A COMMUTATIVITY CONDITION FOR S-UNITAL RINGS

Let R be an s-unital ring, and we prove a commutativity theorem of R satisfying the following conditions: (l ) For each x, y∈ R,there exist bounded positive integers k =k (x,y), s=s (x,y), t =t (x,y)(where, at least one of k, s, t is not equal to 1) such

Finite Groups with Four Relative Commutativity Degrees

It is shown that a finite group G has four relative commutativity degrees if and only if G/Z（G） is a p-group of order p3 and G has no abelian maximal subgroups, or G/Z（G） is a Frobenius group with Frobenius kernel and complement isomorphic to Zp × Zp and Zq, respectively, and the Sylow p-subgroup of G is abelian, where p and q are distinct primes.

Strong Skew Commutativity Preserving Maps on Rings with Involution

Let R be a unital ＊-ring with the unit I. Assume that R contains a symmetric idempotent P which satisfies ARP= 0 implies A = 0 and AR（I - P） = 0 implies A = 0. In this paper, it is shown that a surjective map Ф： R →R is strong skew commutativity preserving （that is, satisfies Ф（A）Ф（B） - Ф（B）Ф（A）＊ ： AB- BA＊ for all A, B ∈R） if and only if there exist a map f ： R → ZSz（R） and an element Z ∈ ZS（R） with Z^2 =I such that Ф（A） =ZA ＋ f（A） for all A ∈ R, where ZS（R） is the symmetric center of R. As applications, the strong skew commutativity preserving maps on unital prime ＊-rings and von Neumann algebras with no central summands of type I1 are characterized.

Two Theorems on the Commutativity of Arbitrary Rings

We prove a theorem on the commutativity of the PI ring and use it to generalize a famous theorem of Herstein.

Weighted multilinear p-adic Hardy operators and commutators on p-adic Herz-type spaces

In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.

Transient AC Overvoltage Suppression Orientated Reactive Power Control of the Wind Turbine in the LCC-HVDC Sending Grid

High-voltage direct current(HVDC) transmission is a crucial way to solve the reverse distribution of clean energy and loads. The line commutated converter-based HVDC(LCCHVDC) has become a vital structure for HVDC due to its high technological maturity and economic advantages. During the DC fault of LCC-HVDC, such as commutation failure, the reactive power regulation of the AC grid always lags the DC control process, causing overvoltage in the AC sending grid, which brings off-grid risk to the wind power generation based on power electronic devices. Nevertheless, considering that wind turbine generators have fast and flexible reactive power control capability, optimizing the reactive power control of wind turbines to participate in the transient overvoltage suppression of the sending grid not only improves the operational safety at the equipment level but also enhances the voltage stability of the system. This paper firstly analyses the impact of wind turbine's reactive power on AC transient overvoltage. Then, it proposes an improved voltage-reactive power control strategy, which contains a reactive power control delay compensation and a power command optimization based on the voltage time series prediction. The delay compensation is used to reduce the contribution of the untimely reactive power of wind turbines on transient overvoltage, and the power command optimization enables wind turbines to have the ability to regulate transient overvoltage, leading to the variation of AC voltage, thus suppressing the transient overvoltage. Finally, the effectiveness and feasibility of the proposed method are verified in a ±800kV/5000MW LCC-HVDC sending grid model based on MATLAB/Simulink.

Impedance Model for Instability Analysis of LCC-HVDCs Considering Transformer Saturation

In line commutated converter based high-voltage direct current(LCC-HVDC)transmission systems,the trans-former saturation can induce harmonic instability,which poses a serious threat to the safe operation of the power system.How-ever,the nonlinear characteristics of the power grids introduced by the transformer saturation considerably limit the application of the conventional analysis methods.To address the issue,this paper derives a linear model for the transformer saturation caused by the DC current due to the converter modulation.Af-terwards,the nonlinear characteristics of power grids with the transformer saturation is described by a complex valued imped-ance matrix.Based on the derived impedance matrix,the sys-tem harmonic stability is analyzed and the mechanism of the transformer saturation induced harmonic instability is revealed.Finally,the sensitivity analysis is conducted to find the key fac-tors that influence the system core saturation instability.The proposed impedance model is verified by the electromagnetic transient simulation,and the simulation results corroborate the effectiveness of the proposed impedance model.Index TermsLine commutated converter based high voltage direct current(LCC-HVDC),transformer saturation,harmonic instability,impedance model.

A Generalization of Torsion Graph for Modules

Let R be a commutative ring with identity and M an R-module. In this paper, we relate a graph to M, say Γ(M), provided tsshat when M=R, Γ(M)is exactly the classic zero-divisor graph.

