Second order elliptic boundary value problems in a domain with edges

The spectrum and essential spectrum of the Dirichlet problem for an arbitrary elliptic operator with real constant coefficients are studied,     

Phase Diagrams and the Metathetic Reactions of Schiff Bases

La présence des reactions metathétiques altére le diagramme de phase des cristaux liquides a base(s) de Schiff et á composants multiples. Au lieu d'un point eutetique les diagrammes de phase montrent un minimum. Pour observer ce minimum, la mètathèses doit conduire à des produits à structures homologues. Les bases de Schiff de la famille des p-n-alkoxybenzylaniline-p-n-alkylaniline forment des systèmes homologues si, soit la chaine “alkyl,” soit la chaine “alkoxy” (mais pas tous les deux) differe par pas plus d'une unitè de méthyléne.     

Unique Maximum Matching Algorithms

We consider the problem of testing the uniqueness of maximum matchings, both in the unweighted and in the weighted case. For the unweighted case, we have two results. First, given a graph with n vertices and m edges, we can test whether the graph has a unique perfect matching, and find it if it exists, in O(m log⁴ n) time. This algorithm uses a recent dynamic connectivity algorithm and an old result of Kotzig characterizing unique perfect matchings in terms of bridges. For the special case of planar graphs, we improve the algorithm to run in O(n log n) time. Second, given one perfect matching, we can test for the existence of another in linear time. This algorithm is a modification of Edmonds' blossom-shrinking algorithm implemented using depth-first search. A generalization of Kotzig's theorem proved by Jackson and Whitty allows us to give a modification of the first algorithm that tests whether a given graph has a unique f-factor, and find it if it exists. We also show how to modify the second algorithm to check whether a given f-factor is unique. Both extensions have the same time bounds as their perfect matching counterparts. For the weighted case, we can test in linear time whether a maximum-weight matching is unique, given the output from Edmonds' algorithm for computing such a matching. The method is an extension of our algorithm for the unweighted case.     

A large volume, portable, real-time PCR reactor

A point-of-care, diagnostic system incorporating a portable thermal cycler and a compact fluorescent detector for real-time, polymerase chain reaction (PCR) on disposable, plastic microfluidic reactors with relatively large reaction volume (ranging from 10 μL to 100 μL) is described. To maintain temperature uniformity and a relatively fast temperature ramping rate, the system utilizes double-sided heater that features a master, thermoelectric element and a thermal waveguide connected to a second thermoelectric element. The waveguide has an aperture for optical coupling between a miniature, fluorescent reader and the PCR reaction chamber. The temperature control is accomplished with a modified, feedforward, variable structural proportional-integral-derivative controller. The temperature of the liquid in the reaction chamber tracks the set-point temperature with an accuracy of ± 0.1 °C. The transition times from one temperature to another are minimized with controllable overshoots (< 2 °C) and undershoots (< 5 °C). The disposable, single-use PCR chip can be quickly inserted into a thermal cycler/reader unit for point-of-care diagnostics applications. The large reaction chamber allows convenient pre-storing of dried, paraffin-encapsulated PCR reagents (polymerase, primers, dNTPs, dyes, and buffers) in the PCR chamber. The reagents are reconstituted "just in time" by heating during the PCR process. The system was tested with viral and bacterial nucleic acid targets.     

Noncovalent self-assembly in aqueous medium: Mechanistic insights from time-resolved cryogenic electron microscopy

