a r X i v :m a t h /0101246v 4 [m a t h .A T ] 4 M a y 2004Annals of Mathematics,158(2003),473–507
Hypersurface complements,Milnor ?bers and higher homotopy groups of arrangments By Alexandru Dimca and Stefan Papadima Introduction The interplay between geometry and topology on complex algebraic vari-eties is a classical theme that goes back to Lefschetz [L]and Zariski [Z]and is always present on the scene;see for instance the work by Libgober [Li].In this paper we study complements of hypersurfaces,with special attention to the case of hyperplane arrangements as discussed in Orlik-Terao’s book [OT1].Theorem 1expresses the degree of the gradient map associated to any homogeneous polynomial h as the number of n -cells that have to be added to a generic hyperplane section D (h )∩H to obtain the complement in P n ,D (h ),of the projective hypersurface V (h ).Alternatively,by results of L?e [Le2]one knows that the a?ne piece V (h )a =V (h )\H of V (h )has the homotopy type of a bouquet of (n ?1)-spheres.Theorem 1can then be restated by saying that the degree of the gradient map coincides with the number of these (n ?1)-spheres.In this form,our result is reminiscent of Milnor’s equality between the degree of the local gradient map and the number of spheres in the Milnor ?ber associated to an isolated hypersurface singularity [M].This topological description of the degree of the gradient map has as a direct consequence a positive answer to a conjecture by Dolgachev [Do]on polar Cremona transformations;see Corollary 2.Corollary 4and the end of
Section 3contain stronger versions of some of the results in [Do]and some related matters.
Corollary 6(obtained independently by Randell [R2,3])reveals a striking feature of complements of hyperplane arrangements.They possess a minimal CW-structure,i.e.,a CW-decomposition with exactly as many k -cells as the k -th Betti number,for all k .Minimality may be viewed as an improvement of the Morse inequalities for twisted homology (the main result of Daniel Cohen in [C]),from homology to the level of cells;see Remark 12(ii).
474ALEXANDRU DIMCA AND STEF AN PAPADIMA
In the second part of our paper,we investigate the higher homotopy groups of complements of complex hyperplane arrangements(asπ1-modules).By the classical work of Brieskorn[B]and Deligne[De],it is known that such a complement is often aspherical.The?rst explicit computation of nontrivial homotopy groups of this type has been performed by Hattori[Hat],in1975. This remained the only example of this kind,until[PS]was published.
Hattori proved that,up to homotopy,the complement of a general position arrangement is a skeleton of the standard minimal CW-structure of a torus. From this,he derived a free resolution of the?rst nontrivial higher homotopy group.We use the techniques developed in the?rst part of our paper to generalize Hattori’s homotopy type formula,for all su?ciently generic sections of aspherical arrangements(a framework inspired from the strati?ed Morse theory of Goresky-MacPherson[GM]);see https://www.doczj.com/doc/f011782671.html,ing the approach by minimality from[PS],we can to generalize the Hattori presentation in Theorem16,and the Hattori resolution in Theorem18.The above framework provides a uni?ed treatment of all explicit computations related to nonzero higher homotopy groups of arrangements available in the literature,to the best of our knowledge.It also gives examples exhibiting a nontrivial homotopy group,πq,for all q;see the end of Section5.
The associated combinatorics plays an important role in arrangement the-ory.By‘combinatorics’we mean the pattern of intersection of the hyperplanes, encoded by the associated intersection lattice.For instance,one knows,by the work of Orlik-Solomon[OS],that the cohomology ring of the complement is de-termined by the combinatorics.On the other hand,the examples of Rybnikov [Ry]show thatπ1is not combinatorially determined,in general.One of the most basic questions in the?eld is to identify the precise amount of topological information on the complement that is determined by the combinatorics.
In Corollary21we consider the associated graded chain complex,with respect to the I-adic?ltration of the group ring Zπ1,of theπ1-equivariant chain complex of the universal cover,constructed from an arbitrary minimal CW-structure of any arrangement complement.We prove that the associated graded is always combinatorially determined,with Q-coe?cients,and that this actually holds over Z,for the class of hypersolvable arrangements introduced in [JP1].We deduce these properties from a general result,namely Theorem20, where we show that the associated graded equivariant chain complex of the universal cover of a minimal CW-complex,whose cohomology ring is generated in degree one,is determined byπ1and the cohomology ring.
There is a rich supply of examples which?t into our framework of generic sections of aspherical arrangements.Among them,we present in Theorem23 a large class of combinatorially de?ned hypersolvable examples,for which the associated graded module of the?rst higher nontrivial homotopy group of the complement is also combinatorially determined.
HYPERSURF ACE COMPLEMENTS475
1.The main results
There is a gradient map associated to any nonconstant homogeneous poly-nomial h∈C[x0,...,x n]of degree d,namely
grad(h):D(h)→P n,(x0:···:x n)→(h0(x):···:h n(x))
where D(h)={x∈P n|h(x)=0}is the principal open set associated to h and h i=?h
476ALEXANDRU DIMCA AND STEF AN PAPADIMA
Euler number is explicitly computed as a sum of the Milnor numberμ(V)and a“singular Milnor number”;see[Da2,Th.1]and[Da3,Th.1or Cor.2].
Corollary2.The degree of the gradient map grad(h)depends only on the reduced polynomial h r associated to h.
This gives a positive answer to Dolgachev’s conjecture at the end of Sec-tion3in[Do],and it follows directly from Theorem1,since D(h)=D(h r).
Let f∈C[x0,...,x n]be a homogeneous polynomial of degree e>0with global Milnor?ber F={x∈C n+1|f(x)=1};see for instance[D1]for more on such varieties.Let g:F\N→R be the function g(x)=h(x)
HYPERSURF ACE COMPLEMENTS477 Our results above have interesting implications for the topology of hyper-
plane arrangements which were our initial motivation in this study.Let A be
a hyperplane arrangement in the complex projective space P n,with n>0.Let
d>0be the number of hyperplanes in this arrangement and choose a linear
equation?i(x)=0for each hyperplane H i in A,for i=1,...,d.
Consider the homogeneous polynomial Q(x)= d i=1?i(x)∈C[x0,...,x n] and the corresponding principal open set M=M(A)=D(Q)=P n\∪d i=1H i.
The topology of the hyperplane arrangement complement M is a central object
of study in the theory of hyperplane arrangements,see Orlik-Terao[OT1].As
a consequence of Theorem1we prove the following:
Corollary4.(1)For any projective arrangement A as above one has
b n(D(Q))=deg(grad(Q)).
(2)In particular:
(a)The following are equivalent:
(i)the morphism grad(Q)is dominant;
(ii)b n(D(Q))>0;
(iii)the projective arrangement A is essential;i.e.,the intersection∩d i=1H i
is empty.
(b)If b n(D(Q))>0then d≤n+b n(D(Q)).As special cases:
(b1)b n(D(Q))=1if and only if d=n+1and up to a linear coordinate
change we have?i(x)=x i?1for all i=1,...,n+1;
(b2)b n(D(Q))=2if and only if d=n+2and up to a linear coordinate
change and re-ordering of the hyperplanes,?i(x)=x i?1for all i=
1,...,n+1and?n+2(x)=x0+x1.
Note that the equivalence of(i)and(iii)is a generalization of Lemma7
in[Do],and(b1)is a generalization of Theorem5in[Do].
To obtain Corollary4from Theorem1all we need is the following:
Lemma5.For any arrangement A as above,(?1)nχ(D(Q)\H)=
b n(D(Q)).
Let A′={H′i}i∈I be an a?ne hyperplane arrangement in C n with com-
plement M(A′)and let?′i=0be an equation for the hyperplane H′i.Consider
the multivalued function
φa:M(A′)→C,φa(x)= i?′i(x)a i
with a i∈C.Varchenko conjectured in[V]that for an essential arrangement A′
and for generic complex exponents a i the functionφa has only nondegenerate
478ALEXANDRU DIMCA AND STEF AN PAPADIMA
critical points and their number is precisely|χ(M(A′))|.This conjecture was proved in more general forms by Orlik-Terao[OT3]via algebraic methods and by Damon[Da2]via topological methods based on[DaM]and[Da1].
In particular Damon shows in Theorem1in[Da2]that the functionφ1 obtained by taking a i=1for all i∈I has only isolated singularities and the sum of the corresponding Milnor numbers equals|χ(M(A′))|.Consider the
morsi?cation
ψ(x)=φ1(x)?
n j=1
b j x j
where b j∈C are generic and small.Then one may think that by the general property of a morsi?cation,ψhas only nondegenerate critical points and their number is precisely|χ(M(A′))|.In fact,as a look at the simple example n=3 andφ1=xyz shows,there are new nondegenerate singularities occurring along the hyperplanes.This can be restated by saying that in general one has
deg(gradφ1)≥|χ(M(A′))|
and not an equality similar to our Corollary4(1).Note that here gradφ1: M(A′)→C n.
The classi?cation of arrangements for which|χ(M(A′))|=1is much more complicated than the one from Corollary4(b1)and the interested reader is referred to[JL].
Theorem1,in conjunction with Corollary4,Part(1),has very interesting consequences.We say that a topological space Z is minimal if Z has the homotopy type of a connected CW-complex K of?nite type,whose number of k-cells equals b k(K)for all k∈N.It is clear that a minimal space has integral torsion-free homology.The converse is true for1-connected spaces;see[PS, Rem.2.14].
The importance of this notion for the topology of spaces which look ho-mologically like complements of hyperplane arrangements was recently noticed in[PS].Previously,the minimality property was known only for generic ar-rangements(Hattori[Hat])and?ber-type arrangements(Cohen-Suciu[CS]). Our next result establishes this property,in full generality.It was indepen-dently obtained by Randell[R2,3],using similar techniques.(See,however, Example13.)The minimality property below should be compared with the main result from[GM,Part III],where the existence of a homologically perfect Morse function is established,for complements of(arbitrary)arrangements of real a?ne subspaces;see[GM,p.236].
Corollary6.Both complements,M(A)?P n and its cone,M′(A)?C n+1,are minimal spaces.
HYPERSURF ACE COMPLEMENTS479 It is easy to see that for n>1,the open set D(f)is not minimal for f generic of degree d>1(just useπ1(D(f))=H1(D(f),Z)=Z/d Z),but the Milnor?ber F de?ned by f is clearly minimal.We do not know whether the Milnor?ber{Q=1}associated to an arrangement is minimal in general.
