Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems

We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables and . The Zakharov system is known to be locally well-posed in and the Klein-Gordon-Schrödinger system is known to be locally well-posed in . Here, we show that the Zakharov and Klein-Gordon-Schrödinger systems are globally well-posed in these spaces, respectively, by using an available conservation law for the norm of and controlling the growth of via the estimates in the local theory.

     

Rumor spreading on random regular graphs and expanders

Broadcasting algorithms are important building blocks of distributed systems. In this work we investigate the typical performance of the classical and well‐studied push model. Assume that initially one node in a given network holds some piece of information. In each round, every one of the informed nodes chooses independently a neighbor uniformly at random and transmits the message to it. In this paper we consider random networks where each vertex has degree d ≥ 3, i.e., the underlying graph is drawn uniformly at random from the set of all d ‐regular graphs with n vertices. We show that with probability 1 ‐ o(1) the push model broadcasts the message to all nodes within (1 + o(1))C_d lnn rounds, where Particularly, we can characterize precisely the effect of the node degree to the typical broadcast time of the push model. Moreover, we consider pseudo‐random regular networks, where we assume that the degree of each node is very large. There we show that the broadcast time is (1 + o(1))Clnn with probability 1 ‐ o(1), where \begin{align*}C = \lim_{d\to\infty}C_d = \frac{1}{\ln2} + 1\end{align*}. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Modules over quantaloids: Applications to the isomorphism problem in algebraic logic and π-institutions

We solve the isomorphism problem in the context of abstract algebraic logic and of π-institutions, namely the problem of when the notions of syntactic and semantic equivalence among logics coincide. The problem is solved in the general setting of categories of modules over quantaloids. We introduce closure operators on modules over quantaloids and their associated morphisms. We show that, up to isomorphism, epis are morphisms associated with closure operators. The notions of (semi-)interpretability and (semi-)representability are introduced and studied. We introduce cyclic modules, and provide a characterization for cyclic projective modules as those having a g-variable. Finally, we explain how every π-institution induces a module over a quantaloid, and thus the theory of modules over quantaloids can be considered as an abstraction of the theory of π-institutions.     

Bounds tightening based on optimality conditions for nonconvex box-constrained optimization

First-order optimality conditions have been extensively studied for the development of algorithms for identifying locally optimal solutions. In this work, we propose two novel methods that directly exploit these conditions to expedite the solution of box-constrained global optimization problems. These methods carry out domain reduction by application of bounds tightening methods on optimality conditions. This scheme is implicit and avoids explicit generation of optimality conditions through symbolic differentation, which can be memory and time intensive. The proposed bounds tightening methods are implemented in the global solver BARON. Computational results on a test library of 327 problems demonstrate the value of our proposed approach in reducing the computational time and number of nodes required to solve these problems to global optimality.     

Formation of alkane‐phosphonic acid self‐assembled monolayers on alumina: an in situ SPR study

The formation process of n‐alkane phosphonic acid CH₃ (CH₂)_n?1 PO(OH)₂ (n = 10,12,14,18) self‐assembled monolayers (SAMs), deposited from ethanol solutions on aluminum oxide, has been monitored in situ using surface plasmon resonance (SPR) spectroscopy. In addition, the two‐solvent approach is used to obtain both film thickness and refractive index of the fully formed adsorbed layers. A densely packed adsorbed layer is formed only for the longest molecules with n = 18. The chain length and solution concentration dependence of formation kinetics are studied, and the existence of two distinct kinetic steps is revealed. Fittings of the experimental results with various kinetic models are performed. Our analysis suggests that during the first kinetic step, a transition from a lying‐down to a standing‐up phase takes place, and the growth of this standing‐up phase is governed by second‐order kinetics. The second slow kinetic step is described by a modified first‐order Langmuir law. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis of 2D Germanane (GeH): a New,Fast, and Facile Approach

Germanane (GeH), a germanium analogue of graphane, has recently attracted considerable interest because its remarkable combination of properties makes it an extremely suitable candidate to be used as 2D material for field effect devices, photovoltaics, and photocatalysis. Up to now, the synthesis of GeH has been conducted by substituting Ca by H in a β‐CaGe₂ layered Zintl phase through topochemical deintercalation in aqueous HCl. This reaction is generally slow and takes place over 6 to 14 days. The new and facile protocol presented here allows to synthesize GeH at room temperature in a significantly shorter time (a few minutes), which renders this method highly attractive for technological applications. The GeH produced with this method is highly pure and has a band gap (E_g) close to 1.4 eV, a lower value than that reported for germanane synthesized using HCl, which is promising for incorporation of GeH in solar cells.     

