Instability in a delay-PDE model of earthquake occurrence

Summary Ductile deformation prior to brittle fracture in rocks causes fracture to take place with a time delay after the critical stress for fracture is reached, in the presence of an increasing load stress. We discuss the stability of a stochastic model of interactive earthquake occurrence under the influence of time delays resulting from the ductile process. A threshold for oscillatory behavior is found for large enough coupling and discrete time delays. The system is stable if the time delays are spread over a broad time interval, even for large coupling.     

A general converse theorem for mean‐value theorems in linear elasticity

We prove a rather general mean‐value formula in the theory of elasticity, which expresses the value of the displacement at the centre of a sphere in terms of certain combinations of integral averages over the sphere itself of the traction and the displacement. We also establish the corresponding converse to this mean‐value formula under minimal smoothness assumptions on the displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

Nitro- and fluoropolyformals. III. Copolyformals from mixtures of fluoro- and nitro-α,ω-diols

Polyformals of fluoro-, nitramine-, and C-nitrodiols show widely differing properties with respect to glass transition temperature, melting transition, and solubility. Polymers with desirable combinations of these properties, e.g., low T_g, high nitro content, and good solubility in polar solvents, were expected to result from acid-promoted copolycondensation of appropriate mixtures of diols with formaldehyde. A series of such condensations were carried out and the polymers obtained from binary mixtures of fluoro- and nitrodiols, different nitrodiols, and fluoro- or nitrodiols and carboranediols, were characterized by GPC, ¹H-NMR, and DSC analysis.     

Convergence of series of translations

For a mean zero norm one sequence (f _n )L ₂[0, 1], the sequence (f _n {nx+y}) is an orthonormal sequence inL ₂([0, 1]²); so if , then converges for a.e. (x, y)[0, 1]² and has a maximal function inL ₂([0, 1]²). But for a mean zerofL ₂[0, 1], it is harder to give necessary and sufficient conditions for theL ₂-norm convergence or a.e. convergence of . Ifc _n 0 and , then this series will not converge inL ₂-norm on a denseG subset of the mean zero functions inL ₂[0, 1]. Also, there are mean zerofL[0, 1] such that never converges and there is a mean zero continuous functionf with a.e. However, iff is mean zero and of bounded variation or in some Lip() with 1/2<1, and if |c _n | = 0(n ^–) for >1/2, then converges a.e. and unconditionally inL ₂[0, 1]. In addition, for any mean zerof of bounded variation, the series has its maximal function in allL _p[0, 1] with 1p<. Finally, if (f _n )L [0, 1] is a uniformly bounded mean zero sequence, then is a necessary and sufficient condition for to converge for a.e.y and a.e. (x _n )[0, 1]. Moreover, iffL [0, 1] is mean zero and , then for a.e. (x _n )[0, 1], converges for a.e.y and in allL _p [0, 1] with 1p<. Some of these theorems can be generalized simply to other compact groups besides [0, 1] under addition modulo one.     

De novo design of a redox-active minimal rubredoxin mimic

Metal-binding sites in metalloproteins frequently occur at the interfaces of elements of secondary structure, which has enabled the retrostructural analysis of natural proteins and the de novo design of helical bundles that bind metal ion cofactors. However, the design of metalloproteins containing beta-structure is less well developed, despite the frequent occurrence of beta-conformations in natural metalloproteins. Here, we describe the design and construction of a beta-protein, RM1, that forms a stable, redox-active 4-Cys thiolate Fe(II/III) site analogous to the active site of rubredoxin. The protein folds into a beta-structure in the presence and absence of metal ions and binds Fe(II/III) to form a redox-active site that is stable to repeated cycles of oxidation and reduction, even in an aerobic environment.     

The ambient gamma dose-rate and the inventory of fission products estimations with the soil samples collected at Canadian embassy in Tokyo during Fukushima nuclear accident

In this study, soil samples were collected at Canadian embassy in Tokyo (about 300 km from Fukushima) on 23 March and 23 May of 2011 for purposes of estimating concentrations of radionuclides in fallout, the total fallout inventory, the depth distribution of radionuclide of interest and the elevated ambient gamma dose-rate at this limited location. Some fission products and actinides were analyzed using gamma-ray spectrometry, alpha spectrometry and liquid scintillation counting. The elevated activity concentration levels of ¹³¹I, ¹³²I, ¹³⁴Cs, ¹³⁷Cs, ¹³⁶Cs, ¹³²Te, ¹²⁹mTe, ¹²⁹Te, ¹⁴⁰Ba and ¹⁴⁰La were measured by the gamma-ray spectrometer in the first sample collected on 23 March. Two months after the accident, the ¹³⁴Cs and ¹³⁷Cs became only detectable nuclides. A mass relaxation depth of 3.0 g/cm² was determined by the activities on the depth distribution of ¹³⁷Cs in a soil core. The total fallout inventory was thus calculated as 225 kBq/m² on March sampling date and 25 kBq/m² on May sampling date. The ambient gamma dose-rates in the sampling area estimated by the fallout fission products inventory and ¹³⁷Cs depth distribution ranged from 184 to 38 nGy/h. There was no detectable americium or plutonium in the soil samples by alpha spectrometry. Although ⁹⁰Sr or ⁸⁹Sr were detected supposedly as a result of this accident, it was less than the detection limit, which was about 0.4 Bq/kg in the soil samples.