BOUNDED-VELOCITY APPROXIMATION
OF MOBILE EUCLIDEAN2-CENTRES?
STEPHANE DUROCHER
School of Computer Science,McGill University
Montr′e al,Qu′e bec,Canada
durocher@cs.mcgill.ca
DAVID KIRKPATRICK
Department of Computer Science,University of British Columbia
Vancouver,British Columbia,Canada
kirk@cs.ubc.ca
Received(received date)
Revised(revised date)
Communicated by(Name)
Given a set P of points(clients)in the plane,a Euclidean2-centre of P is a set of two points(facilities)in the plane such that the maximum distance from any client to its nearest facility is minimized.Geometrically,a Euclidean2-centre of P corresponds to a cover of P by two discs of minimum radius r(the Euclidean2-radius).Given a set of mo-bile clients,where each client follows a continuous trajectory in the plane with bounded velocity,the motion of the corresponding mobile Euclidean2-centre is not necessarily continuous.Consequently,we consider strategies for de?ning the trajectories of a pair of mobile facilities that guarantee a?xed-degree approximation of the Euclidean2-centre while maintaining bounded relative velocity.In an attempt to balance the con?icting goals of closeness of approximation and a low maximum relative velocity,we introduce re?ection-based2-centre functions by re?ecting the position of a mobile client across the mobile Steiner centre and the mobile rectilinear1-centre,respectively.
Keywords:2-centre;motion;approximation;velocity;Euclidean;continuous
1.Introduction
1.1.Motivation
The traditional problems of facility location are de?ned statically;a set of n points is given as input,corresponding to the positions of clients,and a solution consists of a set of k points,corresponding to the positions of facilities,that optimizes some
?Some of these results originally appeared in the?rst author’s doctoral thesis(Ref.22)and in preliminary form at the Fall Workshop on Computational Geometry and Visualization(Ref.23). Funding for this research was made possible by NSERC and the MITACS project on Facility Location Optimization.
1
2Stephane Durocher and David Kirkpatrick
objective function of the input set.In the k-centre problem,the objective is to select locations for k facilities such that the maximum distance from any client to its nearest facility is minimized.A common setting for these problems is to model clients and facilities as points in Euclidean space and to measure distances between these by the Euclidean(?2)distance metric;this de?nes the Euclidean k-centre problem.
Recently,motivated in part by applications in the?eld of mobile computing, there has been considerable interest in recasting a number of familiar questions of facility location in a mobile context(e.g.,Refs.1,2,4,5,11,13,22,24,25,28,32);these include results related to the mobile Euclidean1-centre problem(see Section3).In this paper we consider the mobile Euclidean2-centre problem.A problem instance consists of a set of mobile clients,where each client follows a continuous trajectory through Euclidean space under bounded velocity.A mobile Euclidean2-centre is a pair of mobile facilities de?ned as a function of the instantaneous positions of the clients,such that at any time,the facilities de?ne a Euclidean2-centre of the client set.There exist trajectories for a set mobile clients P,such that any mobile Euclidean2-centre of P is discontinuous.Consequently,for any pair of mobile fa-cilities whose motion has bounded velocity,the distance between some client p in P and the facility nearest to p exceeds the Euclidean2-radius of P.Therefore,we seek strategies for de?ning the positions of a pair of mobile facilities that provide a good approximation to the Euclidean2-centre while maintaining motion that is continuous and whose magnitude of velocity has a low?xed upper bound.Thus, the?tness of a mobile facility is determined not only by the quality of its optimiza-tion of the objective function but also by its maximum velocity.This additional constraint leads to a trade-o?between velocity and approximation factor,requiring new approximation strategies quite di?erent from previous static approximations.
1.2.Main Result
We introduce re?ection-based2-centre functions,a family of approximations to the mobile Euclidean2-centre that involves coordinating the positions of the two facilities without explicit partitioning of the client set.We obtain a solution by using re?ection;the position of the?rst facility is set to coincide with that of a mobile client while the position of the second facility is given by the re?ection of the?rst facility across a mobile centre of re?ection.The choice of re?ection centre is critical to ensuring that both mobile facilities maintain bounded velocity and a good approximation of the mobile Euclidean2-centre.We show that the Steiner centre and the rectilinear1-centre represent good choices for the re?ection centre. Refer to Table1for a summary of the bounds which we derive on the approximation factor and on the maximum relative velocity of these various approximations of the mobile Euclidean2-centre.To the authors’knowledge,no previous bounded-velocity approximations to the mobile Euclidean2-centre have been de?ned.
