Existence and Multiplicity Results for the Nonlinear Klein-Gordon Equation

In this work, we study the multiplicity of solutions for a stationary nonhomogeneous problem associated to the nonlinear one-dimensional Klein-Gordon Equation. We prove that the existence of positive solutions is equivalent to the solvability of a scalar equation 2F(M) = 1, where F is a real function depending on V. Moreover, we prove some existence and multiplicity results for the Dirichlet problem in the superlinear case.     

A general RLC system with complex values

We study a semilinear second-order ordinary differential equation for a complex valued function Q which describes the evolution of a generalized RLC system over an interval [0,?T?]. We solve the Dirichlet and periodic problems under appropriate conditions. Moreover, we give conditions in order to ensure that any solution satisfying an initial condition Q(0)?=?Q ₀, Q′(0)=?I ₀ is defined over [0,?T?].     

Synthesis and characterization of graphene-based nanocomposites with potential use for biomedical applications

In this paper, GaN nanoparticles were synthesized from the complex Ga(H₂NCONH₂)₆Cl₃ in the flow of NH₃ at a mild temperature (350 °C). Further purification was performed by the ethanol-thermal method. The ethanol-thermal method also prompted the GaN nanoparticles to grow into an anisotropic morphology. XRD patterns reveal that GaN nanoparticles have crystallized in a hexagonal wurtzite structure. TEM observation shows that the average size of the as-prepared nanoparticles is about 5–10 nm. The photoluminescence spectrum exhibits a broad green emission band with a peak at 510 nm. It can be known from the first-principle theoretic simulation by the TDDFT method that this fluorescence emission band is attributed to the hydride defects of V _N-H on the surface of GaN nanoparticles.     

Comparative bioavailability of two zolpidem hemitartrate formulations in healthy human Brazilian volunteers using high-performance liquid chromatography coupled to tandem mass spectrometry

To assess the bioequivalence of two zolpidem hemitartrate formulations in 30 healthy volunteers. Plasma samples were obtained over a 24 h period. Plasma concentrations of zolpidem were analyzed by liquid chromatography coupled to tandem mass spectrometry with positive ion electrospray ionization using multiple reaction monitoring. Values of peak concentration (C_max), area under curve (AUC), half-life, elimination constant, volume of distribution and clearance showed statistically significant differences when comparing women (604.34 ng h/ml, 127.36 ng/ml, 4.4 h, 0.18 1/h, 50.56 L and 8.55 L/h, respectively) and men (276.1 ng h/ml, 70.9 ng/ml, 3.3 h, 0.26 1/h, 91.42 L and 24.34 L/h, respectively), receiving the same dose (5 mg), respectively. The geometric means with corresponding 90% confidence interval for Test/Reference percentage ratios were 99.73% (CI 93.69–106.16) for C_max, 97.44% (90% CI = 91.85–103.37%) for area under curve of plasma concentration until the last concentration observed (AUC_last) and 98.30% (90% CI = 92.48–104.49) for the area under curve between the first sample (pre-dosage) and infinity (AUC_0–inf). Since the 90% CI for AUC_last, AUC_0–inf and C_max ratios were within the 80–125% interval proposed by the US Food and Drug Administration, it was concluded that zolpidem hemitartrate formulation (5 mg orodispersible tablet) is bioequivalent to the zolpidem hemitartrate formulation (Patz SL 5 mg sublingual tablet) with regard to both the rate and the extent of absorption. A new formulation of zolpidem 2.5 mg may be useful in women for the same clinical benefits as the 5 mg formulation in men.     

Palladium‐Catalyzed Intramolecular Carbene Insertion into C(sp3)−H Bonds

A palladium‐catalyzed carbene insertion into C(sp³)?H bonds leading to pyrrolidines was developed. The coupling reaction can be catalyzed by both Pd⁰ and Pd^II, is regioselective, and shows a broad functional group tolerance. This reaction is the first example of palladium‐catalyzed C(sp³)?C(sp³) bond assembly starting from diazocarbonyl compounds. DFT calculations revealed that this direct C(sp³)?H bond functionalization reaction involves an unprecedented concerted metalation–deprotonation step.     

Electronic states of a single layer of pentacene: standing-up and flat-lying configurations

The electronic properties of a single layer (SL) of pentacene molecules are investigated by high-resolution UV photoemission and near-edge X-ray absorption spectroscopy in different configurations of the SL, either standing up on an aromatic self-assembled monolayer or planar on a bare Cu(001) substrate. The weakly interacting pentacene molecules in the standing-up SL present a semiconducting character, and the empty states distribution reflects that of gas-phase pentacene, while the planar pentacene-Cu system shows a metallic interface with redistribution of the empty molecular states. The highest-occupied molecular orbital lineshape in the weakly interacting SL shows a double structure, attributed to two nonequivalent molecules in the ordered configuration.     

Some mathematical properties of gauge transformations with respect to the Coulomb gauge: Variational analysis of an energy functional

As gauge invariance of computed magnetic properties, usually partitioned into diamagnetic and paramagnetic terms, is not achieved within the algebraic approximation, unless ad hoc techniques are adopted, a general variational treatment is analyzed, attempting to minimize the term more difficult to evaluate accurately, i.e., the paramagnetic contribution to magnetic susceptibility, by means of a gauge transformation. It is shown that an absolute minimum in a variational sense cannot be determined a priori. However, a “local” minimum of the paramagnetic contribution to magnetic susceptibility can be arrived at by employing general gauge transformations of polynomial form. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 599–606, 2000     

Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.     

Long correlations and Levy models applied to the study of memory effects in high frequency (tick) data

This work is devoted to the study of long correlations, memory effects and other statistical properties of high frequency (tick) data. We use a sample of 25 stocks for this purpose.We verify that the behavior of the return is compatible with that of continuous time Levy processes. We also study the presence of memory effects and long-range correlations in the values of the return.