Abrupt Convergence and Escape Behavior for Birth and Death Chains

We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discrete-time birth-and-death chains on ℤ with drift towards zero. In particular, this includes energy-driven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cut-off paths. Thus, for evolutions defined by one-dimensional energy wells with sufficiently steep walls, cut-off and escape behavior are related by time inversion.     

Effect of sp-hybridized defects on the oscillatory behavior of carbon nanotube oscillators

Using molecular dynamics simulations, we investigate the oscillatory behaviors of carbon nanotube oscillators containing sp³-hybridized defects formed by hydrogen chemisorption. It is found that the presence of these defects significantly affects the kinetic and potential energies of the nanotube systems, which in turn affects their oscillation periods and frequencies. We have also studied the oscillatory characteristics of the oscillators containing sp³-hybridized Stone-Wales defects. Our results show that it is possible to control the motion of the inner nanotube by introducing sp³-hybridized defects on the outer nanotube, which provides a potential way to tune the oscillatory behavior of nanotube oscillators.     

Time and Spacetime: The Crystallizing Block Universe

The nature of the future is completely different from the nature of the past. When quantum effects are significant, the future shows all the signs of quantum weirdness, including duality, uncertainty, and entanglement. With the passage of time, after the time-irreversible process of state-vector reduction has taken place, the past emerges, with the previous quantum uncertainty replaced by the classical certainty of definite particle identities and states. The present time is where this transition largely takes place, but the process does not take place uniformly: evidence from delayed choice and related experiments shows that isolated patches of quantum indeterminacy remain, and that their transition from probability to certainty only takes place later. Thus, when quantum effects are significant, the picture of a classical Evolving Block Universe (‘EBU’) cedes place to one of a Crystallizing Block Universe (‘CBU’), which reflects this quantum transition from indeterminacy to certainty, while nevertheless resembling the EBU on large enough scales.     

Derivations on Real and Complex JB*-Triples

At the regional conference held at the University of California,Irvine, in 1985 [24], Harald Upmeier posed three basic questionsregarding derivations on JB*-triples: (1) Are derivations automatically bounded? (2) When are all bounded derivations inner? (3) Can bounded derivations be approximated by inner derivations? These three questions had all been answered in the binary cases.Question 1 was answered affirmatively by Sakai [17] for C*-algebrasand by Upmeier [23] for JB-algebras. Question 2 was answeredby Sakai [18] and Kadison [12] for von Neumann algebras andby Upmeier [23] for JW-algebras. Question 3 was answered byUpmeier [23] for JB-algebras, and it follows trivially fromthe Kadison–Sakai answer to question 2 in the case ofC*-algebras. In the ternary case, both question 1 and question 3 were answeredby Barton and Friedman in [3] for complex JB*-triples. In thispaper, we consider question 2 for real and complex JBW*-triplesand question 1 and question 3 for real JB*-triples. A real orcomplex JB*-triple is said to have the inner derivation propertyif every derivation on it is inner. By pure algebra, every finite-dimensionalJB*-triple has the inner derivation property. Our main results,Theorems 2, 3 and 4 and Corollaries 2 and 3 determine whichof the infinite-dimensional real or complex Cartan factors havethe inner derivation property.     

Electro-optic detection of femtosecond electromagnetic pulses by use of poled polymers

We report the generation and coherent detection of freely propagating ultrashort baseband electromagnetic pulses. Using optical rectification in ?110? GaAs for wideband emission and electro-optic sampling in a poled polymer for wideband detection, we demonstrate spectral sensitivity that extends from the far infrared (lambda~100 mum) to ~33 THz(lambda = 9 mum) . Over a band of nearly 20 THz, a relatively flat frequency response is observed. We discuss issues that limit the response bandwidth.     

AN INVARIANT FOR HYPERGRAPHS

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Halometallates of 1-methyl-4,4-dimercapto-piperidinium. Evidence of strong hydrogen bonds with participating thiol groups

Chlorometallates of transition and B subgroup elements are readily prepared and precipitated by reaction of the corresponding metallic salts with 1-methyl-4,4-dimercaptopiperidinium chloride. These chlorometallates investigated were [ZnCl₄]^2?, [CdCl₃]^?, [CoCl₄]^2?, [CuCl₅]^3? and [FeCl₄]^2?. Strong SH … Cl interactions, but not NH … Cl, have been evidenced by IR spectroscopy in the zinc, cadmium and cobalt complexes. The SH and NH absorptions are observed at ? 2480 cm^?1 and 3060 cm^?1, respectively. Partial deuteration of the [ZnCl₄]^2? complex with d₁-methanol, shifted these IR signals to 1800 and 2260 cm^?1, clearly evidencing a X-hydrogen type of bond. The SH … Cl interaction is smaller in the [FeCl₄]^2? complex, and practically nonexistent in the [CuCl₅^3? complex.     

Order-preserving representations of the partitions on the finite set

A partial ordering is defined for monotone projections f: N → N, N = {1, 2,…, n}, such that the class of these mappings is a lattice which is isomorphic to the partition lattice. Thus a partition can be uniquely represented by an element of this class of mappings and the partial ordering of partitions is preserved. Algorithms for computing the join and meet of given partitions are presented.     

A new reactivity-based one-pot synthesis of N-acetyllactosamine oligomers

Poly-N-acetyllactosamine oligomer is a type-2 glycan core from which a number of important bioactive glycoconjugates are assembled in vivo. Development of an effective synthesis of N-acetyllactosamine oligomers will therefore provide a new chemoenzymatic entry to this class of complex saccharides. This paper describes the design and synthesis of thioglycoside building blocks, determination of their relative reactivity values, and demonstration of their use in the programmable one-pot synthesis of various N-acetyllactosamine oligomers. Through a combination of segment condensation, the strategy allows for the preparation of larger oligosaccharides with minimal protecting group manipulation, as illustrated in the synthesis of an octasaccharide in a very short period of time.