A note on ∣A∣k summability factors of infinite series

In this note we give an improvement to a recent result obtained by Savas and Rhoade concerning ∣A∣_k summability of infinite series.     

Synthesis, Crystal Structure and ab initio Studies of Cyclohexyl N-Phenylcarbamate

Abstract  

Cyclohexyl N-phenylcarbamate, C₁₃H₁₇NO₂ (I), which is a useful target for biotransformations by fungi, has been synthesized and the structure has been solved by X-ray diffraction. The crystals are triclinic, space group P [`1] \bar{1} , with a = 5.2581 (2) ?, b = 9.5080 (3) ?, c = 12.6165 (4) ?, α = 70.544 (2)°, β = 89.075 (2)°, γ = 80.447 (2)°, M _r = 219.28, V = 585.96 (3) ?³, Z = 2 and R = 0.065. In the title compound the phenyl ring makes a dihedral angle of 30.68(7)° with the carbamate group The molecules are linked into infinite chains via N–H···O hydrogen bonds along the a axis. These hydrogen-bonded chains are further linked by weaker C–H···π interactions. Quantum-mechanical ab initio calculations for the free molecule reproduce well the observed bond lengths and valency angles but show that the crystal packing might be responsible for the rotation of the phenyl ring out of the carbamate plane in the solid state conformation.     

Novel pressure and displacement sensors based on carbon nanotubes

We report newly designed pressure and displacement capacitive sensors based on a flexible paper–CNT structure.The carbon nanotube(CNT)powder was deposited on a thin paper substrate and was pressed at an elevated temperature.The sheet resistance of the paper–CNT films was in the range of 2–4 kΩ/cm2.The paper–CNT films were used to fabricate pressure and displacement sensors.The sensitivities of the pressure and the displacement sensors were found to be17.3 p F·m2/k N and 0.93 10-3p F/μm,respectively.The experimental results were compared with the simulated data and they found good agreement with each other.     

Ecowood Composites Made using Citric-Acidmodified Corn and Oil Palm Starches as the Binder

Mechanics of Composite Materials - The conventional wood-based composites contain an unreacted free formaldehyde, which causes a cancerous effect on humans. To overcome this problem,...     

Study of optoelectronic energy bands and molecular energy levels of tris (8-hydroxyquinolinate) gallium and aluminum organometallic materials from their spectroscopic and electrochemical analysis

For the purpose of investigating electro-molecular absorption bands, energy gaps, E_g and molecular energy levels (ionization potential, IP and electron affinity, EA) of tris (8-hydroxyquinolinate) gallium and aluminum, spectral analysis in conjunction with electrochemical measurements was carried out. UV-Vis-NIR and FTIR spectroscopic measurements were used to assign the electronic and molecular absorption bands in both of the materials. The XRD and scanning electronic microscopy (SEM) technique showed the amorphous nature. From the recorded data of cyclic voltammetry (CV) and materials absorption coefficient, HOMO, LUMO energy levels and energy gaps for Gaq3 and Alq3 were calculated. A bit smaller value of energy gap for Gaq3 (2.80 eV) compared to that of Alq3 (2.86 eV) has been ascribed to the differences in electronic configuration and coordinated bond lengths related to the central metal atom with respect to the quinolinate ligands. A higher value of HOMO energy level for the Alq3 (IP = 6.3 eV) revealed the need of higher potentials to oxidize its molecules comparing to that of Gaq3 (IP = 5.8 eV). It was observed that cationic metals have a direct effect on the physical and chemical behaviors of such organometallic materials that can be exploited to be used in tuning their properties to match the desired application in OSC and/or OLED technologies.     

Dynamic Cross‐Exchange in Halophosphonium Species: Direct Observation of Stereochemical Inversion in the Course of an SN2 Process

The complex fluxional interconversions between otherwise very similar phosphonium bromides and chlorides R₃PX⁺X^? (R=Alk, Ar, X=Cl or Br) were studied by NMR techniques. Their energy barriers are typically ca. 11 kcal mol^?1, but rise rapidly as bulky groups are attached to phosphorus, revealing the importance of steric factors. In contrast, electronic effects, as measured by Hammett analysis, are modest (ρ 1.46) but still clearly indicate negative charge flow towards phosphorus in the transition state. Most significantly, detailed analysis of the exchange pathways unequivocally, and for the first time in any such process, shows that nucleophilic attack of the nucleophilic anion on the tetrahedral centre results in inversion of configuration.     

Modulation instability analysis,optical and other solutions to the modified nonlinear Schrödinger equation

This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrödinger equation, which models the propagation of rogue waves in ocean engineering. The extended Fan sub-equation method with five parameters is used to find exact traveling wave solutions. It has been observed that the equation exhibits a collection of traveling wave solutions for limiting values of parameters. This method is beneficial for solving nonlinear partial differential equations, because it is not only useful for finding the new exact traveling wave solutions, but also gives us the solutions obtained previously by the usage of other techniques (Riccati equation, or first-kind elliptic equation, or the generalized Riccati equation as mapping equation, or auxiliary ordinary differential equation method) in a combined approach. Moreover, by means of the concept of linear stability, we prove that the governing model is stable. 3D figures are plotted for showing the physical behavior of the obtained solutions for the different values of unknown parameters with constraint conditions.     

New lump,lump-kink,breather waves and other interaction solutions to the (3+1)-dimensional soliton equation

This study investigates the (3+1)-dimensional soliton equation via the Hirota bilinear approach and symbolic computations. We successfully construct some new lump, lump-kink, breather wave, lump periodic, and some other new interaction solutions. All the reported solutions are verified by inserting them into the original equation with the help of the Wolfram Mathematica package. The solution's visual characteristics are graphically represented in order to shed more light on the results obtained. The findings obtained are useful in understanding the basic nonlinear fluid dynamic scenarios as well as the dynamics of computational physics and engineering sciences in the related nonlinear higher dimensional wave fields.