From Theorem3we get a substantial strengthening of some of the main results by Orlik and Terao in[OT2].Let A′be the central hyperplane ar-rangement in C n+1associated to the projective arrangement A.Note that Q(x)=0is a reduced equation for the union N of all the hyperplanes in A′. Let f∈C[x0,...,x n]be a homogeneous polynomial of degree e>0with global Milnor?ber F={x∈C n+1|f(x)=1}and let g:F\N→R be the function g(x)=Q(x)
480ALEXANDRU DIMCA AND STEF AN PAPADIMA
Similar results for nonlinear arrangements on complete intersections have
been obtained by Damon in[Da3]where explicit formulas for|C(g)|are given.
The aforementioned results represent a strengthening of those in[D2](in
which the homological version of Theorems1and3above was proved).
The investigation of higher homotopy groups of complements of complex
hypersurfaces(asπ1-modules)is a very di?cult problem.In the irreducible
case,see[Li]for various results on the?rst nontrivial higher homotopy group.
The arrangements of hyperplanes provide the simplest nonirreducible situation
(whereπ1is never trivial,but at the same time rather well understood).This
is the topic of the second part of our paper.
Our results here use the general approach by minimality from[PS],and
signi?cantly extend the homotopy computations therefrom.In Section5,we
present a unifying framework for all known explicit descriptions of nontrivial
higher homotopy groups of arrangement complements,together with a numer-
ical K(π,1)-test.We give speci?c examples,in Section6,with emphasis on
combinatorial determination.A general survey of Sections5and6follows.(To
avoid overloading the exposition,formulas will be systematically skipped.)
Our?rst main result in Sections5and6is Theorem16.It applies to ar-
rangements A which are k-generic sections,k≥2,of aspherical arrangements, A.Here’k-generic’means,roughly speaking,that A and A have the same intersection lattice,up to rank k+1;see Section5(1)for the precise de?nition.
The general position arrangements from[Hat]and the?ber-type aspherical
ones from[FR]belong to the hypersolvable class from[JP1].Consequently
([JP2]),they all are2-generic sections of?ber-type arrangements.At the
same time,the iterated generic hyperplane sections,A,of essential aspherical
arrangements, A,from[R1],are also particular cases of k-generic sections,with k=rank(A)?1.
For such a k-generic section A,Theorem16?rstly says that the comple-
ment M(A)(M′(A))is aspherical if and only if p=∞,where p is a topolog-
ical invariant introduced in[PS].Secondly(if p<∞),one can write down a
Zπ1-module presentation forπp,the?rst higher nontrivial homotopy group of
the complement(see§5(8),(9)for details).Both results essentially follow from
Propositions14and15,which together imply that M(A)and M( A)share the same p-skeleton.
In Theorem18,we substantially extend and improve results from[Hat]and
[R1](see also Remark19).Here we examine A,an iterated generic hyperplane
section of rank≥3,of an essential aspherical arrangement, A.Set M=M(A). In this case,p=rank(A)?1[PS].We show that the Zπ1(M)-presentation of πp(M)from Theorem16extends to a?nite,minimal,free Zπ1(M)-resolution. We infer thatπp(M)cannot be a projective Zπ1(M)-module,unless rank(A)= rank( A)?1,when it is actually Zπ1(M)-free.
HYPERSURF ACE COMPLEMENTS481 In Theorem18(v),we go beyond the?rst nontrivial higher homotopy group.We obtain a complete description of all higher rational homotopy groups,L?:=⊕q≥1πq+1(M)?Q,including both the graded Lie algebra structure of L?induced by the Whitehead product,and the graded Qπ1(M)-module structure.
The computational di?culties related to the twisted homology of a con-nected CW-complex(in particular,to the?rst nonzero higher homotopy group) stem from the fact that the Zπ1-chain complex of the universal cover is very di?cult to describe,in general.As explained in the introduction,we have two results in this direction,at the I-adic associated graded level:Theorem20and Corollary21.
Corollary21belongs to a recurrent theme of our paper:exploration of new phenomena of combinatorial determination in the homotopy theory of arrangements.Our combinatorial determination property from Corollary21 should be compared with a fundamental result of Kohno[K],which says that the rational graded Lie algebra associated to the lower central series?ltration ofπ1of a projective hypersurface complement is determined by the cohomology ring.
In Theorem23,we examine the hypersolvable arrangements for which p=rank(A)?1.We establish the combinatorial determination property of the I-adic associated graded module(over Z)of the?rst higher nontrivial homotopy group of the complement,πp,in Theorem23(i).The proof uses in an essential way the ubiquitous Koszul property from homological algebra.
We also infer from Koszulness,in Theorem23(ii),that the successive quotients of the I-adic?ltration onπp are?nitely generated free abelian groups, with ranks given by the combinatorial I-adic?ltration formula(22).This resembles the lower central series(LCS)formula,which expresses the ranks of the quotients of the lower central series ofπ1of certain arrangements,in combinatorial terms.The LCS formula for pure braid groups was discovered by Kohno,starting from his pioneering work in[K].It was established for all ?ber-type arrangements in[FR],and then extended to the hypersolvable class in[JP1].
Another new example of combinatorial determination is the fact that the generic a?ne part of a union of hyperplanes has the homotopy type of the Folkman complex,associated to the intersection lattice.This follows from Theorem1and Corollary4;see the discussion after the proof of Theorem3.
2.Polar curves,a?ne Lefschetz theory
and degree of gradient maps
The use of the local polar varieties in the study of singular spaces is already a classical subject;see L?e[Le1],L?e-Teissier[LT]and the references
482ALEXANDRU DIMCA AND STEF AN PAPADIMA
therein.Global polar curves in the study of the topology of polynomials is a topic under intense investigations;see for instance Cassou-Nogu`e s and Dimca [CD],Hamm[H],N′e methi[N1,2],Siersma and Tib?a r[ST].For all the proofs in this paper,the classical theory is su?cient:indeed,all the objects being homogeneous,one can localize at the origin of C n+1in the standard way,see [D1].However,using geometric intuition,we?nd it easier to work with global objects,and hence we adopt this viewpoint in the sequel.
We recall brie?y the notation and the results from[CD],[N1,2].Let h∈C[x0,...,x n]be a polynomial(even nonhomogeneous to start with)and assume that the?ber F t=h?1(t)is smooth,for some?xed t∈C.
For any hyperplane in P n,H:?=0where?(x)=c0x0+c1x1+···+c n x n, we de?ne the corresponding polar varietyΓH to be the union of the irreducible components of the variety
{x∈C n+1|rank(dh(x),d?(x))=1}
which are not contained in the critical set S(h)={x∈C n+1|dh(x)=0}of h.
Lemma8(see[CD],[ST]).For a generic hyperplane H,
(i)The polar varietyΓH is either empty or a curve;i.e.,each irreducible
component ofΓH has dimension1.
(ii)dim(F t∩ΓH)≤0and the intersection multiplicity(F t,ΓH)is independent of H.
(iii)The multiplicity(F t,ΓH)is equal to the number of tangent hyperplanes to F t parallel to the hyperplane H.For each such tangent hyperplane H a, the intersection F t∩H a has precisely one singularity,which is an ordinary double point.
The nonnegative integer(F t,ΓH)is called the polar invariant of the hy-persurface F t and is denoted by P(F t).Note that P(F t)corresponds exactly to the classical notion of class of a projective hypersurface;see[L].
We think of a projective hyperplane H as the direction of an a?ne hy-perplane H′={x∈C n+1|?(x)=s}for s∈C.All the a?ne hyperplanes with the same direction form a pencil,and it is precisely this type of pencil that is used in the a?ne Lefschetz theory;see[N1,2].N′e methi considers only connected a?ne varieties,but his results clearly extend to the case of any pure dimensional smooth variety.
Proposition9(see[CD],[ST]).For a generic hyperplane H′in the pencil of all hyperplanes in C n+1with a?xed generic direction H,the?ber F t is homotopy equivalent to a CW-complex obtained from the section F t∩H′by attaching P(F t)cells of dimension n.In particular
P(F t)=(?1)n(χ(F t)?χ(F t∩H′))=(?1)nχ(F t\H′).
HYPERSURF ACE COMPLEMENTS483 Moreover,in this statement‘generic’means that the a?ne hyperplane H′has to verify the following two conditions:
(g1)its direction in P n has to be generic,and
(g2)the intersection F t∩H′has to be smooth.
These two conditions are not stated in[CD],but the reader should have no problem in checking them by using Theorem3′in[CD]and the fact proved by N′e methi in[N1,2]that the only bad sections in a good pencil are the singular https://www.doczj.com/doc/f011782671.html,pletely similar results hold for generic pencils with respect to a closed smooth subvariety Y in some a?ne space C N;see[N1,2],but note that the polar curves are not mentioned there.
Proof of Theorem 1.In view of Hamm’s a?ne Lefschetz theory,see [H,Th.5],the only thing to prove is the equality between the number k n of n-cells attached and the degree of the gradient.
Assume from now on that the polynomial h is homogeneous of degree d and that t=1.It follows from(g1)and(g2)above that we may choose the generic hyperplane H′passing through the origin.
Moreover,in this case,the polar curveΓH,being de?ned by homogeneous equations,is a union of lines L j passing through the origin.For each such line we choose a parametrization t→a j t for some a j∈C n+1,a j=0.It is easy to see that the intersection F1∩L j is either empty(if h(a j)=0)or consists of exactly d distinct points with multiplicity one(if h(a j)=0).The lines of the second type are in bijection with the points in grad(h)?1(D H′),where D H′∈P n is the point corresponding to the direction of the hyperplane H′.It follows that
d·deg(grad(h))=P(F1).
The d-sheeted unrami?ed coverings F1→D(h)and F1∩H′→D(h)∩H give the result,where H is the projective hyperplane corresponding to the a?ne hyperplane(passing through the origin)H′.Indeed,they imply the equalities:χ(F1)=d·χ(D(h))andχ(F1∩H′)=d·χ(D(h)∩H).Hence we have deg(grad(h))=(?1)nχ(F1,F1∩H′)/d=(?1)nχ(D(h),D(h)∩H)=k n.
Remark10.The gradient map grad(h)has a natural extension to the larger open set D′(h)where at least one of the partial derivatives of h does not vanish.It is obvious(by a dimension argument)that this extension has the same degree as the map grad(h).
3.Nonproper Morse theory
For the convenience of the reader we recall,in the special case needed, a basic result of Hamm,see[H,Prop.3],with our addition concerning the condition(c0)in[DP,Lemma3and Ex.2].The?nal claim on the number of cells to be attached is also standard,see for instance[Le1].
