ON MULTIPLICATION AND COMULTIPLICATION MODULES

This article deals with some results concerning multiplication and comultipli- cation modules over a commutative ring.

ON ALMOST PRIME SUBMODULES

In this article, we define almost prime submodules as a new generalization of prime and weakly prime submodules of unitary modules over a commutative ring with identity. We study some basic properties of almost prime submodules and give some characterizations of them, especially for （finitely generated faithful） multiplication modules.

INTERSECTION OF PRIME SUBMODULES AND DIMENSION OF MODULES

The aim of this paper is to study the conditions by which a P-prime sub-module can be expressed as a finite intersection or union of P-prime submodules. Also corresponding to dimension and rank of modules, some equivalent conditions for a ring to be a Dedekind domain are given.

Creation of Multiple Subwavelength Focal Spot Segments Using Phase Modulated Radially Polarized Multi Gaussian Beam

Based on the vector diffraction theory, the effect of complex phase filters on intensity distribution of a radially polarized multi Gaussian beam in the focal region of high NA lens is theoretically investigated. It is observed that a properly designed multi belt complex phase filter can generate subwavelength novel focal patterns including splitting of focal spots and generation of multiple focal spot segments such as eight, six and four focal spots along the optical axis are obtained. We expect that such an investigation is useful for optical manipulation and material processing, multiple high refractive index particle trapping technologies.

Monolithic DWDM source with precise channel spacing

We report a low-cost manufacturing approach for fabricating monolithic multi-wavelength sources for dense wavelength division multiplexing(DWDM)systems that offers high yield and eliminates crystal regrowth and selective area epitaxy steps that are essential in traditional fabrication methods.The source integrates an array of distributed feedback(DFB)lasers with a passive coupler and semiconductor optical amplifier(SOA).Ridge waveguide lasers with sampled Bragg side wall gratings have been integrated using quantum well intermixing to achieve a fully functional four-channel DWDM source with 0.8 nm wavelength spacing and residual errors<0.13 nm.The output power from the SOA is>10 mW per channel making the source suitable for use in passive optical networks(PONs).We have also investigated using multisection phase-shifted sampled gratings to both increase the effective grating coupling coefficient and precisely control the channel lasing wavelength spacing.An 8-channel DFB laser array with 100 GHz channel spacing was demonstrated using a sampled grating with twoπ-phase-shifted sections in each sampling period.The entire array was fabricated by only a single step of electron beam lithography.

Zariski Topologies for Coprime and Second Submodules

Let M be a non-zero module over an associative （not necessarily commutative） ring. In this paper, we investigate the so-called second and coprime submodules of M. Moreover, we topologize the spectrum Spec-s（M） of second submodules of M and the spectrum Spec-c（M） of coprime submodules of M, study several properties of these spaces and investigate their internlay with the algebraic properties of M.

A Prime Submodule Principle

In this paper, we extend the concept of Ako and Ol~ families to submodules, study the behavior of the extended prime submodule principle and use these concepts to give new proofs of some familiar theorems.

Insect group II chitinase OfChtll promotes chitin degradation during larva-pupa molting

The insect group ll chitinase(ChtIl,also known as Cht10)is a unique chitinasewith multiple catalytic and chitin-binding domains.It has been proven genetically to be anessential chitinase for molting.However,Chtll's role in chitin degradation during insectdevelopment remains poorly understood.Obtaining this knowledge is the key to fullyunderstanding the chitin degradation system in insects.Here,we investigated the roleof OfChtll during the molting of Ostrinia furnacalis,a model lepidopteran pest insect.OfChtll was expressed earlier than OfChtI(OfCht5)and OfChi-h,at both the gene andprotein levels during larva-pupa molting as evidenced by quantitative polymerase chainreaction and western blot analyses.A truncated OfChtII,OfChtII-B4C1,was recombinantlyexpressed in Pichia pastoris cells and purified to homogeneity.The recombinant OfChtll-B4C1 loosened compacted chitin particles and produced holes in the cuticle surface asevidenced by scanning electron microscopy.It synergized with OfChtl and OfChi-h whenhydrolyzing insoluble a-chitin.These findings suggested an important role for ChtIl duringinsect molting and also provided a strategy for the coordinatdd degradation of cuticularchitin during insect molting by Chtll,Chtl and Chi-h.

Power distribution analysis for multiple modulation formats in an all-optical sampling wavelength division multiplexing system

An optimal power distribution analysis for an all-optical sampling orthagonal frequency division multiplexing(OFDM) scheme with multiple modulation formats including diferential phase shift keyed(DPSK), diferential quadrature phase shift keyed(DQPSK), and non-return-to-zero(NRZ) is proposed. The noise tolerances of different modulation formats are analyzed, and the optimal input power ratio between phase and intensity modulation formats for the best overall receiving performance is investigated under unchanged total input power. Moreover, this scheme can seamlessly coexist with the traditional WDM channel.

Performance analysis of a low-complexity nonorthogonal multiple access scheme in visible light communication downlinks using pulse modulations

Although Successive Interference Cancellation(SIC)decoding is widely adopted in Nonorthogonal Multiple Access(NOMA)schemes for the recovery of user data at acceptable complexity,the imperfect SIC would cause Error Propagation(EP),which can severely degrade system performance.In this work,we propose an SIC-free NOMA scheme in pulse modulation based Visible Light Communication(VLC)downlinks,including two types of users with different data rate requirements.Low bit-rate users adopt on-off keying,whereas high bit-rate ones use Multiple Pulse Position Modulation(MPPM).The soft decision decoding scheme is exploited by high bit-rate users to decode MPPM signals,which could fundamentally eliminate the detrimental effect of EP;the scheme is also easier and faster to execute compared with the conventional SIC decoding scheme.Expressions of the symbol error rate and achievable data rate for two types of users are derived.Results of the Monte Carlo simulation are provided to confirm the correctness of theoretical results.

Two-Dimensional GaAs/AlGaAs Multiple Quantum Well Spatial Light Modulators

Multiple quantum well spatial light modulators with 128×128 array in 38μm pitch are fabricated using two pproaches, one with an attachment of an optical substrate and another one without. These two fabrication processes are described and compared.