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Technical Notes and CorrespondencesGlobal Stabilization of a Class of Feedforward Systems with Lower-Order NonlinearitiesShihong Ding,Chunjiang Qian,and Shihua LiAbstract—This note considers the problem of global stabilization for aclass of feedforward systems whose nonlinearities are allowed to be lower-order growing,instead of higher-order or linear growing as required by many existing results.To solve the problem,a domination approach is de-veloped to design the stabilizer with a new structure,which is also inte-grated with the adding a power integrator and nested saturation methods.The use of a locally homogeneous stabilizer enables us to relax the growth condition imposed on the nonlinearities and hence enlarges the class of feed-forward systems which are globally stabilizable.Index Terms—Feedforward systems,global stabilization,lower-order nonlinearities.I.I NTRODUCTIONTHIS note considers the global stabilization problem of feedforwardsystems described by_x i =d i x i +1+f i (t;x i +1;...;x n );i =1;...;n 01;_x n =d n u(1)where x =(x 1;...;x n )T2is controlinput,d i ,i =1;...;n are uncertain (possibly time-varying)real pa-rameters satisfying d d i dwith positive constants d and d ,and f i (t;x i +1;...;x n );i =1;...;n 01are continuous unknown func-tions with f i (t;0;...;0)=0.The global stabilization of feedforward systems is a problem of theoretical and practical importance and has at-tracted a great deal of attention from the nonlinear control community.A number of interesting results have been achieved to solve the stabi-lization problem based on two major approaches:the nested saturation design method and the Lyapunov’s direct design method.The nested saturation method was introduced by Teel [1],[2]to globally stabilize a class of nonlinear feedforward systems,and was expanded by many papers,such as [3]–[7].Another effective method for stabilizing feed-forward systems is the forwarding technique [8],[9],[11],[12],which is based on the Lyapunov’s direct design.Both the nested saturation and forwarding methods have been widely used for the stabilization of feedforward systems and many interesting results have been achieved (see surveys in books [13],[14]).Manuscript received March 06,2009;revised August 24,2009.First published January 22,2010;current version published March 10,2010.This work was supported in part by the U.S.National Science Foundation under Grant ECCS-0239105,National Natural Science Foundation of China (Project 60504007),Graduate Innovation Program of Jiangsu Province (Project CX08B_087Z),and the Scientific Research Foundation of Graduate School of Southeast University.Recommended by Associate Editor S.Celikovsky.S.Ding and S.Li are with the School of Automation,Southeast University,Nanjing,Jiangsu 210096,China (e-mail:shihong.ding@;lsh@).C.Qian is with the Department of Electrical and Computer Engineering,Uni-versity of Texas at San Antonio,San Antonio,TX 78249,USA (e-mail:chun-jiang.qian@).Digital Object Identifier 10.1109/TAC.2009.2037455Almost all the aforementioned results on global stabilization of feed-forward systems are based on certain restrictions imposed on the non-linear terms.A common assumption is that the nonlinear functions should satisfy a higher-order growth condition as required in [2].An-other common assumption for the global stabilization of feedforward systems is that the nonlinear terms need some smoothness [3],[6],[15].Nevertheless,the ubiquitous property of all aforementioned conditions is that the nonlinear term f i (t;x i +1;...;x n )should be at least locally linearly growing in variables x i +1;...;x n .An interesting question is to what extent those restrictions can be relaxed to achieve global stabi-lization for the feedforward system (1).For example,is it possible to achieve global stabilization of the following system_x 1=x 2+x 22+x 2=33;_x 2=x 3;_x 3=u (2)using a state-feedback stabilizer?Apparently,the functionf 1(x 2;x 3)=x 22+x 2=33has a nonlinear term x 2=33which is neither higher-order nor continuously differentiable and hence system (2)cannot be handled by existing design methods.In this note,we aim to tackle this question and shall provide a solution to the problem of global stabilization for (1)under a lower-order growth condition.This problem is of theoretical interest since we can enlarge the class of feedforward systems which are globally stabilizable by state feedback.In this note,we introduce a domination approach based on [16],[17],[19]to solve the global stabilization problem of system (1)with lower-order nonlinear terms,which is not solvable by the existing re-sults including [16],[19].Specifically,we first use the technique of adding a power integrator [17]to design a higher-order controller for the linear nominal system.Then using homogeneous properties,we show that the nonlinear system (1)is locally stabilized by the proposed controller even under a lower-order growth stly,we add a series of nested saturations to the higher-order controller obtained for the nominal system.Under the saturated control law,by tuning the sat-uration level,we show that the states of the closed-loop system will enter and stay in a small region where the controller is no longer satu-rated and will finally stabilize system (1).The novelty of the proposed controller lies in its new structure in which most of the controller co-efficients are preset without knowing the nonlinearities and only the saturation level is tunable.Hence,for a family of feedforward systems whose nonlinearities have different growth rates,we can just use the same stabilizer but with different saturation levels.II.P ROBLEM S TATEMENT AND A P RELIMINARY R ESULTThe objective of this note is to design a state feedback controller u (x )which globally stabilizes system (1)in the absence of the commonly required higher-order or linear growth conditions.Specifically,we will show that global stabilization of (1)is achievable under the following assumption.Assumption 2.1:In a neighborhood of the origin,the following in-equalities hold for i =1;...;n 01:j f i (t;x i +1;...;x n )j (j x i +1jpFor simplicity,we assume =p=q with an even number p and an odd number q.Consequentlyr i:=(i01) +1;i=1;...;n+1(4) are ratios of two odd numbers,which will simplify the notation of the controller since(0s)r=0s r.A similar result can be obtained for any real number 0by defining[s]r=sign(s)j s j r[17].Remark2.1:Note that the higher-order growth condition for global stabilization of(1),such as for i=1;...;n01j f i(t;x i+1;...;x n)j (j x i+1j p+111+j x n j p);p>1(5)used in[16]is a special case of Assumption2.1with =0.A distinc-tive feature of Assumption2.1is theflexibility in choosing which enables us to handle a more general class of systems such as(2).How-ever,it should be pointed out that thefirst term j x i+1j px n+ n01=r=rr=r0 )=r=r=r0 )=r0 )=r0 )=r=r0r1 2+ (2r)=r=r0r2x3+ d j 1=r0r2j r2j2r j 1=r2j r1j r1,y= 1=r=r=r0 )=r3 d(2r n0r2)=(2r n)0r+ 1r2(2r n0 )=(2dr1r n)(3 1r2 =(2dr1r n)) =(2r3 21r2r3=(2dr1r n)=(2r).It isobvious that for any constant 2 32( 1):= 1( 1)+n01,thevirtual controller x33=0 2 r2yields_V2 0(n01)( 2r1+ 2r2)+d2 (2r012(x30x33):Following the same line shown in thefirst two steps,we canfindfunctions 33( 1; 2);...; 3n( 1;...; n01)such that for any con-stants 1 31; 2 32( 1);...; n 3n( 1;...; n01)the fol-lowing holds:_Vn(X n)j(6)0(7) 0( 2r1+111+ 2rn)where 1=x1, i=x i0x3i,x3i=0 i01 r i01;i=2;...;n;andV n(X n)=0 )=ri=12ri+n01=r=r0r+111+j x n j p0r).It can be verified thatboth=r=r=rni=12ri+ =rn01i=1(j x i+1jp=r=rn01i=1(j x i+1jp=r=ris homogeneous of degree withrespect to dilation(r)if,for all">0;V("x)="III.G LOBAL S TABILIZATION OF F EEDFORWARD S YSTEMSIn this section,we show that under Assumption 2.1,the problem of global stabilization for system (1)is solvable.Specifically,based on (7)in Section II,we first construct the following bounded control law:u =u n (X n )=0 nr(10)with u 0=0,u i (X i )=0 i [ r )]r,i =1;...;n 01,and (s )=>max ( d +1)=d (r[ d (1+ >max ;...;()+ d+1;2 i n (12);...;r ( d(1+ ());2 j n 01:(13)To show how controller (10)can globally stabilize system (1),we firstintroduce a lemma which will be constantly used in the proof of the main result.Lemma 3.1:Consider the closed-loop system (1)–(10).For i =1;...;n 01,under the condition j x j jr(14)(b )j u i (X i ( t))0u i (X i (t ))j r (1+ j 01);j =i +1;...;n;it canbe seen from (3)thatj f i (1)j rj 1+ i jpr+111+j 1+ n 01j p prpr0rat time instantst k ,i.e.,j x 1(t k )j =rfor all t in a time interval [t k ;t k +1],by continuity ofthe solution,x 1(t k )and x 1(t k +1)have the same sign,i.e.,x 1(t k ) r or x 1(t k ) 0 r ,which in turn implies j u 1(x 1(t k ))0u 1(x 1(t k +1))j =0by the property of saturation function.Hence,we only need to consider the time interval [t k ;t k +1]where j x 1(t )j r.First,by the mean value theorem and the monotone property of s p 01for odd fraction p 1,we have the following inequality:j a p 0b p j p j a 0b j max fj a j p 01;j b j p 01g ;a;b 2I R :(18)Using (18)and the fact that j x r 011j yieldsj u 1(x 1( t 3))0u 1(x 1(t 3))j = 1j x r 1( t 3)0x r 1(t 3)j 1r 2r 1j x 1( t3)0x 1(t 3)j :(19)For j x j (t )j (1+ j 01) rtj d 1x 2(s )+f 1(s;x 2(s );...;x n (s ))j ds[ d(1+ 1)+1] r +( t30t 3)with 1( 1):=( 1r 2=r 1)[ d(1+ 1)+1].This together with (17)and;j =2;...;nj u 1(x 1( t))0u 1(x 1(t ))j 1( 1) r ;j =i;...;nj u i 01(X i 01( t))0u i 01(X i 01(t ))j i 01(1) r ;j =i +1;...;n:(22)Similar to what we did in the initial step,for any final point u i (X i ( t))and starting point u i (X i (t )),we list time series t k ;k =1;2;...;N ,such that j x i (t k )0u i 01(X i 01(t k ))j = rk =0j u i (X i (t k ))0u i (X i (t k +1))j :(23)If j x i (t )0u i 01(X i 01(t ))jr;8t 2[t k ;t k +1].In one of such intervals [t 3; t 3]where j x i (t )0u i 01(X i 01(t ))jr[x i ( t 3)0u i 01(X i 01( t 3))]r0[(x i (t 3)0u i 01(X i 01(t 3)))]ri r i +1ri=r=r:(24)For j x j (t )j (1+ j 01) rtj d i x i +1(s )+f i (s;x i +1(s );...;x n (s ))j ds[ d(1+ i )+1]( t 30t 3) r ;8t 2[t 3; t3],we have j x i (t )j (1+ i 01)r+ ( t30t 3)with i ( 1;...; i )=( i r i +1=r i )[ d(1+ i )+1+ i 01(1)].This together with (23),and+( t 0t )for j x j (t )j (1+ j 01) rg .To this end,we first claim that there exists a time instant t 1such that j x n (t 1)0u n 01(X n 01(t 1))jr=2,for all t 0.We firstconsider the case whenx n (t )0u n 01(X n 01(t ))>r(x n (t )0u n 01(X n 01(t ))=r=rwith which implies that x n (t ) x n (0)0 n r,yieldsrt + n 01r=2;8t 0is also impossible.In conclusion,there exists a time instant t 1such that j x n (t 1)0u n 01(X n 01(t 1))jr;8t t 1:(28)Again,a contradiction argument will be used to prove (28).If (28)is nottrue,there exist two time instants t 012[t 1;+1)and t 0012(t 01;+1)such that x n (t )0u n 01(X n 01(t ))will leave the boundariesr=2at t 01andr at t 001sequentially,i.e.,(a)j x n (t 01)0u n 01(X n 01(t 01))j =r,(c)r;8t 2[t 01;t 001].We first consider the casex n (t 01)u n 01(X n 01(t 01))=r(30)r;t 2[t 01;t 001]:(31)By (31),it can be concluded that for t 2[t 01;t 001],_x n (t )=0d n n [r)]r 0 nr=r (t 0010t 01).This,together with (29),leads tor(t 0010t 01)r(t 0010t 01):(32)Noting the fact that j u n 01(X n 01(t ))j n 01r;8t 2[t 01;t 001].Under thiscondition,it follows from Lemma 3.1thatu n 01(X n 01(t 001))0u n 01(X n 01(t 01))rr +( n 01( 1;...; n 01)0 n )(t 0010t 01)<r.Hence,for 8t t 1X n (t )2Q n =f X n (t ):j x n (t )0u n 01(X n 01(t ))j <rg :(34)Next we will prove that the above relation will also hold at step i .Similar to the first step,we first show that there exists a time instant t i t i 01such that j x n 0i +1(t i )0u n 0i (X n 0i (t i ))jr=2.To give a com-plete picture of the negative case which was not elaborated in the initial step,here we consider in detail the following case x n 0i +1(t )0u n 0i (X n 0i (t ))<0 r12=r0 drUsing (34),for t t i 01,we have j x j (t )j r;tt i 01.By (35),for 8t t i 01,the following inequality holds:_x n 0i +1(t )12=rr=r>0.Itfollows that x n 0i +1(t ) x n 0i +1(t i 01)+ n 0i +1r2>x n 0i +1(t )0u n 0i (X n 0i (t )) x n 0i +1(t i 01)+ n 0i +1rwhich leads to a contradiction as the time goes to infinity.A proof sim-ilar to the initial step can be used to show that the case x n 0i +1(t )0u n 0i (X n 0i (t ))>r=2.Following the line of the proof of the initial step,next we use a con-tradiction argument to prove that j x n 0i +1(t )0u n 0i (X n 0i (t ))j <r=2,(b)j x n 0i +1(t 00i )0u n 0i (X n 0i (t 00i ))j =r=2j x n 0i +1(t )0u n 0i (X n 0i (t ))jr2(37)x n 0i +1(t 00i )0u n 0i (X n 0i (t 00i ))=0rx n 0i +1(t )0u n 0i (X n 0i (t ))0 r ;t 2[t 0i ,t 00i ],which leadsto x n 0i +1(t 00i ) x n 0i +1(t 0i )+ n 0i +1r=x n 0i +1(t 00i )0u n 0i (X n 0i (t 00i ))x n 0i +1(t 0i)0u n 0i (X n 0i (t 0i ))+u n 0i (X n 0i (t 0i ))0u n 0i (X n 0i (t 00i ))+ n 0i +1r20j u n 0i (X n 0i (t 00i))0u n 0i (X n 0i (t 0i ))j + n 0i +1r,it can beconcluded thatj x n 0i +1(t )j (1+ n 0i ) r(1+ j 01),j =n 0i +1;...;n .Hence,by Lemma 3.1,the following holds:u n 0i (X n 0i (t 00i ))0u n 0i (X n 0i (t 0i ))rr( n 0i +10 n 0i (1))(t 00i 0t 0i )>0r=2x n 0i +1(t )0u n 0i (X n 0i (t ))r,or X n 0i +1(t )2Q n 0i +1=f X n 0i +1(t ):j x n 0i +1(t )0u n 0i (X n 0i (t ))j < rgfor n 0i +1 j n ,which completes the inductive proof.Final Step.Proceeding by this way,we can obtain there exists t n 01>0such that for t t n 01;j =2;...;nX j (t )2Q j =f X j (t ):j x j (t )0u j 01(X j 01(t ))j < r(1+ j 01),j =2;...;n .Therefore,by Lemma 3.1,j f 1(t;x 2;...;x n )j rfort t n 01.With the help of these relations,it can be concluded from _x 1(t )=d 1u 1(x 1(t ))+f 1(t;x 2;...;x n )+d 1[x 2(t )0u 1(x 1(t ))]that (a)_x 1(t ) 0 1 r =2,or (b)_x 1(t ) 1 r=2,where 1=d 1(1=2)r 0 d01>0guaranteed by (11).Hence,in either case,there exists a time instant t n such thatfor t t n ,j x 1(t )j r,which implies x 1(t )2Q 1=f x 1:j x 