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Notes on A ∞-algebras,A ∞-categories and non-commutative geometry.I Maxim Kontsevich and Yan Soibelman February 2,2008Contents 1Introduction 21.1A ∞-algebras as spaces ........................21.2Some applications of geometric language ..............31.3Content of the paper .........................41.4Generalization to A ∞-categories ..................6I A ∞-algebras and non-commutative dg-manifolds 72Coalgebras and non-commutative schemes 72.1Coalgebras as functors ........................72.2Smooth thin schemes .........................102.3Inner Hom ...............................113A ∞-algebras 143.1Main de?nitions ...........................143.2Minimal models of A ∞-algebras ...................163.3Centralizer of an A ∞-morphism ...................174Non-commutative dg-line L and weak unit 194.1Main de?nition ............................194.2Adding a weak unit ..........................
205Modules and bimodules
205.1Modules and vector bundles .....................
205.2On the tensor product of A ∞-algebras ...............236Yoneda lemma
236.1Explicit formulas for the product and di?erential on Centr (f )..
236.2Yoneda homomorphism .......................
24
1
II Smoothness and compactness25 7Hochschild cochain and chain complexes of an A∞-algebra25
7.1Hochschild cochain complex (25)
7.2Hochschild chain complex (26)
7.2.1Cyclic di?erential forms of order zero (26)
7.2.2Higher order cyclic di?erential forms (26)
7.2.3Non-commutative Cartan calculus (27)
7.2.4Di?erential on the Hochschild chain complex (28)
7.3The case of strictly unital A∞-algebras (30)
7.4Non-unital case:Cuntz-Quillen complex (31)
8Homologically smooth and compact A∞-algebras32
8.1Homological smoothness (32)
8.2Compact A∞-algebras (34)
9Degeneration Hodge-to-de Rham36
9.1Main conjecture (36)
9.2Relationship with the classical Hodge theory (38)
10A∞-algebras with scalar product39
10.1Main de?nitions (39)
10.2Calabi-Yau structure (40)
11Hochschild complexes as algebras over operads and PROPs43
11.1Con?guration spaces of discs (43)
11.2Con?gurations of points on the cylinder (46)
11.3Generalization of Deligne’s conjecture (48)
11.4Remark about Gauss-Manin connection (50)
11.5Flat connections and the colored operad (50)
11.6PROP of marked Riemann surfaces (54)
12Appendix63
12.1Non-commutative schemes and ind-schemes (63)
12.2Proof of Theorem2.1.1 (65)
12.3Proof of Proposition2.1.2 (66)
12.4Formal completion along a subscheme (67)
1Introduction
1.1A∞-algebras as spaces
The notion of A∞-algebra introduced by Stashe?(or the notion of A∞-category introduced by Fukaya)has two di?erent interpretations.First one is operadic: an A∞-algebra is an algebra over the A∞-operad(one of its versions is the operad of singular chains of the operad of intervals in the real line).Second one
2
is geometric:an A∞-algebra is the same as a non-commutative formal graded
manifold X over,say,?eld k,having a marked k-point pt,and equipped with a vector?eld d of degree+1such that d|pt=0and[d,d]=0(such vector
?elds are called homological).By de?nition the algebra of functions on the non-
commutative formal pointed graded manifold is isomorphic to the algebra of formal series n≥0 i1,i2,...,i n∈I a i1...i n x i1...x i n:= M a M x M of free graded variables x i,i∈I(the set I can be in?nite).Here M=(i1,...,i n),n≥0is a non-commutative multi-index,i.e.an element of the free monoid generated by
I.Homological vector?eld makes the above graded algebra into a complex of
vector spaces.The triple(X,pt,d)is called a non-commutative formal pointed di?erential-graded(or simply dg-)manifold.
It is an interesting problem to make a dictionary from the pure algebraic
language of A∞-algebras and A∞-categories to the language of non-commutative geometry1.One purpose of these notes is to make few steps in this direction.
From the point of view of Grothendieck’s approach to the notion of“space”, our formal pointed manifolds are given by functors on graded associative Artin algebras commuting with?nite projective limits.It is easy to see that such func-tors are represented by graded coalgebras.These coalgebras can be thought of as coalgebras of distributions on formal pointed manifolds.The above-mentioned algebras of formal power series are dual to the coalgebras of distributions.
In the case of(small)A∞-categories considered in the subsequent paper we will slightly modify the above de?nitions.Instead of one marked point one will have a closed subscheme of disjoint points(objects)in a formal graded manifold, and the homological vector?eld d must be compatible with the embedding of this subscheme as well as with the projection onto it.
1.2Some applications of geometric language
Geometric approach to A∞-algebras and A∞-categories clari?es several long-standing questions.In particular one can obtain an explicit description of the A∞-structure on A∞-functors.This will be explained in detail in the subse-quent paper.Here we make few remarks.In geometric terms A∞-functors are interpreted as maps between non-commutative formal dg-manifolds com-muting with homological vector?elds.We will introduce a non-commutative formal dg-manifold of maps between two such spaces.Functors are just“com-mutative”points of the latter.The case of A∞-categories with one object(i.e. A∞-algebras)is considered in this paper.The general case re?ects the di?erence between quivers with one vertex and quivers with many vertices(vertices corre-spond to objects).2As a result of the above considerations one can describe ex-plicitly the A∞-structure on functors in terms of sums over sets of trees.Among other applications of our geometric language we mention an interpretation of
the Hochschild chain complex of an A∞-algebra in terms of cyclic di?erential forms on the corresponding formal pointed dg-manifold(Section7.2).
Geometric language simpli?es some proofs as well.For example,Hochschild cohomology of an A∞-category C is isomorphic to Ext?(Id C,Id C)taken in the
A∞-category of endofunctors C→C.This result admits an easy proof,if one interprets Hochschild cochains as vector?elds and functors as maps(the idea
to treat Ext?(Id C,Id C)as the tangent space to deformations of the derived category D b(C)goes back to A.Bondal).
1.3Content of the paper
Present paper contains two parts out of three(the last one is devoted to A∞-categories and will appear later).Here we discuss A∞-algebras(=non-commutative formal pointed dg-manifolds with?xed a?ne coordinates).We have tried to be precise and provide details of most of the proofs.
Part I is devoted to the geometric description of A∞-algebras.We start with basics on formal graded a?ne schemes,then add a homological vector ?eld,thus arriving to the geometric de?nition of A∞-algebras as formal pointed dg-manifolds.Most of the material is well-known in algebraic language.We cannot completely avoid A∞-categories(subject of the subsequent paper).They appear in the form of categories of A∞-modules and A∞-bimodules,which can be de?ned directly.
Since in the A∞-world many notions are de?ned“up to quasi-isomorphism”, their geometric meaning is not obvious.As an example we mention the notion of weak unit.Basically,this means that the unit exists at the level of cohomology only.In Section4we discuss the relationship of weak units with the“di?erential-graded”version of the a?ne line.
We start Part II with the de?nition of the Hochschild complexes of A∞-algebras.As we already mentioned,Hochschild cochain complex is interpreted
in terms of graded vector?elds on the non-commutative formal a?ne space. Dualizing,Hochschild chain complex is interpreted in terms of degree one cyclic
di?erential forms.This interpretation is motivated by[Ko2].It di?ers from the traditional picture(see e.g.[Co],[CST])where one assigns to a Hochschild chain a0?a1?...?a n the di?erential form a0da1...da n.In our approach we interepret a i as the dual to an a?ne coordinate x i,and the above expression
is dual to the cyclic di?erential1-form x1...x n dx0.We also discuss graphical description of Hochschild chains,the di?erential,etc.
After that we discuss homologically smooth compact A∞-algebras.Those are analogs of smooth projective varieties in algebraic geometry.Indeed,the derived category D b(X)of coherent sheaves on a smooth projective variety X is
A∞-equivalent to the category of perfect modules over a homologically smooth compact A∞-algebra(this can be obtained using the results of[BvB]).The al-gebra contains as much information about the geometry of X as the category
D b(X)does.A good illustration of this idea is given by the“abstract”ver-sion of Hodge theory presented in Section9.It is largely conjectural topic, which eventually should be incorporated in the theory of“non-commutative
4
motives”.Encoding smooth proper varieties by homologically smooth compact A∞-algebras we can forget about the underlying commutative geometry,and try to develop a theory of“non-commutative smooth projective varieties”in an abstract form.Let us brie?y explain what does it mean for the Hodge theory. Let(C?(A,A),b)be the Hochschild chain complex of a(weakly unital)homo-logically smooth compact A∞-algebra A.The corresponding negative cyclic complex(C?(A,A)[[u]],b+uB)gives rise to a family of complexes over the for-mal a?ne line A1form[+2](shift of the grading re?ects the fact that the variable u has degree+2,cf.[Co],[CST]).We conjecture that the corresponding family of cohomology groups gives rise to a vector bundle over the formal line.The generic?ber of this vector bundle is isomorphic to periodic cyclic homology, while the?ber over u=0is isomorphic to the Hochschild homology.If com-pact homologically smooth A∞-algebra A corresponds to a smooth projective variety as explained above,then the generic?ber is just the algebraic de Rham cohomology of the variety,while the?ber over u=0is the Hodge cohomology. Then our conjecture becomes the classical theorem which claims degeneration of the spectral sequence Hodge-to-de Rham.3.
Last section of Part II is devoted to the relationship between moduli spaces of points on a cylinder and algebraic structures on the Hochschild complexes. In Section11.3we formulate a generalization of Deligne’s conjecture.Recall that Deligne’s conjecture says(see e.g.[KoSo1],[McS],[T])that the Hochschild cochain complex of an A∞-algebra is an algebra over the operad of chains on the topological operad of little discs.In the conventional approach to non-commutative geometry Hochschild cochains correspond to polyvector?elds, while Hochschild chains correspond to de Rham di?erential forms.One can contract a form with a polyvector?eld or take a Lie derivative of a form with respect to a polyvector?eld.This geometric point of view leads to a general-ization of Deligne’s conjecture which includes Hochschild chains equipped with the structure of(homotopy)module over cochains,and to the“Cartan type”calculus which involves both chains and cochains(cf.[CST],[TaT1]).We unify both approaches under one roof formulating a theorem which says that the pair consisting of the Hochschild chain and Hochschild cochain complexes of the same A∞-algebra is an algebra over the colored operad of singular chains on con?gurations of discs on a cylinder with marked points on each of the boundary circles.4
Sections10and11.6are devoted to A∞-algebras with scalar product,which is the same as non-commutative formal symplectic manifolds.In Section10we also discuss a homological version of this notion and explain that it corresponds to the notion of Calabi-Yau structure on a manifold.In Section11.6we de?ne an action of the PROP of singular chains of the topological PROP of smooth ori-ented2-dimensional surfaces with boundaries on the Hochschild chain complex of an A∞-algebra with scalar product.If in addition A is homologically smooth
and the spectral sequence Hodge-to-de Rham degenerates,then the above action extends to the action of the PROP of singular chains on the topological PROP of stable2-dimensional surfaces.This is essentially equivalent to a structure of 2-dimensional Cohomological TFT(similar ideas have been developed by Kevin Costello,see[Cos]).More details and an application of this approach to the calculation of Gromov-Witten invariants will be given in[KaKoP].
