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.

The Primary Radical of a Submodule

In this paper we introduced a definition for the primary radical of a submodule with some of its basic properties. We also define the P-radical submodule and review some results about it. We find a method to characterize the primary radical of a finitely generated submodule of a free module.

Hilbert-Schmidtness of Submodules in H^(2)(D^(2))Containing(z)-β(w)

A closed subspace M of the Hardy space H^(2)(D^(2))over the bidisk is called submodule if it is invariant under multiplication by coordinate functions z and w.Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem.This paper proves that every finitely generated submodule M containing(z)-Φ(w)is Hilbert-Schmidt,where 0(z),p(w)are two finite Blaschke products.

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.

Interval Valued Intuitionistic(S,T)-fuzzy H_ν-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.

Overview on Submodule Topologies,Modeling,Modulation,Control Schemes,Fault Diagnosis,and Tolerant Control Strategies of Modular Multilevel Converters

In the present scenario,modular multilevel converters(MMCs)are considered to be one of the most promising and effective topologies in the family of high-power converters because of their modular design and good scalability;MMCs are extensively used in high-voltage and high-power applications.Based on their unique advantages,MMCs have attracted increasing attention from academic circles over the past years.Several studies have focused on different aspects of MMCs,including submodule topologies,modeling schemes,modulation strategies,control schemes for voltage balancing and circulating currents,fault diagnoses,and fault-tolerant control strategies.To summarize the current research status of MMCs,all the aforementioned research issues with representative research approaches,results and characteristics are systematically overviewed.In the final section,the current research status of MMCs and their future trends are emphasized.

Operational Reliability Model of Hybrid MMC Considering Multiple Time Scales and Multi-state Submodule

Environmental and electrical factors such as wind speed,air temperature and switching frequency have significant influences on the operational reliability of hybrid modular multilevel converter(MMC),which is commonly used for the wind power transmission.However,the existing reliability model of hybrid MMC based on statistics cannot accurately reflect the impact of these factors.In this paper,a new operational reliability model of hybrid MMC is presented.The reliability index of the hybrid MMC is coupled with its operation characteristics by calculating multi-term thermal cycling.In addition,an operation strategy of hybrid MMC is proposed to improve its reliability.The multi-state submodule(SM)is developed,which is capable of bypassing specific faulty power modules instead of the whole SM.Case studies show that the proposed operational reliability model could describe the impact of environmental and electrical factors.Also,the proposed operation strategy can improve the reliability of hybrid IMMC by extending the operation time of SMs.

Modules with Finitely Many Submodules

In this paper, we study modules having only finitely many submodules over any ring which is not necessarily commutative. We try to understand how such a module decomposes as a direct sum. We justify that any module V having only finitely many submodules over any ring A is an extension of a cyclic A-module by a finite A-module. Under some assumptions on A, such as commutativity of A, we prove that an A-module V has finitely many submodules if and only if V can be written as a direct sum of a cyclic A-module having only finitely many A-submodules and a finite A-module.

The Existence of Maximal w^＊-closed Submodules in Nest Algebra Modules

Using the technique of annihilators, we characterize the w^＊-closure of the finite-partition submodule R（N, ～） of a weakly closed nest algebra module U completely; and by virtue of this characterization, we obtain a sufficient and necessary condition for U to have a maximal w^＊-closed submodule.

M_(φ)-type Submodules over the Bidisk

Let H^(2)(D^(2))be the Hardy space over the bidisk D^(2),and let M_(φ)=[(z-φ(w))^(2)]be the submodule generated by(z-φ(w))^(2),whereφ(w)is a function in H∞(w).The related quotient module is denoted by N_(φ)=H^(2)(D^(2))ΘM_(φ).In the present paper,we study the Fredholmness of compression operators S_(z),S_(w) on N_(φ).Whenφ(w)is a nonconstant inner function,we prove that the Beurling type theorem holds for the fringe operator F_(w) on[(z-w)^(2)]Θz[(z-w)^(2)]and the Beurling type theorem holds for the fringe operator Fz on M_(φ)ΘwM_(φ)ifφ(0)=0.Lastly,we study some properties of F_(w) on[(z-w^(2))^(2)]Θz[(z-w^(2))^(2)].

Classification of Hardy Submodules and Characteristic Space Theory（A Brief and Selective Survey）

This paper is a brief and selective survey on classification of Hardy Submodules over the polydisk. The survey reports some progress in classification of Hardy submodules

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.