1(t )j <r,j x 2(t )0u 1(x 1(t ))j <rg in which by the construction defined as (10)it is clearthat u i (X i )=0 i [ r)]r =0 i (x i 0x 3i 01)r;i =1;...;n .It implies the saturated control law (10)reduces to the homogeneous controller (7)for X n (t )2Q;8t t n .In addition,by tuning the parameter we can assure that Q where is defined in Lemma ing Lemma 2.1,we obtain that the closed-loop system (1)–(7)is locally strongly stable.Thus it can be concluded that system (1)is globally (strongly)stabilized by controller (10).Remark 3.1:The idea of our proof of the main result is originally inspired by [16]and [17].In this note,we first design a controller for system (6)using the adding a power integrator technique proposed in [17].Note that the adding a power integrator technique in [17]is a top-to-bottom method which is mainly used to design stabilizers for lower-triangular systems.In order to handle the upper-triangular system (1),we first generalize the adding a power integrator technique [17]with the added flexibility in tuning the controller coefficients and then integrate it with the nested saturation scheme [16].The key toolRenabling us to handle the lower-order nonlinearities in this technical note is the use of the higher-order homogeneous controller,while the controller in[16]will still reduce to a linear one.Moreover,a new controller structure is developed by presetting most of the controller coefficients,i.e., i’s,and leaving only one gain,i.e., ,adjustable to obtain the global stabilization results.Specifically,the parameters i’s arefirst determined without knowing the detailed nonlinearities. Then we tune the single gain in the controller to globally stabilize the system.Hence,for a family of feedforward systems whose non-linearities have the same but different growth rates ’s in(3),our domination approach enables us to use the same parameters i’s in the controllers and only tune different ’s to dominate the nonlinearities. With the help of Theorem3.1,now it is possible to design a global stabilizer for system(2).Example3.1:Due to the fact that the nonlinear term f1(x2;x3)= x2=33+x22has a lower-order growing term,the global stabilization problem of system(2)remained unsolved prior to this work.By se-lecting =2,one can verify that p13=2=3>r2=r3=3=5with (r1;r2;r3;r4)=(1;3;5;7),which in turn implies that f1(1)satis-fies Assumption2.1.Therefore,by Theorem3.1,with appropriate con-stants 1; 2; 3and ,system(2)can now be globally stabilized by the following controller:u=0 3 05x3+2 03x2+ 1 01x135=37=5:Next we show that Theorem3.1leads to an interesting result for the strictly feedforward system_x i=d i x i+1+f i(t;x i+2;...;x n);i=1;...;n02;_x n01=x n;_x n=u(44) where d i are uncertain parameters satisfying d d i d with con-stants d>0; d>0,and f i(1);i=1;...;n02are continuous func-tions with f i(t;0;...;0)=0.Unlike most of the existing results that required Lipschitz continuity or higher-order growth condition,now we show that global stabilization of(44)can be achieved under a linear growth condition.Corollary3.1:The strict feedforward system(44)can be globally strongly stabilized if the nonlinear function satisfies a linear growth condition around the origin.Proof:By the linear growth condition,around the origin j f i(t;x i+2;...;x n)j (j x i+2j+111+j x n j); >0where p ij= 1>(i +1)=((j01) +1),i=1;...;n02;j=i+2;...;n for any positive .Hence Assumption2.1holds for(44).It implies Corollary3.1follows immediately by Theorem3.1.Corollary3.1allows us to solve the global robust stabilization problem for the following system.Example3.2:Consider the following system with uncertainties1 d1 2and j d(t)j 1_x1=d1x2+d(t)x3+x23;_x2=x3;_x3=u:(45)It can be verified that around the origin the nonlinear functions satisfy the linear growth condition.Hence,we can designu=0 3 011=7x3+2 09=7x2+ 1 01x19=711=913=11with appropriate coefficients i’s and saturation constant ,which globally stabilizes system(45).Due to the nature of the adding a power integrator technique,the parameters i’s increase significantly along with the system dimension.However,it should be pointed out that our design method in choosing parameters is very conservative for the neatness of the proof.In practice,following the general rules suggested by the proof,we can actually try and test some smaller parameters.This is quite practicable since in our controller the number of the design parameters has been reduced(i.e.,n coefficients i’s and only one ).For system(45),we only need to choose four parameters and one such choice is 1=5; 2=10; 3=60; =0:1which is sufficient to give satisfactory simulation results.R EFERENCES[1]A.R.Teel,“Global stabilization and restricted tracking for multipleintegrators with bounded controls,”Syst.Control Lett.,vol.18,no.3,pp.165–171,1992.[2]A.R.Teel,“A nonlinear small gain theorem for the analysis of controlsystems with saturation,”IEEE Trans.Autom.Control,vol.41,no.9,pp.1256–1270,Sep.1996.[3]X.D.Ye,“Universal stabilization of feedforward nonlinear systems,”Automatica,vol.39,no.1,pp.141–147,2003.[4]W.Lin and X.Li,“Synthesis of upper-triangular non-linear systemswith marginally unstable free dynamics using state-dependent satura-tion,”Int.J.Control,vol.72,no.12,pp.1078–1086,1999.[5]T.Chen and J.Huang,“Disturbance attenuation of feedforward sys-tems with dynamic uncertainty,”IEEE Trans.Autom.Control,vol.53,no.7,pp.1711–1717,Jul.2008.[6]L.Marconi and A.Isidori,“Robust global stabilization of a class ofuncertain feedforward nonlinear systems,”Syst.Control Lett.,vol.41,no.4,pp.281–290,2000.[7]X.D.Ye,J.Huang,and H.Unbehauen,“Decentralized robust stabi-lization for large-scale feedforward nonlinear systems,”Int.J.Control,vol.79,no.12,pp.1505–1511,2006.[8]F.Mazenc and L.Praly,“Adding integrations,saturated controls,andstabilization for feedforward systems,”IEEE Trans.Autom.Control,vol.41,no.11,pp.1559–1578,Nov.1996.[9]M.Jankovic,R.Sepulchre,and P.V.Kokotovic,“Constructive Lya-punov stabilization of nonlinear cascade systems,”IEEE Trans.Autom.Control,vol.41,no.12,pp.1723–1735,Dec.1996.[10]J.Kurzweil,“On the inversion of Lyapunov’s second theorem on sta-bility of motion,”Amer.Math.Soc.Transl.,vol.2,no.24,pp.19–77,1956.[11]F.Mazenc,R.Sepulchre,and M.Jankovic,“Lyapunov functions forstable cascades and applications to global stabilization,”IEEE Trans.Autom.Control,vol.44,no.9,pp.1795–1800,Sep.1999.[12]R.Sepulchre,M.Jankovic,and P.V.Kokotovic,“Integrator for-warding:A new recursive nonlinear robust design,”Automatica,vol.33,no.5,pp.979–984,1997.[13]R.Sepulchre,M.Jankovic,and P.V.Kokotovic,Constructive Non-linear Control.New York:Springer,1997.[14]A.Isidori,Nonlinear Control Systems II.London,U.K.:Springer-Verlag,1999.[15]F.Grognard,R.Sepulchre,and G.Bastin,“Global stabilization of feed-forward systems with exponentially unstable jacobian linearization,”Syst.Control Lett.,vol.37,no.2,pp.107–115,1999.[16]J.Tsinias and M.P.Tzamtzi,“An explicit formula of bounded feedbackstabilizers for feedforward systems,”Syst.Control Lett.,vol.43,no.4,pp.247–261,2001.[17]J.Polendo and C.Qian,“An expanded method to robustly stabilizeuncertain nonlinear systems,”rm.Syst.,vol.8,no.1,pp.55–70,2008.[18]C.Qian and W.Lin,“A continuous feedback approach to global strongstabilization of nonlinear systems,”IEEE Trans.Autom.Control,vol.46,no.7,pp.1061–1079,Jul.2001.[19]C.Qian and J.Li,“Global output feedback stabilization of upper-trian-gular nonlinear systems using a homogeneous domination approach,”Int.J.Robust Nonlin.Control,vol.16,no.9,pp.441–463,2006.[20]H.Hermes,“Homogeneous coordinates and continuous asymptoticallystabilizing feedback controls,”in Differential Equations.New York:Dekker,1991,pp.249–260.R。

