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.     

Templating mesoporous silica with chiral block copolymers and its application for enantioselective separation

In this paper we describe the synthesis of chiral mesoporous silica based on chiral block copolymers of poly(ethylene oxide) and of d-phenylalanine (PEO-b-D-Phe) as a surfactant template. The resulting porous structures are characterized by nitrogen sorption experiments, transmission electron microscopy, and small-angle XRD. It is shown that chiral block copolymers of PEO-b-D-Phe are effective as a surfactant template for the preparation of silica materials with highly ordered periodic mesoporous structures of hexagonal symmetry with a pore size of ca. 5 nm and high surface areas of ca. 700 m2/g. The enantioselectivity feature of this porous silica, after the extraction of the chiral copolymers, was examined by selective adsorption of enantiomers and racemic solutions of valine. The selective adsorption was measured by circular dichroism (CD) spectroscopy. A chiral selectivity factor of 2.34 was found with the D enantiomer of valine adsorbed preferably.     

Difference in the bonding scheme of calix(6)arene and p-sulfonic calix(6)arene to nanoparticles of Fe(2)O(3) and Fe(3)O(4)

Calix(6)arene (C6) and p-sulfonic calix(6)arene (p-C6) formed chemical bonds with Fe(2)O(3) and Fe(3)O(4), respectively. The complexes exhibit different nature of bonding of C6 and p-C6 to the substrates.     

Interpreting weak value amplification with a toy realist model

Constructing an ontology for quantum theory is challenging, in part due to measurement back-action. The Aharonov-Albert-Vaidman weak measurement formalism provides a method to predict measurement results (weak values) when back-action is negligible. The weak value appears analogous to a classical conditional mean, yet can be complex and unbounded. We study weak values in the context of a recent quantum optical experiment involving two-photon interactions. The results of the experiment are reinterpreted within a realist ‘stochastic optics’ model of light. We show that the conditional means of the intensities in the model correspond to the experimentally observed weak values and study the breakdown of the model outside the experimentally probed regime in the limit where the weak value predicts ‘anomalous’ results.     

Solvothermal synthesis of nanocrystalline zinc oxide doped with Mn2+, Ni2+, Co2+ and Cr3+ ions

ZnO nanopowders doped with Mn²⁺, Ni²⁺, Co²⁺ and Cr³⁺ ions have been synthesised for the first time using a solvothermal reaction with microwave heating. The nanopowders were produced from a solution of zinc acetate and manganese (II), chromium (III), nickel (II) and cobalt (II) acetates, using ethylene glycol as a solvent. The content of Ni²⁺, Co²⁺ and Cr³⁺ ions in the solution and in the solid phase were close to each other up to 5 mol%. The doping level of Mn²⁺ ions in the solid is about 50% of that in the solution. No phases or compounds other than ZnO were detected by X-ray diffraction with Mn²⁺, Co²⁺ and Ni²⁺ doping. With Cr³⁺ ions a small amount of chromium oxide was found. None of the powders displayed any luminescence after doping. The Mn²⁺-doped powder displayed a paramagnetic behaviour. ESR and magnetisation investigations have revealed that no clustering of Mn²⁺ ions occurred up to a doping level of 3.9 mol%. The average grain size of powders doped with Ni²⁺, Cr³⁺, Co²⁺ and Mn²⁺ for a 10 mol% ion content in the solution was about 20 nm and the grain size dispersion 30%. With increasing dopant content the grain size decreased. It appears that the solvothermal process employed allows relatively high doping levels of the transition metal ions to be achieved without any dopant clustering or oxide precipitation.     

On the problem of vacuum energy in brane theories

We point out that modern brane theories suffer from a severe vacuum energy problem. To be specific, the Casimir energy associated with the matter fields confined to the brane, is stemming from the one and the same localization mechanism which forms the brane itself, and is thus generically unavoidable. Possible practical solutions are discussed, including in particular spontaneously broken supersymmetry, and quantum mechanically induced brane tension.