Supramolecular systems based on noncovalent bonds are adaptive due to the reversible nature of the noncovalent interactions, enabling stimuli responsiveness, self-healing, facile fabrication, and recyclability. There is much effort devoted to developing new synthetic tools in supramolecular chemistry. Progress in mechanistic understanding is of crucial importance for rational design targeting functional noncovalent nanoscale assemblies. So far, insufficient insight into evolution of noncovalent assemblies hindered our ability to make progress in the field.The typical paradigm in the case of non-covalent self-assembling systems involves the concept of rapid equilibration at ambient conditions. However, when strong noncovalent interactions are involved, kinetic control may dominate the outcome of the self-assembly processes. The ability of water to impose very strong hydrophobic interactions leads to slow transformations between different structural motifs, amenable to structural mechanistic studies. Cryo-TEM emerges as a method that enables direct structural analysis via imaging of “frozen” evolving assemblies. In this review we focus on cryo-TEM imaging of intermediate structures that evolve along a supramolecular transformation pathway. The structures investigated were trapped and directly visualized, in some cases with subnanometer resolution. Direct structural information obtained by time-resolved cryo-TEM proves to be critical for mechanistic understanding of complex multistep self-assembly processes. Such knowledge is necessary to address the challenge related to rational design of novel functional self-assembled materials.     

Fully efficient adiabatic frequency conversion of broadband Ti:sapphire oscillator pulses

By adiabatic difference-frequency generation in an aperiodically poled nonlinear crystal-a nonlinear optical analog of rapid adiabatic passage in a two-level atomic system-we demonstrate the conversion of a 110?nm band from an octave-spanning Ti:sapphire oscillator to the infrared, spanning 1550 to 2450?nm, with near-100% internal conversion efficiency. The experiment proves the principle of complete Landau-Zener adiabatic transfer in nonlinear optical wave mixing. Our implementation is a practical approach to the seeding of high-energy ultrabroadband optical parametric chirped pulse amplifiers.     

Neutrino cosmology after WMAP 7-year data and LHC first Z' bounds

The gauge-extended U(1)(C)×SU(2)(L)×U(1)(I(R))×U(1)(L) model elevates the global symmetries of the standard model (baryon number B and lepton number L) to local gauge symmetries. The U(1)(L) symmetry leads to three superweakly interacting right-handed neutrinos. This also renders a B-L symmetry nonanomalous. The superweak interactions of these Dirac states permit ν(R) decoupling just above the QCD phase transition: 175 is < or approximately equal to T(ν(R))(dec)/MeV is < or approximately equal to 250. In this transitional region, the residual temperature ratio between ν(L) and ν(R) generates extra relativistic degrees of freedom at BBN and at the CMB epochs. Consistency with both WMAP 7-year data and recent estimates of the primordial 4He mass fraction is achieved for 3相似文献   

Beta-elimination in the reactions of .CR1R2CR3R4X radicals with metal powders immersed in aqueous solutions

The reactions of several radicals of the type .CR1R2CR3R4X (where X = OH or NH3+) with metal powders that have been immersed in aqueous solutions were studied. The radicals were formed by radiation chemical techniques. One of the products in all these reactions is the corresponding alkene, R1R2C=CR3R4. The results are in accord with a mechanism in which the radicals react with the metals that are forming transients with metal-carbon sigma bonds. The latter transients decompose via two competing reactions: (a) heterolysis of the metal-carbon sigma bond and (b) beta-elimination of X-. Moreover, the dehalogenation of BrCH2CH2NH3+ and ClCH2(CH3)2COH by metal powders was studied. Also in these reactions, the corresponding alkene is one of the products. This result is consistent with the suggestion that, in the dehalogenation reaction, an alkyl radical is formed in the first step. This radical then reacts with the metal. Alternatively, the transients with metal-carbon sigma bonds in the dehalogenation processes might be formed via a concerted mechanism.     

Search for new physics in lepton+photon+X events with 305 pb(-1) of pp collisions at [square root of s] = 1.96 TeV

We present results of a search for anomalous production of events containing a charged lepton (l, either e or mu) and a photon (gamma), both with high transverse momentum, accompanied by additional signatures X, including missing transverse energy (ET) and additional leptons and photons. We use the same selection criteria as in a previous CDF search but with a substantially larger data set, 305 pb(-1), a pp collision energy of 1.96 TeV, and the CDF II detector. We find 42 lgammaET events versus an expectation of 37.3+/-5.4 events. We observe 31 llgamma+X events versus an expectation of 23.0+/-2.7 events. We find no events similar to the run I eegammagammaET event.