Investigation of the incorporation of electrolyte anions in porous anodic Al2O3 films by employing a suitable probe catalytic reaction

A new method has been developed capable of describing the incorporation of electrolyte anions along the pore wall surface and across both the barrier layer and the pore wall oxide after the establishment of the steady state of growth of porous anodic Al₂O₃ where other methods cannot be applied to obtain reliable results. The knowledge of the nature/composition of anodic oxides as regards the incorporation of species like electrolyte anions is of specific importance for both the understanding of the electrochemical mechanism of oxide production and growth and the scientific and technological applications of porous anodic Al₂O₃ films. The method consists of the selection and use of a suitable catalytic probe reaction on porous anodic oxides at thicknesses varying from a value near zero up to the maximum limiting thickness and the treatment of the experimental reaction rate results by a properly developed mathematical formalism. This method was employed in anodic Al₂O₃ films prepared in H₂SO₄ anodizing electrolyte at a constant bath temperature and different current densities using as a probe reaction the decomposition of HCOOH on these oxides, which is almost exclusively a dehydration reaction, at relatively high reaction temperatures, 350 °C and 390 °C, where the effect of other species except SO₄ ²⁻ incorporated in the oxide on the reaction rate is eliminated. It has been shown that the fraction of the intercrystallite surfaces occupied by SO₄ ²⁻ follows a parabola-like distribution. It has a significant value at the pore base surface, depending on the current density, then it passes through a maximum along the pore wall surface and across both the barrier layer and the pore walls near the pore bases at positions depending on the current density and then becomes almost zero at the mouths of the pores of the oxide with the maximum limiting thickness and at both the Al₂O₃/Al interface and cell boundaries. The maximum value of the surface coverage is almost independent of the current density and is always near 1, showing an almost complete saturation of intercrystalline surfaces at these positions. The above distribution of surface coverage predicts a qualitatively similar distribution of the SO₄ ²⁻ bulk concentration across both the barrier layer and pore wall oxide around the pore bases. The method may be improved and developed further either for a more detailed investigation of the above films or to investigate films prepared in other pore-forming electrolytes. Received: 30 July 1998 / Accepted: 30 September 1998     

Fabrication of hollow titania microspheres with tailored shell thickness

Submicron hollow spheres are an interesting class of materials that receive significant attention nowadays. Closed and mechanically robust homogeneous hollow titania microspheres with as much shell thickness as 130 nm were fabricated by coating polystyrene beads with titania nanoparticles using sol–gel chemistry and subsequently removing the core either via heating or a chemical dissolution process. The thickness of the titania shell deposited on polystyrene core was finely tuned between 100 and 130 nm by varying the concentration of titania precursor, i.e., Ti(OEt)₄ salt from 0.5 to 2 mM during the coating process. The obtained hybrid core–shell particles and hollow microspheres were characterized by scanning electron microscopy, transmission electron microscopy, infrared spectroscopy, X-ray diffraction, and thermo-gravimetric analysis. The approach employed is well suited to the preparation of titania-coated polystyrene hybrid particles and hollow titania spheres, which can find their applications as novel building blocks with unique optical properties for fabrication of advanced materials, catalyst, and drug delivery system.     

Synthesis of novel tantalum oxide sub-micrometer hollow spheres with tailored shell thickness

Sub-micrometer-sized hollow tantalum oxide (Ta2O5) spheres with tunable shell thickness and void size have been fabricated exploiting beta-diketone-functionalized polystyrene (PS) beads as sacrificial templates in a sol-gel process. First, a controlled precipitation of Ta2O5 nanoparticles was carried out on the template surface by hydrolyzing tantalum ethoxide (Ta(OEt)5) at room temperature, and subsequently, the polymer core was removed either via chemical treatment with toluene or calcination at 650 degrees C. The thickness of the tantala shell precipitated on the PS core during the coating process was tuned between 100 and 142 nm by varying the concentration of tantala precursor in the reaction media. The obtained Ta2O5-coated PS particles and hollow microspheres were characterized by scanning electron microscopy, transmission electron microscopy, infrared spectroscopy, X-ray diffraction, and thermogravimetric analysis. Due to the unique optical and dielectric properties, these nanostructured materials are envisaged to be used in applications such as novel building blocks for the fabrication of advanced materials, surface coatings, catalysts, and drug delivery systems.