484ALEXANDRU DIMCA AND STEF AN PAPADIMA
Proposition11.Let A be a smooth algebraic subvariety in C p with dim A=m.Let f1,...,f p be polynomials in C[x1,...,x p].For1≤j≤p, denote byΣj the set of critical points of the mapping(f1,...,f j):A\{z∈A|f1(z)=0}→C j and letΣ′j denote the closure ofΣj in A.Assume that the following conditions hold.
(c0)The set{z∈A||f1(z)|≤a1,...,|f p(z)|≤a p}is compact for any positive numbers a j,j=1,...,p.
(c1)The critical setΣ1is?nite.
(cj)(for j=2,...,p)The map(f1,...,f j?1):Σ′j→C j?1is proper.
Then A has the homotopy type of a space obtained from A1={z∈A|f1(z)=0}by attaching m-cells and the number of these cells is the sum of the Milnor numbersμ(f1,z)for z∈Σ1.
Proof of Theorem3.We set X=h?1(1).Let v:C n+1→C N be the Veronese mapping of degree e sending x to all the monomials of degree e in x and set Y=v(X).Then Y is a smooth closed subvariety in C N and v:X→Y is an unrami?ed covering of degree c,where c=g.c.d.(d,e).To see this,use the fact that v is a closed immersion on C N\{0}and v(x)=v(x′)if and only if x′=u·x with u c=1.
Let H be a generic hyperplane direction in C N with respect to the subva-riety Y and let C(H)be the?nite set of all the points p∈Y such that there is an a?ne hyperplane H′p in the pencil determined by H that is tangent to Y at the point p and the intersection Y∩H′p has a complex Morse(alias non-degenerate,alias A1)singularity.Under the Veronese mapping v,the generic hyperplane direction H corresponds to a homogeneous polynomial of degree e which we call from now on f.
To prove the?rst claim(i)we proceed as follows.It is known that using a?ne Lefschetz theory for a pencil of hypersurfaces{h=t}is equivalent to using(nonproper)Morse theory for the function|h|or,what amounts to the same,for the function|h|2.More explicitly,in view of the last statement at the end of the proof of Lemma(2.5)in[OT2](which clearly applies to our more general setting since all the computations there are local),g is a Morse function if and only if each critical point of h:F\N→C is an A1-singularity. By the homogeneity of both f and h,this last condition on h is equivalent to the fact that each critical point of the function f:X→C is an A1-singularity, condition ful?lled in view of the choice of H and since v:X→Y is a local isomorphism.
Now we pass on to the proof of the claim(ii)in Theorem3.One can derive this claim easily from Proposition9.14in Damon[Da1].However since his proof is using previous results by Siersma[Si]and Looijenga[Lo],we think that our original proof given below and based on Proposition11,longer but more self-contained,retains its interest.
HYPERSURF ACE COMPLEMENTS485 Any polynomial function h:C n+1→C admits a Whitney strati?cation satisfying the Thom a h-condition.This is a constructible strati?cation S such that the open stratum,say S0,coincides with the set of regular points for h and for any other stratum,say S1?h?1(0),and any sequence of points q m∈S0 converging to q∈S1such that the sequence of tangent spaces T q
(h)has a
m
limit T;one has T q S1?T.See Hironaka[Hi,Cor.1,p.248].The requirement of f proper in that corollary is not necessary in our case,as any algebraic map can be compacti?ed.Here and in the sequel,for a mapφ:X→Y and a point q∈X we denote by T q(φ)the tangent space to the?berφ?1(φ(q))at the point q,assumed to be a smooth point on this?ber.
Since in our case h is a homogeneous polynomial,we can?nd a strati?-cation S as above such that all of its strata are C?-invariant,with respect to the natural C?-action on C n+1.In this way we obtain an induced Whitney strati?cation S′on the projective hypersurface V(h).We select our polyno-mial f such that the corresponding projective hypersurface V(f)is smooth and transversal to the strati?cation S′.In this way we get an induced Whitney strati?cation S′1on the projective complete intersection V1=V(h)∩V(f).
We use Proposition11above with A=F and f1=h.All we have to show is the existence of polynomials f2,...,f n+1satisfying the conditions listed in Proposition11.
We will select these polynomials inductively to be generic linear forms as follows.We choose f2such that the corresponding hyperplane H2is transversal to the strati?cation S′1.Let S′2denote the induced strati?cation on V2= V1∩H2.Assume that we have constructed f2,...,f j?1,S′1,...,S′j?1and V1,...,V j?1.We choose f j such that the corresponding hyperplane H j is transversal to the strati?cation S′j?1.Let S′j denote the induced strati?cation on V j=V j?1∩H j.Do this for j=3,...,n and choose for f n+1any linear form.
With this choice it is clear that for1≤j≤n,V j is a complete intersection of dimension n?1?j.In particular,V n=?;i.e.
(c0′){x∈C n+1|f(x)=h(x)=f2(x)=···=f n(x)=0}={0}.
Then the map(f,h,f2,...,f n):C n+1→C n+1is proper,which clearly implies the condition(c0).
The condition(c1)is ful?lled by our construction of f.Assume that we have already checked that the conditions(ck)are ful?lled for k=1,...,j?1. We explain now why the next condition(cj)is ful?lled.
Assume that the condition(cj)fails.This is equivalent to the existence of a sequence p m of points inΣ′j such that
(?)|p m|→∞and f k(p m)→b k(?nite limits)for1≤k≤j?1.
SinceΣj is dense inΣ′j,we can even assume that p m∈Σj.
486ALEXANDRU DIMCA AND STEF AN PAPADIMA
Note thatΣj?1?Σj and the condition c(j?1)is ful?lled.This implies that we may choose our sequence p m in the di?erenceΣj\Σj?1.In this case we get
(??)f j∈Span(d f(p m),dh(p m),f2,...,f j?1)
the latter being a j-dimensional vector space.
Let q m=p m
HYPERSURF ACE COMPLEMENTS487 The main interest in Dolgachev’s paper[Do]is focused on homaloidal polynomials,i.e.,homogeneous polynomials h such that deg(grad(h))=1.In view of the above reformulation of Theorem1it follows that a polynomial h is homaloidal if and only if the a?ne hypersurface V(h)a is homotopy equivalent to an(n?1)-sphere.There are several direct consequences of this fact.
(i)If V(h)is either a smooth quadric(i.e.d=2)or the union of a smooth quadric Q and a tangent hyperplane H0to Q(in this case d=3),then deg(grad(h))=1.Indeed,the?rst case is obvious(either from the topology or the algebra),and the second case follows from the fact that both H0\H and (Q∩H0)\H are contractible.
(ii)Using the topological description of an irreducible projective curve as the wedge of a smooth curve of genus g and m circles,we see that for an irreducible plane curve C of degree d,
b1(C a)=2g+m+d?1.
Using this and the Mayer-Vietoris exact sequence for homology one can derive Theorem4in[Do],which gives the list of all reduced homaloidal polynomials h in the case n=2.This list is reduced to the two examples in(i)above plus the union of three nonconcurrent lines.
(iii)If the hypersurface V(h)has only isolated singular points,say at a1,...,a m,then our formula above gives
deg(grad(h))=(d?1)n?
m
i=1
μ(V(h),a i),
whereμ(V,a)is the Milnor number of the isolated hypersurface singularity (V,a);see[D1,p.161].We conjecture that when n>2and d>2one has deg(grad(h))>1in this situation,unless V(h)is a cone and then of course deg(grad(h))=0.For more details on this conjecture and its relation to the work by A.duPlessis and C.T.C.Wall in[dPW],see[D3].
https://www.doczj.com/doc/f011782671.html,plements of hyperplane arrangements
Proof of Lemma 5.We are going to derive this easy result from [H,Th.5],by using the key homological features of arrangement complements. By Hamm’s theorem,the equality between(?1)nχ(D(Q)\H)=(?1)nχ(D(Q), D(Q)∩H)and b n(D(Q))is equivalent to
(?)b n?1(D(Q)∩H)=b n?1(D(Q)).
All we can say in general is that b n?1(D(Q)∩H)≥b n?1(D(Q)).In the arrangement case,the other inequality follows from two standard facts(see
488ALEXANDRU DIMCA AND STEF AN PAPADIMA
[OT1,Cor.5.88and Th.5.89]):H n?1(D(Q)∩H)is generated by products of cohomology classes of degrees
Proof of Corollary4.(1)This claim follows directly from Theorem1and Lemma5.
(2)(a)To complete this proof we only have to explain why the claims(ii) and(iii)are equivalent.This in turn is an immediate consequence of the well-known equality:deg P A(t)=codim(∩d i=1H i)?1,where P A(t)is the Poincar′e polynomial of D(Q);see[OT1,Cor.3.58,Ths.3.68and2.47].
(2)(b)The inequality can be proved by induction on d by the method of deletion and restriction;see[OT1,p.17].
Proof of https://www.doczj.com/doc/f011782671.html,ing the a?ne Lefschetz theorem of Hamm(see Theorem5in[H]),we know that for a generic projective hyperplane H,the space M has the homotopy type of a space obtained from M∩H by attaching n-cells.The number of these cells is given by
(?1)nχ(M,M∩H)=(?1)nχ(M\H)=b n(M);
see Corollary4above.
To?nish the proof of the minimality of M we proceed by induction.Start with a minimal cell structure,K,for M∩H,to get a cell structure,L,for M,by attaching b n(M)top cells to K.By minimality,we know that K has trivial cellular incidences.The fact that the number of top cells of L equals b n(L)means that these cells are attached with trivial incidences,too,whence the minimality of M.
Finally,M′has the homotopy type of M×S1,being therefore minimal, too.
Remark12.(i)Letμe be the cyclic group of the e-roots of unity.Then there are natural algebraic actions ofμe on the spaces F\N and F∩N occurring in Theorem3.The corresponding weight equivariant Euler polynomials(see [DL]for a de?nition)give information on the relation between the induced μe-actions on the cohomology H?(F\N,Q)and H n?1(F∩N,Q)and the functorial Deligne mixed Hodge structure present on cohomology.
When N is a hyperplane arrangement A′and f is an A′-generic func-tion,these weight equivariant Euler polynomials can be combinatorially com-puted from the lattice associated to the arrangement(see Corollary(2.3)and Remark(2.7)in[DL])by the fact that the weight equivariant Euler polyno-mial of theμe-variety F is known;see[MO]and[St].This gives in particular the characteristic polynomial of the monodromy associated to the function f:N→C.