1.4Generalization to A∞-categories
Let us say few words about the subsequent paper which is devoted to A∞-categories.The formalism of present paper admits a straightforward gener-alization to the case of A∞-categories.The latter should be viewed as non-commutative formal dg-manifolds with a closed marked subscheme of objects. Although some parts of the theory of A∞-categories admit nice interpretation in terms of non-commutative geometry,some other still wait for it.This includes e.g.triangulated A∞-categories.We will present the theory of triangulated A∞-categories from the point of view of A∞-functors from“elementary”categories to a given A∞-category(see a summary in[Ko5],[So1],[So2]).Those“elemen-tary”categories are,roughly speaking,derived categories of representations of quivers with small number of vertices.Our approach has certain advantages over the traditional one.For example the complicated“octahedron axiom”admits a natural interpretation in terms of functors from the A∞-category associated with the quiver of the Dynkin diagram A2(there are six indecomposible objects in the category D b(A2?mod)corresponding to six vertices of the octahedron). In some sections of the paper on A∞-categories we have not been able to pro-vide pure geometric proofs of the results,thus relying on less?exible approach which uses di?erential-graded categories(see[Dr]).As a compromise,we will present only part of the theory of A∞-categories,with sketches of proofs,which are half-geomeric and half-algebraic,postponing more coherent exposition for future publications.
In present and subsequent paper we mostly consider A∞-algebras and cat-egories over a?eld of characteristic zero.This assumption simpli?es many results,but also makes some other less general.We refer the reader to[Lyu], [LyuOv]for a theory over a ground ring instead of ground?eld(the approach of[Lyu],[LyuOv]is pure algebraic and di?erent from ours).Most of the results of present paper are valid for an A∞-algebra A over the unital commutative associative ring k,as long as the graded module A is?at over k.More precisely, the results of Part I remain true except of the results of Section3.2(the minimal model theorem).In these two cases we assume that k is a?eld of characteristic zero.Constructions of Part II work over a commutative ring k.The results of Section10are valid(and the conjectures are expected to be valid)over a ?eld of characteristic zero.Algebraic version of Hodge theory from Section9 and the results of Section11are formulated for an A∞-algebra over the?eld of characteristic zero,although the Conjecture2is expected to be true for any Z-?at A∞-algebra.
Acknowledgments.We thank to Vladimir Drinfeld for useful discussions and
6
to Victor Ginzburg and Kevin Costello for comments on the manuscript.Y.S. thanks to Clay Mathematics Institute for supporting him as a Fellow during a part of the work.His work was also partially supported by an NSF grant.He is especially grateful to IHES for providing excellent research and living conditions for the duration of the project.
Part I
A∞-algebras and
non-commutative dg-manifolds
2Coalgebras and non-commutative schemes Geometric description of A∞-algebras will be given in terms of geometry of non-commutative ind-a?ne schemes in the tensor category of graded vector spaces (we will use Z-grading or Z/2-grading).In this section we are going to describe these ind-schemes as functors from?nite-dimensional algebras to sets(cf.with the description of formal schemes in[Gr]).More precisely,such functors are represented by counital coalgebras.Corresponding geometric objects are called non-commutative thin schemes.
2.1Coalgebras as functors
Let k be a?eld,and C be a k-linear Abelian symmetric monoidal category(we will call such categories tensor),which admits in?nite sums and products(we refer to[DM]about all necessary terminology of tensor categories).Then we can do simple linear algebra in C,in particular,speak about associative algebras or coassociative coalgebras.For the rest of the paper,unless we say otherwise, we will assume that either C=V ect Z k,which is the tensor category of Z-graded
vector spaces V=⊕n∈Z V n,or C=V ect Z/2
k ,which is the tensor category of
Z/2-graded vector spaces(then V=V0⊕V1),or C=V ect k,which is the tensor
category of k-vector spaces.Associativity morphisms in V ect Z k or V ect Z/2
k are
identity maps,and commutativity morphisms are given by the Koszul rule of signs:c(v i?v j)=(?1)ij v j?v i,where v n denotes an element of degree n.
We will denote by C f the Artinian category of?nite-dimensional objects in C(i.e.objects of?nite length).The category Alg C f of unital?nite-dimensional algebras is closed with respect to?nite projective limits.In particular,?nite products and?nite?ber products exist in Alg C f.One has also the categories Coalg C(resp.Coalg C f)of coassociative counital(resp.coassociative counital ?nite-dimensional)coalgebras.In the case C=V ect k we will also use the
notation Alg k,Alg f
k ,Coalg k and Coalg f
k
for these categories.The category
Coalg C f=Alg op
C f
admits?nite inductive limits.
7
We will need simple facts about coalgebras.We will present proofs in the Appendix for completness.
Theorem2.1.1Let F:Alg C f→Sets be a covariant functor commuting with ?nite projective limits.Then it is isomorphic to a functor of the type A→Hom Coalg
C
(A?,B)for some counital coalgebra B.Moreover,the category of such functors is equivalent to the category of counital coalgebras.
Proposition2.1.2If B∈Ob(Coalg C),then B is a union of?nite-dimensional counital coalgebras.
Objects of the category Coalg C f=Alg op
C f can be interpreted as“very thin”
non-commutative a?ne schemes(cf.with?nite schemes in algebraic geometry). Proposition1implies that the category Coalg C is naturally equivalent to the category of ind-objects in Coalg C f.
For a counital coalgebra B we denote by Spc(B)(the“spectrum”of the coalgebra B)the corresponding functor on the category of?nite-dimensional al-gebras.A functor isomorphic to Spc(B)for some B is called a non-commutative thin scheme.The category of non-commutative thin schemes is equivalent to the category of counital coalgebras.For a non-commutative scheme X we denote by B X the corresponding coalgebra.We will call it the coalgebra of distributions on X.The algebra of functions on X is by de?nition O(X)=B?X.
Non-commutative thin schemes form a full monoidal subcategory NAff th C?Ind(NAff C)of the category of non-commutative ind-a?ne schemes(see Ap-pendix).Tensor product corresponds to the tensor product of coalgebras.
Let us consider few examples.
Example2.1.3Let V∈Ob(C).Then T(V)=⊕n≥0V?n carries a structure of counital cofree coalgebra in C with the coproduct?(v0?...?v n)= 0≤i≤n(v0?...?v i)?(v i+1?...?v n).The corresponding non-commutative thin scheme is called non-commutative formal a?ne space V form(or formal neighborhood of zero in V).
De?nition2.1.4A non-commutative formal manifold X is a non-commutative thin scheme isomorphic to some Spc(T(V))from the example above.The di-mension of X is de?ned as dim k V.
The algebra O(X)of functions on a non-commutative formal manifold X of dimension n is isomorphic to the topological algebra k x1,...,x n of formal power series in free graded variables x1,...,x n.
Let X be a non-commutative formal manifold,and pt:k→B X a k-point in X,
De?nition2.1.5The pair(X,pt)is called a non-commutative formal pointed manifold.If C=V ect Z k it will be called non-commutative formal pointed graded
manifold.If C=V ect Z/2
k it will be called non-commutative formal pointed
supermanifold.
8
The following example is a generalization of the Example1(which corre-sponds to a quiver with one vertex).
Example2.1.6Let I be a set and B I=⊕i∈I1i be the direct sum of trivial coalgebras.We denote by O(I)the dual topological algebra.It can be thought of as the algebra of functions on a discrete non-commutative thin scheme I.
A quiver Q in C with the set of vertices I is given by a collection of objects E ij∈C,i,j∈I called spaces of arrows from i to j.The coalgebra of Q is the coalgebra
B Q generated by the O(I)?O(I)-bimodule E Q=⊕i,j∈I E ij,i.e.
B Q?⊕n≥0⊕i
0,i1,...,i n∈I
E i
i1
?...?E i
n?1
i n
:=⊕n≥0B n Q,B0Q:=B I.Elements
of B0Q are called trivial paths.Elements of B n Q are called paths of the length n. Coproduct is given by the formula
?(e i
0i1
?...?e i
n?1
i n
)=⊕0≤m≤n(e i
i1
?...?e i
m?1
i m
)?(e i
m
i m+1
...?...?e i
n?1
i n
),
where for m=0(resp.m=n)we set e i
?1i0=1i
(resp.e i
n
i n+1
=1i
n
).
In particular,?(1i)=1i?1i,i∈I and?(e ij)=1i?e ij+e ij?1j,where e ij∈E ij,and1m∈B I corresponds to the image of1∈1under the natural embedding into⊕m∈I1.
The coalgebra B Q has a counitεsuch thatε(1i)=1i,andε(x)=0for x∈B n Q,n≥1.
Example2.1.7(Generalized quivers).Here we replace1i by a unital simple algebra A i(e.g.A i=Mat(n i,D i),where D i is a division algebra).Then E ij are A i?mod?A j-bimodules.We leave as an exercise to the reader to write down the coproduct(one uses the tensor product of bimodules)and to check that we indeed obtain a coalgebra.
Example2.1.8Let I be a set.Then the coalgebra B I=⊕i∈I1i is a direct sum of trivial coalgebras,isomorphic to the unit object in C.This is a special case of Example2.Notice that in general B Q is a O(I)?O(I)-bimodule. Example2.1.9Let A be an associative unital algebra.It gives rise to the func-
tor F A:Coalg C f→Sets such that F A(B)=Hom Alg
C
(A,B?).This functor describes?nite-dimensional representations of A.It commutes with?nite direct limits,hence it is representable by a coalgebra.If A=O(X)is the algebra of regular functions on the a?ne scheme X,then in the case of algebraically closed ?eld k the coalgebra representing F A is isomorphic to⊕x∈X(k)O?x,X,where O?x,X denotes the topological dual to the completion of the local ring O x,X.If X is smooth of dimension n,then each summand is isomorphic to the topological dual to the algebra of formal power series k[[t1,...,t n]].In other words,this coalgebra corresponds to the disjoint union of formal neighborhoods of all points of X. Remark2.1.10One can describe non-commutative thin schemes more pre-cisely by using structure theorems about?nite-dimensional algebras in C.For example,in the case C=V ect k any?nite-dimensional algebra A is isomorphic
9
to a sum A 0⊕r ,where A 0is a ?nite sum of matrix algebras ⊕i Mat (n i ,D i ),D i are division algebras,and r is the radical.In Z -graded case a similar decompo-sition holds,with A 0being a sum of algebras of the type End (V i )?D i ,where V i are some graded vector spaces and D i are division algebras of degree zero.In Z /2-graded case the description is slightly more complicated.In particular A 0can contain summands isomorphic to (End (V i )?D i )?D λ,where V i and D i are Z /2-graded analogs of the above-described objects,and D λis a 1|1-dimensional superalgebra isomorphic to k [ξ]/(ξ2=λ),deg ξ=1,λ∈k ?/(k ?)2.
2.2Smooth thin schemes
Recall that the notion of an ideal has meaning in any abelian tensor category.A 2-sided ideal J is called nilpotent if the multiplication map J ?n →J has zero image for a su?ciently large n .
De?nition 2.2.1Counital coalgebra B in a tensor category C is called smooth if the corresponding functor F B :Alg C f →Sets,F B (A )=Hom Coalg C (A ?,B )
satis?es the following lifting property:for any 2-sided nilpotent ideal J ?A the map F B (A )→F B (A/J )induced by the natural projection A →A/J is sur-jective.Non-commutative thin scheme X is called smooth if the corresponding counital coalgebra B =B X is smooth.
