An expansion formula for fractional derivatives of variable order

In this work we extend our previous results and derive an expansion formula for fractional derivatives of variable order. The formula is used to determine fractional derivatives of variable order of two elementary functions. Also we propose a constitutive equation describing a solidifying material and determine the corresponding stress relaxation function.     

2,5-Dihydro-1,2-oxaphosphole Derivatives in the Reaction of 3,3-Disubstituted Allenylphosphonic Amidoesters with Electrophilic Reagents

Abstract

The reaction of 3,3-disubstituted allenylphosphonic amidoesters with halogenes, sulfenyl and selenenylchlorides proceeds with five-membered heterocyclization and formation of 2-N,N-dialkylamino-2,5-dihydro-1,2-oxaphosphole 2-oxides:     

Propagation of surface plasmon polaritons through gradient index and periodic structures

We study propagation of surface electromagnetic waves along a metallic surface covered by various layered dielectric structures. We show that strong radiative losses, typical for scattering of a surface wave, can be considerably suppressed when a single dielectric step is substituted by gradient index or periodic layered structure.     

Wave equation for generalized Zener model containing complex order fractional derivatives

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.     

How Fear of Future Outcomes Affects Social Dynamics

Journal of Statistical Physics - Mutualistic relationships among the different species are ubiquitous in nature. To prevent mutualism from slipping into antagonism, a host often invokes a...     

Polymer-Supported Boron Trifluoride

Polystyrene, cross-linked with 7.8% of divinylbenzene, formed a stable complex in chloroform with boron trifluoride containing 0.11% of boron, while cross-linked polystyrene-4-vinylpyridine resins containing 2–2.5% of pyridine rings formed a stable complex with boron trifluoride, containing 1.04% of boron. Both complexes catalyze conversions of aromatic aldehydes, ketones, and acids with alcohols into corresponding acetals, cyclic ketals, and esters; diphenylmethanol converts into ether. The structure of the alcohol plays an important role, with conversions decreasing in the order 1-butanol, 2-butanol, tert-butanol. Both complexes are very stable and in most cases more reactive than the cross-linked polystyrene-A1C1₃ complex.     

Mechanistic investigation and DFT calculation of the new reaction between S-methylisothiosemicarbazide and methyl acetoacetate

A study on the synthesis and mechanistical aspects of formation of 3-methyl-5-oxo-3-pyrazolin-1-carboxamide (MOPC) starting from S-methylisothiosemicarbazide hydrogen iodide and methyl acetoacetate was performed. In the alkaline aqueous solution, the intermediate methyl acetoacetate S-methylisothiosemicarbazone undergoes substitution of CH₃S^? anion by hydroxide anion, cyclization, carbanion formation, and elimination of methanol, thus yielding corresponding Na-enolate salt of pyrazol-5-one derivative. The structure of the compound obtained after protonation of the formed enolate salt was determined by means of spectroscopic techniques and single-crystal X-ray diffraction analysis. The mechanism of conversion of methyl acetoacetate S-methylisothiosemicarbazone into MOPC was investigated by means of the B3LYP functional, and it was found that the reaction is thermodynamically controlled.     

Low-temperature versus oxygen plasma treatment of water-based TiO2 paste for dye-sensitized solar cells

High-temperature treatment steps in fabrication process of dye sensitized solar cell (DSSC) significantly contribute to the manufacturing costs and limit the use of temperature sensitive substrates. Therefore our aim was to develop a simple method for the preparation of water-based TiO₂ paste. The paste is based on peroxotitanic acid (PTA) sol–gel matrix and commercial TiO₂ nanoparticles (P25). Two fabrication processes to decompose/transform the PTA matrix in the printed TiO₂ layer are explored and combined: annealing at temperatures up to 250 °C and/or oxygen plasma treatment. The results show that the PTA matrix in the paste converts to anatase phase and to some extent also attaches to the TiO₂ nanoparticles P25 acting as an interconnecting network within TiO₂ layer. The transformation of the PTA matrix occurs around 250 °C, but in the presence of TiO₂ nanoparticles P25 it starts already at 120 °C. In addition the results reveal that the crystallization is achievable also solely with the oxygen plasma treatment. The efficiency of the TiO₂ layers, exposed to different post-deposition treatments, is evaluated in DSSCs. The results show that oxygen plasma treatment of the TiO₂ layers could efficiently replace temperature curing at 250 °C. Within this study the DSSCs with the efficiency up to 4.2 % measured under standard test conditions (1,000 W/m², AM1.5, 25 °C) were realized.     

Contactless conductivity detector array for capillary electrophoresis

A CE system featuring an array of 16 contactless conductivity detectors was constructed. The detectors were arranged along 70 cm length of a capillary with 100 cm total length and allow the monitoring of separation processes. As the detectors cannot be accommodated on a conventional commercial instrument, a purpose built set‐up employing a sequential injection manifold had to be employed for automation of the fluid handling. Conductivity measurements can be considered universal for electrophoresis and thus any changes in ionic composition can be monitored. The progress of the separation of Na⁺ and K⁺ is demonstrated. The potential of the system to the study of processes in CZE is shown in two examples. The first demonstrates the differences in the developments of peaks originating from a sample plug with a purely aqueous background to that of a plug containing the analyte ions in the buffer. The second example visualizes the opposite migration of cations and anions from a sample plug that had been placed in the middle of the capillary.