HYPERSURF ACE COMPLEMENTS489 (ii)The minimality property turns out to be useful in the context of
homology with twisted coe?cients.Here is a simple example.(More results along this line will be published elsewhere.)Let X be a connected CW-complex
of?nite type.Setπ:=π1(X).For a left Zπ-module N,denote by H?(X,N)
the homology of X with local coe?cients corresponding to N.One knows that
H?(X,N)may be computed as the homology of the chain complex C?( X)?ZπN,where C?( X)denotes theπ-equivariant chain complex of the universal cover of X;see[W,Ch.VI].
Assume now that X is minimal.If N is a?nite-dimensional K-represen-
tation ofπover a?eld K,we obtain,from the above description of twisted
homology,that
dim K H q(X,N)≤(dim K N)·b q(X),for all q.
When X is,up to homotopy,an arrangement complement,and K=C,we thus
recover the main result of[C].(Twisted cohomology may be treated similarly.) Example13.In this example we explain why special care is needed when doing Morse theory on noncompact manifolds as in[OT2]and[R2].Let’s start with a very simple case,where computations are easy.Consider the Milnor ?ber,X?C2,given by{xy=1}.The hyperplane{x+y=0}is generic with respect to the arrangement{xy=0},in the sense of[R2,Prop.2].Set σ:=|x+y|2.When trying to do proper Morse theory with boundary,as in [R2,Th.3],one faces a delicate problem on the boundary.Denoting by B R (S R)the closed ball(sphere)of radius R in C2,we see easily that X∩B R=?, if R2<2,and that the intersection X∩S R is not transverse,if R2=2.In the remaining case(R2>2),it is equally easy to check that the restriction ofσto the boundary X∩S R always has eight critical points(withσ=0).In our very simple example,all these critical points are‘`a gradient sortant’(in the terminology of[HL,Def.3.1.2]).The proof of this fact does not seem obvious, in general.At the same time,this property seems to be needed,in order to get the conclusion of[R2,Th.3](see[HL,Th.3.1.7]).
One can avoid this problem as follows.(See also Theorem3in[R3].)Let
X denote the a?ne Milnor?ber and?:X→C the linear function induced
by the equation of any hyperplane.Then for a real number r>0,let D r be
the open disc|z| points,it follows that X has the same homotopy type(even di?eo type)as the cylinder X r=??1(D r)for r>>0.Fix such an r.For R>>r,we have that Y=X r∩B R has the same homotopy type as X r. Moreover,if the hyperplane?=0is generic in the sense of L?e/N′e methi, it follows that the real function|?|has no critical points on the boundary of Y except those corresponding to the minimal value0which do not matter. In the example treated before,one can check that the critical values 490ALEXANDRU DIMCA AND STEF AN PAPADIMA corresponding to the eight critical points tend to in?nity when R→∞;i.e., the eight singularities are no longer in Y for a good choice of r and R! Note that Y is a noncompact manifold with a noncompact boundary,but the sets Y r0={y∈Y||?(y)|≤r0}are compact for all0≤r0 The idea behind Proposition11is the same:one can do Morse theory on a noncompact manifold with corners if there are no critical points on the boundary,and this is achieved by an argument similar to the above and based on the conditions(cj);see[H]for more details. 5.k-generic sections of aspherical arrangements The preceding minimality result(Corollary6)enables us to use the gen-eral method of[PS]to get explicit information on higher homotopy groups of arrangement complements,in certain situations.We begin by describing a framework that encompasses all such known computations.(For the basic facts in arrangement theory,we use reference[OT1].) Let A={H1,...,H n}be a projective hyperplane arrangement in P(V), with associated central arrangement,A′={H′1,...,H′n},in V.Let M(A)?P(V)and M′(A)?V be the corresponding arrangement complements.Denote by L(A)the intersection lattice,that is the set of intersections of hyperplanes from A′,X(called?ats),ordered by reverse inclusion.We will assume that A is essential.(We may do this,without changing the homotopy types of the complements and the intersection lattice,in a standard way;see[OT1, p.197].)Then there is a canonical Whitney strati?cation of P(V),S A,whose strata are indexed by the nonzero?ats,having M(A)as top stratum;see[GM, III3.1and III4.5].Thus,the genericity condition from Morse theory takes a particularly simple form,in the arrangement case. To be more precise,we will need the following de?nition.Let U?V be a complex vector subspace.We say that U is L k(A)-generic(0≤k (1)codim V(X)=codim U(X∩U),for all X∈L(A),codim V(X)≤k+1. It is not di?cult to see that(1)forces k≤dim U?1and that P(U)is transverse to S A if and only if U is L k(A)-generic,with k=dim U?1.Consider also the restriction,A U:={P(U)∩H1,...,P(U)∩H n},with complement M(A)∩P(U). A direct application of[GM,Th.II5.2]gives then the following: (2)If k=dim U?1and U is L k(A)-generic,then the pair(M(A), M(A)∩P(U))is k-connected. HYPERSURF ACE COMPLEMENTS491 The next proposition,which will provide our framework for homotopy computations by minimality,upgrades the above implication(2)to the level of cells,for the case of an arbitrary L k(A)-generic section,U. Proposition14.Let A be an arrangement in P(V),and let U?V be a subspace.Assume that both