Zebra Factorizations in Free Semigroups

Let $S$ be a semigroup of words over an alphabet $A$. Let $\Omega(S)$ consist of those elements $w$ of $S$ for which every prefix and suffix of $w$ belongs to $S$. We show that $\Omega(S)$ is a free semigroup. Moreover, $S$ is called separative if also the complement $S^c = A^+\setminus S$ is a semigroup. There are uncountably many separative semigroups over $A$, if $A$ has at least two letters. We prove that if $S$ is separative, then every word $w \in A^+$ has a unique minimum factorization $w = z_1z_2 \cdots z_n$ with respect to $\Omega(S)$ and $\Omega(S^c)$, where $z_i \in \Omega(S) \cup \Omega(S^c)$ and $n$ is as small as possible.     

Exciplex intermediates in photoinduced electron transfer of porphyrin-fullerene dyads

The photoinduced electron transfer in differently linked zinc porphyrin-fullerene dyads and their free-base porphyrin analogues was studied in polar and nonpolar solvents with femto- to nanosecond absorption and emission spectroscopies. A new intermediate state, different from the locally excited (LE) chromophores and the complete charge-separated (CCS) state, was observed. It was identified as an exciplex. The exciplex preceded the CCS state in polar benzonitrile and the excited singlet state of fullerene in nonpolar toluene. The behavior of the dyads was modeled by using a common kinetic scheme involving equilibria between the exciplex and LE chromophores. The scheme is suitable for all the studied porphyrin-fullerene compounds. The rates of reaction steps depended on the type of linkage between the moieties. The scheme and Marcus theory were applied to calculate electronic couplings for sequential reactions, and consistent results were obtained.     

Lipid membrane formation by vesicle fusion on silicon dioxide surfaces modified with alkyl self-assembled monolayer islands

Using atomic force microscopy, we have investigated the formation of the dipalmitoylphosphatidylcholine (DPPC) membrane by the vesicle fusion method on SiO2 surfaces modified with self-assembled monolayer (SAM) islands of octadecyltrichlorosilane (OTS) with sizes comparable to those of the vesicles. OTS-SAM islands with various sizes and coverages can be constructed on the SiO2 surfaces prepared by thermal oxidation followed by partial hydroxylation in a H2O2/H2SO4 solution. When vesicles are sufficiently smaller than the SiO2 domains, DPPC bilayers and DPPC/OTS layers form on the SiO2 and OTS domains, respectively. However, the adhesion of larger vesicles onto SiO2 is prevented by the OTS islands; therefore only DPPC/OTS layers form without formation of DPPC bilayers on the SiO2 domains. On surfaces with domains on the scale of tens to hundreds of nanometers, the relative size between the hydrophilic domains and the vesicles becomes an important factor in the membrane formation by the fusion of vesicles.     

Comparative study for differentiation of aquatic humic-type organic constituents by capillary zone electrophoresis using polyvinyl alcohol-coated capillary

Capillary zone electrophoresis (CZE) with UV detection (254 nm) was applied to characterize aquatic dissolved humic matter (DHM) from different environmental sources (lake, river and sea waters, in all 15 different samples). A series of separation examples of DHMs using a polyvinyl alcohol (PVA)-coated silica open tubular capillary were carried out in a phosphate buffer (40 mM) as a background electrolyte at neutral acidity (pH 6.8). The separative power of electropherograms was reasonable and the reproducibility was above the mark. Each electropherogram was characteristic of the corresponding humic sample. Special functional fulvic and humic acids or their overall mixtures separated with XAD, DAX and DEAE sorbing solids as well as the original dissolved organic matter (DOM) were nicely differentiated according to their environmental sources. The PVA coating of open tubular silica capillaries seems to be very potential in electrophoretic characterization and separation of different humic solutes at neutral acidities with low sample concentrations thus permitting a workable technique, in a growing series of CZE studies, for better compared results from different studies.     

Graph theoretic approach to parallel gene assembly

We study parallel complexity of signed graphs motivated by the highly complex genetic recombination processes in ciliates. The molecular gene assembly operations have been modeled by operations of signed graphs, i.e., graphs where the vertices have a sign + or −. In the optimization problem for signed graphs one wishes to find the parallel complexity by which the graphs can be reduced to the empty graph. We relate parallel complexity to matchings in graphs for some natural graph classes, especially bipartite graphs. It is shown, for instance, that a bipartite graph G has parallel complexity one if and only if G has a unique perfect matching. We also formulate some open problems of this research topic.     

The Equation x<Superscript>i</Superscript> = y<Superscript>j</Superscript>z<Superscript>k</Superscript> in a Free Semigroup

The equation xⁱ = y^jz^k has only periodic solutions in a free semigroup. This result was first proven by Lyndon and Schützenberger. We present a very short proof of this classical result. Moreover, we establish that the power of two or more of a primitive word cannot be factorized into conjugates of a different word.     

Intensity fluctuations and degree of polarization in three-dimensional thermal light fields

The normalized intensity fluctuations of arbitrary electromagnetic wave fields obeying Gaussian statistics are expressed in terms of the three-dimensional degree of polarization. This general formulation implies an important physical result concerning the polarization of planar fields and the dimensionality of the formalism. The results are expected to be particularly useful in intensity interferometry.     

Ultra-Wideband Signal Impact on the Performances of IEEE 802.11b and Bluetooth Networks

This paper presents the results of a coexistence study investigating the impact of ultra-wideband (UWB) interference on IEEE 802.11b and Bluetooth networks. The results are based on the experimental test measurements made at the University of Oulu, Finland. Simple high-power UWB transmitters are used to interfere with victim networks. Preliminary results show that only under extreme interference conditions with thousands of equivalent Federal Communications Commission– (FCC)-compliant devices in close proximity, will the IEEE 802.11b and Bluetooth networks experience significant performance degradation. The impact of the UWB interference on the IEEE 802.11b network was insignificant if the distance to UWB transmitters was greater than 40 cm. The impact on Bluetooth was even less noticeable. In our study, several high-power UWB transmitters that greatly exceed the FCC radiation regulations have been used, and the measurement settings presents the worst case scenario because of the very short distance between the interferers and the victim system. Effectively our study approximates the use of thousands of FCC-complaint UWB devices in the same space.     

On Upper Bounds for Minimum Distance and Covering Radius of Non-binary Codes

We consider upper bounds on two fundamental parameters of a code; minimum distance and covering radius. New upper bounds on the covering radius of non-binary linear codes are derived by generalizing a method due to S. Litsyn and A. Tietäväinen lt:newu and combining it with a new upper bound on the asymptotic information rate of non-binary codes. The upper bound on the information rate is an application of a shortening method of a code and is an analogue of the Shannon-Gallager-Berlekamp straight line bound on error probability. These results improve on the best presently known asymptotic upper bounds on minimum distance and covering radius of non-binary codes in certain intervals.