An integral bound for the strain energy in nonlinear elasticity in terms of the boundary displacements

For the displacement boundary value problem in nonlinear elastostatics with zero body force, an integral bound for the strain energy is obtained in terms of theL ₂-norms of the given boundary displacements and their tangential derivatives (assumed sufficiently small). The constants involved depend upon the strain energy density function and upon the geometry of the domain.     

Selective activation of organic molecules by elemental fluorine

Reactions on tertiary hydrogen atoms, attached to unactivated saturated carbons, are very rare and usually inefficient. The electron density however, of a carbon-tertiary hydrogen bond is relatively high and therefore there is a chance it will react with a strong electrophile. One of the strongest electrophiles existing is, of course, the electrophilic fluorine. Two main sources for such an unusual species exist. One source is the various fluoroxy compounds like CF₃OF or CF₃COOF ant the other is the elemental fluorine itself.Indeed, when fluorine is allowed to react, at low temperatures, with various alkylcyclohexanol esters, a highly regio- and an absolutely stereospecific electrophilic substitution on the tertiary unactivated hydrogen takes place as for example:

The radical pathway possibility of these reactions is excluded and it is believed that they are of ionic nature. By dehydrofluorination, a double bond is introduced in sites that no other reagent is known to do, thus activating the molecule towards further chemical transformations. The influence of the electron-withdrawing group on the reaction center will also be discussed.The described reaction is not restricted only to cyclic compounds as aliphatic chains also react as expected, i.e.

The scope of these unusual reactions in both alicyclic and aliphatic fields will be evaluated.     

Comment on the magnetic interaction in nuclei

The contributions of the relativistic electromagnetic corrections to the Coulomb energy shifts are examined carefully in this note. In previous calculations, some of the terms were neglected or their contributions were not evaluated properly. In this note, we consider the appropriate expressions of the electromagnetic interactions and discuss their contributions to Coulomb energy shifts.     

Anomalous transport in scale-free networks

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.     

Memory in the occurrence of earthquakes

We study the statistics of the recurrence times tau between earthquakes above a certain magnitude M in six (one global and five regional) earthquake catalogs. We find that the distribution of the recurrence times strongly depends on the previous recurrence time tau0, such that small and large recurrence times tend to cluster in time. This dependence on the past is reflected in both the conditional mean recurrence time and the conditional mean residual time until the next earthquake, which increase monotonically with tau0. As a consequence, the risk of encountering the next event within a certain time span after the last event depends significantly on the past, an effect that has to be taken into account in any effective earthquake prognosis.     

Dynamic of the Fluorescence of the Complex Zn++/Bis-N-Carbazolyl-Distyrylbenzene

The discrimination between similar concentrations of the different metal ions is one of the important roles of fluorescent sensors. Here we present the study of the fluorescence dynamic of the chromophore bis-N-carbazolyl-distyrylbenzene (BCDSB) in acetonitrile/water (mmol/L), doped with metal ions such as K+; Ca++; Mg++; Zn++(10 micromol/L). BCDSB has the fluorescence with lambda(max) at 448 nm by excitation at lambda(exc) = 378 nm, lifetime 1.089 ns: quantum yield of the fluorescence is 0.68. With continuation of irradiation fluorescence quenching has been registered for all investigated metal ions. However, in the presence of Zn++ oscillation of the intensity was observed. The energy activation of the oscillation as much as 15 kcal/mol was estimated. We believe, that the specificity of the complex Zn++/BCDSB, is in an asymmetrical structure, formed via binding sites of Zn++ with the electron-enriched binding sites of the BCDSB, excited in n(pi)* state. This asymmetrical complex structure can cause the photoinduced structural fluctuation in the complex coordination.     

Efficient immunization strategies for computer networks and populations

We present an effective immunization strategy for computer networks and populations with broad and, in particular, scale-free degree distributions. The proposed strategy, acquaintance immunization, calls for the immunization of random acquaintances of random nodes (individuals). The strategy requires no knowledge of the node degrees or any other global knowledge, as do targeted immunization strategies. We study analytically the critical threshold for complete immunization. We also study the strategy with respect to the susceptible-infected-removed epidemiological model. We show that the immunization threshold is dramatically reduced with the suggested strategy, for all studied cases.