On uniqueness for nonlinear elliptic equation involving the Pucci's extremal operator

In this article we study uniqueness of positive solutions for the nonlinear uniformly elliptic equation in RN, limr→∞u(r)=0, where denotes the Pucci's extremal operator with parameters 0<λ?Λ and p>1. It is known that all positive solutions of this equation are radially symmetric with respect to a point in RN, so the problem reduces to the study of a radial version of this equation. However, this is still a nontrivial question even in the case of the Laplacian (λ=Λ). The Pucci's operator is a prototype of a nonlinear operator in no-divergence form. This feature makes the uniqueness question specially challenging, since two standard tools like Pohozaev identity and global integration by parts are no longer available. The corresponding equation involving is also considered.     

Modeling the quantum evolution of the universe through classical matter

It is well known that the canonical quantization of the Friedmann–Lemaître–Robertson–Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor $\left<a\right>(t)$ never vanishes and, as $t\rightarrow \infty $ , we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS). We then show that this single fluid with an implict EoS is equivalent to two non-interacting fluids, one of them representing stiff matter with negative energy density. In the case of two non-interacting scalar fields, one of them of the phantom type, we find their potential energy. In both cases we find that quantum mechanics changes completely the configuration of matter for small values of time, by adding a fluid or a scalar field with negative energy density. As time passes, the density of negative energy decreases and we recover the ordinary content of the classical universe. The more the initial wave function of the universe is concentrated around the classical big bang singularity, the more it is necessary to add negative energy, since this type of energy will be responsible for the removal of the classical singularity.     

Hurst exponent footprints from activities on a large structural system

This paper presents Hurst exponent footprints from pseudo-dynamic measurements of significantly varied activities on a damaged bridge structure during rehabilitation through continuous monitoring. The system is interesting due to associated uncertainty in large-scale structures and significant presence of human intervention arising from fundamentally different processes. Investigations into the variation of computed Hurst exponents on time series of limited lengths are carried out in this regard. The Hurst exponents are compared with respect to specific events during the rehabilitation, as well as with the data collection locations. The variations of local Hurst exponents about the values computed for each activity are presented. The scaling of Hurst exponents for different activities is also investigated; these are representative of the extent of multifractality for each event. The extent of multifractality is assessed along with its source and time dependency.     

Forty years of metrology with synchrotron radiation at SURF

The Canadian Light Source, the University of Western Ontario, IBM Canada and BigBangwidth during 2006 developed the Remote Beamline Access (RBA) system. This system was demonstrated using a standalone soft X-ray machine as well on the VESPERS beamline. The RBA system serves as a proof of concept and basis for ScienceStudio, which is now under development.     

A class of methods for diffusion-convection equations

A class of method with a free parameter(s) is considered for the solution of the diffusion–convection equation. This class is obtained using interpolation function approach and so, some classic methods appears when s take specific values. In order to obtain a non–oscillatory numerical solution some restrictions will be placed on s. Choosing two suitable methods of that class, an algorithm will be established and computational requirements will be considered     

Convergence results for a class of nonlinear fractional heat equations

In this article we study various convergence results for a class of nonlinear fractional heat equations of the form $\left\{ \begin{gathered} u_t (t,x) - \mathcal{I}[u(t, \cdot )](x) = f(t,x),(t,x) \in (0,T) \times \mathbb{R}^n , \hfill \\ u(0,x) = u_0 (x),x \in \mathbb{R}^n , \hfill \\ \end{gathered} \right.$ where I is a nonlocal nonlinear operator of Isaacs type. Our aim is to study the convergence of solutions when the order of the operator changes in various ways. In particular, we consider zero order operators approaching fractional operators through scaling and fractional operators of decreasing order approaching zero order operators. We further give rate of convergence in cases when the solution of the limiting equation has appropriate regularity assumptions.     

Electrolyte effects on amorphous and supercooled sugar systems

The purpose of the present work was to analyze the modification of sugar thermal transitions in the presence of salts. Solid systems consisted of freeze-dried solutions of trehalose or sucrose, with or without salts (potassium and magnesium chlorides, acetates or citrates at 5:1 sugar:salt molar ratio). The freeze-dried systems were humidified at water activities 0.22 and 0.43 at 25 °C and then incubated at 70 °C. The presence of electrolytes affected the kinetics of several relaxation phenomena in sugar systems. Trehalose and sucrose crystallization was delayed in systems containing salts and this effect was dependent on water–cation interactions and on the size of the anion, being citrate the most inhibiting anion. The delaying effect of ions on sugar crystallization correlated with the degree of changes observed in the asymmetry of the sugar melting peak, and with the magnitude of enthalpy relaxations. Salts decreased peak and onset temperatures of trehalose melting crystals and increased the difference between these temperatures compared to the system without salt. Systems containing potassium citrate and MgCl₂ showed the highest Δc_p, relaxation enthalpies in the amorphous state and crystallization delay, and reflected higher anomalies in trehalose melting behavior.     

New multifunctional heterobinuclear palladium (II) complexes based on organometallic dithiocarbazate ligands

In the research of new compounds with multifunctional applications, heterobinuclear palladium (II) complexes based on organometallic dithiocarbazates (DTCZs) have been isolated. The organometallic DTCZ ligands of the general formula [{(η⁵-C₅H₄)-CH=NNHC(S)SCH₃}]MLn [MLn = Re (CO)₃ ( 2a ); Mn (CO)₃ ( 2b ); FeCp ( 2c )] were prepared by the reaction between formyl organometallic precursors ( 1a−c ) with S-methyldithiocarbazate. Subsequently, a two-step reaction of 2a−c with: (i) K₂[PdCl₄] and (ii) PPh₃ yielded heterobinuclear complexes [Pd{MLn(η⁵-C₅H₄)-CH=NNHC(S)SCH₃}–(Cl)(PPh₃)] [MLn = Re (CO)₃ ( 3a ); Mn (CO)₃ ( 3b ); FeCp ( 3c )]. All compounds were characterized by conventional spectroscopic techniques (infrared spectroscopy, nuclear magnetic resonance spectroscopy, mass spectrometry and elemental analysis). In addition, the molecular structures of 2a , 2c and 3c were determined by single-crystal X-ray diffraction. The new palladium (II) complexes ( 3a−c ) were evaluated as antiproliferative agents against non-small cell lung cancer cells (H1299 cells). Complexes 3a and 3b containing cyrhetrenyl- and cymantrenyl-DTCZ ligands, respectively, were more active than their ferrocenyl analogue 3c . The activity was associated with the electron-withdrawing properties of the (η⁵-C₅H₄)M (CO)₃ moieties and their better lipophilicity than that of the ferrocenyl analogue. In addition, we studied the capacity of metalloligands ( 2a−c ) and palladium (II) complexes ( 3a−c ) to remove methylene blue in water under UV–visible light irradiation. The results established that the complexes showed moderate efficiency and were less active than their corresponding free ligands.