Linearized Asymptotic Stability for Fractional Differential Equations

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector \{\lambda \in \C : |\arg \lambda| > \frac{\alpha \pi}{2}\} where $\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable

Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

Scalar sextet in the 331 model with right-handed neutrinos

A Higgs sextet is introduced in order to generate Dirac and Majorana neutrino masses in the 331 model with right-handed neutrinos. As will be seen, the present sextet introduction leads to a rich neutrino mass structure. The smallness of neutrino masses can be achieved via, for example, a seesaw limit. The fact that the masses of the charged leptons are not effected by their new Yukawa couplings to the sextet is convenient for generating small neutrino masses.Comment: RevTeX4, 5 pages, no figure. To appear in Phys. Rev. D. Misprints removed (v.2

Solvability of singular integral equations with rotations and degenerate kernels in the vanishing coefficient case

By means of Riemann boundary value problems and of certain convenient systems of linear algebraic equations, this paper deals with the solvability of a class of singular integral equations with rotations and degenerate kernel within the case of a coefficient vanishing on the unit circle. All the possibilities about the index of the coefficients in the corresponding equations are considered and described in detail, and explicit formulas for their solutions are obtained. An example of application of the method is shown at the end of the last section

Novel preconcentration technique for on-line coupling to high-speed narrow-bore capillary gas chromatography: sample enrichment by equilibrium (ab)sorption, II: Coupling to a portable micro gas chromatograph

The technique of equilibrium (ab)sorption has been proven to be a powerful method for preconcentration of gaseous samples for high-speed narrow-bore capillary gas chromatography (GC) in general and field-portable GC instruments, often referred as micro GCs, in particular. Using a simple experimental set-up equipped with the open-tubular enrichment column it is possible to produce a homogeneously enriched sample plug, allowing reproducible injections of an enriched sample into the micro GC. Using a non-polar trapping column enrichment factors found for n-alkanes in the range of C7 to C10 ranged from 15 to 150 and agree well with calculated values. Using a highly retentive Thermocap column, the enrichment factor observed for heptane was above 500. As the use of this new preconcentration method requires only minimum modification of the micro GC, the chromatographic performance of the instrument was not compromised by direct coupling to the preconcentration device. Examples of on-line enrichment with portable micro GC analysis of VOCs from air are shown. These examples clearly demonstrate the potentials of the new method in field analysis