Evaluation of Poly(Glycidyl Methacrylate) Nanocoating for Chiral Separation with Glu-β-CD as Chiral Selector in Capillary Electrophoresis

In this paper, a capillary coated with poly(glycidyl methacrylate) nanoparticles (PGMA NPs) was prepared and applied to construct a capillary electrophoresis (CE) enantioseparation system with glucosyl-β-cyclodextrin (Glu-β-CD) as a chiral selector. The PGMA NP coating can be easily introduced through a simple ring-opening reaction. Two basic drugs were used as models to evaluate the separation performance of the PGMA coating. Under the optimal conditions selected, the separation of the two enantiomers was obtained.

On n-generalized commutators and Lie ideals of rings

Let [Formula: see text] be an associative ring. Given a positive integer [Formula: see text], for [Formula: see text] we define [Formula: see text], the [Formula: see text]-generalized commutator of [Formula: see text]. By an [Formula: see text]-generalized Lie ideal of [Formula: see text] (at the [Formula: see text]th position with [Formula: see text]) we mean an additive subgroup [Formula: see text] of [Formula: see text] satisfying [Formula: see text] for all [Formula: see text] and all [Formula: see text], where [Formula: see text]. In the paper, we study [Formula: see text]-generalized commutators of rings and prove that if [Formula: see text] is a noncommutative prime ring and [Formula: see text], then every nonzero [Formula: see text]-generalized Lie ideal of [Formula: see text] contains a nonzero ideal. Therefore, if [Formula: see text] is a noncommutative simple ring, then [Formula: see text]. This extends a classical result due to Herstein [Generalized commutators in rings, Portugal. Math. 13 (1954) 137–139]. Some generalizations and related questions on [Formula: see text]-generalized commutators and their relationship with noncommutative polynomials are also discussed.

The fineness properties of Morita contexts

Let [Formula: see text] be a Morita context. For generalized fine (respectively, generalized unit-fine) rings [Formula: see text] and [Formula: see text], it is proved that [Formula: see text] is generalized fine (respectively, generalized unit-fine) if and only if, for [Formula: see text] and [Formula: see text], [Formula: see text] implies [Formula: see text] and [Formula: see text] implies [Formula: see text]. Especially, for fine (respectively, unit-fine) rings [Formula: see text] and [Formula: see text], [Formula: see text] is fine (respectively, unit-fine) if and only if, for [Formula: see text] and [Formula: see text], [Formula: see text] implies [Formula: see text] and [Formula: see text] implies [Formula: see text]. As consequences, (1) matrix rings over fine (respectively, unit-fine, generalized fine and generalized unit-fine) rings are fine (respectively, unit-fine, generalized fine and generalized unit-fine); (2) a sufficient condition for a simple ring to be fine (respectively, unit-fine) is obtained: a simple ring [Formula: see text] is fine (respectively, unit-fine) if both [Formula: see text] and [Formula: see text] are fine (respectively, unit-fine) for some [Formula: see text]; and (3) a question of Cǎlugǎreanu [1] on unit-fine matrix rings is affirmatively answered.

Isomorphism between Endomorphism Rings of Modules over A Semisimple Ring

Our question is what ring R which all modules over R are determined, up to isomorphism, by their endomorphism rings? Examples of this ring are division ring and simple Artinian ring. Any semi simple ring does not satisfy this property. We construct a semi simple ring R but R is not a simple Artinian ring which all modules over R are determined, up to isomorphism, by their endomorphism rings.

Power commuting traces of bilinear maps on invertible elements

Let [Formula: see text] be a unital simple ring. Under a mild technical restriction on [Formula: see text], we characterize bilinear mappings [Formula: see text] satisfying [Formula: see text], and [Formula: see text] for all unit [Formula: see text] and [Formula: see text], where [Formula: see text]. As an application we describe bijective linear maps [Formula: see text] satisfying [Formula: see text] for all invertible [Formula: see text]. Precisely, we will show that [Formula: see text] is an isomorphism.

An Optical Five Channel Demultiplexer-Based Simple Photonic Crystal Ring Resonator for WDM Applications

We have proposed simple ring resonator 5-channel demultiplexer based on optical channel drop filter analysis that is applicable at third communication window (1550 nm) range. Our proposed base filter is the important part in designing the demultiplexer, inclusive one ring resonator contains one square dielectric rod at core. Demultiplexer structure introduced by arranging five filter with different ring core refractive index. Insomuch every ring core have individual refractive index, thus each ring have diverse resonant wavelength. Numerical results by the finite difference time domain (FDTD) method show quality factor (Q) and transmission efficiency of fundamental channel drop filter are 1038 and 93 %, respectively. It is found that transmission efficiency in designed demultiplexer is more than 90 % for each channel; channel spacing is less than 4.2 nm. The average crosstalk value, total footprint of demutiplexer is −17.85 dB, 689.61 μm2, respectively. Small size with a very simple ring design can be benefit in photonic integrated circuit.

Simulative Study of Simple Ring Resonator Based Brewster Plate for Power System operation Stability

<span>This study has outlined the simulative study of simple ring resonator based Brewster plate in the air. The obtained results are achieved with the variations of space length, curvature radius and phase angle of the </span><span>spherical mirror</span><span>. Beam radius criterion and stability parameters are measured with the variations of </span><span>refractive index</span><span> and thickness of Brewster plate in the air. The negative and positive effects of increasing operating parameters are observed on the performance of ring resonator system efficiency. </span>