Perfect difference families,perfect difference matrices,and related combinatorial structures

The existence problems of perfect difference families with block size k, k=4,5, and additive sequences of permutations of length n, n=3,4, are two outstanding open problems in combinatorial design theory for more than 30 years. In this article, we mainly investigate perfect difference families with block size k=4 and additive sequences of permutations of length n=3. The necessary condition for the existence of a perfect difference family with block size 4 and order v, or briefly (v, 4,1)‐PDF, is v≡1(mod12), and that of an additive sequence of permutations of length 3 and order m, or briefly ASP (3, m), is m≡1(mod2). So far, (12t+1,4,1)‐PDFs with t<50 are known only for t=1,4−36,41,46 with two definiteexceptions of t=2,3, and ASP (3, m)'s with odd 3<m<200 are known only for m=5,7,13−29,35,45,49,65,75,85,91,95,105,115,119,121,125,133,135,145,147,161,169,175,189,195 with two definite exceptions of m=9,11. In this article, we show that a (12t+1,4,1)‐PDF exists for any t⩽1,000 except for t=2,3, and an ASP (3, m) exists for any odd 3<m<200 except for m=9,11 and possibly for m=59. The main idea of this article is to use perfect difference families and additive sequences of permutations with “holes”. We first introduce the concepts of an incomplete perfect difference matrix with a regular hole and a perfect difference packing with a regular difference leave, respectively. We show that an additive sequence of permutations is in fact equivalent to a perfect difference matrix, then describe an important recursive construction for perfect difference matrices via perfect difference packings with a regular difference leave. Plenty of perfect difference packings with a desirable difference leave are constructed directly. We also provide a general recursive construction for perfect difference packings, and as its applications, we obtain extensive recursive constructions for perfect difference families, some via incomplete perfect difference matrices with a regular hole. Examples of perfect difference packings directly constructed are used as ingredients in these recursive constructions to produce vast numbers of perfect difference families with block size 4. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 415–449, 2010     

Lateral distribution of EAS muons measured for the primary cosmic ray energy around 100 TeV

The muonic component of the extensive air showers (EAS) is of great importance for the astroparticle physics. It carries the information about the properties of primary cosmic ray (CR) particles, such as their mass, and electromagnetic and hadronic nature. It provides a sensitive test for the hadronic interaction models, which are inevitable for describing the cascade shower development of cosmic rays in EAS experiments. The YangBaJing Hybrid Array (YBJ-HA) experiment has been in operation since the end of 2016. Surface detectors are used for the measurements of primary energy, angular direction and core position of a shower event, while underground muon detectors are used for measuring the density of muons at various locations. Using the data obtained by the YBJ-HA experiment,this work reports the first measurement of the lateral muon distribution for the primary cosmic ray energy in the 100TeV region. The punch-through effect is evaluated via MC simulation.     

Influence of the long-range forces in non-Gaussian random-packing dynamics

In this paper, we perform molecular dynamics (MD) simulations to study the random packing of spheres with different particle size distributions. In particular, we deal with non-Gaussian distributions by means of the Lévy distributions. The initial positions as well as the radii of five thousand non-overlapping particles are assigned inside a confining rectangular box. After that, the system is allowed to settle under gravity towards the bottom of the box. Both the translational and rotational movements of each particle are considered in the simulations. In order to deal with interacting particles, we take into account both the contact and long-range cohesive forces. The normal viscoelastic force is calculated according to the nonlinear Hertz model, whereas the tangential force is calculated through an accurate nonlinear-spring model. Assuming a molecular approach, we account for the long-range cohesive forces using a Lennard-Jones (LJ)-like potential. The packing processes are studied assuming different long-range interaction strengths.     

Transmission control by asymmetric electromagnetically induced transparency-like metamaterials in transverse electromagnetic waveguide

We numerically and experimentally present passive and active electromagnetically induced transparency-like metamaterials in a TEM waveguide under normal excitation. Asymmetry of the metamaterial unit cell leads to the splitting of the radiative resonance. Surface current distributions are analyzed to account for each resonance. Moreover, by implementing a varactor diode to one of the gaps of the double-split ring resonator, electromagnetically induced transmission-like band is shifted in frequency and the corresponding bandwidth is modulated. A modulation ratio of 29.5 dB in transmission is experimentally demonstrated by only increasing the bias voltage 4 volts.     

Entropic Kullback-Leibler type distance measures for quantum distributions

Entropic distance measures for quantum mechanical probability distributions, which are characterized by nodal structure and symmetry holes, are considered. We illustrate how the Kullback-Leibler (KL) distance is not well defined in some instances and propose instead the use of the cumulative residual Kullback-Leibler (CRKL) distance. The KL and CRKL measures are compared and contrasted for some representative quantum mechanical systems: The particle in an infinite well, the harmonic oscillator, and hydrogenic systems. We present cases where CRKL can be used to obtain distances whereas KL cannot be used, and also highlight examples where the KL and CRKL measures yield different behaviors and interpretations. An extension of the CRKL definition is obtained for application to harmonic oscillator systems defined over [−∞, ∞]. Distance measures for two-variable (particle) distributions are also considered to address generalizations of the mutual information correlation measure. The use of CRKL in measuring distances between orbitals is also discussed.     

Baryon structure from Lattice QCD

We present recent lattice results on the baryon spectrum, nucleon electromagnetic and axial form factors, nucleon to △ transition form factors as well as the △ electromagnetic form factors. The masses of the low lying baryons and the nucleon form factors are calculated using two degenerate flavors of twisted mass fermions down to pion mass of about 270 MeV. We compare to the results of other collaborations. The nucleon to △ transition and △ form factors are calculated in a hybrid scheme, which uses staggered sea quarks and domain wall valence quarks. The dominant magnetic dipole nucleon to △ transition form factor is also evaluated using dynamical domain wall fermions. The momentum frame are extracted using the form factors transverse density distributions of the △ in the infinite determined from lattice QCD.     

2+1维广义Calogero-Bogoyavlenskii-Schiff方程的无穷多对称及其约化

通过潘勒卫检验,得到了2+1维广义Calogero-Bogoyavlenskii-Schiff方程可积的条件.在这个基础上,得到了GCBS方程的双线性形式,从而根据形式级数展开法得到了无穷多对称.根据这个对称可以得到GCBS方程的约化. 关键词： 无穷多对称 截断对称 对称约化 GCBS方程     

On the Quantitative Click Conjugation of Molecular Weight Distributions: What Can Theoretically Be Expected?

The assessment of the success of a click conjugation for block copolymer formation often occurs via ill‐defined criteria based on the qualitative shape of the size exclusion chromatography (SEC) distribution as well as unsuitable characteristics of these molecular weight distribution such as the peak molecular weight, M_p. The data presented herein illustrate that from the shape of the SEC distribution, w(log M) versus log M, of the click product—under the assumption of a 100% efficient conjugation reaction—a conclusion about the effectiveness of the click conjugation cannot be derived. It is demonstrated that under certain conditions multi‐modal molecular weight distributions are obtained from two well‐defined monomodal initial distributions. Similarly, the comparison of peak maxima between the conjugate and the initial SEC distributions is a poorly defined criterion to assess the success of a conjugation. The only reliable assessment for the success of the click coupling reaction is the true number average molecular weight, , of the SEC distribution of the click product, as well as a plot of the concentration or number distributions, c versus M, of the precursors and product polymer.

     

Properties of a simple bilinear stochastic model: Estimation and predictability

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distributions from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others.