The growth and composition of anodic films on GaP

Anodic films have been grown on GaP in a variety of buffered anodizing solutions with pH ranging from 3 to 10. The films were grown at constant current densities from 1 to 100 mA/cm². Films with thicknesses in the range 500–1000 Å resulted from the higher current densities. The films were analyzed using the Rutherford backscattering of 1·7–2 MeV ⁴He ions in conjunction with ion channeling. This analysis revealed two distinct types of films; those with uniform composition as a function of depth and those with non-uniform profiles. The uniform films have Ga:P:O composition ratios typically ～1:2:5:8 whereas the non-uniform films have typical integrated Ga:P:O ratios of ～1:1·5:5. In the non-uniform films, which are the majority of those grown, Ga is piled up at the film-electrolyte interface; associated with this Ga excess is a corresponding P deficiency at the interface. This indicates that Ga migrates through the films during anodizing and forms a Ga-rich outer layer. In the uniform films it appears that much of the migrating Ga is continually being dissolved in the electrolyte during anodization.     

High resolution polar Kerr effect measurements of Sr2RuO4: evidence for broken time-reversal symmetry in the superconducting state

The polar Kerr effect in the spin-triplet superconductor Sr2RuO4 was measured with high precision using a Sagnac interferometer with a zero-area Sagnac loop. We observed nonzero Kerr rotations as big as 65 nanorad appearing below Tc in large domains. Our results imply a broken time-reversal symmetry state in the superconducting state of Sr2RuO4, similar to 3He-A.     

A sequential parametric convex approximation method with applications to nonconvex truss topology design problems

We describe a general scheme for solving nonconvex optimization problems, where in each iteration the nonconvex feasible set is approximated by an inner convex approximation. The latter is defined using an upper bound on the nonconvex constraint functions. Under appropriate conditions, a monotone convergence to a KKT point is established. The scheme is applied to truss topology design (TTD) problems, where the nonconvex constraints are associated with bounds on displacements and stresses. It is shown that the approximate convex problem solved at each inner iteration can be cast as a conic quadratic programming problem, hence large scale TTD problems can be efficiently solved by the proposed method.     

Abundance of hilbertian domains

We construct an abundance of Hilbertian domains: LetK be an abelian extension of ? such that {ord(a)|a εG(K/?)} is unbounded, let ? _K be its ring of integers, and lete ≥ 2 be an integer. Then, for almost all σ εG (?) ^e , each ring between ? _K andK · (σ) is Hilbertian.     

Duality and equilibrium prices in economics of uncertainty

A random variable (RV) X is given aminimum selling price (S) $$S_U \left( X \right): = \mathop {\sup }\limits_x \left\{ {x + EU\left( {X - x} \right)} \right\}$$ and amaximum buying price (B) $$B_p \left( X \right): = \mathop {\inf }\limits_x \left\{ {x + EP\left( {X - x} \right)} \right\}$$ whereU(·) andP(·) are appropriate functions. These prices are derived from considerations ofstochastic optimization with recourse, and are calledrecourse certainty equivalents (RCE's) of X. Both RCE's compute the “value” of a RV as an optimization problem, and both problems (S) and (B) have meaningful dual problems, stated in terms of theCsiszár φ-divergence $$I_\phi \left( {p,q} \right): = \sum\limits_{i = 1}^n {q_i \phi \left( {\frac{{p_i }}{{q_i }}} \right)} $$ a generalized entropy function, measuring the distance between RV's with probability vectors p and q. The RCES _U was studied elsewhere, and applied to production, investment and insurance problems. Here we study the RCEB _P, and apply it to problems ofinventory control (where the attitude towards risk determines the stock levels and order sizes) andoptimal insurance coverage, a problem stated as a game between the insurance company (setting the premiums) and the buyer of insurance, maximizing the RCE of his coverage.     

Cyclicity of bicyclic operators and completeness of translates

We study cyclicity of operators on a separable Banach space which admit a bicyclic vector such that the norms of its images under the iterates of the operator satisfy certain growth conditions. A simple consequence of our main result is that a bicyclic unitary operator on a Banach space with separable dual is cyclic. Our results also imply that if is the shift operator acting on the weighted space of sequences , if the weight ω satisfies some regularity conditions and ω(n) = 1 for nonnegative n, then S is cyclic if . On the other hand one can see that S is not cyclic if the series diverges. We show that the question of Herrero whether either S or S* is cyclic on admits a positive answer when the series is convergent. We also prove completeness results for translates in certain Banach spaces of functions on .     

Heterogeneous Electrocatalytic Oxygen Evolution Reaction by a Sol-Gel Electrode with Entrapped Na3[Ru2(μ-CO3)4]: The Effect of NaHCO3

The Na₃[Ru₂(μ-CO₃)₄] complex is acting as a water oxidation catalyst in a homogeneous system. Due to the significance of heterogeneous systems and the effect of bicarbonate on the kinetic, we studied the bicarbonate effect on the heterogeneous electrocatalyst by entrapping the Na₃[Ru₂(μ-CO₃)₄] complex in a sol-gel matrix. We have developed two types of sol-gel electrodes, which differ by the precursor, and are demonstrating their stability over a minimum of 200 electrochemical cycles. The pH increases affected the currents and k_cat for both types of electrodes, and their hydrophobicity, which was obtained from the precursor type, influenced the electrocatalytic process rate. The results indicate that NaHCO₃ has an important role in the catalytic activity of the presented heterogeneous systems; without NaHCO₃, the diffusing species is probably OH⁻, which undergoes diffusion via the Grotthuss mechanism. To the best of our knowledge, this is the first study to present a simple and fast one-step entrapment process for the Na₃[Ru₂(μ-CO₃)₄] complex by the sol-gel method under standard laboratory conditions. The results contribute to optimizing the WSP, ultimately helping expand the usage of hydrogen as a green and more readily available energy source.