Modification of Polylactide Nonwovens with Carbon Nanotubes and Ladder Poly(silsesquioxane)

Electrospun nonwovens of poly(L-lactide) (PLLA) modified with multiwall carbon nanotubes (MWCNT) and linear ladder-like poly(silsesquioxane) with methoxycarbonyl side groups (LPSQ-COOMe) were obtained. MWCNT and LPSQ-COOMe were added to the polymer solution before the electrospinning. In addition, nonwovens of PLLA grafted to modified MWCNT were electrospun. All modified nonwovens exhibited higher tensile strength than the neat PLA nonwoven. The addition of 10 wt.% of LPSQ-COOMe and 0.1 wt.% of MWCNT to PLLA increased the tensile strength of the nonwovens 2.4 times, improving also the elongation at the maximum stress.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Current air quality analytics and monitoring: A review

This review summarizes the different tools and concepts that are commonly applied in air quality monitoring. The monitoring of atmosphere is extremely important as the air quality is an important problem for large communities. Main requirements for analytical devices used for monitoring include a long period of autonomic operation and portability. These instruments, however, are often characterized by poor analytical performance. Monitoring networks are the most common tools used for monitoring, so large-scale monitoring programmes are summarized here. Biomonitoring, as a cheap and convenient alternative to traditional sample collection, is becoming more and more popular, although its main drawback is the lack of standard procedures. Telemonitoring is another approach to air monitoring, which offers some interesting opportunities, such as ease of coverage of large or remote areas, constituting a complementary approach to traditional strategies; however, it requires huge costs.     

Mono-Aryl/Alkylthio-Substituted (Hetero)acenes of Exceptional Thermal and Photochemical Stability by the Thio-Friedel–Crafts/Bradsher Cyclization Reaction

The highly substituted mono-aryl/alkylthio-(hetero)acenes prepared in this study have been found to be thermally more stable (T_decomp.=331–354 °C) than the known di-aryl/alkylthio-substituted acenes by an average of 25 °C. They are also much more photostable at 254 and 365 nm (in both argon and air) than the parent anthracene and other reported anthracenes. The most photostable aryl/alkylthio-anthracenes at 254 nm were found to be 60–70 (in air) and 130 (in argon) times more stable in solution than the unsubstituted anthracene, and much more stable than known EDG/EWG-substituted anthracenes (EDG=electron-donating group, EWG=electron-withdrawing group) with an extended aromatic core. Furthermore, the acenes showed significantly higher photostability at 365 nm in both air and argon. The anthracenes were obtained by the novel thio-Friedel–Crafts/Bradsher cyclization reaction of hitherto unknown [o-(1,3-dithian-2-yl)aryl](aryl)methyl thioethers. The developed approach provides a general access to mono-aryl/alkylthio-substituted (hetero)acene frameworks containing at least three fused (hetero)aromatic rings. The characteristic feature of this approach, which leads to highly substituted acenes, is that the substituents, unlike in other methods, may be introduced at an early stage of the synthesis. DFT and TD-DFT calculations confirmed the stabilizing role of the aryl/alkylthio substituent in the mono-aryl/alkylthio-substituted anthracenes, which are the most stable anthracenes prepared to date. Their high photostability is mainly due to the quenching of singlet oxygen by the acene and the quenching of the acene S₁ state by molecular oxygen.     

Stability of vertices in random boolean cellular automata

Based on computer simulations, Kauffman (Physica D, 10, 145-156, 1984) made several generalizations about a random Boolean cellular automaton which he invented as a model of cellular metabolism. Here we give the first rigorous proofs of two of Kauffman's generalizations: a large fraction of vertices stabilize quickly, consequently the length of cycles in the automaton's behavior is small compared to that of a random mapping with the same number of states; and reversal of the states of a large fraction of the vertices does not affect the cycle to which the automaton moves.     

Cycles in a random graph near the critical point

Let G(n, M) be a graph chosen at random from the family of all labelled graphs with n vertices and M(n) = 0.5n + s(n) edges, where s³(n)n^?2→∞ but s(n) = o(n). We find the limit distribution of the length of shortest cycle contained in the largest component of G(n, M), as well as of the longest cycle outside it. We also describe the block structure of G(n, M) and derive from this result the limit probability that G(n, M) contains a cycle with a diagonal. Finally, we show that the probability tending to 1 as n-→∞ the length of the longest cycle in G(n, M) is of the order s²(n)/n.     

Reliability and expectation bounds for coherent systems with exchangeable components

Sharp upper and lower bounds are obtained for the reliability functions and the expectations of lifetimes of coherent systems based on dependent exchangeable absolutely continuous components with a given marginal distribution function, by use of the concept of Samaniego's signature. We first show that the distribution of any coherent system based on exchangeable components with absolutely continuous joint distribution is a convex combination of distributions of order statistics (equivalent to the k-out-of-n systems) with the weights identical with the values of the Samaniego signature of the system. This extends the Samaniego representation valid for the case of independent and identically distributed components. Combining the representation with optimal bounds on linear combinations of distribution functions of order statistics from dependent identically distributed samples, we derive the corresponding reliability and expectation bounds, dependent on the signature of the system and marginal distribution of dependent components. We also present the sequences of exchangeable absolutely continuous joint distributions of components which attain the bounds in limit. As an application, we obtain the reliability bounds for all the coherent systems with three and four exchangeable components, expressed in terms of the parent marginal reliability function and specify the respective expectation bounds for exchangeable exponential components, comparing them with the lifetime expectations of systems with independent and identically distributed exponential components.