Commuting Space of Primary and Secondary Schools in the Context of Child Friendly Cities:A Case Study of Bajiao Street of Shijingshan District

With the continuous promotion of the construction of child friendly cities,the school commuting space is an important component of the construction of child friendly roads.Based on the background of child friendly cities,the commuting space of 11 primary and secondary schools in Bajiao Street is analyzed through literature analysis and field research methods.Firstly,the relevant literature on school commuting space is sorted out,and the characteristics of school commuting space are summarized,including transportation,landscape,culture,leisure,and security.Secondly,the characteristics of commuting space of primary and secondary schools in Bajiao Street are analyzed from three aspects:in front of the school gate,path space,and node space.This paper aims to provide reference and guidance for the future construction of children’s walking school commuting and promote the construction of a child friendly city.

The Construction and Analysis of Linear Ring Spaces

This paper proposes the novel algebraic structure of a linear ring space. A linear ring space is an order triad consisting of two rings, and a linear map between the two rings. The definition of quasi-linearity is discussed, in addition to the examination of properties and classifications of linear ring spaces. Particularly, the ring of holomorphic functions on a region of the complex plane is examined, and the manner in which it generates an iterated linear ring space under the complex derivative operator. This notion is then generalized to all rings with nth order linear and surjective operators. Basic operator theory regarding the classifications of linear ring maps is also covered.

Commutativity Conditions for Rings and Generalized 2-CN Rings

Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions:(1)if for each x∈R\N(R)and each y∈R,(xy)^(k)=x^(k)y^(k)for k=m,m+1,n,n+1,where m and n are relatively prime positive integers,then R is commutative;(2)if for each x∈R\J(R)and each y∈R,(xy)^(k)=y^(k)x^(k)for k=m,m+1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented.

A Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces by Using New Commutativity Condition

We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.

Definite Answer for Riemann Hypothesis Zeta 3/2 Function Provided by New Material Yb2Si2O7 in Quantum Mechanics

This paper indicates the problem of the famous Riemann hypothesis (RH), which has been well-verified by a definite answering method using a Bose-Einstein Condensate (BEC) phase. We adopt mathematical induction, mappings, and laser photons governed by electromagnetically induced transparency (EIT) to examine the existence of the RH. In considering the well-developed as Riemann zeta function, we find that the existence of RH has a corrected and self-consistent solution. Specifically, there is the only one pole at s = 1 on the complex plane for Riemann’s functions, which generalizes to all non-trivial zeros while s > 1. The essential solution is based on the BEC phases and on the nature of the laser photon(s). This work also incorporates Heisenberg commutators [ x^,p^]=1/2in the field of quantum mechanics. We found that a satisfactory solution for the RH would be incomplete without the formalism of Heisenberg commutators, BEC phases, and EIT effects. Ultimately, we propose the application of qubits in connection with the RH.

Analysis of Commuting Modal Shift in Consideration of Social Interaction of Consciousness for Environment

It is the matter for achievement of the low carbon transport system that the excessive use of private vehicles can be controlled appropriately.Not only improvement of service level of modes except private vehicle,but also consciousness for environmental problem of individual trip maker is important for eco-commuting promotion.On the other hand,consciousness for environment would be changed by influence of other person.Accordingly,it is aimed in the study that the structure of decision-making process for modal shift to the eco-commuting mode in the local city is described considering environmental consciousness and social interaction.For the purpose,the consciousness for the environment problem and the travel behavior of the commuter at the suburban area in the local city are investigated by the questionnaire survey.The covariance structure about the eco-consciousness is analyzed with the database of the questionnaire survey by structural equation modeling.As the result,it can be confirmed with the structural equation model that the individual environmental consciousness is strongly related with the intention of self-sacrifice and is influenced with the local interaction of the individual connections.On the other hand,the intention of modal shift for the commuting mode is analyzed with the database of the questionnaire survey.It can be found out that the environmental consciousness is not statistically significant for commuting mode choice with the present poor level of service of public transport.However,the intention of self-sacrifice for the prevention of the global warming is statistically confirmed as the factor of modal shift with the operation of eco-commuting bus service with the RP/SP integrated estimation method.As the result,the multi-agent simulation system with social interaction model for eco consciousness is developed to measure the effect of the eco-commuting promotion.For the purpose,the carbon dioxide emission is estimated based on traffic demand and road network condition in the traffic environment model.On the other hand,the relation between agents is defined based on the small world network.The proposed multi-agent simulation is applied to measure the effect of the eco-commuting promotion such as improvement of level of service on the public transport or education of eco-consciousness.The effect of the promotion plan can be observed with the proposed multi-agent system.Finally,it can be concluded that the proposed multi-agent simulation with social interaction for eco-consciousness is useful for planning of eco-commuting promotion.