Proposition 2.2.2For any quiver Q in C the corresponding coalgebra B Q is smooth.
Proof.First let us assume that the result holds for all ?nite quivers.We remark that if A is ?nite-dimensional,and Q is an in?nite quiver then for any morphism f :A ?→B Q we have:f (A ?)belongs to the coalgebra of a ?nite sub-quiver of Q .Since the lifting property holds for the latter,the result follows.Finally,we need to prove the Proposition for a ?nite quiver Q .Let us choose a basis {e ij,α}of each space of arrows E ij .Then for a ?nite-dimensional algebra A the set F B Q (A )is isomorphic to the set {((πi ),x ij,α)i,j ∈I },where πi ∈A,π2i =πi ,πi πj =πj πi ,if i =j , i ∈I πi =1A ,and x ij,α∈πi Aπj satisfy the condition:there exists N ≥1such that x i 1j 1,α1...x i m j m ,αm =0for all m ≥N .Let now J ?A be the nilpotent ideal from the de?nition of smooth coalgebra and (π′i ,x ′ij,α)be elements of A/J satisfying the above constraints.Our goal is to lift them to A .We can lift the them to the projectors πi and elements x ij,αfor A in such a way that the above constraints are satis?ed except of the last one,which becomes an inclusion x i 1j 1,α1...x i m j m ,αm ∈J for m ≥N .Since J n =0in A for some n
we see that x i 1j 1,α1...x i m j m ,αm =0in A for m ≥nN .This proves the result.
Remark 2.2.3a)According to Cuntz and Quillen (see [CQ2])a non-commutative algebra R in V ect k is called smooth if the functor Alg k →Sets,F R (A )=Hom Alg k (R,A )satis?es the lifting property from the De?nition 3applied to all (not only ?nite-dimensional)algebras.We remark that if R is smooth in the sense of Cuntz and Quillen then the coalgebra R dual representing the func-tor Coalg f k →Sets,B →Hom Alg f k
(R,B ?)is smooth.One can prove that any 10
smooth coalgebra in V ect k is isomorphic to a coalgebra of a generalized quiver (see Example 3).
b)Almost all examples of non-commutative smooth thin schemes consid-ered in this paper are formal pointed manifolds,i.e.they are isomorphic to Spc (T (V ))for some V ∈Ob (C ).It is natural to try to “globalize”our results to the case of non-commutative “smooth”schemes X which satisfy the property that the completion of X at a “commutative”point gives rise to a formal pointed manifold in our sense.An example of the space of maps is considered in the next subsection.
c)The tensor product of non-commutative smooth thin schemes is typically non-smooth,since it corresponds to the tensor product of coalgebras (the latter is not a categorical product).
Let now x be a k -point of a non-commutative smooth thin scheme X .By de?nition x is a homomorphism of counital coalgebras x :k →B X (here k =1is the trivial coalgebra corresponding to the unit object).The completion X x of X at x is a formal pointed manifold which can be described such as follows.As a functor F X x :Alg f C →Sets it assigns to a ?nite-dimensional algebra A the set of such homomorphisms of counital colagebras f :A ?→B X which are compositions A ?→A ?1→B X ,where A ?1?B X is a conilpotent extension of x (i.e.A 1is a ?nite-dimensional unital nilpotent algebra such that the natural embedding k →A ?1→B X coinsides with x :k →B X ).
Description of the coalgebra B X x is given in the following Proposition.
Proposition 2.2.4The formal neighborhood X
x corresponds to the counital sub-coalgebra B X x ?B X which is the preimage under the natural projection B X →B X /x (k )of the sub-coalgebra consisting of conilpotent elements in the non-counital coalgebra B/x (k ).Moreover, X
x is universal for all morphisms from nilpotent extensions of x to X .
We discuss in Appendix a more general construction of the completion along a non-commutative thin subscheme.
We leave as an exercise to the reader to prove the following result.
Proposition 2.2.5Let Q be a quiver and pt i ∈X =X B Q corresponds to a vertex i ∈I .Then the formal neighborhood X pt i is a formal pointed manifold corresponding to the tensor coalgebra T (E ii )=⊕n ≥0E ?n ii ,where E ii is the space of loops at i .
2.3Inner Hom
Let X,Y be non-commutative thin schemes,and B X ,B Y the corresponding coalgebras.
Theorem 2.3.1The functor Alg C f →Sets such that
A →Hom Coalg C (A ??
B X ,B Y )
11
is representable.The corresponding non-commutative thin scheme is denoted by Maps(X,Y).
Proof.It is easy to see that the functor under consideration commutes with ?nite projective limits.Hence it is of the type A→Hom Coalg
C
(A?,B),where B is a counital coalgebra(Theorem1).The corresponding non-commutative thin scheme is the desired Maps(X,Y).
It follows from the de?nition that Maps(X,Y)=Hom
(X,Y)is a non-commutative thin scheme, which satis?es the following functorial isomorphism for any Z∈Ob(NAff th C): Hom NAff th
C
(Z,Hom
(X,Y)for X=Spec(A),where A is a?nite-dimensional unital algebra and Y is arbitrary.The situation is similar to the case of“commutative”algebraic geometry,where one can de?ne an a?ne scheme of maps from a scheme of?nite length to an arbitrary a?ne scheme.On the other hand,one can show that the category of non-commutative ind-a?ne schemes admit inner Hom’s (the corresponding result for commutative ind-a?ne schemes is known. Remark2.3.2The non-commutative thin scheme Maps(X,Y)gives rise to a quiver,such that its vertices are k-points of Maps(X,Y).In other words, vertices correspond to homomorphisms B X→B Y of the coalgebras of distribu-tions.Taking the completion at a k-point we obtain a formal pointed manifold. More generally,one can take a completion along a subscheme of k-points,thus arriving to a non-commutative formal manifold with a marked closed subscheme (rather than one point).This construction will be used in the subsequent paper for the desription of the A∞-structure on A∞-functors.We also remark that the space of arrows E ij of a quiver is an example of the geometric notion of bitangent space at a pair of k-points i,j.It will be discussed in the subsequent paper.
Example2.3.3Let Q1={i1}and Q2={i2}be quivers with one vertex such
that E i
1i1
=V1,E i
2
i2
=V2,dim V i<∞,i=1,2.Then B Q
i
=T(V i),i=1,2
and Maps(X B
Q1,X B
Q2
)corresponds to the quiver Q such that the set of vertices
I Q=Hom Coalg
C (B Q
1
,B Q
2
)= n≥1Hom(V?n1,V2).
De?nition2.3.4Homomorphism f:B1→B2of counital coalgebras is called a minimal conilpotent extension if it is an inclusion and the induced coproduct on the non-counital coalgebra B2/f(B1)is trivial.
Composition of minimal conilpotent extensions is simply called a conilpotent extension.De?nition2.2.1can be reformulated in terms of?nite-dimensional
12
coalgebras.Coalgebra B is smooth if the functor C→Hom Coalg
C
(C,B)satis?es the lifting property with respect to conilpotent extensions of?nite-dimensional counital coalgebras.The following proposition shows that we can drop the condition of?nite-dimensionality.
Proposition2.3.5If B is a smooth coalgebra then the functor Coalg C→Sets such that C→Hom Coalg
C
(C,B)satis?es the lifting property for conilpotent extensions.
Proof.Let f:B1→B2be a conilpotent extension,and g:B1→B and arbitrary homomorphism of counital coalgebras.It can be thought of as homomorphism of f(B1)→B.We need to show that g can be extended to B2. Let us consider the set of pairs(C,g C)such f(B1)?C?B2and g C:C→B de?nes an extension of counital coalgebras,which coincides with g on f(B1).We apply Zorn lemma to the partially ordered set of such pairs and see that there exists a maximal element(B max,g max)in this set.We claim that B max=B2. Indeed,let x∈B2\B max.Then there exists a?nite-dimensional coalgebra B x?B2which contains x.Clearly B x is a conilpotent extension of f(B1)∩B x. Since B is smooth we can extend g max:f(B1)∩B x→B to g x:B x→B and,?nally to g x,max:B x+B max→B.This contradicts to maximality of (B max,g max).Proposition is proved.
Proposition2.3.6If X,Y are non-commutative thin schemes and Y is smooth then Maps(X,Y)is also smooth.
Proof.Let A→A/J be a nilpotent extension of?nite-dimensional unital algebras.Then(A/J)??B X→A??B X is a conilpotent extension of counital coalgebras.Since B Y is smooth then the previous Proposition implies that the
induced map Hom Coalg
C (A??B X,B Y)→Hom Coalg
C
((A/J)??B X,B Y)is
surjective.This concludes the proof.
Let us consider the case when(X,pt X)and(Y,pt Y)are non-commutative formal pointed manifolds in the category C=V ect Z k.One can describe“in coordinates”the non-commutative formal pointed manifold,which is the for-mal neighborhood of a k-point of Maps(X,Y).Namely,let X=Spc(B)and
Y=Spc(C),and let f∈Hom NAff th
C (X,Y)be a morphism preserving marked
points.Then f gives rise to a k-point of Z=Maps(X,Y).Since O(X)and O(Y)are isomorphic to the topological algebras of formal power series in free graded variables,we can choose sets of free topological generators(x i)i∈I and (y j)j∈J for these algebras.Then we can write for the corresponding homomor-phism of algebras f?:O(Y)→O(X):
f?(y j)= I c0j,M x M,
where c0j,M∈k and M=(i1,...,i n),i s∈I is a non-commutative multi-index
(all the coe?cients depend on f,hence a better notation should be c f,0
j,M
).Notice
13
that for M=0one gets c0j,0=0since f is a morphism of pointed schemes. Then we can consider an“in?nitesimal deformation”f def of f
f?def(y j)= M(c0j,M+δc0j,M)x M,
whereδc0j,M are new variables commuting with all x i.Thenδc0j,M can be thought of as coordinates in the formal neighborhood of f.More pedantically it can be spelled out such as follows.Let A=k⊕m be a?nite-dimensional graded unital algebra,where m is a graded nilpotent ideal of A.Then an A-point of the formal
neighborhood U f of f is a morphismφ∈Hom NAff th
C (Spec(A)?X,Y),such
that it reduces to f modulo the nilpotent ideal m.We have for the corresponding homomorphism of algebras:
φ?(y j)= M c j,M x M,
where M is a non-commutative multi-index,c j,M∈A,and c j,M→c0j,M under the natural homomorphism A→k=A/m.In particular c j,0∈m.We can treat coe?cients c j,M as A-points of the formal neighborhood U f of f∈Maps(X,Y). Remark2.3.7The above de?nitions will play an important role in the subse-quent paper,where the non-commutative smooth thin scheme Spc(B Q)will be assigned to a(small)A∞-category,the non-commutative smooth thin scheme
Maps(Spc(B Q
1),Spc(B Q
2
))will be used for the description of the category of
A∞-functors between A∞-categories,and the formal neighborhood of a point
in the space Maps(Spc(B Q
1),Spc(B Q
2
))will correspond to natural transforma-
tions between A∞-functors.
3A∞-algebras
3.1Main de?nitions
From now on assume that C=V ect Z k unless we say otherwise.If X is a thin scheme then a vector?eld on X is,by de?nition,a derivation of the coalgebra B X.Vector?elds form a graded Lie algebra V ect(X).