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LTE_3GPP_36.213-860(中文版)

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贫富差距英文(共10篇)

贫富差距英文(共10篇)

贫富差距英文(共10篇)贫富差距英文（一）: 有关贫富差距的英文作文While china continue to amaze the outside world with its stories of rapid economic growth,the country"s Gini Co-efficient-a standard measure of income inequality has exceed the 0.40 threshold viewed as danger level.Although china has lifted hundreds of millions of people out of absolute poverty during the period of reform and opening,has transformed from planning economy system to marked-orientedsystem,the gap between the rich and poor remains in rural-urban income as well as in every social classes are widening that will confine the long-term development of national economy as whole.The per capita disposable income of city dwellers released in 2023 was 8,472 yuan (US$1,024),compared with 2,622 yuan (US$317) of farmers that account for 80% of the national population. approx. 25% of chinese population is in the upper middle class to rich. But the larger segment-about 75% is in the low middle class to poor.Even though the past year of 2023 appears a good one for the country"s some 800 million farmers thanks to a substantial recovery in grain price and cuting tax,the task to uplift the farmer income,to narrow the disparity and inequality which will affect society stabilization in rural-urban development level is arduous. to achieve a coordinated development between urban and rural areas and to resolve issues concerning agriculture, farmers and rural areas,Wen called for reforms to increase assistance and protection for agriculture, to speed up urbanization, to let cities play a bigger role in promotingthe development of rural areas and to coordinate the development of urban and rural areas, by unifying the management of issues like labor, family, compulsory education, and taxation.贫富差距英文（二）: 跪求英语作文一篇,贫富差距,The world"s wealth continues to be unevenly distributed.For many years now,poor nations have complained that wealthy countries provide only enough aid to keep them poor and never enough to become self-sufficient; wealthy nations complain that the amount is sufficient but the management of the aid is poor.Discuss the reasons for both of the conflicting opinion.英语,400字It’s certainly true that without a profit motive,the rational thing to do would be to sit at home all day and play video games —or whatever other pursuit you might choose if you never had to worry about paying the bills.And history shows that government efforts to try to equalize wealth or manage economies usually backfire. Inequality of wealth,by itself,isn’t new.In the past few decades,there’s evidence that the gap in some countries is widening – including the U.S.But super-rich folks like Forbes 400billionaires and greedy corporate executives are hardly a recent phenomenon.A hundred years ago,the wealth gap between the richest robber baron and the poorest farmer was wider than the current spread between a $100-million-a-year CEO and the worst-paid worker.And if you factor in modern health care,“conveniences” like cars,TVs andcellphones,the average American today probably enjoys a standard ofliving on a par with some of the richest Americans a century ago.So a widening income gap and wealth inequity doesn’t seem to have hurt progress.The issue isn’t whether money is a potent incentive for keeping us all busy trying to buy or build a bigger house or inventing the next cool electronic device.The question is whether the playing field is level.Equality of opportunity isn’t just a matter of fairness.No society can expect to thrive if it doesn’t fully tap the talent and ability of its entire workforce — including those who happen to be born poor.Economists talk about “human capital” like any other input to their economic models.In theory,free markets will allocate that human capital to the best use by rewarding best work that the market values the most highly.贫富差距英文（三）: Definition of Wealth gap （贫富差距的英文定义）最好是详细具体一点的定义诠释.谢谢!Wealth gap refers to disparities in the distribution of economic assets and income. The term typically refers to inequality among individuals and groups within a society, but can also refer to inequality among nations. Economic Inequality generally refers to equality of outcome, and is related to the idea of equality of opportunity. It is a contested issue whether economic inequality is a positive or negative phenomenon, both on utilitarian and moral grounds.Wealth gap has existed in a wide range of societies and historical periods; its nature, cause and importance are open to broad debate. Acountry"s economic structure or system (for example, capitalism or socialism), ongoing or past wars, and differences in individuals" abilities to create wealth are all involved in the creation of economic inequality.There are various Numerical indexes for measuring economic inequality. Inequality is most often measured using the Gini coefficient, but there are also many other methods.贫富差距英文（四）: 如何缩小贫富差距英语How to reduce the gap between rich and poor贫富差距英文（五）: 把increasingly用在下面这句话里“贫富差距越来越大”.要英文的.the gap between rich and poor has increasingly widened贫富差距英文（六）: 求一篇关于人们之间距离（gap between people）的英语文章,不是关于贫富差距或者两代人之间的代沟.就是说说现在人们之间的距离感是近了还是远了.