A and the restriction A U are essential.If U is L k(A)-generic(0≤k (i)Both X and Y are minimal CW-complexes. (ii)At the level of k-skeletons,X(k)=Y(k),and the restriction of j to X(k) is the identity. Proof.If k If k=dim U?1,it is not di?cult to see that A U may be obtained from A by taking dim V?dim U successive generic hyperplane sections.Therefore, the method of proof of Corollary6shows that,up to homotopy,M(A)∩P(U) is the k-skeleton of a minimal CW-structure for M(A). Let A be an arrangement in P(V),and let U?V be a proper subspace which is L0(A)-generic.Assume that both A and A U are essential.The preceding proposition leads to the following combinatorial de?nition: (3)k(A,U):=sup{0≤? and to the next topological counterpart: (4)p(A,U):=sup{q≥0|b r(M(A))=b r(M(A U)),for all r≤q}. Proposition15.k(A,U)=p(A,U). Proof.The inequality k(A,U)≤p(A,U)follows from Proposition14. Denoting by r and r′the ranks of A and A U respectively,we know that b s(M(A U))=0,for s≥r′,and b s(M(A))=0,for s 492ALEXANDRU DIMCA AND STEF AN PAPADIMA To this end,we will use three well-known facts(see[OT1]).Firstly,the natural map,H?M(A)→H?M(A U),is onto.Secondly,the natural map, H?M(B)→H?M(A),is monic.Together with de?nition(4)above,these two facts imply that the natural map,H?M(B)→H?M(B U),is an isomorphism, up to degree q.The combinatorial description of the cohomology algebras of arrangement complements by Orlik-Solomon algebras may now be used to deduce the independence of B U from B. Description of the k-generic framework We want to apply Theorem2.10from[PS]to an(essential)arrangement A in P(U),with complement M:=M(A).Setπ=π1(M).The method of[PS] requires both M and K(π,1)to be minimal spaces,with cohomology algebras generated in degree1.By Corollary6(and standard facts in arrangement cohomology)all these assumptions will be satis?ed,as soon as K(π,1)is(up to homotopy)an arrangement complement,too. This in turn happens whenever A is a k-generic section,k≥2,of an (essential)aspherical arrangement, A.That is,if there exists A in P(V), U?V,with M( A)aspherical,such that A= A U,and with the property that U is L k( A)-generic,as in(1)above. Indeed,Proposition14guarantees that in this case we may replace,up to homotopy,the inclusion M(A)?→M( A)by a cellular map between minimal CW-complexes,j:X→Y,which restricts to the identity on k-skeletons.In particular,Y is a K(π,1)and j is a classifying map. Let us recall now from[PS,Def.2.7]the order ofπ1-connectivity, (5)p(M):=sup{q|b r(M)=b r(Y),for all r≤q}. Set p=p(M).It follows from Proposition15that p=∞if and only if U=V. Moreover,Propositions14and15imply that k≤p and that we may actually construct a classifying map j with the property that j|X(p)=id(with the convention X(∞)=X). We will also need theπ-equivariant chain complexes of the universal cov-ers, X and Y,associated to the above Morse-theoretic minimal cell structures: (6)C?( X):={d q:H q X?Zπ?→H q?1X?Zπ}q, and (7)C?( Y):={?q:H q Y?Zπ?→H q?1Y?Zπ}q. They have the property that C≤p( X)=C≤p( Y).(Here we adopt the conven-tion of turning left Zπ-modules into right Zπ-modules,replacing the action of x∈πby that of x?1.) wifi万能钥匙V2.0官方PC电脑版 免费使用教程 大家伙都知道WiFi万能钥匙是一款自动获取周边免费Wi-Fi热点信息并建立连接的android手机必备工具。所有的热点信息基于云端数据库，内置全国数万Wi-Fi热点数据，随时随地轻松接入无线网络，最大化使用各种联网的移动服务，扫除无网断网的状态，特别适合商务人群、移动人群和重度网虫，不过万能钥匙只能为手机用户带来方便，电脑用户却是无福消受，不过不要担心，万能钥匙官方已经考虑到这个问题了，这不WiFi万能钥匙电脑版出炉了，WiFi 万能钥匙pc版支持电脑解锁连接附近共享WiFi，下载安装后可获得像手机端同样的连接WiFi体验。使用户能够实现任何地方不断网，享受丰富多彩的互联网生活。 WiFi万能钥匙常见问题： 1.为什么要使用WiFi万能钥匙？ WiFi万能钥匙是一款android手机必备的搜索连接管理Wi-Fi热点的工具。内置逾万条的Wi-Fi热点数据；用户可分享使用已知的Wi-Fi热点信息；智能关闭Wi-Fi热点功能非常省电；支持网页认证一键连接，方便省心。 2.什么是万能钥匙自动解锁？ 若该加密Wi-Fi热点已共享，则可以使用万能钥匙进行连接使用；若该加密Wi-Fi热点尚未共享，则您可以共享该热点。 3.为什么我的Wi-Fi功能会自动关闭？ 若勾选了“一键省电”的功能，该功能会在屏幕锁定后或无网络传输时自动关闭Wi-Fi功能。这样做，省电同时也省心，无须再手动关闭Wi-Fi功能了。也可以取消“一键省电”设置，自行调整选项。 4.咖啡馆、机场商场等地点的网络是开放网络，需要通过网页认证，我使用WiFi万能钥匙后，每次连接还需要打开网页吗？ WiFi万能钥匙是支持网页认证的，只需要网页认证连接一次该Wi-Fi热点，今后就无须再打开网页进行认证了。 用六个步骤建立平衡计分卡 作者：杨序国 目前，平衡计分卡应用与推广的热潮正从国外袭入国内。根据Gartner Group 的调查表明，到2000年为止，在《财富》杂志公布的世界前1000位公司中有40%的公司采用了平衡计分卡系统。在最近由William M. Mercer 公司对214个公司的调查中发现，88%的公司提出平衡计分卡对于员工报酬方案的设计与实施是有帮助的，并且平衡计分卡所揭示的非财务的考核方法在这些公司中被广泛运用于员工奖金计划的设计与实施中。然而，国内不少企业设计与实施的平衡计分卡与真正的平衡计分卡的初衷存在一些背离。在国外，平衡计分卡被比作飞机驾驶舱内的仪表盘，里面有各种指标，管理层借此观察企业运行是否良好。而国内的公司更多的只是单纯将平衡计分卡作为一种绩效考评工具，往往以解决价值分配问题为初衷，而不是作为一种战略实施划执行工具，首先以支撑企业战略目标的达成为目的。 如图1所示（图略），建立平衡计分卡是一个系统化的过程。这里必须强调的是，必须根据公司战略来制定平衡计分卡，再按照战略与平衡计分卡来制定战略的实施计划，而不是相反。否则平衡计分卡就成为对战略实施计划的监测工具和绩效管理工具，这与KPI没有什么区别。这是多数公司会犯的错误。 下表1是笔者2003年上半年在深圳特区某高科技民营企业做BSC咨询项目时的工作计划表： 表1：BSC项目时间表 第一阶段：战略明确与前期工作 第一步，制定公司战略。 公司战略的制定虽不是本文所要解决的问题，但要明白公司在生命周期不同的阶段有不同的战略重点，如表2： 表2：处于生命周期不同阶段的公司的战略重点 第二步，调查与明确客户价值定位 客户的价值定位就是为什么客户从您的公司，而不是从您的竞争对手那里购买产品？他们会为了什么（价格、质量、时间、功能、服务、关系、品牌、形象）而付出钞票？公司如何比竞争对手做得更好？公司的产品/服务是否能为客户提供与众不同的价值？如何让公司的产品/服务优于竞争对手？ 所谓三电平是指逆变器交流侧每相输出电压相对于直流侧有三种取值，正端电压(+Vdc/2)、负端电压(-Vdc/2)、中点零电压(0)。二极管箱位型三电平逆变器主电路结构如图所示。逆变器每一相需要4个IGBT开关管、4个续流二极管、2个箱位二极管;整个三相逆变器直流侧由两个电容C1、C2串联起来来支撑并均衡直流侧电压，C1=C2。通过一定的开关逻辑控制，交流侧产生三种电平的相电压，在输出端合成正弦波。 三电平逆变器的工作原理 以输出电压A相为例，分析三电平逆变器主电路工作原理，并假设器件为理想器件，不计其导通管压降。定义负载电流由逆变器流向电机或其它负载时的方向为正方向。 (l) 当Sa1，、Sa2导通，Sa3、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流从正极点流过主开关Sa1、Sa2，该相输出端电位等同于正极点电位，输出电压U=+V dc/2; 若负载电流为负方向，则电流流过与主开关管Sa1、Sa2反并联的续流二极管对电容C1充电，电流注入正极点，该相输出端电位仍然等同于正极点电位，输出电压U=+V dc/2。