De?nition3.1.1A non-commutative thin di?erential-graded(dg for short) scheme is a pair(X,d)where X is a non-commutative thin scheme,and d is a vector?eld on X of degree+1such that[d,d]=0.
We will call the vector?eld d homological vector?eld.
Let X be a formal pointed manifold and x0be its unique k-point.Such a point corresponds to a homomorphism of counital coalgebras k→B X.We say that the vector?eld d vanishes at x0if the corresponding derivation kills the image of k.
14
De?nition3.1.2A non-commutative formal pointed dg-manifold is a pair((X,x0),d) such that(X,x0)is a non-commutative formal pointed graded manifold,and
d=d X is a homological vector?eld on X such that d|x
=0.
Homological vector?eld d has an in?nite Taylor decomposition at x0.More precisely,let T x
X be the tangent space at x0.It is canonically isomorphic to
the graded vector space of primitive elements of the coalgebra B X,i.e.the set of
a∈B X such that?(a)=1?a+a?1where1∈B X is the image of1∈k under
the homomorphism of coalgebras x0:k→B X(see Appendix for the general
de?nition of the tangent space).Then d:=d X gives rise to a(non-canonically
de?ned)collection of linear maps d(n)
X :=m n:T x
X?n→T x
X[1],n≥1called
Taylor coe?cients of d which satisfy a system of quadratic relations arising from the condition[d,d]=0.Indeed,our non-commutative formal pointed manifold is isomorphic to the formal neighborhood of zero in T x
X,hence the corresponding non-commutative thin scheme is isomorphic to the cofree tensor
coalgebra T(T x
0X)generated by T x
X.Homological vector?eld d is a derivation
of a cofree coalgebra,hence it is uniquely determined by a sequence of linear maps m n.
De?nition3.1.3Non-unital A∞-algebra over k is given by a non-commutative formal pointed dg-manifold(X,x0,d)together with an isomorphism of counital coalgebras B X?T(T x
X).
Choice of an isomorphism with the tensor coalgebra generated by the tangent space is a non-commutative analog of a choice of a?ne structure in the formal neighborhood of x0.
From the above de?nitions one can recover the traditional one.We present it below for convenience of the reader.
De?nition3.1.4A structure of an A∞-algebra on V∈Ob(V ect Z k)is given by a derivation d of degree+1of the non-counital cofree coalgebra T+(V[1])=⊕n≥1V?n such that[d,d]=0in the di?erential-graded Lie algebra of coalgebra derivations.
Traditionally the Taylor coe?cients of d=m1+m2+...are called(higher) multiplications for V.The pair(V,m1)is a complex of k-vector spaces called the tangent complex.If X=Spc(T(V))then V[1]=T0X and m1=d(1)X is the?rst Taylor coe?cient of the homological vector?eld d X.The tangent cohomology groups H i(V,m1)will be denoted by H i(V).Clearly H?(V)=⊕i∈Z H i(V)is an associative(non-unital)algebra with the product induced by m2.
An important class of A∞-algebras consists of unital(or strictly unital)and weakly unital(or homologically unital)ones.We are going to discuss the de?-nition and the geometric meaning of unitality later.
Homomorphism of A∞-algebras can be described geometrically as a mor-phism of the corresponding non-commutative formal pointed dg-manifolds.In the algebraic form one recovers the following traditional de?nition.
15
De?nition 3.1.5A homomorphism of non-unital A ∞-algebras (A ∞-morphism for short)(V,d V )→(W,d W )is a homomorphism of di?erential-graded coalge-bras T +(V [1])→T +(W [1]).
A homomorphism f of non-unital A ∞-algebras is determined by its Taylor coe?cients f n :V ?n →W [1?n ],n ≥1satisfying the system of equations 1≤l 1<..., f l 2?l 1(a l 1+1,...,a l 2),...,f n ?l i ?1(a n ?l i ?1+1,...,a n ))= s +r =n +1 1≤j ≤s (?1)?s f s (a 1,...,a j ?1,m V r (a j ,...,a j +r ?1),a j +r ,...,a n ).Here ?s =r 1≤p ≤j ?1de g (a p )+j ?1+r (s ?j ),γi = 1≤p ≤i ?1(i ?p )(l p ?l p ?1?1)+ 1≤p ≤i ?1ν(l p ) l p ?1+1≤q ≤l p deg (a q ),where we use the notation ν(l p )= p +1≤m ≤i (1?l m +l m ?1),and set l 0=0. Remark 3.1.6All the above de?nitions and results are valid for Z /2-graded A ∞-algebras as well.In this case we consider formal manifolds in the category V ect Z /2k of Z /2-graded vector spaces.We will use the correspodning results without further comments.In this case one denotes by ΠA the Z /2-graded vector space A [1]. 3.2Minimal models of A ∞-algebras One can do simple di?erential geometry in the symmetric monoidal category of non-commutative formal pointed dg-manifolds.New phenomenon is the possi-bility to de?ne some structures up to a quasi-isomorphism. De?nition 3.2.1Let f :(X,d X ,x 0)→(Y,d Y ,y 0)be a morphism of non-commutative formal pointed dg-manifolds.We say that f is a quasi-isomorphism if the induced morphism of the tangent complexes f 1:(T x 0X,d (1)X )→(T y 0Y,d (1)Y )is a quasi-isomorphism.We will use the same terminology for the corresponding A ∞-algebras. De?nition 3.2.2An A ∞-algebra A (or the corresponding non-commutative formal pointed dg-manifold)is called minimal if m 1=0.It is called contractible if m n =0for all n ≥2and H ?(A,m 1)=0. The notion of minimality is coordinate independent,while the notion of contractibility is not. It is easy to prove that any A ∞-algebra A has a minimal model M A ,i.e.M A is minimal and there is a quasi-isomorphism M A →A (the proof is similar to the one from [Ko1],[KoSo2]).The minimal model is unique up to an A ∞-isomorphism.We will use the same terminology for non-commutative formal pointed dg-manifolds.In geometric language a non-commutative formal pointed dg-manifold X is isomorphic to a categorical product (i.e.corresponding to the completed free product of algebras of functions)X m ×X lc ,where X m is minimal and X lc is linear contractible.The above-mentioned quasi-isomorphism corresponds to the projection X →X m . The following result (homological inverse function theorem)can be easily deduced from the above product decomposition. 16 Proposition3.2.3If f:A→B is a quasi-isomorphism of A∞-algebras then there is a(non-canonical)quasi-isomorphism g:B→A such that fg and gf induce identity maps on zero cohomologies H0(B)and H0(A)respectively. 