Properties of the period function for some Hamiltonian systems and homogeneous solutions of a semilinear elliptic equation

In this work we study the period function T of solutions to the conservative equation x^″(t)+f(x(t))=0. We present conditions on f that imply the monotonicity and convexity of T. As a consequence we obtain the criterium established by C. Chicone and find conditions easier to apply. We also get a condition obtained by Cima, Gasull and Mañosas about monotonicity and, following some of their calculations, present results on the period function of Hamiltonian systems where H(x,y)=F(x)+n^-1|y|ⁿ. Using the monotonicity of T, we count the homogeneous solutions to the semilinear elliptic equation Δu=γu^γ-1 in two dimensions.     

Effects of brain polarization on reaction times and pinch force in chronic stroke

Background  

Previous studies showed that anodal transcranial DC stimulation (tDCS) applied to the primary motor cortex of the affected hemisphere (M1_{affected hemisphere}) after subcortical stroke transiently improves performance of complex tasks that mimic activities of daily living (ADL). It is not known if relatively simpler motor tasks are similarly affected. Here we tested the effects of tDCS on pinch force (PF) and simple reaction time (RT) tasks in patients with chronic stroke in a double-blind cross-over Sham-controlled experimental design.     

Supporting hydrogen based transportation: case studies with Global MARKAL Model

Steadily growing prices of oil and emissions coming from conventional vehicles, might force a switch to an alternative and less polluting fuel in the coming future. In this article we analyze the potential influence of selected factors for successful market penetration of hydrogen fuel cell vehicles in hydrogen based private transportation economy. Using a world scale, full energy system, bottom-up, optimization model (Global MARKAL Model—GMM) we address the possibility of supporting the fuel cell vehicle technology to become competitive in the markets. In a series of optimizations we evaluate the potential influence of governmental supports and the internalization of externalities related to CO₂ and local pollution emissions originating from the transportation sector, as well as preferential crediting options and demonstration projects promoting fuel cell vehicles. The results suggest that the crucial element is the price of fuel cells and their further potential to reduce costs. This reduction of costs may be triggered by governmental support such as direct subsidies to fuel cells, preferential crediting options for the buildup of hydrogen infrastructure as well as penalization of emitters of CO₂ and/or local pollutants.     

Bentonitic earth catalyzed rearrangement of aryl 1,1-dimethylpropargyl ethers. Synthesis of 2,2-dimethyl-2H-1-benzopyrans

Mexican Bentonitic earth (Tonsil) catalyzed the Claisen rearrangement of aryl 1,1-dimethylpropargyl ethers under mild conditions to provide 2,2-dimethyl-2H-1-benzopyrans. The synthesis of encecalin 2f and desmethoxyencecalin 2i , two biologically active products among other natural products ( 2b, 2e ) was performed by this procedure.     

Far infrared reflectivity of narrow band materials

The application of a Fourier spectrometer to the study of the electronic structure in the far infrared of some intermediate valence or heavy fermion materials or of highT _c superconductors showed that FT-reflectivity is a powerful tool of investigation at very low energies. A very careful control of the experimental conditions and of the reference measurements is necessary to eliminate spurious reflectivities.The results show optical transitions at very low energy and permit to evaluate the electronic structures and the effective mass of the carriers in the vicinity of the Fermi level.     

Kinetics of the gas-phase thermal elimination of (β-bromo ethyl)-pyrazole

Pyrazole elimination and vinyl bromide were found as products in the Flash Vacuum Pyrolysis of (β-Bromo ethyl)-pyrazole. To obtain kinetic parameters (E_a) we carried out competitive reactions using (β-chloro ethyl)-pyrazole as an internal standard. A thermochemical study to calculate Δ(ΔH${}_{\text{?}}^{\text{°}}$ ) for this reaction was carried out.     

Functionalized azabicycloalkane amino acids by nitrone 1,3-dipolar intramolecular cycloaddition

[reaction: see text] An efficient and operationally simple method for the synthesis of functionalized azaoxobicyclo[X.3.0]alkane amino acids has been devised. The key step is an intramolecular nitrone cycloaddition on 5-allyl- or 5-homoallylproline that was found to be completely regio- and stereoselective.     

Adsorption of silanes bearing nitrogenated Lewis bases on SiO2/Si (100) model surfaces

The present paper describes the one-pot procedure for the formation of self-assembled thin films of two silanes on the model oxidized silicon wafer, SiO2/Si. SiO2/Si is a model system for other surfaces, such as glass, quartz, aerosol, and silica gel. MALDI-TOF MS with and without a matrix, XPS, and AFM have confirmed the formation of self-assembled thin films of both 3-imidazolylpropyltrimethoxysilane (3-IPTS) and 4-(N-propyltriethoxysilane-imino)pyridine (4-PTSIP) on the SiO2/Si surface after 30 min. Longer adsorption times lead to the deposition of nonreacted 3-IPTS precursors and the formation of agglomerates on the 3-IPTS monolayer. The formation of 4-PTSIP self-assembled layers on SiO2/Si is also demonstrated. The present results for the flat SiO2/Si surface can lead to a better understanding of the formation of a stationary phase for affinity chromatography as well as transition-metal-supported catalysts on silica and their relationship with surface roughness and ordering. The 3-IPTS and 4-PTSIP modified SiO2/Si wafers can also be envisaged as possible built-on-silicon thin-layer chromatography (TLC) extraction devices for metal determination or N-heterocycle analytes, such as histidine and histamine, with "on-spot" MALDI-TOF MS detection.