Bounded-Velocity Approximation of Mobile Euclidean2-Centres3
1.3.Overview
This paper is organized as follows.Section2recalls the de?nition of a Euclidean2-centre,motivates the necessity of approximation,and formalizes the measures used for comparing the quality of di?erent approximations.Section3provides a brief overview of related work.In Section4we introduce re?ection-based approximations to the Euclidean2-centre and derive bounds on their respective maximum relative velocities and approximation factors.Section5compares the various approximation strategies considered and mentions directions for future research.
2.Mobile Euclidean2-Centre:De?nition and Properties
2.1.Euclidean k-Centre of a Set of Points
Given a set of points P in R2,a fundamental problem of geometry and data analysis concerns the characterization and computation of points that are central to P.
A natural,and for many applications the default,metric for measuring distance between points is the Euclidean distance metric.We now recall the de?nition of a Euclidean k-centre of a set P,where k denotes the number of facilities serving P. De?nition1.Given a?nite set P in R2,a Euclidean k-centre of P is a set of k points,{Ξ1(P),...,Ξk(P)},that minimizes
max p∈P
min
i∈{1,...,k}||
p?Ξi(P)||.(1)
We refer to the value of(1)as the Euclidean k-radius of P.It is straightfor-ward to show that a Euclidean k-centre is invariant under similarity transformations. Geometrically,a Euclidean k-centre of P corresponds to the centres of k discs whose union covers the points of P such that the radius of the largest disc is minimized. Although the Euclidean1-centre of P is unique,when k≥2,a Euclidean k-centre of P is not unique in general.For example,four points located at the vertices of the unit square in the plane have two distinct possible2-centres,located at the midpoints of opposite pairs of edges of the square.
The Euclidean k-centre problem is also known as planar k-centre,15,21min-max multicentre,17,29minimax radius clustering,12and minimax location-allocation problem.20
In this paper we refer to values of k≤2.We denote the Euclidean1-centre of a set P byΞ(P)and a Euclidean2-centre of P by{Ξ1(P),Ξ2(P)}.
2.2.Mobile Clients and Mobile Facilities
We consider continuous motion in R2.Since a point refers to a?xed position in Euclidean space,we refer to a client in the context of motion.That is,each client’s position traces a continuous trajectory through the Euclidean plane,de?ned as a function over a continuous temporal dimension.
4Stephane Durocher and David Kirkpatrick
De?nition2.Let T=[0,t f]denote a time interval.Set P={p1,...,p n}is a set of mobile clients if for every i,p i:T→R2is a bounded continuous function that de?nes the position of client i in R2at every instant t∈T.
We consider clients whose motion is continuous and we assume that each client’s velocity is bounded by a constantσ>0.That is,
?p∈P,?t1,t2∈T,||p(t1)?p(t2)||≤σ|t1?t2|.(2) Throughout this article we assume a constant upper bound ofσ=1on the velocity of clients since we are interested in relative velocity.We make no assumption on the continuity of higher derivatives,only that the rate of change in position is bounded.
For every t∈T,let P(t)={p(t)|p∈P}denote the set of points corresponding to the positions of clients in P at time t.We de?ne the mobile Euclidean1-centre and a mobile Euclidean2-centre as a direct extensions of their respective static de?nitions:Ξ(P(t))and{Ξ1(P(t)),Ξ2(P(t))}.Since a Euclidean2-centre is not unique,a mobile Euclidean2-centre of P is a pair of mobile facilities that realizes any Euclidean2-centre of P(t)at time t.
2.3.Discontinuity of Mobile Euclidean2-Centres
Bereg et al.13show that the relative velocity of the Euclidean1-centre has no?nite upper bound.Speci?cally,for anyσ≥0,Bereg et al.give an example of four mobile clients in R2,each moving in a linear trajectory with unit velocity,such that their Euclidean1-centre moves with average velocity at leastσover some time interval whose length depends onσ.
The unbounded velocity of the Euclidean1-centre is easily shown to imply a similar property for the Euclidean2-centre.22Unlike the Euclidean1-centre which is continuous,22we show that a continuous mobile Euclidean2-centre does not always exist.
Proposition1.There exists a set of mobile clients P such that any mobile Eu-clidean2-centre of P is discontinuous.
See Appendix A for an example of four mobile clients that realize such a set P. This same example can be used to show that the rectilinear2-centre and2-means clustering are also discontinuous.See Section4.1for a discussion of the rectilinear 2-centre and2-means clustering.
2.4.Approximating the Euclidean2-Centre:Comparison Measures Continuity of motion and,more speci?cally,a?nite upper bound on velocity impose natural constraints on any physical moving object.Scenarios involving vehicles, mobile robots,or people with wireless communication devices suggest that bounds on velocity are necessary in many applications(e.g.,Refs.9,16,18,19,34,37).
