The dual form of Beck type identities

The Ramanujan Journal - Inspired by Andrews and Merca’s recent work on the number of even parts over all partitions into distinct parts, we introduce a new kind of Beck type identities, which...     

Separation and analysis of triazine herbcide residues by capillary electrophoresis

Triazines are widely used in agriculture around the world as selective pre‐ and post‐emergence herbicides for the control of broad leaf and grassy weeds. With high toxicity and persistence, triazines can contaminate the environment and crops, so the development of rapid and sensitive methods for the determination of different triazines is necessary. Capillary electrophoresis comprises a group of techniques used to separate chemical mixtures. Analytical separation is based on different electrophoretic mobilities. This review focuses on the analysis of triazine herbicides with different modes of capillary electrophoresis, including capillary zone electrophoresis, micellar electrokinetic capillary electrophoresis, capillary electrochromatography and nonaqueous capillary electrophoresis. Determinations of triazines in various matrices such as surface water, groundwater, vegetables, soil and grains are emphasized. Copyright © 2014 John Wiley & Sons, Ltd.     

The behavior of differential forms under purely inseparable extensions

Let F be a field of characteristic 2. In this paper we give a complete computation of the kernel of the homomorphism $H_2^{m+1}(F)?H_2^{m+1}(L)$ induced by scalar extension, where $L/F$ is a purely inseparable extension (of any degree), $H_2^{m+1}(F)$ is the cokernel of the Artin–Schreier operator $?:{\mathrm{\Omega }}_F^m?{\mathrm{\Omega }}_F^m/\mathrm{d}{\mathrm{\Omega }}_F^{m?1}$ given by: $x\frac{\mathrm{d}{x}_1}{x_1}\wedge ?\wedge \frac{\mathrm{d}{x}_m}{x_m}?(x^2?x)\frac{\mathrm{d}{x}_1}{x_1}\wedge ?\wedge \frac{\mathrm{d}{x}_m}{x_m}+\mathrm{d}{\mathrm{\Omega }}_F^{m?1}$, where ${\mathrm{\Omega }}_F^m$ is the space of absolute m-differential forms over F and d is the differential operator. Other related results are included.     

Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Microelectromechanical Systems for Nanomechanical Testing: Electrostatic Actuation and Capacitive Sensing for High-Strain-Rate Testing

Experimental Mechanics - There have been relatively few studies on mechanical properties of nanomaterials under high strain rates, mainly due to the lack of capable nanomechanical testing devices....