Prime Submodules and Flat Modules

In this paper, some characterizations of prime submodules in flat modules and, particularly, in free modules are given. Furthermore, the height of prime submodules and some saturated chain of prime submodules are also given.

Group Action on Fuzzy Modules

In this article, we introduce the notion of fuzzy G-module by defining the group action of G on a fuzzy set of a Z-module M. We establish the cases in which fuzzy submodules also become fuzzy G-submodules. Notions of a fuzzy prime submodule, fuzzy prime G-submodule, fuzzy semi prime submodule, fuzzy G-semi prime submodule, G-invariant fuzzy submodule and G-invariant fuzzy prime submodule of M are introduced and their properties are described. The homomorphic image and pre-image of fuzzy G-submodules, G-invariant fuzzy submodules and G-invariant fuzzy prime submodules of M are also established.

On Co-Primarily Packed Modules

Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If where Na is a primary submodule of M for each , then for some . When there exists such that;N is called Strongly Coprimarily Packed submodule. In this paper, we list some basic properties of this concept. We end this paper by explaining the relations between p-compactly packed and coprimarily packed submodules, and also the relations between strongly p-compactly packed and strongly coprimarily packed submodules.

Cancellation of Modules with Finite Goldie Dimension

In this paper, we show that if C is a module with finite Goldie dimension, and A ＋ C≌B ＋ C, then there are essential submodules A＇△ A, B＇△ B such that A＇≌ B＇.

DC Traction Power Supply System Based on Modular Multilevel Converter Suitable for Energy Feeding and De-icing

A novel DC traction power supply system suitable for energy feeding and de-icing is proposed in this paper for an urban rail transit catenary on the basis of the full bridge submodule (FBSM) modular multilevel converter (MMC). The FBSM-MMC is a novel type of voltage source converter (VSC) and can directly control the output DC voltage and conduct bipolar currents, thus flexibly controlling the power flow of the urban rail transit catenary. The proposed topology can overcome the inherent disadvantages of the output voltage drop in the diode rectifier units, increase the power supply distance and reduce the number of traction substations. The flexible DC technology can coordinate multiple FBSM-MMCs in a wide area and jointly complete the bidirectional control of catenary power flow during the operation of the electric locomotive, so as to realize the local consumption and optimal utilization of the recovered braking energy of the train. In addition, the FBSM-MMCs can also adjust the output current when the locomotive is out of service to prevent the catenary from icing in winter. The working modes of the proposed topology are illustrated in detail and the control strategy is specially designed for normal locomotive operations and catenary de-icing. Simulation cases conducted by PSCAD/EMTDC validate the proposed topology and its control strategy.

Research on a Multiport Parallel Type Hybrid Circuit Breaker for HVDC Grids:Modeling and Design

This paper proposes a star type multiport hybrid circuit breaker(Star-HCB)topology for protection of multiterminal DC transmission.Reliability and stability of high voltage DC(HVDC)grids are determined by their capabilities to withstand DC-side faults.In order to maintain reliability of HVDC grids,both ends of each line should be equipped with hybrid circuit breakers(HCB).This method will increase expenditure of the HVDC,especially the meshed topology.The n-port Star-HCB consists of ultra-fast mechanical disconnectors,load current switch and only one transferring branch which is formed by improved half-bridge sub-module.Compared with existing traditional hybrid circuit breakers and other multiport hybrid circuit breakers,the proposed topology can realize the same short-circuit blocking goal using fewer components.Detailed mathematical transient process calculation and timedomain simulation of the proposed Star-HCB are given to verify its superiority.

Dual Zariski Spaces of Modules

Let R be a commutative ring with identity,M be an R-module,L(M)denote the set of all submodules of M and g■(M)\{OM}.For any submodule N of M,we set gV^(d)(N)={K∈g:K■N}and gζ^(d)(M)=(GV^(d)(N):N■L(M)).Consider χ■L(R)\{R},where L(R)is the set of all ideals of R.We set χV(I)=(J∈x:I■J)and χζ(R)={xV(I):I■L(R)}for any ideal I of R.In this paper,we investigate when,for arbitrary χ and g as above,χζ(R)and gζ^(d)(M)form a topology and a semimodule,respectively.We investigate the structure of gζ^(d)(M)in the case that it is a semimodule.