A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz continuous gradient, then we prove that our method obtains an ?-optimal solution in $\mathcal{O}(n^{2}/\epsilon)$ iterations, where n is the number of blocks. For the class of problems with cheap coordinate derivatives we show that the new method is faster than methods based on full-gradient information. Analysis for the rate of convergence in probability is also provided. For strongly convex functions our method converges linearly. Extensive numerical tests confirm that on very large problems, our method is much more numerically efficient than methods based on full gradient information.     

The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

Enumerative Properties of NC (B) (p,q)

We determine the rank generating function, the zeta polynomial and the M?bius function for the poset NC ^(B) (p, q) of annular non-crossing partitions of type B, where p and q are two positive integers. We give an alternative treatment of some of these results in the case q = 1, for which this poset is a lattice. We also consider the general case of multiannular noncrossing partitions of type B, and prove that this reduces to the cases of non-crossing partitions of type B in the annulus and the disc.     

Tensor product surfaces of euclidean plane curves

Recently B.Y. CHEN initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold [3]. In [6] the particular case of tensor product of two Euclidean plane curves was studied. The minimal one were classified, and necessary and sufficient conditions for such a tensor product to be totally real or complex or slant were established. In the present paper we study for tensor product of Euclidean plane curves the problem of B.Y. CHEN: to what extent do the properties of the tensor product immersion f ? h of two immersions f, h determines the immersions f, h ? [3]     

Silver–titanium dioxide nanocomposites as effective antimicrobial and antibiofilm agents

Recent studies have revealed the existence of liver cancer stem cells (CSCs). Therefore, there is an urgent need for new and effective treatment strategies specific to liver CSCs. In this work, the poly(d,l-lactide-coglycolide) nanoparticles containing paclitaxel were prepared by emulsification-solvent evaporation method. The nanoparticles decorated with anti-CD133 antibody, termed targeted nanoparticles, were prepared by carbodiimide chemistry for liver CSCs. The physicochemical characteristics of the nanoparticles (i.e., encapsulation efficiency, particle size distribution, morphology, and in vitro release) were investigated. Cellular uptake and accumulation in tumor tissue of nanoparticles were observed. To assess anti-tumor activity of nanoparticles in vitro and in vivo, cell survival assay and tumor regression study were carried out using liver cancer cell lines (Huh7 and HepG2) and their xenografts. Particle size of targeted nanoparticles was 429.26 ± 41.53 nm with zeta potential of ?11.2 mV. Targeted nanoparticles possessed spherical morphology and high encapsulation efficiency (87.53 ± 5.9 %). The accumulation of targeted nanoparticles depends on dual effects of passive and active targeting. Drug-loaded nanoparticles showed cytotoxicity on the tumor cells in vitro and in vivo. Targeted nanoparticles resulted in significant improvement in therapeutic response through selectively eliminating CD133 positive subpopulation. These results suggested that the novel nanoparticles could be a promising candidate with excellent therapeutic efficacy for targeting liver CSCs.     

高Tc超导谐振器微波特性研究

研究了高Ｔｃ超导谐振器的微波特性特别是表面电阻Ｒｓ和磁场穿透深度λ,给出了Ｒｓ随温度变化的曲线以及穿透深度的测量结果。实验中采用了由ＹＢａ２Ｃｕ３Ｏ７薄膜和蓝宝石片构成的平行板谐振器。     

Nuclear size dependence of inclusive particle production

The inclusive production of π⁺, π^?, K⁺, K^?, p and $\text{p}$ for protons incident on carbon and tungsten targets was studied at the Internal Target Area of the Fermilab. We assume an A^α dependence for the inclusive cross sections and report here on the variation of α with incident momentum, transverse momentum and particle species.     

Pomeranchuk-like theorems on integrated cross sections and average spin polarization parameters

Pomeranchuk-like theorems on the integrated cross sections and on the average spin polarization parameters of different meson-baryon reactions are obtained by using the improvements of the usual triangular isospin inequalities on integrated cross sections.     

A linear filtering problem in complete correlated actions

In the last paper, the geometry of the Sz.-Nagy-Foia model for contraction operators on Hilbert spaces was used to advantage in several problems of multivariate analysis. The lifting of intertwining operators, one of the basic results from the Sz.-Nagy-Foia theory, is now recognized as the most adequate operatorial form of the deep classical results of the extrapolation theory. The labeling of the exact intertwining dilations given by [1]Acta Sci. Math. (Szeged) 40 9–32] and the recursive methods used there open a broad perspective for using the Sz.-Nagy-Foia model in multivariate filtering theory. In this paper, using the notion of correlated action (see [5 and 6] Rev. Roumaine Math. Pures Appl. 23, No. 9 1393–1423]) as a time domain, a linear filtering problem is formulated and its solution in terms of the coefficients of the analytic function which factorizes the spectral distribution of the known data and the coefficients of an analytic function which describes the cross correlations is given. In some special cases it is shown that the filter coefficients can be determined using recursive methods from the intertwining dilation theory, of the autocorrelation function of the known data and an intertwining operator, interpreted as the initial estimator given by the prior statistics.     

Investigation of lifetimes in dipole bands of 141Eu

Lifetimes have been measured for dipole bands in ¹⁴¹Eu using DSAM. The deduced B(M1) and B(E2) values as well as B(M1)/B(E2) ratios are compared with calculations in the framework of the TAC (Tilted Axis Cranking) and SPAC (Shears mechanism with Principal Axis Cranking) models. The dipole bands can be interpreted as magnetic rotational bands.Received: 6 April 2004, Revised: 14 May 2004, Published online: 13 July 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.10.Re Collective levels - 21.10.Tg Lifetimes - 27.60. + j