Abstract:
This special issue comprises of eleven selected papers from the 3rd International Conference on Ubiquitous Information Management and Communication (ICUIMC 2009). From 358 papers submitted in the conference, 106 papers were selected for presentation. Among them, eleven qualified papers have been selected as the papers for this special issue, which deal with state-of-the-art software technology. Explosive growth of information on the Internet has made data search algorithm a critical issue nowadays. Thus, five papers focus on data search algorithm: “Energy Valid Scope for Location-Dependent Spatial Queries in Mobile Environments,” by Ken C. K. Lee, Wang-Chien Lee, Hong Va Leong, Brandon Unger, and Baihua Zheng, designed an algorithm to compute the valid scope where clients receive the same query result, thus eliminating the waste of sending many LDSQs to the server by nearby clients. “Small Knowledge Canvas: Software for Managing Fragmental Knowledge,” by Akiko Hino and Katsumi Tanaka, introduces the concept of “Small knowledge canvas” to utilize the fragmental knowledge, and thus they design a Web browsing model and context extraction algorithm to enrich the bookmark for personal context. “Improving Search and Information Credibility Analysis from Interaction between Web1.0 and Web2.0 Contents,” by Katsumi Tanaka, Satoshi Nakamura, Hiroaki Ohshima, Yusuke Yamamoto, Yusuke Yanbe, and Makoto Kato, proposes a new idea for improving the Web search performance and increasing the information credibility of search results by the usage of Web 1.0 and Web2.0 contents in a complementary manner. “Pivoted Table Index for Querying Product-Property-Value Information,” by Hyunja Lee and Junho Shim, proposes two storage-schemas: a vertical schema as a primary table structure for the triple information in RDBMS and a pivoted table index created from the basic vertical table as an additional index structure for accelerating query triple (product–attribute–value) information. “Metadata Management for Integration and Analysis of Earth Observation Data,” by Akira Takahashi, Masashi Tatedoko, Toshiyuki Shimizu, Hiroko Kinutani, and Masatoshi Yoshikawa, proposes a conceptual model of earth observation data store and manage earth observation. The model is a simple quintuple with information extracted from conventional data models, and it is used to uniquely determine portions of earth observation data, and thus easy to add annotations to data.

Abstract:
In this paper we will first present a generalization of the wedge product of association schemes to table algebras and give a necessary and sufficient condition for a table algebra to be the wedge product of two table algebras. Then we show that if the duals of two commutative table algebras are table algebras, then the dual of their wedge product is a table algebra, and is also isomorphic to the wedge product of the duals of those table algebras in the reverse order. Some applications to association schemes are also given.

Abstract:
We study the problem of the product property for the Lempert function with many poles and consider some properties of this function mostly for plane domains.

Abstract:
Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning Cross Approximation (CA) algorithm to kernel matrices which merges the merits of PCD and CA, and proves as well as numerically exemplifies that it solves large kernel systems two-order more efficiently than those resorts to regularization. As a by-product, a diagonal-pivoted CA technique is also shown efficient in eigen-decomposition of large covariance matrices in an uncertainty quantification problem.

Abstract:
We prove that the pluricomplex Green function has the product property $g_{D_1\times D_2}=\max\{ g_{D_1},g_{D_2}\}$ for any domains $D_1\subset\Bbb C^n$ and $D_2\subset\Bbb C^m$.

Abstract:
In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks property. A more general inequality for integrals of a class of composite functions is also given by using this property.

Abstract:
We show that the Cartesian product of three hereditarily infinite dimensional compact metric spaces is never hereditarily infinite dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.

Abstract:
We introduce and study a Rokhlin-type property for actions of finite groups on (not necessarily unital) C*-algebras. We show that the corresponding crossed product C*-algebras can be locally approximated by C*-algebras that are stably isomorphic to closed two-sided ideals of the given algebra. We then use this result to prove that several classes of C*-algebras are closed under crossed products by finite group actions with this Rokhlin property.

Abstract:
Let $C$ be an irreducible smooth projective curve defined over an algebraically closed field. We prove that the symmetric product ${\rm Sym}^d(C)$ has the diagonal property for all $d \geq 1$. For any positive integers $n$ and $r$, let ${\mathcal Q}_{{\mathcal O}^{\oplus n}_C}(nr)$ be the Quot scheme parametrizing all the torsion quotients of ${\mathcal O}^{\oplus n}_C$ of degree $nr$. We prove that ${\mathcal Q}_{{\mathcal O}^{\oplus n}_C}(nr)$ has the weak point property.

Abstract:
In this paper we generalize to unbounded convex subsets C of hyperbolic spaces results obtained by W.A. Kirk and R. Espinola on approximate fixed points of nonexpansive mappings in product spaces $(C\times M)_\infty$, where M is a metric space and C is a nonempty, convex, closed and bounded subset of a normed or a CAT(0)-space. We extend the results further, to families $(C_u)_{u\in M}$ of unbounded convex subsets of a hyperbolic space. The key ingredient in obtaining these generalizations is a uniform quantitative version of a theorem due to Borwein, Reich and Shafrir, obtained by the authors in a previous paper using techniques from mathematical logic. Inspired by that, we introduce in the last section the notion of uniform approximate fixed point property for sets C and classes of self-mappings of C. The paper ends with an open problem.