3.3Centralizer of an A∞-morphism Let A and B be two A∞-algebras,and(X,d X,x0)and(Y,d Y,y0)be the corre-sponding non-commutative formal pointed dg-manifolds.Let f:A→B be a morphism of A∞-algebras.Then the corresponding k-point f∈Maps(Spc(A),Spc(B)) Maps(X,Y)f(completion at gives rise to the formal pointed manifold U f= the point f).Functoriality of the construction of Maps(X,Y)gives rise to a homomorphism of graded Lie algebras of vector?elds V ect(X)⊕V ect(Y)→ V ect(Maps(X,Y)).Since[d X,d Y]=0on X?Y,we have a well-de?ned homo-logical vector?eld d Z on Z=Maps(X,Y).It corresponds to d X?1Y?1X?d Y under the above homomorphism.It is easy to see that d Z|f=0and in fact morphisms f:A→B of A∞-algebras are exactly zeros of d Z.We are going to describe below the A∞-algebra Centr(f)(centralizer of f)which corresponds to the formal neighborhood U f of the point f∈Maps(X,Y).We can write (see Section2.3for the notation) c j,M=c0j,M+r j,M, where c0j,M∈k and r j,M are formal non-commutative coordinates in the neigh-borhood of f.Then the A∞-algebra Centr(f)has a basis(r j,M)j,M and the A∞-structure is de?ned by the restriction of the homological vector d Z to U f. As a Z-graded vector space Centr(f)= n≥0Hom V ect Z k(A?n,B)[?n].Let φ1,...,φn∈Centr(f),and a1,...,a N∈A.Then we have m n(φ1,...,φn)(a1,...,a N)= I+R.Here I corresponds to the term=1X?d Y and is given by the following expression 17 f a 1 a N φ1φ n f + root i φI=Σtrees T ?+m B j Similarly R corresponds to the term d X ?1Y and is described by the following picture R=Σa 1 a N e A m j .edges e, trees T root + φ1 ?+Comments on the ?gure describing I . 1)We partition a sequence (a 1,...,a N )into l ≥n non-empty subsequences. 2)We mark n of these subsequences counting from the left (the set can be empty). 3)We apply multilinear map φi ,1≤i ≤n to the i th marked group of 18 elements a l. 4)We apply Taylor coe?cients of f to the remaining subsequences. Notice that the term R appear only for m1(i.e.n=1).For all subsequences we have n≥1. From geometric point of view the term I corresponds to the vector?eld d Y, while the term R corresponds to the vector?eld d X. Proposition3.3.1Let d Centr(f)be the derivation corresponding to the image of d X⊕d Y in Maps(X,Y). One has[d Centr(f),d Centr(f)]=0. Proof.Clear. Remark3.3.2The A∞-algebra Centr(f)and its generalization to the case of A∞-categories discussed in the subsequent paper provide geometric description of the notion of natural transformaion in the A∞-case(see[Lyu],[LyuOv]for a pure algebraic approach to this notion). 4Non-commutative dg-line L and weak unit 4.1Main de?nition De?nition4.1.1An A∞-algebra is called unital(or strictly unital)if there exists an element1∈V of degree zero,such that m2(1,v)=m2(v,1)and m n(v1,...,1,...,v n)=0for all n=2and v,v1,...,v n∈V.It is called weakly unital(or homologically unital)if the graded associative unital algebra H?(V) has a unit1∈H0(V). The notion of strict unit depends on a choice of a?ne coordinates on Spc(T(V)), while the notion of weak unit is“coordinate free”.Moreover,one can show that a weakly unital A∞-algebra becomes strictly unital after an appropriate change of coordinates. The category of unital or weakly unital A∞-algebras are de?ned in the nat-ural way by the requirement that morphisms preserve the unit(or weak unit) structure. In this section we are going to discuss a non-commutative dg-version of the odd1-dimensional supervector space A0|1and its relationship to weakly unital A∞-algebras.The results are valid for both Z-graded and Z/2-graded A∞-algebras. De?nition4.1.2Non-commutative formal dg-line L is a non-commutative for-mal pointed dg-manifold corresponding to the one-dimensional A∞-algebra A? k such that m2=id,m n=2=0. The algebra of functions O(L)is isomorphic to the topological algebra of formal series k ξ ,where degξ=1.The di?erential is given by?(ξ)=ξ2. 19 4.2Adding a weak unit Let(X,d X,x0)be a non-commutative formal pointed dg-manifold correspod-ning to a non-unital A∞-algebra A.We would like to describe geometrically the procedure of adding a weak unit to A. Let us consider the non-commutative formal pointed graded manifold X1= L×X corresponding to the free product of the coalgebras B L?B X.Clearly one can lift vector?elds d X and d L:=?/?ξto X1. Lemma4.2.1The vector?eld =d X+ad(ξ)?ξ2?/?ξ d:=d X 1 satis?es the condition[d,d]=0. Proof.Straightforward check. It follows from the formulas given in the proof thatξappears in the ex-pansion of d X in quadratic expressions only.Let A1be an A∞-algebras cor-responding to X1and1∈T pt X1=A1[1]be the element of A1[1]dual toξ(it corresponds to the tangent vector?/?ξ).Thus we see that m A12(1,a)= m A12(a,1)=a,m A12(1,1)=1for any a∈A and m A1n(a1,...,1,...,a n)=0for all n≥2,a1,...,a n∈A.This proves the following result. Proposition4.2.2The A∞-algebra A1has a strict unit. Notice that we have a canonical morphism of non-commutative formal pointed dg-manifolds e:X→X1such that e?|X=id,e?(ξ)=0. De?nition4.2.3Weak unit in X is given by a morphism of non-commutative formal pointed dg-manifolds p:X1→X such that p?e=id. It follows from the de?nition that if X has a weak unit then the associative algebra H?(A,m A1)is unital.Hence our geometric de?nition agrees with the pure algebraic one(explicit algebraic description of the notion of weak unit can be found e.g.in[FOOO],Section205). 5Modules and bimodules 5.1Modules and vector bundles Recall that a topological vector space is called linearly compact if it is a pro-jective limit of?nite-dimensional vector spaces.The duality functor V→V?establishes an anti-equivalence between the category of vector spaces(equipped with the discrete topology)and the category of linearly compact vector spaces. All that can be extended in the obvious way to the category of graded vector spaces. Let X be a non-commutative thin scheme in V ect Z k. 全面预算管理常见错误 全面预算管理常见错误 全面预算反映的是公司未来某一特定期间(如一个会计年度)的全部生产、经营活动的财务计划。如若一个公司的全面预算管理做得好，显然会达到提升战略管理能力、有效监控与考核、高效使用企业资源、有效管理经营风险等目的。 那么，我们在应用全面预算管理工具时常犯的错误是什么?以创维为例： 1.缺乏重视：一把手和参与者都没把它当回事 每年的全面预算管理参与者大多采取应付态度，总以为这是集团布置的任务，与自己的实际工作没有太大关系。一把手也没有从内心重视这项工作，总以为这是财务的事，把这项工作完全交给财务人员来做，自己不关心，也不交流，在汇报或答辩时照本宣科。 2.