General constructions of biquandles and their symmetries

Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set theoretic solutions of the well-known Yang-Baxter equation. The first half of this paper proposes some natural constructions of biquandles from groups and from their simpler counterparts, namely, quandles. We completely determine all words in the free group on two generators that give rise to (bi)quandle structures on all groups. We give some novel constructions of biquandles on unions and products of quandles, including what we refer as the holomorph biquandle of a quandle. These constructions give a wealth of solutions of the Yang-Baxter equation. We also show that for nice quandle coverings a biquandle structure on the base can be lifted to a biquandle structure on the covering. In the second half of the paper, we determine automorphism groups of these biquandles in terms of associated quandles showing elegant relationships between the symmetries of the underlying structures.     

Real analysis related to the Monge-Ampère equation

In this paper we consider a family of convex sets in , , , , satisfying certain axioms of affine invariance, and a Borel measure satisfying a doubling condition with respect to the family The axioms are modelled on the properties of the solutions of the real Monge-Ampère equation. The purpose of the paper is to show a variant of the Calderón-Zygmund decomposition in terms of the members of This is achieved by showing first a Besicovitch-type covering lemma for the family and then using the doubling property of the measure The decomposition is motivated by the study of the properties of the linearized Monge-Ampère equation. We show certain applications to maximal functions, and we prove a John and Nirenberg-type inequality for functions with bounded mean oscillation with respect to

     

粒度空间约简及其粗糙集模型研究

针对交可约粒度空间中覆盖、基和粒结构的关系,结合偏序关系的哈斯图,给出一种约简粒度空间的方法.另外,通过限定上、下近似算子的取值范围,重新定义了交可约粒度空间上的粗糙集模型,并讨论了其相关性质.     

基于失效情景的应急设施选址问题

非常规突发事件巨大的破坏力以及发生时间、地点和规模的不确定性,使应急系统内设施有可能被破坏而失效,因此选址时必须考虑设施失效情景的发生.给出以最大限度覆盖用户需求为目标,基于失效设施数目具有不确定性情景的设施选址双层随机规划模型;通过计算模型上下界,给出减小规模的等价模型,降低了双层规划求解难度;最后实验验证了模型的合理性,并给出新增选址方案.     

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Universal fluorescent labeling of amplification products using locked nucleic acids

Amplification/hybridization‐based genetic analyses using primers containing locked nucleic acids (LNAs) present many benefits. Here, we developed a novel design for universal fluorescent PCR using LNAs. Universal fluorescent PCR generates intermediate nonlabeled fragments and final fluorescent fragments in a two‐step amplification process that uses locus‐specific primers with universal tails and universal fluorescent primers. In this study, a few standard nucleotides were replaced with LNAs only in the fluorescent universal primers. The sequence of the fluorescent universal primer significantly affected the amplification efficiency. For primers with three LNAs, the fluorescent primers with stable M13(‐47) sequences provided the most efficient signal (approximately tenfold higher than the primers with M13(‐21) sequences at lower Tm values). Moreover, AT‐rich LNA substitutions in the fluorescent primers produced much lower amplification efficiencies than GC‐rich substitutions. GC‐rich LNAs produced greater differences in Tm values among primers, and resulted in the preferential production of fluorescently labeled amplicons. The specificity and sensitivity of LNA‐containing fluorescent primers were assessed by genotyping eight STRs in Japanese individuals, and full STR profiles could be generated using as little as 0.25 ng of genomic DNA. The method permitted clear discrimination of alleles and represents sensitive STR genotyping at a reduced cost.     

Entrapment of pH Universal Indicator into Sol‐Gel Matrix

This study involves the behavior of universal indicator entrapped into the sol‐gel matrix. The encapsulation of universal indicator has been prepared by acid catalyzed sol‐gel reaction of tetraethylorthosilicate (TEOS) in the presence of universal indicator to produce transparent monolithic silica doping with universal indicator. The immobilized universal indicator pH‐indicator shows behavior similar to its solution counterpart. The UV/VIS spectra indicate that the universal indicator retains its structure during the sol‐gel reactions in terms of response to pH. The universal indicator can be regarded as uniformly distributed in the sol‐gel matrix. The use of SDS surfactant has positive effects on the immobilized universal indicator monolithic disk due to homogenizing the polymerizing system. This observation has been confirmed using polarized microscopy.     

Universal point sets for planar three-trees

For every $n\in \mathbb{N}$, we present a set $S_n$ of $O(n^{3/2}\log n)$ points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of $S_n$. This is the first subquadratic upper bound on the cardinality of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.