通常标识为所谓的“1”状态，如图所示。 “1”状态“0”状态 “-1”状态 (2) 当Sa2、Sa3导通，Sa1、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流 从O点顺序流过箱位二极管D a1，主开关管Sa2:，该相输出端电位等同与0点电位，输出电压U=O;若负载电流为负方向，则电流顺序流过主开关管Sa3和箱位二极管D a2，电流注入O点，该相输出端电位等同于O点电位，输出电压U=0，电源对电容C2充电。即通常标识的“0”状态，如图所示。 扫描仪驱动安装步骤 一、安装 注意：安装扫描仪驱动前，请不要启动扫描仪。 1、打开光盘，双击“电子档案扫描必备软件”->“扫描仪软 件”->“扫描仪驱动” 2、双击“setup.exe”图标，点击“下一步” 3、点击“下一步” 4、点击“下一步” 5、点击“是” 6、选择要安装的目录，建议不与操作系统安装在同一磁盘 里，点击“下一步” 7、点击“下一步” 8、点击“下一步” 9、点击“下一步” 10、点击“完成” 二、更新 1、打开光盘，双击“电子档案扫描必备软件”->“扫描仪软 件”->“扫描仪补丁”->“ScannPatch” 2、双击“FhkSp”图标，显示“安装成功”，点击“确定”。 三、安装扫描仪设置软件 1、打开光盘，双击“电子档案扫描必备软件”->“扫描仪软 件”->“ScandAll”，双击“ScandAllPRO”的图标 2、去掉“安装Scan to Microsoft SharePoint。”前面的选项 “√”，点击“ok” 3、点击“下一步” 4、选择“我接受许可证协议中的条款”，点击“下一步” 5、点击“下一步” 6、选择要安装的目录，建议不与操作系统安装在同一磁盘 里，点击“下一步” 7、点击“下一步” 8、点击“下一步” 9、点击“完成” 四、配置扫描仪 1、打开扫描仪开关，启动扫描仪 2、双击桌面快捷方式图标，打开扫描仪配置软件 3、点击菜单栏中的“扫描”->“选择扫描仪” 4、如下图所示，选择扫描仪fi-6130，点击选择 5、点击菜单栏中的“扫描”->“设置” 6、进入设置界面，在“图像模式”下拉选项中，选择“灰度” 7、点击下面的“选项”按钮 8、在“旋转”选项卡中，“自动检测尺寸和偏斜”选项中，选 择“自动页面尺寸检测”。 9、在“工作/缓存”选项卡中，“预先抓纸”选项中，选择“重 叠检测（超声波）”。 三电平逆变器的主电路结构及其工作原理 所谓三电平是指逆变器交流侧每相输出电压相对于直流侧有三种取值，正端电压(+Vdc/2)、负端电压(-Vdc/2)、中点零电压(0)。二极管箱位型三电平逆变器主电路结构如图所示。逆变器每一相需要4个IGBT开关管、4个续流二极管、2个箱位二极管;整个三相逆变器直流侧由两个电容C1、C2串联起来来支撑并均衡直流侧电压，C1=C2。通过一定的开关逻辑控制，交流侧产生三种电平的相电压，在输出端合成正弦波。 三电平逆变器的工作原理 以输出电压A相为例，分析三电平逆变器主电路工作原理，并假设器件为理想器件，不计其导通管压降。定义负载电流由逆变器流向电机或其它负载时的方向为正方向。 (l) 当Sa1，、Sa2导通，Sa3、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流从正极点流过主开关Sa1、Sa2，该相输出端电位等同于正极点电位，输出电压U=+V dc/2; 若负载电流为负方向，则电流流过与主开关管Sa1、Sa2反并联的续流二极管对电容C1充电，电流注入正极点，该相输出端电位仍然等同于正极点电位，输出电压U=+V dc/2。通常标识为所谓的“1”状态，如图所示。 “1”状态“0”状态 “-1”状态 (2) 当Sa2、Sa3导通，Sa1、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流 从O点顺序流过箱位二极管D a1，主开关管Sa2:，该相输出端电位等同与0点电位，输出电压U=O;若负载电流为负方向，则电流顺序流过主开关管Sa3和箱位二极管D a2，电流注入O点，该相输出端电位等同于O点电位，输出电压U=0，电源对电容C2充电。即通常标识的“0”状态，如图所示。 (3) 当Sa3、Sa4导通，Sa1、Sa2关断时，若负载电流为正方向，则电流从负极点流过与主开 关Sa3、Sa4反并联的续流二极管对电容C2进行充电，该相输出端电位等同于负极点电位，输出电压U=-V dc/2;若负载电流为负方向，则电源对电容C2充电，电流流过主开关管Sa3、Sa4注入负极点，该相输出端电位仍然等同于负极点电位，输出电压U=-V dc/2。通常标识为“-1”状态，如图所示。 慧眼扫描仪驱动安装使用指南 1、慧眼扫描仪使用平台说明 原有“综合纳税服务平台”不支持慧眼扫描仪，使用慧眼扫描仪必须给企业用户安装百旺的“网上受理”系统，而且“网上受理”系统也不支持虹光扫描仪。当前我公司负责人正在联系总参，欲将“网上受理”系统做出调整让其支持虹光扫描仪，但短时间内实现不了。 “网上受理”和“纳服平台”互不兼容，在同一台电脑上不能安装两个平台，否则会导致双方都不能实现认证操作。 2、慧眼X30扫描仪驱动安装注意事项 （1）慧眼扫X30描仪本身有平板扫描和高速扫描两种方式，但是现在扫描仪不能自动检测扫描，安装完驱动之后，网上受理平台扫描认证直接调用的是高速扫描，平板暂不能使用。此问题已联系厂家做出修改，正在处理中。 （2）X30扫描仪直接安装扫描货运发票没有问题，但是扫描增值税发票有问题，有些数据项没有办法扫描到，或者切割错误，这个是扫描仪安装注册表参数的问题，需要修改注册表参数，然后再使用扫描增值税发票。X30需要修改的注册表参数是：HKEY_CURRENT_USER\Software\LANXUM\67LU\TWAIN\Last Settings\ADF Front\1下Paper Settings的参数由默认的0改为4. X30修改注册表操作步骤如下： 安装过慧眼X30扫描仪之后，需要修改注册文件，如果不修改注册文件，货运认证没有问题，但是增值税扫描认证有些认证项无法扫描出来。 注册表修改入下图所示： XP 系统：点击“开始——运行”，页面如下图所示： 打开运行窗口，输入“regedit”，页面如下图所示： 点击【确定】按钮，或者直接回车，会打开注册表页面，如下图所示： 网络打印机及网络扫描仪的安装方法 2011-02-17 02:11 P.M. 一、网络打印机的安装 1.电脑开机后放入光盘——打开桌面“我的电脑”——点击“DVD驱动器”——安装打印机驱动和扫描仪驱动 2.点击“开始”——点击“运行”——输入“cmd”后点确定——输入“ipconfig”——IP Address为IP地址，subnet mask为子网掩码，default gateway 为默认网关 3.打开复印机——找到系统设置——选择“指定”—— 按“IP”给复印机指定一个IP地址。例如电脑的IP地址为192.168.1.102，则可给复印机指定IP为192.168.1.103或192.168.1.104等（指定IP要注意不能与其他电脑IP相同） 按“子网掩码”——输入与电脑子网掩码相同的子网掩码。例如电脑子网掩码为255.255.255.0，则复印机的子网掩码也要设为255.255.255.0后退菜单——菜单向下按找到网关——给复印机指定的网关要与电脑相同。例如电脑的默认网关为192.168.1.1，则复印机的默认网关也要为192.168.1.1 4.点击“开始”——“设置”——“控制面板”——点击“打印机和其他硬 件”（经典视图下点击“打印机和传真”）——找到将要安装的打印机——点击右键“属性”——点击上方“端口”——点击中下方“添加端口”——选择“standard TCP/IP port”——点击“新端口”——“下一步”——输入复印机的IP地址——“下一步”即可（若提示网络上没有找到设备。则检查网线是否连接好。若确信连接好后仍有提示则说明复印机与该电脑不再同一网段）完成添加端口后点击“确定”即可。 点击“开始”——“运行”——输入“cmd”点确定——输入“ping空格复印机IP地址”。例如复印机IP地址为192.168.1.105，则输入“ping 192.168.1.105”——若出现有255字样说明打印机安装成功。 二、网络扫描仪的安装 1.点击“开始”——“程序”——找到扫描仪的驱动“Type TWAIN ”——“Network”——选择“使用特定扫描仪”——点击“搜索扫 描仪”——确定后在“IP地址或主机名：”中输入复印机的IP地址然后点“确定” 2.打开word软件——点击“插入”菜单——“图片”——“来自扫描仪或照相机”——在“设备”中选择安装好的扫描仪——点击“自动插入”即可。 三、问题解决 1.若网络打印机或网络扫描仪不能成功使用 点击“开始”——“运行”——输入“cmd”点确定——输入“ping空格复印机IP地址”。例如复印机IP地址为192.168.1.105，则输入“ping 192.168.1.105”——是否出现有255字样。若不出现则说明电脑没有正确与复印机连接。解决方法为确定IP地址、子网掩码、默认网关的指定是否正确。（此方法叫做检测是否ping通） 可ping通后——打开IE浏览器——在地址栏中输入复印机的IP地址——在 如何防止wifi万能钥匙蹭网 一个，你可以把SSID广播关闭了。 第二，也是最有效的一个，MAC地址过滤，只允许特定的MAC地址的设备接入无线路由器。我现在就是用的这个，设置了这个以后我直接不设密码，除了我没人能加入我的无线路由。 设置复杂密码即可关闭无线路由PIN码连接...还有就是自己不使用wifi万能钥匙软件，因为使用该软件后会分享你自己无线的密码，该软件之所以破解率高！或者使用时不点击分享功能！ 万能钥匙蹭网其实就是内置密码库一个个测试密码一般都是些简单的防止它很简单那就是设置问题了设置时最好密码加数字大小写和写要想更安全加上特殊字符@%*,? 这样谁也无法破解了 在无线路由器中有三种方法防止别人非法连接无线信号：1、将无线信号进行加密。设置加密后，无线客户端只有知道正确的密码才可以连接上该无线网络，安全级别最高。推荐使用WEP或WPA加密方式。2、开启无线MAC地址过滤。通过设定规则，仅让允许的无线客户端进行连接，而禁止其他用户连接。3、在路由器中禁用SSID广播。禁用SSID广播后，无线网卡识别不了路由器的无线网络名称，也就连接不上该无线网络。 360防蹭网 【简易步骤】： 打开【360安全卫士】—【功能大全】—【流量防火墙】—【防蹭网】—【立即启动】即可。 wifi万能钥匙（安卓）此乃神器啊！顾名思义是破解wifi的软件！这里就不多说了，自己下载试试就知道了！现在教你如何提取wifi万能钥匙蹭网后路由器的密码！首先：机子必须root（没root的自行度娘）然后安装RE管理器，打开RE管理器允许获取最高权限！然后按依次打开data/misc/wifi 找到并打开wpa_supplicant.conf这个文件！就会看见一页的数据！ssid是wifi名称、psk是密码！这样你就能用你的笔记本输密码上网了！ [三电平逆变器的主电路结构及其工作原理]三电平逆变器 工作原理 三电平逆变器的主电路结构及其原理 所谓三电平是指逆变器侧每相输出电压相对于直流侧有三种取值，正端电压(+Vdc/2)、负端电压(-Vdc/2)、中点零电压(0)。二极管箱 位型三电平逆变器主电路结构如图所示。逆变器每一相需要4个IGBT 开关管、4个续流二极管、2个箱位二极管;整个三相逆变器直流侧由两个电容C1、C2串联起来来支撑并均衡直流侧电压，C1=C2。通过一定的开关逻辑控制，交流侧产生三种电平的相电压，在输出端合成正弦波。 三电平逆变器的工作原理 以输出电压A相为例，分析三电平逆变器主电路工作原理，并假 设器件为理想器件，不计其导通管压降。定义负载电流由逆变器流向电机或其它负载时的方向为正方向。 (l) 当Sa1、Sa2导通，Sa3、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流从正极点流过主开关Sa1、Sa2，该相输出端电位等同于正极点电位，输出电压U=+Vdc/2;若负载电流为负方向，则电流流过与主开关管Sa1、Sa2反并联的续流二极管对电容C1 充电，电流注入正极点，该相输出端电位仍然等同于正极点电位，输出电压U=+Vdc/2。