无格局观：一把手心中没有一盘棋 全面预算管理的前提是战略管理和业务规划，要求管理者尤其是一把手首先要对自己所管公司所处的行业环境、竞争对手及自己所处的地位、拥有的优劣势，所应采取的战略、目标、发展路径、资源及获取方式，以及产品、客户、市场、组织形式、流程、能力等均要有清晰的认识。如果一把手对公司的这一盘生意没有谱，显然是无法把全面预算管理工具运用好，结果大多是走形式了。在这方面管理者要熟练运用SWOT、波特五力分析模型、行业对标分析、平衡积分卡(战略地图)等战略分析工具。 3.关联性差：战略与业务规划脱节，一把手缺乏系统思维能力 表现在战略和业务规划的因果关系不清晰，或者是业务规划不关注发展战略，只关注公司的短期目标，想到哪就是哪，年度业务规划与发展战略完全没有关联。目标不关联、路径不关联、评价不关联，这样的预算显然不是真正的全面预算。 4.两线作战：业务与预算是两套班子 我们常常看到产业公司的预算和其业务规划是脱节的，业务与预算是两套班子，两线作战，业务运作过程中资源不足时再来找资源，找不到就搁浅。像这样没有资源保障的业务规划往往是空话，是没 有意义的。可见，任何业务规划必须配置相应的资源，一把手必须 懂得推动某项业务，计算其投入与产出，这样才能避免业务或管理 上的空谈。 5.不会分解：一把手缺乏把战略细化为行动的能力 一般来讲发展战略必须分解为长中短期目标、路径，且要细化为年度经营目标，要落实到具体的行动，通过预算层层分解，成为年 度指标、季度指标、月份目标，落实到每个业务单元的日常经营上。 6.监控缺失：集团管理报表严重偏科 战略监控的常用工具是管理报告和业绩评价。尽管创维集团有一定的基础，但凌乱而不系统，表现在用于月度或季度经营分析的管 理报表过于侧重利润表的分析，而对业务、资产负债的关注不足， 缺少反映现金流、资产负债的流动性指标，缺乏行业特性指标(如A 计划的可比门店增长)。同时现今使用的管理报表过于偏重预算的达 成情况、历史纵向的对比分析，缺少横向的行业对标分析。更要命 的是管理报表与战略主体、法人主体、会计主体及会计核算体系完 全分离，增加了财务人员的工作量。 7.工具滞后：数据运算平台难以负荷 现有的经营分析信息系统(OA)不能承载更多的数据和功能，表现在数据运算平台难以负荷，常有逻辑错误，BUG频出，且难以实现 与会计核算系统的衔接。系统维护工作量大、成本高，可见该信息 系统已严重滞后，急需更换。 8.定位不清：集团管理边界模糊，可执行性差 集团整体战略与产业公司业务战略混为一谈，各自定位不清，导致管理边界模糊，可执行性差。比如“核心产业做强，相关产业做大”的集团发展战略，在实际执行中就碰到集团做什么，产业公司 身体仓库管理系统 1、模块说明：每个模块一般可分为六组：基本资料、日常作业、凭证打印、清单与报表、 批次处理、查询作业 1.1 基本资料：产品类别设定、编码原则设定、产品编码、仓别设定、单据性质设定 1.1.1 产品类别设定：此为后续报表数据收集索引和分类之依据 1.1.2 编码原则设定：据此不同公司可采取不同的分段和方式进行自动编码，包 括产品编码、供应商编码、客户资料编码、人员编码等， 都要依此进行自定义。 Eg: A 一般产品编码通用原则为：大分类(3码)+中分类(3码)+小分类(3码)+ 流水码(4码)，共计13码左右即可。 Eg: B 编码不必赋予太多特殊意义，亦造成编码上的混乱，以简单明了，易 识别为原则。 1.1.3 产品编码：包括基本项目、采购、生管、仓库、业务、品管、生产、财务 会计、其它，其可根据不同部门使用状况来分类定义，同 时便于基础资料的收集与输入，及日后使用之管理和维护。 1.1.4 仓别设定：此为各仓别属性设定之基础 1.1.5 单据性质设定：此为各“日常作业”之单据性质设定基础。 Eg：A库存异动单对库存的影响可分为：增加、减少 调拨单对库存的影响为：平调 成本开帐/调整单对成本的影响可分为：增加、减少 Eg：B可依不的部门或个人进行单据别的区别使用和管理。 Eg：C单据的编码方式：单别+单据号，或可采用自由编码的方式进行等 Eg：D单据表尾的备注与签核流程等。 Eg：E单据电脑审核流程。 1.2 日常作业：库存异动建立作业、调拨建立作业、成本开帐/调整建立作业、盘点资 料建立作业、批号管理建立作业、借入/出建立作业、借入/出还回作 业 1.2.1 库存异动建立作业：此单据适用于非生产性物料的异动(或增或减)，及库存 盘盈亏之调整用，如没有上线制令管理系统亦可通过 此作业进行库存异动作业。 1.2.2 调拨单建立作业：此单据适用于各仓之间的物料调拨之用，不对库存变化 产生影响。 1.2.3 成本开帐/调整建立作业：此单据适用于系统开帐之各仓库存成本资料的输 入，亦是日常“成本重计作业”所产生之单据。 1.2.4 盘点资料建立作业：此单据适用于盘点时库存数量之输入 1.2.5 批号管理建立作业：此单据适用于物料在产品生产过程中的使用和追溯的 管理，及先进先出原理 1.2.6 借入/出建立作业：此单据适用于所有借入/出作业记录之凭证 1.2.7 借入/出还回建立作业：此单据适用所有借入/出还回作业记录之凭证，如无 法归还之作业，则通过进货或销货来做关联性作 业。 1.3 凭证打印：库存异动单凭证、调拨单凭证、成本开帐/调整单凭证、盘点清单凭证、 批号管理凭证、借入/出凭证、借入/出还回凭证 Lotus Notes的六个使用技巧 目前人民银行系统内部使用的是Lotus Domino邮件系统，此系统是一个很好的群件工作平台，它有很好的电子邮件系统，领先的全文检索和复制功能。它还具有极强的安全措施，可以可靠地保证信息安全性，具有系统管理方便、使用简单的优点。笔者在使用过程遇到一些问题，取得了一些经验，介绍如下，供同仁参考。 一、在一台计算机装多个ID 的LOTUS 如果是多个用户使用同一台机器收发各自邮件可采用以下方法： 1、首先进行工作场所的设置：任选一个除办公室外的工作场所（因为办公室场所默认为第一个安装用户所用） （1）基本页面：改场所类型为“局域网”，场所名称可以由用户自行设定，这个名称将显示在右下角的场所列表中。 （2）服务器页面：宿主/邮件服务器填写你的邮件服务器名称。 （3）端口页面：使用的端口选择TCP/IP、LAN0 （4）邮件页面：邮件文件位置选择“在服务器”；邮件文件填写第二用户的邮件文件位置（如mail1\aaa.nsf）；Notes邮件网络域填写公司的网络域名程；收件人姓名自动查找选择“先本地后服务器”；发送外出邮件选择“通过Domino服务器” 2、当第一次打开邮箱时，系统要求输入最后一次使用NOTES的用户的密码，如果为当前用户可直接输入密码进入邮箱，否则请连续点击密码输入窗的“取消”按钮，在弹出的选择到切换到的标识符窗口中选择第二用户的ID文件，打开后输入密码，进入欢迎页面，之后在右下角的场所列表中，选择第二用户的工作场所，邮件箱即可打开。如果NOTES已打开的状态下切换用户，请首先切换用户ID，之后到Lotus的右下角场所选择框中直接选择该用户的工作场所即可。注意：用户的ID和他的工作场所一定要配套使用，否则会出现无法转发邮件等问题。 二、服务器的Mail.box文件被破坏的解决方法 如果收发服务器上的邮箱(Mail.box)被破坏，运行Fixup服务器程序，如果这不能解决问题，可以压缩Mail.box，如果仍然有问题，执行下面的步骤： 1、关闭Lotus Domino服务。 2、重新将notes\data\目录下的Mail.box文件更名，如可以把它改为Mail_old.box。 3、重新启动Lotus Domino服务，服务器会自动生成一个新的Mail.box文件。 4、从Mail_old.box中将未被破坏的文档拷贝到新生成的Mail.box中。 三、删除已经发出去的邮件 有时在给多个用户发邮件时，由于工作失误，将邮件发错，想删除发给这些用户的邮件，请立即与邮件管理员联系，因为所用用户发出的邮件 都要放在一个外出邮箱mail.box中，如果此时发出的邮件在mail.box中没有发出，可请管理员将此mail.box中的邮件直接删除（注意：在使用 此方法时，用户要快速与邮件管理员联系，否则邮件会从mial.box中发出），如果此邮件已经从mail.box中发出，则只能通过管理员在服务器 端打开所有收到此邮件的邮箱，并一个一个删除，这种方法只对本单们内的用户邮箱进行删除。 四、设置邮箱的大小，当超过邮箱大小时能够报警由于服务器硬盘空间是有限的，并且在用户邮箱大太时，会使服务器工作在超负荷状态下，为了更加合理的使用Lotus Notes系统，对每个用户邮箱进行大小设置以防止数据库无限制的膨胀，对用户邮箱的大小设置可以采用下面的操作： （1）单击“文件”菜单，选择“文件”，选择“服务器管理…”，选择要管理的服务器，单 投标书中常常容易出现的问题 一、封面 1. 封面格式是否与招标文件要求格式一致，文字打印是否有错字。 2. 封面标段、里程是否与所投标段、里程一致。 3. 企业法人或委托代理人是否按照规定签字或盖章，是否按规定加盖单位公章，投标单位名称是否与资格审查时的单位名称相符。 4. 投标日期是否正确。 二、目录 5. 目录内容从顺序到文字表述是否与招标文件要求一致。 6. 目录编号、页码、标题是否与内容编号、页码（内容首页）、标题一致。 三、投标书及投标书附录 7. 投标书格式、标段、里程是否与招标文件规定相符，建设单位名称与招标单位名称是否正确。 8. 报价金额是否与“投标报价汇总表合计”、“投标报价汇总表”、“综合报价表”一致，大小写是否一致，国际标中英文标书报价金额是否一致。 9. 投标书所示工期是否满足招标文件要求。 10. 投标书是否按已按要求盖公章。 11. 法人代表或委托代理人是否按要求签字或盖章。 12. 投标书日期是否正确，是否与封面所示吻合。 四、修改报价的声明书（或降价函） 13. 修改报价的声明书是否内容与投标书相同。 14. 降价函是否按招标文件要求装订或单独递送。 五、授权书、银行保函、信贷证明 15. 授权书、银行保函、信贷证明是否按照招标文件要求格式填写。 16. 上述三项是否由法人正确签字或盖章。 17. 委托代理人是否正确签字或盖章。 18. 委托书日期是否正确。 19. 委托权限是否满足招标文件要求，单位公章加盖完善。 20. 信贷证明中信贷数额是否符合业主明示要求，如业主无明示，是否符合标段总价的一定比例。 六、报价 21. 报价编制说明要符合招标文件要求，繁简得当。 22. 报价表格式是否按照招标文件要求格式，子目排序是否正确。 23. “投标报价汇总表合计”、“投标报价汇总表”、“综合报价表”及其他报价表是否按照招标文件规定填写，编制人、审核人、投标人是否按规定签字盖章。 24. “投标报价汇总表合计”与“投标报价汇总表”的数字是否吻合，是否有算术错误。 25. “投标报价汇总表”与“综合报价表”的数字是否吻合，是否有算术错误。 26.“综合报价表”的单价与“单项概预算表”的指标是否吻合，是否有算术错误。“综 仓库管理系统 ——使用手册 目录 第1章系统概述 (1) 1.1引言 (1) 1.2系统特点....................................................... 错误！未定义书签。第2章系统安装 ............................................ 错误！未定义书签。 2.1系统环境要求............................................... 错误！未定义书签。 2.2单机版的安装............................................... 错误！未定义书签。 2.3网络版的安装............................................... 错误！未定义书签。 2.3.1 程序包文件介绍....................................................... 错误！未定义书签。 2.3.2 数据库的安装与配置............................................... 错误！未定义书签。 2.3.3 客户端的安装与配置............................................... 错误！未定义书签。 2.4系统注册....................................................... 错误！未定义书签。第3章基本操作 (2) 3.1系统启动 (2) 3.2重新登录 (2) 3.3修改密码 (2) 3.4记录排序 (3) 3.5快速查找功能 (3) 3.7窗口分隔 (3) 3.8数据列表属性设置 (3) 3.9数据筛选 (4) 3.10数据导入 (4) 3.11报表设计 (5) 消防预算通常易错易漏问题 一、通用 1、水电费、配合费、管理费、检测费漏算或者未跟甲方明确 2、蓝图和电子图不一致（核对版本） 3、防火封堵漏算或者多算 4、强弱电界面不清导致漏算，如风机控制柜、水泵控制柜及控制柜到电机的电线电缆 及桥架和管子，还有消防桥架 5、因风机连锁线、强启线甚至多线在强电系统图或者动力平面图上导致漏算 6、支架，有时因集中计算支架反而整体漏项，漏量或者是漏上定额。 7、末端试水或者放空管包括水箱、水池的溢流排水、浮球阀等，因界面不清漏项 8、试压、管道冲洗和调试漏计 9、过楼板套管和穿墙套管漏计 10、卡箍管配件漏计量或者是漏上定额 11、减压阀组应拆散计算（减压阀+闸阀、过滤器等）、且要再计算书上标明，以免 时间长记不住 12、管道保温容易漏项:○1、屋顶和汽车坡道处○2、地下室天窗周边或者半地下室自然 排烟口处○3、楼层未封闭的连廊、凹廊立管或者水平管 13、做结算时间跨度长容易出现重复抛量 14、新定额软件中容易出现主材价格一样或者独立费主材重复。 二、消火栓 1、消防箱规格尺寸不明确，如单、双栓自救盘减压稳压等，箱子大小尺寸、带不带灭 火器等，小于200mm厚度的箱子全部为旋转式消火栓栓头 2、减压孔板漏算，通常因系统图或者平面图一笔带过而忽略 3、消火栓DN65的立管长度容易弄错（因标高没有仔细弄清楚） 4、高低区顶端设置自动排气阀，同时配有截止阀或者铜球阀 5、实验消火栓别漏项、还有有的实验消火栓旁边有一个DN65的阀门 6、消火栓DN65的支管有事会设置蝶阀，平面图看不出来，系统图或者施工设计说明 会有，容易漏算。 