Bounded-Velocity Approximation of Mobile Euclidean 2-Centres 5
Given its discontinuity,a Euclidean 2-centre may be un?t for certain applications and impossible to maintain exactly within speci?c mobile contexts.A pair of mobile facilities that approximate the Euclidean 2-centre while maintaining some ?xed upper bound on maximum velocity may be better suited.We refer to a pair Υ={Υ1,Υ2},where Υi :P (R 2)→R 2,as a 2-centre function .
In analogy to (2),we say 2-centre function Υ={Υ1,Υ2
}has maximum (relative)
velocity v max if ?t 1,t 2∈T,max i ∈{1,2}||Υi (P (t 1))?Υi (P (t 2))||≤v max |t 1?t 2|,(3)
for all time intervals T and all sets of mobile clients P de?ned on T .If Υhas bounded relative velocity then {Υ1(P (t )),Υ2(P (t ))}cannot always coincide with a Euclidean 2-centre of P (t );that is,max p ∈P min i ∈{1,2}||p (t )?Υi (P (t ))||must exceed the Euclidean 2-radius of P for some sets of mobile clients P .We formalize this notion and quantify it in terms of the approximation factor of Υ.
De?nition 3.A 2-centre function Υ={Υ1,Υ2
}is a λ-approximation of the
Euclidean 2-centre if ?P ∈P (R 2),max p ∈P min i ∈{1,2}||p ?Υi (P )||≤λmax q ∈P min j ∈{1,2}||q ?Ξj (P )||.(4)
2.5.General Lower Bounds on Comparison Measures
We establish lower bounds on the maximum relative velocity and approximation factor of any mobile 2-centre function.Proposition
2.A mobile 2-centre function with maximum relative velocity less than 1+√3/2cannot guarantee any bounded approximation of the Euclidean 2-centre.
See Appendix A for a proof of Proposition 2.This property highlights a sig-ni?cant di?erence between approximations of the mobile Euclidean 1-centre and approximations of the mobile Euclidean 2-centre;in particular,several approxi-mations of the mobile Euclidean 1-centre have been considered that guarantee an approximation factor of 2while requiring at most unit velocity 13,22,25in R 2.
Bereg et al.11show that for any λ>1there exists a bounded-velocity approxi-mation of the Euclidean 1-centre with approximation factor λ.Again,the situation di?ers when approximating the Euclidean 2-centre:
Proposition 3.A continuous mobile 2-centre function in R 2
cannot guarantee a
λ-approximation of the Euclidean 2-centre for any λ<√2.
See Appendix A for a proof of Proposition 3.
6Stephane Durocher and David Kirkpatrick
3.Related Work
A Euclidean2-centre of a set of n points is straightforward to?nd in linear time in R (e.g.,Ref.22).A considerable number of results have appeared related to the static Euclidean2-centre in R2,including both deterministic and randomized algorithms for?nding exact or approximate solutions(e.g.,Refs.6,7,15,21,26,27,33,35,39)and algorithms for the corresponding decision problem(e.g.,Ref.31).Currently,the algorithm with the best running time is by Chan15who gives a deterministic solution to the exact problem in R2,requiring O(n log2n log2log n)time.The current best lower bound is?(n log n)time,shown by Segal.38Agarwal and Sharir8mention a generalization of Drezner’s algorithm21from R2to R d to give an algorithm requiring O(n d+1)time.
With respect to motion,most of the previous work in this area is related to the mobile Euclidean1-centre.These results serve as a benchmark against which we can contrast our results on the mobile Euclidean2-centre.
Bereg et al.11,13,14show that the velocity of the mobile Euclidean1-centre is unbounded in R2.They consider the centre of mass and the rectilinear1-centre as bounded-velocity approximations and derive tight bounds of(2?2/n)and[(1+√2)/2]on their respective approximation factors and tight bounds of1and√2on their respective relative velocities,where n is the number of mobile clients.Durocher and Kirkpatrick25examine the Steiner centre as a bounded-velocity approximation of the mobile Euclidean1-centre and show tight bounds of approximately1.1153 on its approximation factor and4/πon its relative velocity.Durocher22shows that no bounded-velocity approximation is possible for the Euclidean3-centre.
Agarwal and Har-Peled4maintain the approximate mobile1-centre in R2under ?∞and?2distance metrics.Their approximations do not require continuity or bounded velocity in the motion of the mobile facility;their objective,rather,is to minimize the number of events processed and the update cost per event using a kinetic data structure(KDS)to maintain a(1+?)-approximation on the extent of the client positions.As shown by Bereg et al.,11the maximum relative velocity of an approximation to the mobile Euclidean1-centre is inversely proportional to its approximation factor.That is,a(1+?)-approximation of the Euclidean1-centre de?ned in terms of a variable?cannot guarantee any?xed upper bound on velocity.