最好是在网络,杂志或者英文报纸上的文章.More ways to communicate:that the relationship between the countries,as small as between family members,it is necessary to reduce barriers to,first of all to be able to communicate.In order to communicate,no matter how the other side,should take the initiativethemselves.A small group of course,respect the elderly,but also set aside the older generation.To learn from each other.Young to respect and filial piety of the old,old people,then the hearing would also like to hear,do not always think that old conservative,old knowledge,the experience of the old useless,in fact,not always true.Countries,governments,relevant departments have to do community work,education of young people.But the old initiative also concerned about the next generation of young people to understand,tolerance,not always in accordance with their own standards of young people in the past,which could not,it could not.Especially to young people with an open mind to learn new knowledge and new technologies,it is very important because it is young and you do not have a common language,can communicate an important condition.The old heart of the elderly who can not be old,which means we must always learn to keep up efforts to understand and adapt to the new.In order to realize lifelong learning,new knowledge and new skills to master at least not lag too much.It is also very important.Not as good,social change,scientific and technological progress too fast,the elderly lagged too far behind,and sometimes their children do not mouth that was also the essence of the look down.You can not force young people think highly of smth,you have to study hard to catch up with the times.In fact,unless you really do not mind the old hands and feet were effective,and even the sixties and seventies-year-old Qi Bashi-year-old Granny old man can still learn newKnowledge of new technology,memory may be not so satisfactory,sometimes understanding than do young people also strong.You continue to use new knowledge and new skills to enrich your own,they could still feel young,youngpeople will respect you more and more willing to communicate with you,the generation gap will naturally shallow and even filled the- Human beings are not "cold-blooded" We fear loneliness.It was lonely fear.When we met in the physical,mental and spiritual desire to have been met.On the need to munication is not good,even if a bright and sunny outside,was also a dark andhumid.However,good communication,and even the coldest winter in the hearts of happy flowers will bloom.贫富差距英文（七）: 英语翻译1在发展中国家,伴随着经济增长,贫富差距也随之增长在建筑领域里,有一部分的建筑师只为富人服务.有一部分建筑师在为穷人做设计.我认为这样的分支只能使贫富差距显得越来越大.我想做的是设计这两者之间的关系,通过设计来让更多的“强者”主动接触曾被他们忽视的“弱者”,从而提高后者的社会地位,缩小贫富差距.我不知道什么时候人人才能真正的平等.也许永远不可能实现.但我还是希望通过自己的设计可以缩小这个距离.2在发展中国家,大多农民都以为自己是农民而感到自卑.3总有一天,他们会因为自己是农民而自豪.【贫富差距英文】In developing countries,along with the increasing of the economy,the disparity between disparity wealthily and poverty is also go up.In architecture,some of the architect noly service for wealthily individuals while mang others like to disign foe poverties.I beleive that the status quo of this issue lead to the gap becoming bigger and bigger.What am I want to do is disign the hypotaxis of these twosides,make more"overmatch" tough those "weakling",then reduse the staton,sefuce the disparity.I do not know what is equality,might be never come ture,but I want to do that2 In developing countries,most famers are inferiority,owing to famers.3 They will be pround os them in some day楼主,累死我了.这都是我亲笔翻译的.【贫富差距英文】贫富差距英文（八）: 英语翻译1、加拿大是一个非常富裕同时贫富差距很小的国家；2、加拿大是一个由移民组成的多元文化的年轻国度,还有待形成统一的国家认同；3、加拿大是全球最主要的贸易大国之一；4、加拿大在世界军事力量对比中处于中间力量的国家,紧邻美国这个超级大国,但热爱和平1、加拿大是一个非常富裕同时贫富差距很小的国家Canada is an extremely wealthy at the same time gap between rich and poor very small country.2、加拿大是一个由移民组成的多元文化的年轻国度,还有待形成统一的国家认同Canada is one multicultural young state which is composed by the immigration,but also waits for forms the unified national approval 3、加拿大是全球最主要的贸易大国之一Canada is one of global most main trade great nations4、加拿大在世界军事力量对比中处于中间力量的国家,紧邻美国这个超级大国,但热爱和平Canada is in the intermediary force in the world military force contrast the country,close neighbor US this superpower,but deeply loves peace贫富差距英文（九）: 英语翻译人和人之间权利和财力的差别,使得贫富差距扩大化,解决这个问题不仅是政府的责任,广大民众也应该齐心协力,为了人的生活更加美好,相处更加和睦. 大量的人口从农村前往城市,使得城市人口极具增加,带来了许多问题,比如说就业紧张,环境问题等等一系列.人和人之间权利和财力的差别,使得贫富差距扩大化,解决这个问题不仅是政府的责任,广大民众也应该齐心协力,为了人的生活更加美好,相处更加和睦. 大量的人口从农村前往城市,使得城市人口极具增加,带来了许多问题,比如说就业紧张,住房问题,环境问题等等一系列.The power distinction and wealth difference among people has led to the enlargement of the difference between the poor and the rich.The settlement of this problem is not only the goverment"s duty but also broad mass should work together to make people lead a better life and live in more harmony with one anotherLots of people has poured into the city from the countryside ,which keep the population of city drastically increasing with occurrence of many problems ,such as intense employment and housing problems and environmental problems..贫富差距英文（十）: 英语翻译经过30年来改革开放,伴随着经济的迅猛发展,我国的贫富差距也日益扩大,社会公平问题日益凸显,住房公积金领域的种种不公平现象也受到社会各界的格外关注.住房公积金制度建立的初衷是通过政策性互助资金的让渡解决中低收入家庭的住房问题,维护社会公平,保障社会稳定.但许多数据表明,现行住房公积金制度由于种种原因,实际上并没有充分发挥这种保障功能,甚至在一定程度上拉大了社会各群体之间的收入差距.同时,住房公积金制度在各地区的发展极不平衡,采取的是各自为政的封闭式管理,导致住房公积金制度的效率不高.本文从公平与效率的角度出发,对我国住房公积金制度的运行现状进行了实证分析,证实了我国住房公积金制度在促进城镇住房建设、提高城镇居民的居住水平、改善住房消费结构等方面发挥了重要作用；通过对住房公积金制度中的种种不公平及效率不高的现象进行剖析,找出住房公积金制度存在的不足之处；通过借鉴国外公积金及住房政策的成功经验,结合我国城乡实情,提出了以公平为体、效率为基完善城镇住房公积金制度和建立农村住房公积金制度,最终在全国范围内构建立体结构住房公积金政策金融管理体系的对策.After 30 years of reform and opening,along with rapid economic development,China"s widening wealth gap,social equity issues become increasingly prominent area of the housing provident fund various inequities are particularly concerned by the community.Housing provident fund system was originally conceived as mutual funds by transferring policy to solve the housing problems of low-income households,maintaining social justice,security and socialstability.However,many data indicate that the existing housing fund system for various reasons,did not actually give full play to such security functions,and even to some extent widened between different groups in society income gap.Meanwhile,the housing provident fund system in unbalanced regional development,to the fragmentation of closed-end management of a housing provident fund system is not efficient.From the perspective of fairness and efficiency of our housing fund system running status of an empirical analysis,confirmed that the housing provident fund system in China to promote urban housing construction and improve the living standards of urban residents to improve the structure of housing consumption has played an importanteffect; through the various housing provident fund system in the unfair and the phenomenon of high-efficiency analysis,the housing provident fund system to identify deficiencies in existing Department; by reference Guowai fund and housing policy of the successful experience,combined with China"s Cheng Xiang truth,made Le body of fairness,efficiency-based system to improve the urban housing fund and the establishment of rural housing accumulation fund system,and eventually build a nationwide three-dimensional structure of the financial management system of housing provident fund policy response.贫富差距英文作文中国贫富差距ppt英文。

u(t x) = Gamma d

u(t x) = Gamma d

t! 1
lim e?itH Pc
L2 s ?
= 0; s > 0;
(1.8)
where L2 ; s 2 R; denotes the weighted L2 space consisting of all functions, f , that are locally in L2 and s such that (1 + jxj2)s=2 f (x) 2 L2 , with norm,
@ d2 i @t u(t; x) = ? dx2 u(t; x) + V (x)u(t; x) + f (x; juj) ju(t; x)j ; u(0; x) = (x); u(t; x)
(1.1)
where u is a complex-valued function de ned for t; x 2 R. For each xed x 2 R, f (x; ) 2 C 1(R; R); @ @x f (x; ) 2 C (R; R); f (x; 0) = 0 and,
t! 1
lim u(t) ? e?itE0 P0
L2 s ?