三、喷淋 1、DN25的登高管 2、下喷、侧喷及支管、或者因支管标高不明确导致支管量不准及支架误差很大 3、湿式报警阀组排水管上的管道及附件：流量计、闸阀、压力表等 4、喷淋系统水流指示器旁边的泄水阀及泄水管不能漏算 5、屋顶水箱至喷淋干管的补水管不要漏算，还有消防水箱的进水管通常是机电总包做， 但是不排除消防单位做，界面要核实。 四、自动报警 1、报警主机漏计（主机+CRT+电源+广播主机+电话主机等、电源监控主机、防火门监 控主机、漏电保护主机、可燃气体探测器主机等） 2、消报按钮和消火栓数量对应不起来 3、防火阀或者正压送风口和模块对应不起来 4、卷帘门模块漏计 5、吊顶登高的管线漏计 6、金属软管及对应的线漏计（模块、消火栓按钮） 7、短路隔离器漏算，或者数量少算，最多32个点位一个短路隔离器。 智能仓库管理系统 需求规格说明书 拟制：仇璐佳日期：2010年3月17日星期三审核：日期： 批准：日期： 文档编号：DATA-RATE-SRS-01 创建日期：2010-03-17 最后修改日期：2020-04-24 版本号：1.0.0 电子版文件名：智能仓库管理系统-需求规格说明书- 文档修改记录 基于web智能仓库管理系统详细需求说明书（Requirements Specification） 1．引言 1．1 编写目的 本系统由三大模块构成，分别是：系统设置，单据填开，库存查询。 其中： 系统设置包括：管理员的增加，修改，删除，以及权限管理；仓库内货物的基本资料的增加，修改，删除；工人，客户等的基本资料的增加，修改，删除。 单据填开模块包括：出库单，入库单，派工单，等单据的填开及作废操作。 库存查询系统包括：库存情况的查询，各项明细的查询，工人工资的查询，正在加工产品查询等。 报表导出模块包括：按月，按季度，按年的报表导出功能。 1．2 背景说明 (1)项目名称：基于web智能仓库管理系统 (2)项目任务开发者：东南大学成贤学院06级计算机（一）班仇璐佳，软件基本运行环境为Windows环境，使用MyEclipse7.1作为开发工具，使用struts2作为系统基本框架，Spring作为依赖注入工具，hibernate对MySql所搭建的数据库的封装，前台页面采用ext的js框架，动态能力强，界面友好。 (3)本系统可以满足一般企业在生产中对仓库管理的基本需求，高效，准确的完成仓库的进出库，统计，生产，制造等流程。 1．3 术语定义 静态数据－－系统固化在内的描述系统实现功能的一部分数据。 1引言 (2) 1.1编写目的 (2) 1.2背景 (2) 1.3定义 (3) 1.4参考资料 (3) 2任务概述 (3) 2.1目标 (3) 2.2用户的特点 (9) 2.3假定和约束 (9) 3需求规定 (9) 3.1对功能的规定 (9) 3.2对性能的规定 (9) 3.2.1精度 (9) 3.2.2时间特性要求 (9) 3.2.3灵活性 (9) 3.3输人输出要求 (9) 3.4数据管理能力要求 (10) 3.5故障处理要求 (10) 3.6其他专门要求 (10) 4运行环境规定 (11) 4.1设备 (11) 4.2支持软件 (11) 4.3接口 (11) 4.4控制 (11) 软件需求说明书 1引言 1.1编写目的 企业的物资供应管理往往是很复杂的，烦琐的。由于所掌握的物资种类众多，订货，管理，发放的渠道各有差异，各个企业之间的管理体制不尽相同，各类统计计划报表繁多，因此物资管理必须实现计算机化，而且必须根据企业的具体情况制定相应的方案。 根据当前的企业管理体制，一般物资供应管理系统，总是根据所掌握的物资类别，相应分成几个科室来进行物资的计划，订货，核销托收，验收入库，根据企业各个部门的需要来发放物资设备，并随时按期进行库存盘点，作台帐，根据企业领导和自身管理的需要按月，季度，年来进行统计分析，产生相应报表。为了加强关键物资，设备的管理，要定期掌握其储备，消耗情况，根据计划定额和实际消耗定额的比较，进行定额的管理，使得资金使用合理，物资设备的储备最佳。 所以一个完整的企业物资供应管理系统应该包括计划管理，合同托收管理，仓库管理，定额管理，统计管理，财务管理等模块。其中仓库管理是整个物资供应管理系统的核心。 开发本系统的目的在于代替手工管理、统计报表等工作，具体要求包括： 数据录入：录入商品信息、供货商信息、名片、入库信息、出库信息、退货信息等信息； 数据修改：修改商品信息、供货商信息、名片、帐号等信息； 统计数据：统计仓库里面的商品的数量，种类，并计算库存总价值； 数据查询：输入查询条件，就会得到查询结果； 数据备份：定期对数据库做备份，以免在数据库遇到意外破坏的时候能够恢复数据库，从而减少破坏造成的损失。 二、仓库信息管理系统分析与设计 （一）《仓库信息管理系统》的需求建模 1、需求分析 仓库信息管理系统要能完成以下功能： 仓库存放的货物品种繁多，堆存方式以及处理方式也非常复杂，随着业务量的增加，仓库管理者需要处理的信息量会大幅上升，因此往往很难及时准确的掌握整个仓库的运作状态。针对这一情况，为了减轻仓库管理员和操作员的工作负担，此系统在满足仓库的基本管理功能基础上发挥信息系统的智能化。 根据要求可将系统分为四个模块 （1）用户登录模块 普通操作员和管理人员登录此系统，执行仓库管理的一些操作，但是普通操作员和管理人员所能执行的功能不一样。 （2）仓库管理模块 管理员工作需要登陆系统，才能够进行操作，系统中的各项数据都不允许外人随便查看和更改，所以设置登陆模块是必须的。可以执行仓库进货，退货，领料，退料；商品调拨，仓库盘点等功能。（3）业务查询模块 在用户登录系统后，可以执行库存查询，销售查询，仓库历史记录查询。 （4）系统设置模块 显示当前仓库系统中的信息,在系统中可以执行供应商设置，仓库设置。 2、功能模块分析 （1）登录模块 ①普通操作员：显示当天仓库中的所有库存的信息。 ②管理员：修改仓库中的库存信息。 ③用户注销：在用户执行完仓库功能时，注销。 ④用户退出。 （2）管理模块 ①仓库库存的进货与退货； ②仓库中的库存需要领料和退料功能； ③仓库也可以完成不同地区的商品在此仓库的商品调拨任务； ④用户人员也可以在当天之后对仓库中的库存进行盘点。 （3）查询模块 ①显示当前仓库商品信息，并执行库存查询； ②显示仓库信息，对商品的销售量进行查询； ③此系统还可以对仓库历史记录进行查询。 （4）设置模块 ①供应商设置 ②仓库设置 3、工作内容及要求 ①进一步细化需求分析的内容，识别出系统的参与者，并完成用例图； ②将用例图中的每个用例都写成相应的事件流文档； ③进一步使用活动图来描述每个用例，为后续的系统设计做好准备； 装饰预算100误区 装饰预算100误区 第一章地面工程 1、楼梯装饰定额中，包括了踏步、休息平台和楼梯踢脚线，但不包括楼梯底面抹灰。 注解：常误解楼梯间首层地面的踢脚线也包含在楼梯装饰定额中。其实，楼梯间首层地面的踢脚线不包含在楼梯装饰定额中，楼梯装饰定额中只含楼梯踢脚线，而不是楼梯间踢脚线。楼梯底面抹灰应执行天棚相应子目，往往漏算。 2、台阶、坡道、散水定额中，仅含面层的工料费用，不包括垫层。 注解：经常只计算台阶、坡道、散水的面层，而漏算相应的垫层。 3、块料面层、木地板、活动地板，按图示尺寸以平方米计算。扣除柱子所占的面积，门窗洞口、暖气槽和壁龛的开口部分工程量并入相应面层内。 注解：门窗洞口的地面经常漏算。 4、块料踢脚、木踢脚按图示长度以米计算。 注解：门窗洞口的长度经常减掉，而侧面的踢脚往往漏算。 5、地面灰土垫层中的素土，定额中一般利用原土，故不考虑买土的费用。 注解：特殊情况下，需要买土，而买土的费用常漏算。 6、石材图案镶贴应按镶贴图案的矩形面积计算，成品拼花按设计图案的面积计算。 注解：石材拼花常单独计算，而石材拼花的工程量未扣除，应按“算多少扣多少”的原则执行。 7、波打线一般为块料楼（地）面沿墙边四周所做的装饰线；宽度不等。波打线按图示尺寸以平方米计算。注解：地面四周的波打线常与地面面层合并计算，其实应单独计算。 8、找平层、整体面层按房间净面积以平方米计算，不扣除墙垛、柱、间壁墙及面积在0.3平方米以内孔洞所占面积，但门窗洞口、暖气槽的面积也不增加。 注解：计算找平层、整体面层时常误把间壁墙所占面积减掉。 9、楼梯面层工程量按楼梯间净水平投影面积以平方米计算。楼梯井宽在500mm以内者不予扣除，超过50 0mm者应扣除其面积。 注解：计算时，常先计算单层的楼梯面层工程量，然后乘于楼层数减1的（n—1）。当楼顶为上人屋面时，楼梯常通到楼顶，此时单层的楼梯面层工程量应乘于楼层数，而不是楼层数减1。 10、台阶按水平投影面积计算。不包括牵边、侧面装饰，其装饰应按展开面积计算，套用零星项目的相应子目。 注解：牵边、侧面装饰常漏算。 11、装饰面板踢脚线定额中一般不含收口装饰线条，应执行装饰线条的相应子目。 注解：装饰面板踢脚线上部的收口装饰线条常漏算。 1引言 (3) 1.1编写目的 (3) 1.2背景 (3) 1.3定义 (3) 1.4参考资料 (3) 2程序系统的结构 (4) 3用户登录界面程序设计说明 (5) 3.1程序描述 (5) 3.2功能 (5) 3.3性能 (5) 3.4输人项 (6) 3.5输出项 (6) 3.6算法 (6) 3.7流程逻辑 (6) 3.8接口 (7) 3.9存储分配 (7) 4仓库管理模块（02）设计说明 (7) 4.1程序描述 (7) 4.2功能 (8) 4.3性能 (8) 4.4输人项 (8) 4.5输出项 (8) 4.6算法 (8) 4.7流程逻辑 (9) 4.8接口 (10) 5仓库查询模块（03）设计说明 (11) 5.1程序描述 (11) 5.2功能 (11) 5.3性能 (11) 5.4输人项 (11) 5.5输出项 (11) 5.6算法 (12) 5.7流程逻辑 (12) 6系统设置模块（04）设计说明 (13) 6.1程序描述 (13) 6.2功能 (13) 6.3性能 (13) 6.4输人项 (13) 6.5输出项 (13) 6.6算法 (14) 6.7流程逻辑 (14) 6.8接口 (14) 6.9测试计划 (14) 详细设计说明书 1引言 1.1编写目的 本文档为仓库管理系统详细设计文档(Design Document)，对作品进行系统性介绍，对使用的技术机制进行分析，对各个模块进行功能描述，并给出主要数据流程和系统结构 本文档的预期读者是本系统的需求用户、团队开发人员、相关领域科研人员 1.2背景 项目名称：仓库管理系统--详细设计说明书 项目任务开发者：大连交通大学软件学院R数学072班张同骥06，软件基本运行环境为Windows环境 1.3定义 Mysql：数据库管理软件 DBMS：数据库管理系统 Windows 2003/XP：运行环境 JSP ：软件开发语言 Myeclipse ：开发工具 1.4参考资料 《软件工程应用实践教程》清华大学出版社 《系统分析与设计》清华大学出版社 《数据库系统概论》高等教育出版社 《Windows网络编程》清华大学出版社 《VC技术》清华大学出版社 预算编制精要及常见问题 2009-12-09 09:15:34| 分类：造价经验| 标签：|字号大中小订阅 在此给大家推荐我的淘宝网店，里面有一套完整的图纸+计算底稿，分不同地区编制的，希望对各位初学者有所帮助。店铺地址： https://www.doczj.com/doc/e84278709.html,土建造价员 A：施工图预算的编制 施工图预算是考验业务人员技术水平高低的唯一文件。施工图预算质量的好坏，直接影响到施工图结算质量的好坏，预算是结算的基础。因此，想快速、准确的编制施工图预算，应从下面七个方面着手进行。 一、认真熟悉图纸，做好图纸会审前的准备工作。 施工图纸是建筑工程的"语言"。在计算之前，要认真熟悉图纸，认真阅读设计说明，了解设计者的意图。一般先粗看后精读，使该工程在头脑中形成立体图形，知道它的结构形式，内外装饰的要求，采用了哪些新型建筑材料等。看图顺序一般先由结构图开始，最后看施工图，注重核对结构图和施工图的标高、尺寸是否一致，发现互相矛盾的地方或不清楚的地方要随时记录下来，在图纸会审时提出来，由设计单位解答清楚。 预算编制前的看图，没有必要从施工的角度去动脑筋。这种看图方法纯粹是从预算编制角度出发，为了排除预算编制过程中的障碍而进行的。有的人在动手计算预算工程量前，象现场施工人员一样，花费很大的精力和很长的时间去看图，其实是不必要的。也有的人在预算工程量计算前不看图，提笔就开算，这种做法势必在工程量计算过程中，随时去翻阅有关图纸，造成工作混乱，降低了工作效率，并且容易发生差错，也是不可取的。 二、熟练掌握工程量计算规则，提高计算速度。 工程量要计算的既快又准，和熟练掌握工程量计算规则和计算方法关系密切。土建工程的特点是：图纸张数多、施工项目杂、需要计算的工程量大，因此在计算工程量时一定要把计算式写清楚，每一项工程量都要标明来源图纸的编号或所采用的标准图集号、页数及构件编号，并把所需砂浆的种类标号及砼的标号注明，使计算式不但自己能看懂，更重要的是甲方审核时也能看的懂。计算方法:首先 确定"三线一面"的尺寸做为基数，运用"统筹法"的基本原理来计算工程量，避免 出现漏项、重复计算和计算错误等现象的发生，做到工程量计算的即快又准。总之，土建工程的工程量计算，是一项比较复杂的艰苦工作，责任心要求很强，它是土建预算编制的关键环节。计算方法正确，不但能提高计算工程量的速度，还能保证土建预算的编制质量，为确定科学合理的工程造价起到可靠保证。 三、了解现行的施工规范，保证预算的准确性。 （仓库管理）仓库管理系统软件设计说明书改后 仓库管理系统 软件设计说明书 目录 1. 介绍 (1) 1.1 目的 (1) 1.2 范围 (1) 1.3 定义、缩写词 (1) 1.4 内容概览 (1) 2. 体系结构表示方法 (1) 3. 系统要达到的目标和限制 (2) 4. 用例视图 (2) 4.1 系统用例图 (2) 4.2 产品类别 (3) 4.3 检索产品 (4) 4.4 产品详细 (5) 4.5 管理员注册 (6) 4.6 查看订单 (7) 4.7 下订单 (8) 4.8 管理员登录系统 (9) 4.9 管理员退出系统 (10) 4.10 日常管理 (11) 4.11 商品信息管理 (12) 4.12 供应信息管理 (12) 4.13 名片信息管理 (13) 4.14 配送状态处理 (14) 5. 