带有对合的素环的微分恒等式

Let R be a prime ring of characteristic different from two with the second involution∗andαan automorphism of R.An additive mapping F of R is called a generalized(α,α)-derivation on R if there exists an(α,α)-derivation d of R such that F(xy)=F(x)α(y)+α(x)d(y)holds for all x,y∈R.The paper deals with the study of some commutativity criteria for prime rings with involution.Precisely,we describe the structure of R admitting a generalized(α,α)-derivation F satisfying any one of the following properties:(i)F(xx∗)−α(xx∗)∈Z(R),(ii)F(xx∗)+α(xx∗)∈Z(R),(iii)F(x)F(x∗)−α(xx∗)∈Z(R),(iv)F(x)F(x∗)+α(xx∗)∈Z(R),(v)F(xx∗)−F(x)F(x∗)∈Z(R),(vi)F(xx∗)−F(x∗)F(x)=0 for all x∈R.Also,some examples are given to demonstrate that the restriction of the various results is not superfluous.In fact,our results unify and extend several well known theorems in literature.

Research on the Voltage Supporting Capability of Multi-VSC-HVDC Subsystems Operation Strategy to Receiving-end LCC-HVDC Network in Weak AC Grid

For the hybrid multi-infeed HVDC system in which the receiving-end grid is a strong AC grid including LCC-HVDC subsystems and multiple VSC-HVDC subsystems,it has higher voltage support capability.However,for weak AC grid,the voltage support capability of the multi-VSC-HVDC subsystems to the LCC-HVDC subsystem(voltage support capability-mVSCs-LCC)can resist the risk of commutation failure.Based on this consideration,this paper proposes an evaluation index called Dynamic Voltage Support Strength Factor(DVSF)for the hybrid multi-infeed system,and uses this index to qualitatively judge the voltage support capability-mVSCs-LCC in weak AC grid.In addition,the proposed evaluation index can also indirectly judge the ability of the LCC-HVDC subsystem to suppress commutation failure.Firstly,the mathematical model of the power flow of the LCC and VSC networks in the steady-state is analyzed,and the concept of DVSF applied to hybrid multi-infeed system is proposed.Furthermore,the DVSF index is also used to qualitatively judge the voltage support capability-mVSCs-LCC.Secondly,the influence of multiple VSC-HVDC subsystems with different operation strategies on the DVSF is analyzed with reference to the concept of DVSF.Finally,the indicators proposed in this paper are compared with other evaluation indicators through MATLAB simulation software to verify its effectiveness.More importantly,the effects of multi-VSC-HVDC subsystems using different coordinated control strategies on the voltage support capability of the receiving-end LCC-HVDC subsystem are also verified.

THE FRACTIONAL TYPE MARCINKIEWICZ INTEGRALS AND COMMUTATORS ON WEIGHTED HARDY SPACES

This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).

BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THEω-TYPE CALDER′ON-ZYGMUND OPERATOR ON LORENTZ SPACE

In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).

BAND-DOMINATED OPERATORS ON BERGMAN-TYPE SPACES

In this paper,we study band-dominated operators on Bergman-type spaces and prove that the C*-algebra of band-dominated operators is equal to the essential commutant of Toeplitz operators with a symbol in the set of bounded vanishing Lipschitz functions.On the Bergman space and the Fock space,we show that the C*-algebra of band-dominated operators equals the Toeplitz algebra.

BOUNDEDNESS OF THE CALDER´ON COMMUTATOR WITH A ROUGH KERNEL ON TRIEBEL-LIZORKIN SPACES

In this paper,we consider the boundedness on Triebel-Lizorkin spaces for the d-dimensional Calder´on commutator defined by TΩ,af(x)=p.v.∫R_(d)Ω(x−y)/|x−y|^(d+1)(a(x)−a(y))f(y)dy,where Ω is homogeneous of degree zero,integrable on Sd−1 and has a vanishing moment of order one,and a is a function on Rd such that∇a∈L^(∞)(R^(d)).We prove that if 1<p,q<∞andΩ∈L(log L)^(2 q)(S^(d−1))with q=max{1/q,1/q′},then TΩ,a is bounded on Triebel-Lizorkin spaces˙F_(p)^(0)q(R^(d)).