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.     

On ω-limit Sets of Triangular Maps on the Unit Cube

We consider Sturm–Liouville eigenvalue problems of second order with arbitary seperated boundary conditions and perform a suitabl discretization of them. The obtained discrete Sturm–Liouville eigenvalue problems are examined and the asymptotic behavior of their eigenvalue as the norm of the partition tends to zero is investigated.     

直觉I-Fuzzy拓扑空间的杨忠道定理

以L~*-格值上Lukasiewicz蕴含算子为工具引入了直觉I-Fuzzy拓扑空间中导集概念,接着给出它的一些性质,最后证明了直觉I-Fuzzy拓扑空间中导集的杨忠道定理.     

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.     

A Minty variational principle for set optimization

Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so-called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. Löhne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity assumptions. The variational inequality is based on a new Dini directional derivative for set-valued functions which is defined in terms of a “lattice difference quotient.” A residual operation in a lattice of sets replaces the inverse addition in linear spaces. Relationships to families of scalar problems are pointed out and used for proofs. The appearance of improper scalarizations poses a major difficulty which is dealt with by extending known scalar results such as Diewert's theorem to improper functions.     

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.     

Genotyping of exons 1 to 20 in Duchenne muscular dystrophy by universal multiplex PCR and short‐end capillary electrophoresis

One rapid CE method was established to diagnose Duchenne muscular dystrophy (DMD). DMD is a severe recessive inherited disorder frequently caused by gene deletions. Among them, exons 1–20 account for nearly 30% of occurrences. In this study, the universal multiplex PCR was used to enhance the fluorescently labeling efficiency, which was performed only by one universal fluorescent primer. After PCR, a short‐end injection CE (short‐end CE) speeded up the genotyping of the DMD gene. This method involved no extra purification, and was completed within 9 min. The CE conditions contained a polymer solution of 1.5% hydroxylethylcellulose in 1× TBE buffer at 6 kV for separation. This method was applied to test six DMD patients and one healthy male person. The results showed good agreement with those of multiplex ligation‐dependent probe amplification. This method can be applied for clinical diagnosis of DMD disease. Accurate diagnosis of the DMD gene is the best way to prevent the disease.