The Averaged Robbins – Monro Method for Linear Problems in a Banach Space

We consider a recursive method of Robbins–Monro type to solve the linear problem Ax=V in a Banach space. The bounded linear operator A and the vector V are assumed to be observable with some noise only. According to Polyak and Ruppert we use gains converging to zero slower than 1/n and take the average of the iterates as an estimator for the solution of the linear problem. Under weak conditions on the noise processes almost sure and distributional invariance principles are shown.     

New Kinds of Fuzzy Ideals in BCI-algebras*

Following the seminal work of Xi on the definition of fuzzy ideal in BCI-algebras, three new kinds of definitions of fuzzy ideal of BCI-algebras are proposed. First, by the use of the relations between fuzzy points and fuzzy sets, the definition of a (s,t]-fuzzy ideals of BCI-algebras is introduced. The acceptable nontrivial concepts obtained in this manner are the - fuzzy ideals and -fuzzy ideals. Second, based on the concept of falling shadow, a theoretical approach of fuzzy ideal is established and the fuzzy ideal based on t-norm is proposed. Finally, by the use of the implication operators of fuzzy logic, an R-fuzzy ideals is proposed and relations between the (s,t]-fuzzy ideals and R-fuzzy ideals are discussed. *Foundation Item:Supported by NNSF of China(60274016). Biography:Zhang Guang-ji(1947-),male,Professor     

Ordinary p-Laplacian systems with nonlinear boundary conditions

This paper is concerned with the existence of solutions for the boundary value problem

     

Invariants of 2 × 2 matrices, irreducible {\hbox{SL}(2, \mathbb{C})} characters and the Magnus trace map

We obtain an explicit characterization of the stable points of the action of on the cartesian product G  ^{× n} by simultaneous conjugation on each factor in terms of the corresponding invariant functions. From this, a simple criterion for the irreducibility of representations of finitely generated groups into G is derived. We also obtain analogous results for the action of on the vector space of n-tuples of 2 × 2 complex matrices. For a free group F _n of rank n, we show how to generically reconstruct the 2 ^n-2 conjugacy classes of representations F _n → G from their values under the map considered in Magnus [Math. Zeit. 170, 91–103 (1980)], defined by certain 3n − 3 traces of words of length one and two.      

beta-Barrel transmembrane proteins: Geometric modelling, detection of transmembrane region, and structural properties

The location of the membrane lipid bilayer relative to a transmembrane protein structure is important in protein engineering. Since it is not present on the determined structures, it is essential to automatically define the membrane embedded protein region in order to test mutation effects or to design potential drugs. beta-Barrel transmembrane proteins, present in nature as outer membrane proteins (OMPs), comprise one of the two transmembrane protein fold classes. Lately, the number of their determined structures has increased and this enables the implementation and evaluation of structure-based annotation methods and their more comprehensive study. In this paper, we propose two new algorithms for (i) the geometric modelling of beta-barrels and (ii) the detection of the transmembrane region of a beta-barrel transmembrane protein. The geometric modelling algorithm combines a non-linear least square minimization method and a genetic algorithm in order to find the characteristics (axis, radius) of a shape with axial symmetry which best models a beta-barrel. The transmembrane region is detected by profiling the external residues of the beta-barrel along its axis in terms of hydrophobicity and existence of aromatic and charged residues. TbB-Tool implements these algorithms and is available in . A non-redundant set of 22 OMPs is used in order to evaluate the algorithms implemented and the results are very satisfying. In addition, we quantify the abundance of all amino acids and the average hydrophobicity for external and internal beta-stranded residues along the axis of beta-barrel, thus confirming and extending other researchers' results.     

Properties and performance of BaxSr1−xCo0.8Fe0.2O3−δ materials for oxygen transport membranes

The present paper discusses the oxygen transport properties, oxygen stoichiometry, phase stability, and chemical and mechanical stability of the perovskites (BSCF) and (SCF) for air separation applications. The low oxygen conductive brownmillerite phase in SCF is characterized using in-situ neutron diffraction, thermographic analysis and temperature programmed desorption but this phase is not present for BSCF under the conditions studied. Although both materials show oxygen fluxes well above 10 ml/cm²·min at T=1,273 K and pO₂=1 bar for self-supporting, 200 μm-thick membranes, BSCF is preferred as a membrane material due to its phase stability. However, BSCF’s long-term stable performance remains to be confirmed. The deviation from ideal oxygen stoichiometry for both materials is high: δ>0.6. The thermal expansion coefficients of BSCF and SCF are 24×10⁻⁶ and 30×10⁻⁶ K⁻¹, respectively, as determined from neutron diffraction data. The phenomenon of kinetic demixing has been observed at pO₂<10⁻⁵ bar, resulting in roughening of the surface and enrichment with alkaline earth metals. Stress–strain curves were determined and indicated creep behavior that induces undesired ductility at T=1,073 K for SCF. Remedies for mechanical and chemical instabilities are discussed.     

Precoloring extension on unit interval graphs

In the precoloring extension problem a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [Precoloring extension. III. Classes of perfect graphs, Combin. Probab. Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete on unit interval graphs.     

The Gold Partition Conjecture

We present the Gold Partition Conjecture which immediately implies the – Conjecture and tight upper bound for sorting. We prove the Gold Partition Conjecture for posets of width two, semiorders and posets containing at most elements. We prove that the fraction of partial orders on an -element set satisfying our conjecture converges to when approaches infinity. We discuss properties of a hypothetical counterexample.     

基于明暗度分类和改进二分法的车牌字符分割

车牌字符分割易受到车牌倾斜及边界、杂点的干扰,致使复杂条件下的车牌图像分割准确率不高,针对该缺点提出一种鲁棒性强的分割算法。在车牌预处理阶段进行图像明暗度分类及灰度图增强,以此为基础进行倾斜校正及上下边界定位;在字符切分阶段采用改进二分法进行分割,之后对1,2,6,7四个字符实现了边界精确定位。实验表明,该算法实时性较好,能够有效克服车牌对比度不高、模糊、粘连和倾斜的缺点。     

鄂尔多斯盆地宜川地区上古生界烃源岩评价

依据氢指数（HI）、降解率（PC/TOC）等两个方面的地球化学指标,按照煤系地层烃源岩有机质类型划分标准,对研究区的山西-太原组烃源层的有机质类型作剖析,进行上古生界烃源岩系统评价。研究认为,本溪组烃源岩主要是泥岩,有机质丰度平均2.51%,泥岩干酪根母质类型主体属腐殖型干酪根,即Ⅲ型干酪根;太原组暗色泥岩有机质丰度平均2.26%,煤层比较发育,有机质丰度平均81.66%;山西组的泥岩比较发育,泥岩有机质丰度平均2.26%,煤层有机质丰度平均72.66%。本区上古生界干酪根显微组分都以镜质组为主,显示干酪根母质为腐殖型,即Ⅲ型干酪根,热成熟度演化较高,Ro都大于2.5%,Tmax为490℃以上,表明泥岩已达到过成熟阶段,本区暗色泥岩及煤层属中等—好气源岩,此次烃源岩的认识对该区下一步的勘探提供重要的依据。