= 0:
(1.10)
For functions u(t; x) de ned for t; x 2 R, we denote u(t) for u(t; ). Equation (1.10) gives us also a time-dependent characterization of the stability of the bound state 0 . It tells us that given any initial state in L2 , = rei 0 + with 2 Hc, the solution to (1.5) is the sum of the periodic orbit of the bound state, e?itE0 rei 0, and a dispersive solution, e?itH , that propagates out to in nity as t ! 1 and whose local energies tend to zero. As we show below, this situation persists in the nonlinear case. There is an invariant center manifold, consisting of the orbits of periodic localized solutions, such that all small solutions to (1.1) approach particular orbits in the center manifold as t ! 1. Invariant manifold theorems have been extensively 3
体验英语unit 7

体验英语unit 7

体验英语unit 7, book 3Why do people get addicted to drugs?A:The illegal drug trade touches millions of lives in both developed and developing countries. Its most negative impact is concentrated amongst the most disadvantaged of our societies. The UN estimates that some 180 million people worldwide —4.2 per cent of people aged 15 years and above —were consuming drugs in the late 1990s.B:Economic reliance on the drug trade, and drug addiction, leaves many individuals open to exploitation by criminals and criminal organizations, and threatens the health of men, women and children, the rule of law, and ultimately, the vitality and strength of all our communities. However, for the first time in recent history, global production of drugs such as heroin and cocaine is no longer growing, but shows signs of stabilization and even decline. This makes combined efforts an increasingly viable能养活的；能生育的；可行的option to achieve the targets set out in the 1998 UN Special Session which aim at a substantial reduction if not elimination of drug production by the year 2008. Progress is also being reported from the demand side, where there are signs of stabilization or even decline in some of the main markets.Risk is the probability of losing something of value.Since we value life above other things,the greatest risk for most people is the risk of death.Of course,we hope to live a longer life.Other things we value include health,safety,money,property,relationships and happiness. One way to manage risk in life is through rational planning.By balancing the most likely risks against the most likely rewards,we can make better decisions and give greater consideration to the long-term outcomes.Talk to your classmate(s) how you should avoid doing things that appear to be pleasant at first but are really harmful in the end. You may talk about drug abuse, smoking, alcoholism, addiction to computer games, etc. Cigarette Smoking is harmful to(Affects My Health) our health.1. John started smoking when he was very young. At the beginning, he did it for fun, but some time later, he became an addicted smoker, and his health began going downhill. He’s not alone —for people who smoke more than 20 cigarettes daily are more likely to have frequent coughs, chest pains and other troubles. Smoking also has been associated with mental health conditions. Youngsters who smoke cigarettes regularly have been shown to have more difficulty concentrating their mind on what they aredoing. According to a survey, teen smokers are more likely to be absent-minded in class than non-smoking teenagers.2.Some people talk about smoking as if it were a fun thing to do. All I can think is, “if they only knew.” I grew up in a family free of smokers. We all believed it was stupid to spend money to damage health. However, when I was 16, I was involved with a group of teenagers who would do anything that looked cool. At that time we thought it was surely a cool thing to have a cigarette between your fingers and look grown-up. By and by I became an addicted smoker. Half a year ago I felt pain in my chest, so my parents took me to the hospital and I had a scan of my lungs.I couldn’t believe my eyes when I saw the results. The scan showed several dark marks on the image of my lungs. Since I saw that scan I haven’t smoked a si ngle cigarette.Ecstasy Affects Mental HealthJim had been suffering from extreme anxiety since his early twenties. Trying Ecstasy did make him feel high and help his condition, but only for a short period of time; in the end, it increased his anxiety, paranoia[,pærə'nɔiə]偏执狂，妄想狂, and feelings of unreality不真实；非现实. And he isn’t alone — for people whoalready suffer from anxiety disorders, use of Ecstasy is more likely to worsen their conditions. Ecstasy also has been associated with other mental health conditions such as depression. Youngsters who use Ecstasy weekly have been shown to frequently experience depression in which they want to kill themselves sometimes. According to a survey, teens who use Ecstasy weekly are three times more likely to have such thoughts than non-using teenagers.(Feel dizzy//my whole body aches,I am aching all over//how’s your appetite?what’s appetite like?fair,I don’t have much appetite,I’ve got no appetite.the sight of food simply turns my stomach//you look pale,I have a slitting headache and a sore throat//I feel warm,I have got a fever//I am tired all the time//I am suffering from insomnia,often wake up in the middle of the night,in the early hours of the morning//I’ve gained,lost 3 kilograms this past month//my weight falls from---kilos to---kilos//take a hot bath or shower helps relieve stress//have you tried any of the sleeping medications available?//I don’t need as much sleep as others//have you experienced any other symptoms?,I had a lot of indigestion//I have a pain in my neck//I am out of breath,I am short of breath,Ihave a high blood pressure//I feel like vomiting//my problem seems to be a minor case of food poinsoning//I take a hip-bath 坐浴hip bone 髋骨,spine瘠骨//I hurt my left foot,I missed one step while coming down the stairs//you have a sprained ankle,it’s slightly swollen,how does it feel,rather painful//I will give you an X-ray to see if there is anything wrong with the bone//A people with anorexia厌食症develops joint and muscle problems.There’s a lack of iron in the blood.As the sickness progresses, a young woman’s breathing,heartbeat and blood pressure rates slow down.The important substance calcium is lost from the bones,causing bones to break.//cure you of the disease//take medicine//recover from the //do not prescribe sb sth,pills,tablets//unable to find out your problem//checks-up//have his blood tested//have sb x-rayed//take an x-ray picture of your bone//examine the patient very carefully//responsible//stay young//remain healthy//professional//psychology/--logicalneed//frightened//scared to death//make the patient feel relaxed//hospitable//benevolent//exhausted//feels sick/ill from overwork//fatigue)The doctor consoles the patient by saying that he is in no danger and advises him to do more walking.The patient answers that he always does so because he is a postman.Think about it:They think it is a fun, harmless drug.It seriously damaged her health. Besides, she lost her strength, motivation, dreams, friends, apartment, money and most of all, her sanity明智；头脑清楚；精神健全；通情达理.Summary of passage A: the writer uses her personal experiences with the drug ecstasy to warn others of its dangerous effects. She, a normal woman grew up in a small town in the state of Pennsylvania but moved to New York to try to realize her dream of working in theater and it was there she first came into contact with drugs. Many of her acting school friends were drug users and in an effort to fit in, she began to use them too. Her story was typical of many drug addicts. She went from someone who used drugs for fun to someone who couldn’t live without them. Finally she had some kind of a breakdown. Luckily her mother drove to NY to rescue her and she ended up back in Pennsylvania in hospital. She recalls her horror at seeing a brain scan which the doctorshad done and which showed that Ecstasy had had permanent effects on her brain.Read about it:She was a popular kid that everyone liked.She thought that it couldn’t be harmful/bad.Because she thought that it was normal.It took away her sanity.Translation:A lot of people believe that sleeping pills help them sleep. All I can think is, “if they only knew.”My dream came true when I first flew up into the blue sky in an airplane.The country boy was exposed to many strange things in the city. He felt greatly shocked as if he had entered a future world. Within only one year after graduation from college, he went from a student who pursued his dream to a person who didn’t care about a thing.I have been given permission to do the interview in that area, and that’s not something that everyone gets.Important structures:My dream came true when I got the notice to inform me that I had been admitted to the university.I had gone from a fresh college graduate to an experienced engineer in five years.The more we take from the Earth now, the more we will pay back in the future.Standing on the top of the mountain, I felt as if I had melted in the beautiful scenery.I couldn’t believe my eyes when I saw my disabled mother walking to me.Passage B:Think about it:There was a war on drugs in New Haven and the police gathered there to arrest the drug gang.The drug bust突击搜捕毒品及贩毒者arrested almost all the drug dealers on the list.Summary of passage B: The article uses the personal experience of a policeman to talk about the war on drugs in the U.S.A. White’s hometown, New Haven, is presented as a typical town---safe and peaceful