通常标识为所谓的“1”状态，如图所示。 “1”状态“0”状态 “-1”状态 (2) 当Sa2、Sa3导通，Sa1、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流从O点顺序流过箱位二极管Da1，主开关管Sa2:，该相输出端电位等同与0点电位，输出电压U=O;若负载电流为负方向，则电流顺序流过主开关管Sa3和箱位二极管Da2，电流注入O点，该相输出端电位等同于O点电位，输出电压U=0，电源对电容C2充电。即通常标识的“0”状态，如图所示。 (3) 当Sa3、Sa4导通，Sa1、Sa2关断时，若负载电流为正方向，则电流从负极点流过与主开关Sa3、Sa4反并联的续流二极管对电容C2进行充电，该相输出端电位等同于负极点电位，输出电压U=-Vdc/2;若负载电流为负方向，则电源对电容C2充电，电流流过主开关管Sa3、Sa4注入负极点，该相输出端电位仍然等同于负极点电位，输出电压U=-Vdc/2。通常标识为“-1”状态，如图所示。 三电平逆变器工作状态间的转换 1、安装fi-6130z的TWAIN驱动 打开V10.21.310文件夹，双击setup.exe运行安装程序； 重启电脑后，接上扫描的USB数据线到电脑后面的USB接口，给扫描仪通电，在电脑右下角会提示“发现新硬件”，然后如果显示“新硬件已安装成功，可以使用”的字样，则驱动安装成功，如果提示“设备安装失败，不能正常使用”的字样，则驱动安装失败。 2、在后督系统中，选择菜单栏的“扫描”-“初始化”，点击“TWAIN Driver”，单击“确定”， 选择“FUJITSU fi-6130zdj”，然后单击“选择”； 3、新建批次，点击菜单栏下的“扫描”-“开始（特殊）”，调出富士通扫描仪的“TWAIN 驱动（32）” （1）将分辨率设置成200x200；（2）扫描类型设置为ADF(双面)；（3）图像模式设置为彩色； 设置完后，点击“选项”； （1）将旋转角度改为“自动”；（2）自动检测尺寸和偏斜改为“自动页面尺寸检测”； （1）将缓存模式改为“使用双内存”；（2）多页送纸检测选择为“重叠检测（超声波）； 勾选“JPEG转送”，点击“确定”返回到“TWAIN驱动（32）”对话框； 创建“普通票据”的扫描模板 点击“设置” 点击“添加” 键入“普通票据扫描”，然后点击“确定”； 创建“长页票据扫描”的模板 （1）将扫描类型选择为“长页（双面）”；（2）将“长度”设置为“1600毫米”，点击确定； 长页票据扫描模板中，“选项”里的设置需要将“旋转角度”改为“0度”，“缓存模式”改为“使用扫描仪的内存”，其他设置同普通票据扫描模板一致； 添加“长页票据扫描”模板； 打印机 一、网络打印机的安装 1.电脑开机后放入光盘——打开桌面“我的电脑”——点击“DVD驱动器”——安装打印机驱动和扫描仪驱动 2.点击“开始”——点击“运行”——输入“cmd”后点确定——输入“ipconfig”——IP Address为IP地址，subnet mask为子网掩码，default gateway 为默认网关 3.打开复印机——找到系统设置——选择“指定”—— 按“IP”给复印机指定一个IP地址。例如电脑的IP地址为192.168.1.102，则可给复印机指定IP为192.168.1.103或192.168.1.104等（指定IP要注意不能与其他电脑IP相同） 按“子网掩码”——输入与电脑子网掩码相同的子网掩码。例如电脑子网掩码为255.255.255.0，则复印机的子网掩码也要设为255.255.255.0后退菜单——菜单向下按找到网关——给复印机指定的网关要与电脑相同。例如电脑的默认网关为192.168.1.1，则复印机的默认网关也要为192.168.1.1 4.点击“开始”——“设置”——“控制面板”——点击“打印机和其他硬 件”（经典视图下点击“打印机和传真”）——找到将要安装的打印机——点击右键“属性”——点击上方“端口”——点击中下方“添加端口”——选择“standard TCP/IP port”——点击“新端口”——“下一步”——输入复印机的IP地址——“下一步”即可（若提示网络上没有找到设备。则检查网线是否连接好。若确信连接好后仍有提示则说明复印机与该电脑不再同一网段）完成添加端口后点击“确定”即可。 点击“开始”——“运行”——输入“cmd”点确定——输入“ping空格复印机IP地址”。例如复印机IP地址为192.168.1.105，则输入“ping 192.168.1.105”——若出现有255字样说明打印机安装成功。 二、网络扫描仪的安装 1.点击“开始”——“程序”——找到扫描仪的驱动“Type TWAIN ”——“Network”——选择“使用特定扫描仪”——点击“搜索扫 描仪”——确定后在“IP地址或主机名：”中输入复印机的IP地址然后点“确定” 2.打开word软件——点击“插入”菜单——“图片”——“来自扫描仪或照相机”——在“设备”中选择安装好的扫描仪——点击“自动插入”即可。 三、问题解决 1.若网络打印机或网络扫描仪不能成功使用 点击“开始”——“运行”——输入“cmd”点确定——输入“ping空格复印机IP地址”。例如复印机IP地址为192.168.1.105，则输入“ping 192.168.1.105”——是否出现有255字样。若不出现则说明电脑没有正确与复印机连接。解决方法为确定IP地址、子网掩码、默认网关的指定是否正确。（此方法叫做检测是否ping通） 三电平逆变器的主电路结构 及其工作原理 -标准化文件发布号：（9556-EUATWK-MWUB-WUNN-INNUL-DDQTY-KII 三电平逆变器的主电路结构及其工作原理 所谓三电平是指逆变器交流侧每相输出电压相对于直流侧有三种取值，正端电压 (+Vdc/2)、负端电压(-Vdc/2)、中点零电压(0)。二极管箱位型三电平逆变器主电路结构如图所示。逆变器每一相需要4个IGBT开关管、4个续流二极管、2个箱位二极管;整个三相逆变器直流侧由两个电容C1、C2串联起来来支撑并均衡直流侧电压，C1=C2。通过一定的开关逻辑控制，交流侧产生三种电平的相电压，在输出端合成正弦波。 三电平逆变器的工作原理 以输出电压A相为例，分析三电平逆变器主电路工作原理，并假设器件为理想器件，不计其导通管压降。定义负载电流由逆变器流向电机或其它负载时的方向为正方向。 (l) 当Sa1，、Sa2导通，Sa3、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流从正极点流过主开关Sa1、Sa2，该相输出端电位等同于正极点电位，输出电压 U=+V dc/2;若负载电流为负方向，则电流流过与主开关管Sa1、Sa2反并联的续流二极管对电容C1充电，电流注入正极点，该相输出端电位仍然等同于正极点电位，输出电压U=+V dc/2。通常标识为所谓的“1”状态，如图所示。 “1”状态“0”状态 “-1”状态 (2) 当Sa2、Sa3导通，Sa1、Sa4关断时，若负载电流为正方向，则电源对电容C1充电，电流 从O点顺序流过箱位二极管D a1，主开关管Sa2:，该相输出端电位等同与0点电位，输出电压U=O;若负载电流为负方向，则电流顺序流过主开关管Sa3和箱位二极管D a2，电流注入O点，该相输出端电位等同于O点电位，输出电压U=0，电源对电容C2充电。即通常标识的“0”状态，如图所示。 (3) 当Sa3、Sa4导通，Sa1、Sa2关断时，若负载电流为正方向，则电流从负极点流过与主开 关Sa3、Sa4反并联的续流二极管对电容C2进行充电，该相输出端电位等同于负极点电位，输出电压U=-V dc/2;若负载电流为负方向，则电源对电容C2充电，电流流过主开关管Sa3、Sa4注入负极点，该相输出端电位仍然等同于负极点电位，输出电压U=-V dc/2。通常标识为“-1”状态，如图所示。 驱动安装正确顺序 驱动程序安装的一般顺序 ==一般安装顺序== 驱动程序安装的一般顺序： 主板芯片组（Chipset）→显卡（VGA）→声卡（Audio）→网卡（LAN）→无线网卡（Wireless LAN）→红外线（IR）→触控（Touchpad）→PCMCIA 控制器（PCMCIA）→读卡器(Flash Media Reader)→调制解调器（Modem）→其它（如电视卡、CDMA上网适配器等等）。不按顺序安装很有可能导致某些软件安装失败。 第一步，安装操作系统后，首先应该装上操作系统的Service Pack（SP）补丁。我们知道驱动程序直接面对的是操作系统与硬件，所以首先应该用SP 补丁解决了操作系统的兼容性问题，这样才能尽量确保操作系统和驱动程序的无缝结合。 第二步，安装主板驱动。主板驱动主要用来开启主板芯片组内置功能及特性，主板驱动里一般是主板识别和管理硬盘的IDE驱动程序或补丁，比如Intel芯片组的INF驱动和VIA的4in1补丁等。如果还包含有AGP补 丁的话，一定要先安装完IDE驱动再安装AGP补丁，这一步很重要，也是很多造成系统不稳定的直接原因。 第三步，安装DirectX驱动。这里一般推荐安装最新版本，目前DirectX的最新版本是DirectX 9.0C。可能有些用户会认为：“我的显卡并不支持DirectX 9，没有必要安装DirectX 9.0C”，其实这是个错误的认识，把DirectX等同为了Direct3D。DirectX是微软嵌在操作系统上的应用程序接口（API），DirectX由显示部分、声音部分、输入部分和网络部分四大部分组成，显示部分又分为Direct Draw（负责2D加速）和Direct 3D（负责3D加速），所以说Direct3D只是它其中的一小部分而已。而新版本的DirectX改善的不仅仅是显示部分，其声音部分（DirectSound）——带来更好的声效；输入部分（Direct Input）——支持更多的游戏输入设备，并对这些设备的识别与驱动上更加细致，充分发挥设备的最佳状态和全部功能；网络部分（DirectPlay）——增强计算机的网络连接，提供更多的连接方式。只不过是DirectX在显示部分的改进比较大，也更引人关注，才忽略了其他部分的功劳，所以安装新版本的DirectX的意义并不仅是在显示部分了。当然，有兼容性问题时另当别论。 第四步，这时再安装显卡、声卡、网卡、调制解调器等插在主板上的板卡类驱动。 第五步，最后就可以装打印机、扫描仪、读写机这些外设驱动。 建立平衡计分卡实务案例 用六个步骤建立平衡计分卡 目前，平衡计分卡应用与推广的热潮正从国外袭入国内。根据Gartner Group 的调查表明，到2000年为止，在《财富》杂志公布的世界前1000位公司中有40%的公司采用了平衡计分卡系统。在最近由William M. Mercer 公司对214个公司的调查中发现，88%的公司提出平衡计分卡对于员工报酬方案的设计与实施是有帮助的，并且平衡计分卡所揭示的非财务的考核方法在这些公司中被广泛运用于员工奖金计划的设计与实施中。然而，国内不少企业设计与实施的平衡计分卡与真正的平衡计分卡的初衷存在一些背离。在国外，平衡计分卡被比作飞机驾驶舱内的仪表盘，里面有各种指标，管理层借此观察企业运行是否良好。而国内的公司更多的只是单纯将平衡计分卡作为一种绩效考评工具，往往以解决价值分配问题为初衷，而不是作为一种战略实施划执行工具，首先以支撑企业战略目标的达成为目的。 建立平衡计分卡是一个系统化的过程。这里必须强调的是，必须根据公司战略来制定平衡计分卡，再按照战略与平衡计分卡来制定战略的实施计划，而不是相反。否则平衡计分卡就成为对战略实施计划的监测工具和绩效管理工具，这与KPI没有什么区别。这是多数公司会犯的错误。 下表1是笔者2003年上半年在深圳特区某高科技民营企业做BSC咨询项目时的工作计划表： 表1：BSC项目时间表 第一阶段：战略明确与前期工作 第二阶段：制定平衡计分卡 第三阶段，制定战略与测评指标的实施计划 第四阶段，战略监测、反馈与修正 2004全年战略考察与流程重组利用BSC这一战略管理工具每月、每季进行定期战略考察与反馈，并针对公司流程绩效差距对公司流程进行分解与分析，予以重组或优化。