The use of partition polynomial series in Laplace inversion of composite functions with applications in fractional calculus

This paper presents an analytical method towards Laplace transform inversion of composite functions with the aid of Bell polynomial series. The presented results are used to derive the exact solution of fractional distributed order relaxation processes as well as time‐domain impulse response of fractional distributed order operators in new series forms. Evaluation of the obtained series expansions through computer simulations is also given. The results are then used to present novel series expansions for some special functions, including the one‐parameter Mittag‐Leffler function. It is shown that truncating these series expansions when combined with using potential partition polynomials provides efficient approximations for these functions. At the end, the results are shown to be also useful in studying asymptotical behavior of partial Bell polynomials. Numerical simulations as well as analytical examples are provided to verify the results of this paper.     

Coupled nonlinear size-dependent behaviour of microbeams

The nonlinear resonant behaviour of a microbeam, subject to a distributed harmonic excitation force, is investigated numerically taking into account the longitudinal as well as the transverse displacement. Hamilton’s principle is employed to derive the coupled longitudinal-transverse nonlinear partial differential equations of motion based on the modified couple stress theory. The discretized form of the equations of motion is obtained by applying the Galerkin technique. The pseudo-arclength continuation technique is then employed to solve the discretized equations of motion numerically. Different types of bifurcations as well as the stability of solution branches are determined. The numerical results are presented in the form of frequency-response and force-response curves for different sets of parameters. The effect of taking into account the longitudinal displacement is highlighted.     

Nonlinear resonant behavior of microbeams over the buckled state

The present study investigates the nonlinear resonant behavior of a microbeam over its buckled (non-trivial) configuration. The system is assumed to be subjected to an axial load along with a distributed transverse harmonic load. The axial load is increased leading the system to lose the stability via a pitchfork bifurcation; the postbuckling configuration is obtained and the nonlinear resonant response of the system over the buckled state is examined. More specifically, the nonlinear equation of motion is obtained employing Hamilton’s principle along with the modified couple stress theory. The continuous system is truncated into a system with finite degrees of freedom; the Galerkin scheme is employed to discretize the nonlinear partial differential equation of motion into a set of ordinary differential equations. This set of equations is solved numerically employing the pseudo-arclength continuation technique; first a nonlinear static analysis is performed upon this set of equations so as to obtain the onset of buckling (supercritical pitchfork bifurcation) and the buckled configuration of the microbeam. The frequency-response and force-response curves of the system are then constructed over the buckled configurations. A comparison is made between the frequency-response curves obtained by means of the modified couple stress and the classical theories. The effect of different system parameters on the frequency-response and force-response curves is also examined.     

The reaction of 2,4,6-tris(trimethylsiloxy)-1,3,5-triazine with chlorocarbenium ions: a new access to 1-oxa-3-azabutatrienium and 2-azaallenium salts

Chlorocarbenium salts - of the Vilsmeier-Arnold type react with the silylated isocyanuric acid to give 1-oxa-3-azabutatrienium salts under mild conditions. From reactions of diarylchloromethenium salts - with and ketones or tertiary carboxamides high yields of 2-azaallenium salts were obtained. A few chloro substituted 2-azaallenium salts were prepared from and carbonyl compounds. The mechanisms of the new reactions are discussed.     

A Silicon-Based Arrayed Waveguide Grating Operating in Two Communication Channels

Abstract

This article proposes a silicon-based arrayed waveguide grating operating in two wavelength bands simultaneously with central wavelengths of 1,550.12 nm and 1,310.12 nm. If input light to an arrayed waveguide grating consists of wavelengths around 1,550.12 nm, the proposed system will act as a four-channel demultiplexer with channel spacing of 0.8 nm. On the other hand, when input wavelengths are distributed around 1,310.12 nm, the same arrayed waveguide grating will divide the input to seven channels with channel spacing of 0.33 nm.     

A study on spatially extended phase objects using speckle photography

We present an application of an improved speckle photography technique for spatially extended phase objects. A contour mapping of a thin lens displaying its phase variation is presented. A theoretical analysis is investigated followed by the experimental presentation. Reasonable interference fringes are obtained and compared with the fringes obtained for hot air. The phase information of the object is extracted using the point-by-point technique.     

IBMA–metal containing polymers

A new convenient route to metal containing polymers is described. This method involves emulsion co(ter) polymerization of a polar hydrocarbon soluble monomer, N-isobutoxymethylacrylamide (IBMA), with styrene or styrene/butadiene, followed by addition of metals. Metal incorporation is effected by latex or solution techniques. Preparative, atomic adsorption, spectroscopic, film observation, and dilute solution data are presented in support of metal complexation. Structures for the complexes are proposed.     

Circular chromatic index of graphs of maximum degree 3

This paper proves that if G is a graph (parallel edges allowed) of maximum degree 3, then χ′_c(G) ≤ 11/3 provided that G does not contain H₁ or H₂ as a subgraph, where H₁ and H₂ are obtained by subdividing one edge of K (the graph with three parallel edges between two vertices) and K₄, respectively. As χ′_c(H₁) = χ′_c(H₂) = 4, our result implies that there is no graph G with 11/3 < χ′_c(G) < 4. It also implies that if G is a 2‐edge connected cubic graph, then χ′_c(G) ≤ 11/3. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 325–335, 2005     

Predicted rate enhancements of dephosphorylation in functional oximate comicelles

The rate enhancements of dephosphorylation of p-nitrophenyldiphenyl phosphate by comicelles of cetyltrimethylammonium bromide with a functional cosurfactant are due wholly to increased concentration of the nucleophile in the micelle.     

Floating switch with large-signal capability

Electronic switches using field-effect devices are widely used, but suffer from a low ratio of signal-waveform amplitude to control-waveform amplitude. A switch configuration is described using two devices and overcoming this disadvantage.