Fritz John Necessary Optimality Conditions of the Alternative-Type

An alternative-type version of the Fritz John optimality conditions is established at points not necessarily optimal, which covers situations where no result appearing elsewhere is applicable. As a by-product, a versatile formulation of these necessary Fritz John optimality conditions along with a simple proof is provided. This encompasses several versions appearing in the literature. A variant of the KKT conditions is also presented.     

Optimality conditions for a unified vector optimization problem with not necessarily preordering relations

This paper studies a general vector optimization problem which encompasses those related to efficiency, weak efficiency, strict efficiency, proper efficiency and approximate efficiency among others involving non necessarily preordering relations. Based on existing results about complete characterization by scalarization of the solution set obtained by the same authors, several properties of (generalized) convexity and lower semicontinuity of the composition of the scalarizing functional and the objective vector function are studied. Finally, some optimality conditions are presented through subdifferentials in the convex and nonconvex case.     

Classical and Quantum Theories of Spin

A great effort has been devoted to formulating a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in connecting classical and quantum theories rests in finding a parameter that plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneering works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level, we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail.     

The problem of time in parametrized theories

A common feature of reparametrization invariant theories is the difficulty involved in identifying an appropriate evolution parameter and in constructing a Hilbert space on states. Two well known examples of such theories are the relativistic point particle and the canonical formulation of quantum gravity. The strong analogy between them (specially for minisuperspace models) is considered in order to stress the correspondence between the localization problem and the problem of time, respectively. A possible solution for the first problem was given by the proper time formulation of relativistic quantum mechanics. Thus, we extrapolate the main outlines of such a formalism to the quantum gravity framework. As a consequence, a proposal to solve the problem of time arises.     

Direct Laser Interference Patterning of Zirconia Using Infra-Red Picosecond Pulsed Laser: Effect of Laser Processing Parameters on the Surface Topography and Microstructure

This study investigates the influence of processing parameters when applying direct laser interference patterning (DLIP) on the morphology and microstructure of zirconia surfaces using a 10 ps-pulsed laser source with 1064 nm wavelength. An experimental testing matrix is built with different values of laser fluence (5.7 – 18.2 J cm⁻²) and pulse overlap (66 – 98%). Surface morphology and microstructure are characterized by confocal microscopy and scanning electron microscopy. Homogeneous line-like patterns with periodic spatial repetition of 5.0 µm, with varying depths, widths, and aspect ratio, are fabricated using proper processing parameters (5.7 – 7.6 J cm⁻² and 92 – 96%). Structures with maximum depth of 1.5 µm and sharp edges are obtained (7.6 J cm⁻² and 96% overlap). Ablated regions presented a morphology typical of photophysical ablation mechanism, with signs of molten material at the surface. Sub-micrometric pores and nanodroplets are registered for all conditions, while sub-micrometric cracks developed only for higher fluences. A processing window conducing to homogenous DLIP structures is set based on experimental data. Periodic structures with multiscale topographic features are successfully obtained on zirconia surfaces using DLIP technology in this study. These outcomes open new perspectives for fabrication of multifunctional zirconia surfaces for advanced biomedical and engineering applications.     

Hypersurfaces in the Lorentz-Minkowski space satisfying Lkψ?=?Aψ?+?b

We study hypersurfaces in the Lorentz-Minkowski space \mathbbLⁿ⁺¹{\mathbb{L}^{n+1}} whose position vector ψ satisfies the condition L _k ψ = Aψ + b, where L _k is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed k = 0, . . . , n − 1, A ? \mathbbR^(n+1)×(n+1){A\in\mathbb{R}^{(n+1)\times(n+1)}} is a constant matrix and b ? \mathbbLⁿ⁺¹{b\in\mathbb{L}^{n+1}} is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature, open pieces of totally umbilical hypersurfaces \mathbbSⁿ₁(r){\mathbb{S}^n_1(r)} or \mathbbHⁿ(-r){\mathbb{H}^n(-r)}, and open pieces of generalized cylinders \mathbbS^m₁(r)×\mathbbR^n-m{\mathbb{S}^m_1(r)\times\mathbb{R}^{n-m}}, \mathbbH^m(-r)×\mathbbR^n-m{\mathbb{H}^m(-r)\times\mathbb{R}^{n-m}}, with k + 1 ≤ m ≤ n − 1, or \mathbbL^m×\mathbbS^n-m(r){\mathbb{L}^m\times\mathbb{S}^{n-m}(r)}, with k + 1 ≤ n − m ≤ n − 1. This completely extends to the Lorentz-Minkowski space a previous classification for hypersurfaces in \mathbbRⁿ⁺¹{\mathbb{R}^{n+1}} given by Alías and Gürbüz (Geom. Dedicata 121:113–127, 2006).     

Novel Heat Controller for Thermogenerators Working on Uncontrolled Stoves

This paper describes the development of a thermogenerator designed for uncontrolled firewood household stoves. It was built on BiTe thermoelectric (TE) modules, and it uses a water pot as a cooling device that also serves as a hot water source. An original heat controller was developed; it has low thermal resistance (R) during low-power operation, but its R can be continuously increased according to the stove temperature so that the TE never overheats while its power generation is optimized.     

A High-Valent Non-Heme μ-Oxo Manganese(IV) Dimer Generated from a Thiolate-Bound Manganese(II) Complex and Dioxygen

This study deals with the unprecedented reactivity of dinuclear non-heme Mn^II–thiolate complexes with O₂, which dependent on the protonation state of the initial Mn^II dimer selectively generates either a di-μ-oxo or μ-oxo-μ-hydroxo Mn^IV complex. Both dimers have been characterized by different techniques including single-crystal X-ray diffraction and mass spectrometry. Oxygenation reactions carried out with labeled ¹⁸O₂ unambiguously show that the oxygen atoms present in the Mn^IV dimers originate from O₂. Based on experimental observations and DFT calculations, evidence is provided that these Mn^IV species comproportionate with a Mn^II precursor to yield μ-oxo and/or μ-hydroxo Mn^III dimers. Our work highlights the delicate balance of reaction conditions to control the synthesis of non-heme high-valent μ-oxo and μ-hydroxo Mn species from Mn^II precursors and O₂.     

Gibberellic acid production by free and immobilized cells in different culture systems

Gibberellic acid production was studied in different fermentation systems. Free and immobilized cells of Gibberella fujikuroi cultures in shakeflask, stirred and fixed-bed reactors were evaluated for the production of gibberellic acid (GA₃). Gibberellic acid production with free cells cultured in a stirred reactor reached 0.206 g/L and a yield of 0.078 g of GA₃/g biomass.