战略管理部人力资源部 第一步，制定公司战略 柯尼卡美能达网络扫描安装步骤 一、机器设置 开机——效用/计数器——管理员管理——输入密码（默认密码为：12345678）——管理员管理2——网络设置——网络设置1——基本设置——DHCP改为“输入IP”（一定要改为输入IP否侧开关机后会自动取消）——输入IP地址，子网掩码和网关——点击输入——关机（大约三分钟）开机。 二、FTP安装设置 在任意磁盘建立扫描后所放置的文件夹 安装FTP软件——打开FTP软件——选择路径（扫描完成后所放置的文件夹）——选择Anonymous——完成 三、IE浏览器设置 打开IE浏览器输入本复印机所设置的IP地址进入页面——传真/扫描——进入建立页面——选择“TX:PCCFTP服务器”——输入单触键名——FTP地址“为本PCIP地址”——匿名改为“是”——目录（文件路径）为“/”（别的选项默认即可不用更改）——完成 四、PCIP地址查询 双击网上邻居——查看网络连接——右键单击本地连接——属性——常规——双击Internet协议（TCP/IP）即可看到本机PC的IP地址 双击屏幕右下角小电脑图标——详细信息也可看到本PC的IP地址 五、检查网络与机器是否连接正常 单击开始——运行——输入“ping +复印机的IP地址-t ”如出现正常的数字跳动即为连接正常，如果没有需要进行IP从新设定，检查本机与复印机的网关设定 六、注意事项 1、如果电脑有开机密码把匿名改为“不是”——输入用户名和密码 2、FTP设置取消Anonymous选项——输入本PC的开机密码和用户名 3、复印机IP地址和PCIP地址须在同一个域里 4、如果电脑与复印机直接连接须用交叉线（注：彩机C200E以上，黑白机282以上,直接用网线即可） 柯尼卡美能达网络打印设置 一、机器设置 开机——效用/计数器——管理员管理——输入密码（默认密码为：12345678）——管理员管理2——网络设置——网络设置1——基本设置（283以上需设到网口4上）——DHCP改为“输入IP”（一定要改为输入IP否侧开关机后会自动取消）——输入IP地址，子网掩码和网关——点击输入——开关机 二、驱动安装 wifi采集心得 1.如何玩转wifi万能钥匙 采集wifi必备品，这个对于脸皮薄的可以使用。下载请看群文件（wifi万能钥匙） 先讲解一下万能钥匙几个功能吧 ①什么是深度解锁 深度解锁是利用万能钥匙内置的16位密码来对热点进行尝试解锁。一般就是只能解开一些简单的密码，比如1-8，1-9，8个8等等。深度解锁解开的几率是比较低的。 如何进入深度解锁？ 当一个热点没有被分享的时候，也就是点击热点进行万能钥匙深度解锁的时候，提示“未能找到热点信息”，就会有一个提示框让你是否进入深度解锁。 （个人不建议在采集时间去深度破解，有些时间不如先采集别的以后留着捡漏用！） ②什么是垦荒？ 垦荒的原理和深度解锁是一样的，在楼上已经说明。这里不再多说。只不过垦荒比深度解锁方便可以一次性解锁多个热点，并且可以后台运行，在垦荒的同时可以聊QQ玩游戏。 如何进入垦荒？ 进入垦荒的条件比较苛刻。 随着万能钥匙使用的人数增多，越来越多的人分享了热点。所以现在走到哪里都会有可以解锁的热点（至少我是这样的）。 进入垦荒的条件是，目前搜索到的wifi没有可用的，也就是一键查询后所有的热点均无蓝钥匙（附近有开放的wifi也不可以，因为万能钥匙默认开放的wifi也是可以使用的）。就会有提示是否进入垦荒。 （如果采集累了坐下休息那就垦荒下吧说不定有意外收获！） ③什么是一键查询万能钥匙 一键查询万能钥匙是用来查询手机搜索出来wifi可以解锁的功能，这个是我们采集经常用到的功能之一。选着一键查询万能钥匙必须是联网的才可以查询，不然没有办法查询数据密码。一键查询后，在列表中就会出现 一些蓝色小钥匙，这就代表可以解锁的wifi，点击它选着自动连接就可以了，80%几率连成功。 （个人建议普通街道每150米一查询，商业街每80米一查询。本人就是靠这个功能赚钱的） ④钥匙地图 地图是用来查看可以解锁的热点用的， 同时这个页面不用打开GPS，就可以省电、快速的确定自己的所 柯尼卡美能达163V打印机、扫描仪驱动 安装程序及步骤 2011-05-27 首先，要确保有打印机自带的光盘，或者到柯尼卡美能达的官方网站下载驱动程序，不过可能不好下载。 一、打印机安装程序及步骤： 1、插好打印机与电脑连接的USB插口。 2、关闭打印机电源开关。 3、点击“开始”—“打印机和传真”，如果在“开始”中 找不到“打印机和传真”的话则点击“控制面板”—“打印机和传真”。 4、在左侧“打印机任务”栏，点击“添加打印机”。 5、打开打印机电源开关。 6、电脑自动出现添加打印机向导。点击“下一步”—“连 接到此计算机的本地打印机”—“自动检测并安装即插即用打印机（A）”。 7、按照说明步骤点击确定即可。 二、打印机安装程序及步骤： 1、插好打印机与电脑连接的USB插口。 2、关闭打印机电源开关。 3、插入磁盘—打开磁盘点击打印机安装驱动（Printer）。 4、按照提示操作即可。 三、扫描驱动安装程序及步骤： 1、插好打印机与电脑连接的USB插口。 2、关闭打印机电源开关。 3、插入磁盘，点击“Instscan”—选择语言“简体中文”—选择驱动程序的机型“KONICA MINOLTA 163Scanner”点击”—输入IP地址—确定即可。 4、打开打印机电源开关。电脑提示发现新硬件并可以安装使用。 5、打开光盘，点击“Instscan”—选择语言“简体中文”—选择驱动程序的机型“KONICA MINOLTA 163Scanner”点击”—“升级驱动程序”—“完成”—“完成”即可。 6、由于柯尼卡美能达163V所带的扫描仪属于虚拟扫描，所以扫描时要从word、excel、photo shop中才能扫描。具体步骤如下： ①：打开word文档—插入—图片—来自扫描仪或照相机—设备“KONICA MINOLTA 163Scanner”—自定义插入，出现一个选项框“文稿尺寸”（根据自己的需要选择）—扫描模式（有文本和照片两个选项，不是照片扫描的话就选择文本）—分辨率（150×150dpi标准分辨率用于标准尺寸字符如打印文档等；300×300dpi较高分辨率用于小字符如报纸等，此分辨率为默认模式；600×600dpi最高分辨率用于扫描图像数据）—扫描类型（出栈扫描即用户点击扫描按钮开 摘要 三相三电平逆变器具有输出电压谐波小，/ dv dt小，EMI小等优点，是高压大功率逆变器应用领域的研究热点，三相二极管中点箝位型三电平逆变器是三相三电平逆变器的一种主要拓扑，已经得到了广泛的应用。三相T型三电平逆变器，是基于三相二极管中点箝位型三电平逆变器的一种改进拓扑。这种逆变器中，每个桥臂通过反向串联的开关管实现中点箝位功能，是逆变器输出电压有三种电平。该拓扑比三相二极管中点箝位型三电平拓扑结构每相减少了两个箝位二极管，可以降低损耗并且减少逆变器体积，是一种很有发展前景的拓扑。 本设计采用正弦脉宽调制（SPWM），本文介绍了三相T型三电平逆变器的设计，介绍其结构和基本工作原理，及SPWM控制法的原理，并利用SPWM控制的方法对三电平逆变器进行设计与仿真。本设计采用SIMULINK对T型三电平逆变电路建立模型，并进行仿真。 关键词： T型三电平逆变器、正弦脉宽调制、SIMULINK仿真 目录 第一章绪论 (6) 1.1研究背景及意义 .. 1.2三电平逆变器拓扑分类 第一章 T型三电平逆变器工作原理分析 (6) 1.1逆变器的结构 1.2本章小结 第二章正弦脉波调制（SPWM） (7) 3.1 PWM与SPWM的工作原理 3.2三电平逆变电路SPWM的实现 3.3本章小结 第三章电路仿真与参数计算 (10) 4.1逆变器的基本要求 4.2电路图 4.3调制电路 4.4L-C滤波电路 4.5结果分析 第四章课程设计小结 (14) 参考文献 (15) 第一章绪论 1.1 研究背景及意义 近年来，随着经济的飞速发展，人类对能源的需求也大幅度增加，而传统能源面临着枯竭的危机。在这种情况下，我们不得不加速开发新型能源。各国的专家致力于新能源的开发与利用，光伏发电、风力发电、生物发电等各种新型发电技术已经得到了一定的应用，并且正在蓬勃的发展，尤其是光伏发电，因其成本低、稳定性较好，控制简单等优点，在各国得到了广泛的应用。受地区气象条件的影响，太阳能光伏电池板输出的直流电压极不稳定，而且电压幅值低，容量小。为了高效利用太阳能，需要将不稳定的光伏电池串、并联组合，并且经过多级电力电子变换器组合输出恒频交流电压并网运行。而把这些初始能源转化为可用电能的桥梁就是逆变器。随着开关器件的不断发展，逆变器的拓扑、调制方式和控制策略也在不断发展，控制理论在逆变器的控制上得到了很好的应用，这一切都保证了优良的供电质量。在一些高电压、大功率的应用场合，传统的两电平逆变器由于开关器件耐压限制，无法满足需求。在这种情况下，如何将低耐压开关器件应用于高电压大功率场合成为各国专家研究的热点，由此，多电平逆变器技术应运而生。多电平的概念最早是由日本专家南波江章(A.Nabae)等人在 1980 年提出的[1]，通过改变主电路的拓扑结构、增加开关器件的方式，在开关器件关断的时候将直流电压分散到各个器件两端，实现了低耐压开关器件在大功率场合应用。 1.2三电平逆变器拓扑分类 常见的多电平的电路拓扑主要有三种：二极管箝位型逆变器、飞跨电容箝位型逆变器和具有独立直流电源的级联型逆变器。本文研究的 T 型三电平逆变器可以说是中点箝位型逆变器的改进拓扑，其优势主要体现在减少了电流通路中的开关器件数量，减少了传导损耗。而且与二极管箝位型三电平逆变器相比，T 型三电平逆变器的每个桥臂少用了两个箝位二极管，其控制方法和二极管箝位型三电平逆变器类似[2]。T 型三电平逆变器融合了两电平和三电平逆变器的优势，既有两电平逆变器传导损耗低，器件数目少的优点，又有三电平逆变器输出波形好，效率高的优点，是很有发展前景的一种三电平逆变器拓扑。 平衡计分卡系统实施步骤（new） 学习导航 通过学习本课程，你将能够： ●了解实施平衡计分卡系统的前期准备； ●学会如何将战略转化为可操作的行动； ●掌握平衡计分卡系统实施步骤。 平衡计分卡系统实施步骤（new） 一、实施平衡计分卡系统的前期准备 应用平衡计分卡的过程实际上就是对战略中心型组织框架的导入过程，实质就在于如何把握战略中心型组织框架导入的时机。 1.不适合使用平衡计分卡的情况 在下列两种情况下，企业的平衡计分卡实施成功率会很低： 企业高层不认可 平衡计分卡不是一个简单的人力资源绩效考核系统。为了提高企业的执行力，它必须从高层做起、从战略做起，而且要协调各个部门之间的关系和相互的责任。 不具备合适的企业文化 平衡计分卡是一套全员动员、全员参与的管理系统，如果一个企业没有学习、创新、积极发展、不断改进的文化，就不适合实施平衡计分卡，否则在实施过程中会有很多人持反对意见、设置障碍。 2.导入的时机选择 企业战略变革 一个企业的经营环境发生了变化，迫使企业必须改变策略时，就需要实施平衡计分卡；企业发生了重大的高层人事变动，如新的高层主管与大多数员工还没有建立管理的默契时，也需要运用平衡计分卡作为一个系统来促进全员的沟通。 业绩不佳 当企业出现业绩不佳时，价值观会出现差距，员工也会有不同的想法，应用平衡计分卡让员工的想法、价值观趋于一致；当产品或者服务的质量不好时，也需要平衡计分卡改善不足和弥补缺陷；同时，导入平衡计分卡还能提升企业业务操作环节的效率。 图1 导入战略中心型组织框架的时机示意图 业务增长期 当企业要进行一些新的业务管理时，也是导入平衡计分卡的良好时机。比如，并购新的企业后，被并购企业与并购企业在文化、战略以及想法上都不同，就需要通过战略中心型组织的框架促使双方更好地沟通，更好地执行公司的战略；同样，企业在全球进行地区性扩张以及建立新的公司时，由于地区的差异，很多东西不能面对面沟通，就需要使用平衡计分卡。 资源整合阶段 企业的目标是形成新的组织架构，当企业进行各种类型的整合时，可以用平衡计分卡来勾勒各个组织架构需要做的重点事情。 3.组织实施平衡计分卡项目失败的原因 根据平衡计分卡协会的调查，在全球实施平衡计分卡的众多企业中，有将近50%没有取得最后成功，主要原因体现在三方面，如图2所示。wifi万能钥匙V2.0官方PC电脑版免费使用教程
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