in 1960 but a drug war zone by 1990.Thetext describe as a big and successful coordinated drugs bust involving not just a national security task force made up of the police, US marshals元帅,执行官vt配置,集合, the FBI but also overseas operations such as in Columbia. Since the bust New Haven has become a safer place to live and White is confident that the war on drugs can be won.Translation:With the beginning of the war came ten years of killing and destruction.We shall continue to do what we have always been doing. Most of them had been up since the morning before yesterday. But none of them will sleep tonight either.Born and raised in Chengdu, Li Ming still remembers the time when he lived in a/the quadrangle.How dare you treat a young child in such a cruel manner in broad daylight?Prescription drug abuse by teenagers and young adults is a growing problem in the United States. Data from the Partnership for a Drug Free America's annual tracking study suggests: -- 1 in 5 teens has abused a prescription pain medication药物治疗-- 1 in 5 report abusing prescription stimulants and tranquilizers['træŋkwilaizə]镇定剂-- 1 in 10 has abused cough medication 药物The Partnership for a Drug-Free America is doing a great job with educating parents, young adults and teenagers on the realrisks associated with the misuse of prescription drugs and other commonly abused substances. Kids as young as 12 are being experimented with prescription drugs non- medically - to get high or to self-medicate. Pharmaceuticals[,fɑ:mə'sju:tikəl] adj. 制药（学）的n. 药物are more readily accessible to children than illicit违法的；不正当的drugs because they are typically stored in medicine cabinets at homes. The National Survey on Drug Use and Health identifies 4 types of prescription drugs that are commonly abused - painkillers止痛药, stimulants, sedatives镇静剂and tranquilizers. An astonishing eleven percent of teenagers (ages 12-17) reported non-medical use of painkillers and four percent reported non- medical use of stimulants. Painkillers are the most commonly abused prescription drug among teenagers, especially younger teens. Stimulant abuse is most commonly found in older teenagers and college students than in younger teens. Females are more likely to be current abusers of prescription drugs than males (4.3 vs. 3.6 percent) [Source: 2002 National Survey on Drug Use and Health]. Many argue that online pharmacies are a great resource for teenagers looking to obtain dangerous and addictive prescription drugs for non-medical uses. William Hill, CEO and founder of (), says, "I couldn't agree more! Online pharmacies can pose serious risks to consumers of all ages, especially minors. To help protect children, parents should enable the Parental Controls which are available on most computers today. Parents should also be open with their children informing them of the deadly dangers associated with the misuse of prescription drugs." When asking Hill how consumers can protect themselves from rogue小淘气；流氓online pharmacies, he replied, "Consumers should make certain that any online pharmacy they conduct business with is properly licensed and governed by the U.S. or Canada." He adds, " was designed to put legitimate patients in touch with legitimate pharmacies while conducting business over the Internet in a highly secure, private environment." There's no doubt that rogue online pharmacies contribute largely to the ever-growing problem of prescription drugs being misused and abused by teenagers in the United States, although it seems the real problem and largest contributing factor to this nearing epidemic流行病can be found in unsecured medicine cabinets. So parents, please secure the location in which you store prescription medications in your home. To view a list of online pharmacies identified by the FDA (Food and Drug Administration) as running illegal operations visit, /standards_scamlist.asp. About is the Internet's mostpopular destination that offers consumers prescription drug price comparison and licensed online pharmacy referral参照；转诊病人services. Led by a talented team of e-commerce experts, offers price comparisons on over 13,000 medications being sold by approximately 50 of the Internet's largest and most reputable pharmacies which are all licensed in their governing countries, including the U.S. and Canada. is the most secure and convenient way for consumers to search and perform up-to-date price comparisons of prescription drugs.The pressure to excel in middle school is stressing out students from affluent neighborhoods, making them more likely to become depressed, and to smoke, drink, and abuse drugs.A new study reveals a correlation between achievement pressures, depression, and substance abuse as students feel anxious to do well not only in school but in outside activities as well. As a result, the youths turn to alcohol and other substances to 'self-medicate.' According to the researchers, overwhelming and unrealistic goals are key to the pressure many of these children feel, and are what eventually leads to the behavioral problems. And it's not only pressure to achieve specific academic goals, they say, but general feelings of isolation, especially from their mothers, that may be to blame. For girls in particular, a lack of after-school adult supervision was linked to problems.The study, conducted with more than 300 sixth and seventh graders in an affluent Northeastern community, revealed that seventh graders were three times as likely to use drugs than sixth graders. Boys in seventh grade who were considered popular and well-liked among their peers were more likely to be regular users of cigarettes, alcohol, and illegal drugs than were sixth grade boys and girls. The fact that they used these substances, however, drew out negative responses from their peers. The study also showed that: Seven percent of sixth-grade boys and 8% of sixth-grade girls smoked cigarettes. Six percent of seventh-grade girls and 7% of seventh grade boys had smoked marijuana[,mæriju'ɑ:nə] n. 大麻；大麻毒品at least once in the year prior to the study. Seventh-grade girls who had good relationships with their fathers were more likely to have better grades. The study also showed that students who had the closest relationships with their mothers were least likely to smoke, use drugs and alcohol, or to show any symptoms ofdistress.It is really a sad thing to see someone waste their life away with drug abuse and addiction, Family and friends are the ones that feel the worst and feel helpless when they are unable to reach their loved one, Of course, they do reach out, but the person may not be ready to admit that there is a problem. Drugs crumble family relationships and friendships, It destroys the life of good people and families with children, It is a traumatic外伤的；创伤的and destructive thing and as long as people have a hard time dealing with their daily issues, drugs will always play a partin their lives. When families are destroyed,, it is hard to pick up the pieces and this disease is taking over the nation and the world, However, there is help from Christian drug rehab treatment facilities that target the reasons for the behavior to find the right solutions. Drug addiction, if not treated, will cause other issues such as domestic abuse, child abuse and other issues, Due to their drug habit, a father or mother will neglect their children in exchange for the drugs.The drug addict has no control over their habit; at least that is what they think when they are doing the drug, Due to this control issue, they may be emotionally distorted because of not having a clear idea of how to stop the abuse of drugs.The whole family is affected by the drug abuse to such an extent that they are constantly fighting over the issue, This will let the drug add ict get deeper and deeper their drug habit because they don’t do wellwith arguments and pressure.For drug addicts who go on to enter a Christian drug rehab(rehabilitation)修复treatment center and come out on top, it makes the family better and it will prove to be a rewarding experience to all those who are involved, Family members that are involved in the treatment and recovery process are usually the ones that experience the delight of seeing their loved one get clean. The treatment process for the recovering drug addict has to be structured and organized. Discipline has to be shown because without it, the drug addict will slip back the old habits. Support needs to be introduced immediately, The drug addict has to be confident that there are people behind their success, They have to be responsible and accountable for everything that goes on during their treatment,.If you know someone who is abusing drugs, be sure to show them some type of understanding and don’t point fingers because this can happen to anyone at anytime. Drug addicts feel that they are not loved enough. They feel that the drugs are their only friend and so that is why it becomes so important to them, How family members react to their loves ones who are abusing drugs is important to them.However, a lot of family members will allow embarrassment and shame to dictate how they treat their loved one. Offering them love and support will help them to get to that place of promise where they can enjoy life without substance abuse.These are practices that I do whenever I am trying to release a pattern that no longer serves my highest good. I am using smoking as an example but you can fill in any other habit instead of smoking like drinking, drugs and other addictive behaviors. Sometimes addictive