 1$ be a real number and $x \in [0,1)$ be an irrational number. Denote by $k_n(x)$ the exact number of partial quotients in the continued fraction expansion of $x$ given by the first $n$ digits in the $β$-expansion of $x$ ($n \in \mathbb{N}$). In this paper, we show a central limit theorem and a law of the iterated logarithm for the random variables sequence $\{k_n, n \geq 1\}$, which generalize the results of Faivre and Wu respectively from $β=10$ to any $β>1$.

math.NT↗
arXiv2016

Random Continued fractions: Lévy constant and Chernoff-type estimate

Given a stochastic process $\{A_n, n \geq 1\}$ taking values in natural numbers, the random continued fractions is defined as $[A_1, A_2, \cdots, A_n, \cdots]$ analogue to the continued fraction expansion of real numbers. Assume that $\{A_n, n \geq 1\}$ is ergodic and the expectation $E(\log A_1) < \infty$, we give a Lévy-type metric theorem which covers that of real case presented by Lévy in 1929. Moreover, a corresponding Chernoff-type estimate is obtained under the conditions $\{A_n, n \geq 1\}$ is $ψ$-mixing and for each $0< t< 1$, $E(A_1^t) < \infty$.

math.NT↗
arXiv2015

Local dimensions in Moran constructions

We study the dimensional properties of Moran sets and Moran measures in doubling metric spaces. In particular, we consider local dimensions and $L^q$-dimensions. We generalize and extend several existing results in this area.

math.CA↗
arXiv2015

Probing the Electroweak Phase Transition at the LHC

We study the correlation between the value of the triple Higgs coupling and the nature of the electroweak phase transition. We use an effective potential approach, including higher order, non-renormalizable terms coming from integrating out new physics. We show that if only the dimension six operators are considered, large positive deviations of the triple Higgs coupling from its Standard Model (SM) value are predicted in the regions of parameter space consistent with a strong first order electroweak phase transition (SFOEPT). We also show that at higher orders sizable and negative deviations of the triple Higgs coupling may be obtained, and the sign of the corrections tends to be correlated with the order of the phase transition. We also consider a singlet extension of the SM, which allows us to establish the connection with the effective field theory (EFT) approach and analyze the limits of its validity. Furthermore, we study how to probe the triple Higgs coupling from the double Higgs production at the LHC. We show that selective cuts in the invariant mass of the two Higgs bosons should be used, to maximize the sensitivity for values of the triple Higgs coupling significantly different from the Standard Model one.

hep-ph↗
arXiv2015

Existence and exponential stability of positive almost periodic solution for Nicholson's blowflies models on time scales

In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using the fixed point theorem in Banach space and the time scale calculus theory, we obtain some sufficient conditions for the existence and exponential stability of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales. Finally, we present an illustrative example to show the effectiveness of obtained results. Our results show that under a simple condition the continuous-time Nicholson's blowflies models and their discrete-time analogue have the same dynamical behaviors.

math.CA↗
arXiv2015

Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales

In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results. Our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new.

math.DS↗
arXiv2015

Benefit of Multipath TCP on the Stability of Network

Multipath-TCP receives a lot of attention recently and can potentially improve quality of service for both private and commercial users. It leverages the multiple available paths and send packets through all the available paths. The growing of Mutipath TCP has received a growing interest from both researchers who publish a growing number of articles on the topic and the vendors since Apple has decided to use Multipath TCP on its smartphones and tablets to support the Siri voice recognition application. In this paper, we study the performance of Multipath TCP from its impact on the stability of the network. In particular, we study three scenarios, Internet, which is the largest networks and involves heterogeneous traffic, data center, which is smaller but has different traffic patterns compared with Internet scale network and wireless network, whose energy consumption also needs to be considered. Our study shows that stability is affected but not seriouly for Internet and wireless network, but datacenter network stability is seriously affected due to its bursty traffic pattern.

cs.NI↗
arXiv2015

Almost automorphic funtions on time scales and almost automorphic solutions to shunting inhibitory cellular neural networks on time scales

In this paper, we first propose a new concept of almost periodic time scales, a new definition of almost automorphic functions on almost periodic time scales, and study some their basic properties. Then we prove a result ensuring the existence of an almost automorphic solution for both the linear nonhomogeneous dynamic equation on time scales and its associated homogeneous equation, assuming that the associated homogeneous equation admits an exponential dichotomy. Finally, as an application of our results, we establish the existence and global exponential stability of almost automorphic solutions to a class of shunting inhibitory cellular neural networks with time-varying delays on time scales. Our results about the shunting inhibitory cellular neural network with time-varying delays on time scales are new even for the both cases of differential equations(the time scale $\mathbb{T}=\mathbb{R})$ and difference equations(the time scale $\mathbb{T}=\mathbb{Z})$.

math.DS↗