逻辑视图 (16) 5.1 总览 (16) 5.2 主要Package的介绍 (17) 6. 过程视图 (19) 6.1 管理员盘点 (19) 6.2 产品管理 (20) 6.3 订单处理数据 (22) 6.4 仓库物流管理 (23) 6.5 管理员查询 (24) 7. 部署视图 (24) 8. 流程逻辑 (25) 9. 规模和性能 (26) 10. 质量 (26) 软件设计说明书 1. 介绍 1.1 目的 本文档为仓库管理系统详细设计文档(Design Document)，对作品进行系统性介绍，对使用的技术机制进行分析，对各个模块进行功能描述，并给出主要数据流程和系统结构 本文档的预期读者是本系统的需求用户、团队开发人员、相关领域科研人员 1.2 范围 对作品进行系统性介绍，对使用的技术机制进行分析，对各个模块进行功能描述，并给出主要数据流程和系统结构 1.3 定义、缩写词 Mysql：数据库管理软件 DBMS：数据库管理系统 Windows 2003/XP：运行环境 JSP ：软件开发语言 Myeclipse ：开发工具 1.4 内容概览 ?仓库管理系统 管理员将各项产品进行编排设备号，位置号，从而有效划分区域管理 ?设置系统 设置各项分类的标签，便于其他人进行查询及复查 ?仓库查询系统 进入系统后客户或者管理员有效快捷查询产品各项目录 ?用户登录系统 用户如果要进行查询操作，需要输入正确的用户名和密码，如果输入错误，则停留在登录页； 2. 体系结构表示方法 这篇文档使用一系列视图反映系统架构的某个方面； 用例视图：概括了架构上最为重要的用例和它们的非功能性需求； 逻辑视图：展示了描述系统关键方面的重要用例实现场景(使用交互图)； 部署视图：展示构建在处理节点上的物理部署以及节点之间的网络配置(使用部署图)； 一、关于AppendItemValue 试试下面这个简单的例子： Dim ws As New notesuiworkspace Dim uidoc As notesuidocument Dim doc As notesdocument Set uidoc=ws.currentdocument Set doc=uidoc.document For i=1 To 10 Call doc.appenditemvalue("myitem",i) Next Call doc.save(True,True ) 这个程序用以对当前文档增加10个ITEM，名字都叫myitem，但值从1到10不等。结果如何？用调试方式进行观察，发现：确实增加了10个ITEM，名字都叫myitem，但值却都是1！这与NOTES中的帮助不符。帮助里宣称： If the document already has an item called itemName$, AppendItemVa lue does not replace it. Instead, it creates another item of the same name, and gives it th e value you specify. ^^^^^^^^^^^^^^^^^^^^ 从4.6到5.0结果都一样。 二、区分NOTES的前台类与后台类 由于两者的使用范围不一，在写程序时应注意这一点，尤其写代理时。如果在后台服务器运行的代理里加一句： Dim ws As New notesuiworkspace 代理运行日志报错：Unkown Error. 三、关于NOTES与OLE的共享域 NOTES提供了一个很好的功能：共享域。NOTES用共享域来与OLE应用程序交换彼此信息。但除非确有必要与OLE应用程序共享信息，建议在设计表单时，选上：禁止共享域。 笔者曾在一个表单中创建了一个作者域AUTHOR，又在它的RTF域中嵌入MS-WORD文档： CALL UIDOC.CREATOBJECT("MYDOC","WORD.DOCUMENT.8","") 似乎一切都正常。但当我变更了NOTES的作者域AUTHOR（因笔者试图通过作者域的改变来控制NOTES文档的修改进而达到流程控制的目的），因为流程的需要，我把它变成了两个值，在NOTES中显示为： user1/co1/server1,user2/co1/server2 然后对RTF域中所嵌入的WORD文档进行了修改，然后退出，保存。结果问题出现了，NOTES 报错：你不是文档的作者，不能保存！ 什么原因？当时我明明是用user1/co1/server1进行修改的！后来，仔细调试，把AUTHOR 常见错误之一：不做上年预算回顾和分析 很多公司在启动新一年预算时，只是简单地照搬上年预算流程和预算模板，或者机械地执行上级预算指导意见，对上年预算执行情况的回顾和总结不够重视，这极易导致当年预算的失败。因为预算是企业管理的龙头，企业管理模式经常会随市场竞争环境的变化进行调整。预算回顾的作用在于，通过对上年度预算执行情况的回顾，发现预算执行中的问题，再从这些问题中找出调整企业管理模式的必要性，从而对既有的预算模式进行适度调整。不进行预算回顾就启动预算的另一个危险在于，当所有相关部门有条不紊地按上一年度预算模式组织预算编制时，企业高层可能已经在酝酿着管理模式的变革了，当管理模式变革开始时，按旧模式进行的预算编制可能刚完成一半，这时候预算工作只能全部推倒重来。 常见错误之二：预算仅是财务部门的事情 相信很多做预算的财务同仁都有同样的感触，即预算工作的最大困难在于公司上下都把预算当作财务部门的事，往往不予配合，财务人员最后只能是盲人摸象，勉强拼凑出一个整体的预算。要解决这个问题，首先，在预算启动时，可以由财务人员和业务领导共同组成预算管理委员会，统筹负责预算编制工作，这样业务部门就会积极参与预算编制了。其次，在预算编制过程中，应专门安排时间组织预算汇报会，由业务部门领导向公司管理层汇 报。由于有向公司管理层汇报的压力，业务部门领导通常会认真准备预算，财务部门在此过程中也可以获得非常充实的非财务信息。最后，预算编制人员在向业务部门催要预算表格时，不要单纯地要求其上报下年的预算，要先积极提供翔实的上年经营财务数据供业务部门参考，从而获得业务部门的支持和配合。 常见错误之三：预算编制脱离公司战略 为了适应市场竞争的需要，公司战略要经常调整，包括业务组合的调整、组织机构的调整、责任主体的重新定义，等等。而在实际工作中，预算启动往往要早于公司战略调整。由于流程繁琐，预算编制通常在下半年即开始启动，而公司领导往往是等年底看到当年年报、获取经营业绩信息后，才决定对现有战略进行调整，由此就导致了预算与战略的脱节。解决这个问题的关键在于，应由公司高层管理者担任预算管理委员会主席，因为他们掌握着公司战略调整的最新信息，这样所有的预算工作在战略调整酝酿的初期就能有所准备和预留。 常见错误之四：预算与核算能力相脱节 预算编制要充分考虑企业当前的核算能力与核算水平，否则，就会造成预算编制很漂亮却无法执行的局面。比如，公司打算在新的一年里按项目进行预算和考核，但目前的财务核算体系却是以期间作为收入成本费用核算的单位，由于项目核算必然要涉及 《管理信息系统》报告书 2013-2014 学年第 1 学期 仓库管理系统 专业： 信息管理与信息系统 班级： 2班 姓名： XXXXX 学号： 20113444 电话： XXXXXXXXXX 指导教师：王老师 信息科学与工程学院 2013.12.13 1引言 1.1背景 随着社会经济的发展和工业生产的加速，仓库的进出更为频繁，仓库信息更为重要。传统仓库管理完全由人来完成，以手工记录为主，当企业的物流业务成长到一定规模之后，随着订单数量的增加，客户需求不断个性化，执行效率就成为物流发展的瓶颈，单纯依靠人力资源的增加已不能提升出入库执行的速度，反而带来成本的大幅度上升与差错频频。计算机信息管理技术的迅速发展恰恰解决了这个问题，它使计算机技术与现代的管理技术相互配合，来更加准确、高速地完成工业企业日常的仓库管理工作。使企业能够以最少的人员来完成更多的工作。 随着我国市场经济的进一步开展，强大的信息保障，有力的电子化管理，使各大企业在国内经济市场的大潮中把现代高科技的信息技术发挥的淋漓尽致。越来越多有远见的企业家，不惜重金从国外购买高新技术，高的投资、合理的管理往往换来巨大的利润。经营的物质技术手段由简单落后转变成 高科技与人工手段并存，进而更多地将高科技应用到零售商业。国内实施WMS的条件日益成熟。主 要是物流业在过去的两年里随着国家经济的发展，而日新月异，现代一体化物流的管理思想日益为企业所接受，对仓库有了新定位和认识，从而对管理系统也提出了新的要求。所以从仓库管理的周期来考虑，一个能够高效管理的仓库系统就是一个优秀的仓库系统。 1.2开发目的及意义 对于中小型企业，仓库管理工作主要是进货商品的入库管理和销售商品的出库管理及库存商品的保管管理。现有的管理工作主要依靠手工完成，工作量大，且效率不高。为了能更好地利用现代信息技术的成果，提高管理工作的效率和水平，以适应企业发展的需要，决定开发库存管理系统。 商品流通的仓储及配送中心的出入库，库存、配送等管理，能够使管理工作节省人力。减少差错、提高工作效率，并保障。商品流转的顺利进行应用计算机系统与手持终端的结合可以方便、准确地完成商品流转的相关管理。 LotusScript 是完全面向对象的编程语言。它通过预定义的类与 Domino 接口。Domino 监控用户代码的编译和加载，并且自动包含 Domino 的类定义。 访问现有的对象最好使用 LotusScript，例如：根据其他文档的值来更改一个文档中的值。LotusScript 提供了一些公式没有的功能，例如：操作数据库存取控制列表 (ACL) 的能力。 写script关键是取对象，查看对象的属性，所以你要学会看notes提供的Script帮助。下面是我收集的一些script例子。一般是比较技巧的程序，要学习一般script编写，请下载lotusScript学习库！ LotusScript 是完全面向对象的编程语言。它通过预定义的类与 Domino 接口。Domino 监控用户代码的编译和加载，并且自动包含 Domino 的类定义。 访问现有的对象最好使用 LotusScript，例如：根据其他文档的值来更改一个文档中的值。LotusScript 提供了一些公式没有的功能，例如：操作数据库存取控制列表 (ACL) 的能力。 写script关键是取对象，查看对象的属性，所以你要学会看notes提供的Script帮助。下面是我收集的一些script例子。一般是比较技巧的程序，要学习一般script编写，请下载lotusScript学习库！ 怎样判断视图中没有文档？ set doc = vw.getfirstdocument() if doc is nothing then end if 如何将查询结果放到一个文件夹里？ 下面是将搜索结果放到名叫newfolder的文件夹中，并跳转到该文件夹上 Sub Click(Source As Button) Dim docs As notesdocumentcollection Dim doc As notesdocument ........... q=doc.query(0) Set docs = db.ftsearch(q, 0) Call docs.PutAllInFolder( "newfolder" ) Call w.OpenDatabase( "","","newfolder") End Sub 如何删掉数据库中所有私有视图 Dim session As New notessession Dim db As notesdatabase Dim doc As notesdocument Set db=session.currentdatabase 编制投标书常见错误115例 一、封面 1、封面格式是否与招标文件要求格式一致，文字打印是否有错字。 2、封面标段、里程是否与所投标段、里程一致。 3、企业法人或委托代理人是否按照规定签字或盖章，是否按规定加盖单位公章，投标单位名称是否与资格审查时的单位名称相符。 4、投标日期是否正确。 二、目录 5、目录内容从顺序到文字表述是否与招标文件要求一致。 6、目录编号、页码、标题是否与内容编号、页码（内容首页）、标题一致。 三、投标书及投标书附录 7、投标书格式、标段、里程是否与招标文件规定相符，建设单位名称与招标单位名称是否正确。 8、报价金额是否与“投标报价汇总表合计”、“投标报价汇总表”、“综合报价表”一致，大小写是否一致，国际标中英文标书报价金额是否一致。 9、投标书所示工期是否满足招标文件要求。 10、投标书是否按已按要求盖公章。 11、法人代表或委托代理人是否按要求签字或盖章。 12、投标书日期是否正确，是否与封面所示吻合。 四、修改报价的声明书（或降价函） 13、修改报价的声明书是否内容与投标书相同。 14、降价函是否按招标文件要求装订或单独递送。 五、授权书、银行保函、信贷证明 15、授权书、银行保函、信贷证明是否按照招标文件要求格式填写。 16、上述三项是否由法人正确签字或盖章。 17、委托代理人是否正确签字或盖章。 18、委托书日期是否正确。 19、委托权限是否满足招标文件要求，单位公章加盖完善。 20、信贷证明XX贷数额是否符合野猪明示要求，如野猪无明示，是否符合标段总价的一定比例。 六、报价 21、报价编制说明要符合招标文件要求，繁简得当。 22、报价表格式是否按照招标文件要求格式，子目排序是否正确。 23、“投标报价汇总表合计”、“投标报价汇总表”、“综合报价表”及其他报价表是否按照招标文件规定填写，编制人、审核人、投标人是否按规定签字盖章。全面预算管理常见错误
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投标书中常常容易出现的问题
仓库管理系统使用手册
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仓库管理系统需求分析说明书
仓库管理系统(软件需求说明书)
仓库管理系统说明书
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lotus notes 开发常用方法
预算编制常见错误
仓库管理系统需求说明书
Lotus script的一些常用方法
编制投标书容易出现的错误
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