patterns emerge from emotional charges. You get stressed at work for example and you take a smoke. Whenever emotional charges occur, they need to be cleared.1. Buy a small notebook that can easily fit into a shirt pocket or purse. Whenever you engage in the habit that you are trying to release, write down the date, time, the people you were with and the reason why you felt drawn to engaging in the pattern that you are trying to release.2. What you are trying to do is to identify the triggers that are supporting the old habit. Also a lot of time we have unconscious agreements with others to support us in maintaining our old habits. If you conscientiously do this for a week, you will know exactly what the triggers are for your habit and who in your life is supporting you in doing this behavior.3. After a week, take out the notebook and make a list of the triggers/reasons you indulged in the habit and the people who appear to be supporting the habit. Post both of these lists up in your home and take time throughout the day to look at both lists. This will help you to understand what the underlying foundation of the pattern is.4. For triggers, begin to recondition yourself. Say for example that you want to give smoking and that you have a trigger that after you eat you usually smoke or whenever you have a break you smoke. After you eat or have a break, instead of smoking - take 30 deep breaths instead.5. For the people list, look at who is on it and begin to evaluate the relationship. If some of them are people in your work group that the major thing you have in common with is smoking, tell them that you are trying to give up smoking and that you will no longer want to take smoking breaks together. Explain to them that it is not personal that you just have a hard time for the present watching others smoke when you cannot.6. If the people on the list are family members, you need to explain to them that you are trying to give up cigarettes and ask them to support you in this.7. For those periods when you are just dying to smoke, for the first week, make a promise to yourself that if you still feel this strongly fifteen minutes from now you will smoke. If you do feel that way fifteen minutes later, go ahead and smoke. During week two change the time period to a half hour. During week three change the period to an hour.8. I feel that energy healing can help support people who are serious about letting go of addictive behaviour. Energy healing focuses on the underlying root cause of imbalances rather than on the symptoms.9. Another valuable thing to discover is what is your energetic reward from engaging in the bad habit. How are you benefiting from it. Once you identify what the energetic payback is to you, you can figure out another way to get the payback without indulging in the bad habit or addictive behavior.Different Kinds Of Stress--- Tension headache is one of the most common complaints of people who are constantly stressed out. This type of headache can occur at any age and can affect almost anyone; it can definitely affect a person's daily activity since it comes with an annoying and painful headache that can be felt not only in the head but also in the scalp头皮and neck. Discussed in this article are important tips on how to get rid of stress headaches.You have surely heard of the concept of different kinds of stress before. We generally differentiate between: constructive stress (eustress) and destructive stress (distress). Constructive stress is very healthy in the workplace since it gives you a drive towards success, keeps you excited, and can lead to a creative state of flow. The primal reaction reaction to danger is what is referred to as distress. The human biology doesn't care any more about getting any kind of work done, it just wants to fight or flight. That's when you keep thinking about what a prick your co-worker/boss is and can't concentrate on your work anymore.-Out Of The Stress-Consciousness I honestly don't want to give you the same advice that you get everywhere else concerning stress-management: T ake a vacation, spend time with your family, work out, volunteer for charity work, get together with your friend and eathealthy. Poof, all your problems will be gone. Next client please.(...as if ...)Sure, that advice has its place and you will feel much better after a good workout, for example. But let's not kid ourselves, the next day it will be the same old story and the same stress appears again. Fact is: You will never get out of being stressed by other people or circumstances in your workplace as long as you percieve them as being a danger. Even if this is unconscious. The perception of danger is the turning point of eustress(productivity) crossing over into distress.-Making The Unconscious Conscious Now is the time for some good self-honesty.1. Remember the last time you got into some seriously uncomfortable stress in the workplace2. Do what you would do naturally and review the major troubles you have in that situation3. Now let's shift your focus from the situation or person(well, where did I know from that it was outside ofyourself ...) to yourself. Which of your beliefs play into this trouble?4. What are you afraid of? If you don't know, just guess. What could you maybe afraid of? Make a list of possibilities without judging. It's not necessary. When the situation occurs next time youwill be able to point more and more in the direction of which of your guesses was the most accurate.5. Really picture in your mind what the worst possible outcome of the situation may be.6. What would you do given the circumstance that the worst case scenario really happened? Could you deal with that inany way?7. What is the most probable outcome of the situation? Our goal is to get more and more of our common sense into our animalistic fear-reactions. For example, when the stress arises from meeting a deadline or you will loose your job, this can be a very scary situation to be in. The only way to get out of being paralyzed by the stress ahead is in fact to get less outcome-dependent. This seems to be one of the big ironies of life, since independence from the outcome usually produces better outcomes. Don't just skim the above steps and go "Yeah, yeah. Done that". T ake your time and really do this analysis. It will get you further in the long run than anyvacation-workout-volunteering-quickfix. To combine productivity and relaxation, simply avoid destructive stress in the workplace -- which might prove tobe a much harder task than it sounds. Eustress is the flow you are looking for to happily be productive at work.Teachers' efforts to increase the number of students interested in science, technology, engineering and math careers received a boost today from NBC News with the release of a comprehensive collection of science and technology videos spanning the greatest scientific milestones of our era and the latest scientific discoveries. Students and teachers can explore both historic and current developments in science, such as the discovery of atomic energy, the beginning moments of the space race, and the latest findings about climate change. The Science and Technology curriculum includes more than 1,000 two-to-five minute clips of current and historic scientific discoveries and technological innovations that K-12 educators can use to expand and deepen discussions as well as spur interest by students to pursue careers in these fields. The video resources are continually updated with new developments in science and are correlated to curriculum; the curriculum spans over 70 years of history and includes resources on traditional subjects such as Biology and Chemistry as well as high interest topics like Forensics and Environmental Science. The science and technology resources are available online at HotChalk (/nbc.html), a free, easy-to-use web-based learning management system designed specifically for K-12 educators. HotChalk helps teachers easily and quickly develop customized lesson plans and assignments, locate and integrate curriculum materials, and manage assignments and grading. The specific subject matter can be searched by topic and includes the following subject areas: Earth Sciences, Astronomy and Space Science, Life Sciences and Biology, Physical Sciences, Chemistry,and Physics, Environmental Science, Forensic Science and, Computer Science and Technology. All of the curriculum resources are exclusive features of NBC News Archives on Demand, a significant effort by NBC News to set a new standard in bringing life-relevant learning to classrooms. Available on HotChalk (/nbc.html), the Archives are continually updated and comprised of thousands of video, audio, and image and text resources. The content has been organized specifically for classroom instruction, allowing teachers of history, government, civics, English language, writing/composition, and now science classes to create richer, timelier lesson plans with engaging curriculum that brings concepts to life and creates relevancy between concepts and real-world applications for this generation of wired kids. About NBC News NBC News, /, has been a leading source of global news and information for more than 70 years, first on radio, and today via broadcast and cable television, the Internet, radio and cell phones. Operating around the clock with bureaus in key cities in the United States and overseas, NBC News provides immediate coverage and in-depth reporting of major events to a worldwide audience. SOURCE NBC News。