4.Re?ection-Based2-Centre Functions
4.1.Motivation and De?nition
Generalizations of strategies that provide bounded-velocity approximations to the mobile Euclidean1-centre suggest themselves as natural candidates for de?ning a 2-centre function.In particular,as discussed by Bereg et al.,11the rectilinear1-centre and the centre of mass both provide bounded-velocity approximations of the Euclidean1-centre(see Sections4.5and4.6for de?nitions).Both have natural gen-eralizations to two facilities,namely,the rectilinear2-centre and the2-means centre,
7
Bounded-Velocity Approximation of Mobile Euclidean2-Centres
Fig.1.Given a properly-selected re?ection centre F,when the clients of P form two clusters,client p0and its re?ection q across F(P)de?ne an approximation to the Euclidean2-centre.
neither of which is continuous(see Section2.3).As a result,neither the rectilinear 2-centre nor the2-means centre de?ne a bounded-velocity2-centre function.
A natural strategy for?nding a static approximation to the Euclidean2-centre problem involves partitioning the clients into two sets and subsequently identify-ing an approximation to the Euclidean1-centre of each partition.Such strategies generalize poorly to the mobile setting because discontinuities in the position of a mobile2-centre function can result from changes in the partition of the client set. Thus,it is not clear that a continuous mobile2-centre function can be de?ned in terms of partitions of the client set.
Nevertheless,if the clients of P form two obvious clusters,then a2-centre func-tionΥshould position one facility close to each cluster.In particular,when the clients of P coincide at two points a and b,the Euclidean2-radius of P is zero,and Υ1(P)andΥ2(P)must coincide with a and b in order to guarantee any?xed upper bound on approximation factor.When this occurs,observe that any client p0in P and its re?ection across the midpoint of P coincide with{a,b}.
As described by Durocher,22a natural de?nition for a bounded-velocity Eu-clidean2-centre of P in one dimension is provided by partitioning P acrossΞ(P) and identifying the Euclidean1-centre of each partition;the position of the?rst facility is speci?ed by the Euclidean1-centre of the partition with greater diameter while the position of the second facility can be viewed as the re?ection of the?rst facility across the Euclidean1-centre of P.This strategy does not generalize to higher dimensions because the Euclidean1-centre does not induce a partition of the clients in two or more dimensions.Furthermore,the unbounded velocity of the Eu-clidean1-centre in two or more dimensions precludes it from being used to de?ne a bounded-velocity facility.Instead,we identify a mobile centre of re?ection,denoted F,that remains central to P while moving under bounded velocity.A client of P, say p0,is selected arbitrarily and the position of the?rst facility is set to coincide with that of p0.The position of the second facility,q,is found by re?ecting p0across F.See Figure1.
De?nition4.Given a?nite set of mobile clients P in R2,an arbitrarily-selected client p0in P,and a function F:P(R2)→R2,a re?ection-based2-centre
8Stephane Durocher and David Kirkpatrick
function consists of two facility functions,Υ1andΥ2,whose positions are given by the position of client p0(t)and its re?ection across F(P(t)).
We refer to F as the re?ection centre.We select bounded-velocity approxima-tions of the mobile Euclidean1-centre as natural candidates for F.These include the mobile centre of mass,the mobile rectilinear1-centre,and the mobile Steiner centre.For comparison,we also examine the case when F is the mobile Euclidean 1-centre.Sections4.5through4.7respectively begin with de?nitions for the centre of mass,the rectilinear1-centre,and the Steiner centre and follow with a deriva-tion of bounds on the maximum relative velocity and approximation factor of the corresponding re?ection-based2-centre function.
Given a?xed choice for client p0,invariance under similarity transformations of a re?ection-based2-centre function follows if the corresponding property holds for the re?ection centre.The rectilinear1-centre is invariant under translation and uniform scaling,but not under re?ection or rotation whereas the Euclidean1-centre,the Steiner centre,and the centre of mass are invariant under all similarity transformations.22
4.2.Maximum Velocity
As we now show,if an upper bound is known on the relative velocity of the re?ec-tion centre,F,then an upper bound on the relative velocity of the corresponding re?ection-based2-centre function is straightforward to establish.The worst case is achieved when the re?ection centre F and the client p0being re?ected move toward or away from each other at their respective maximum velocities.
Proposition4.Let a and b denote mobile clients or mobile facility functions with respective maximum velocities v a and v b.The maximum velocity of the re?ection of a across b is2v b+v a.Furthermore,this bound is tight if the maximum velocities of a and b are simultaneously realizable in opposite directions.
Proof.Choose any time interval T and any v a,v b>0.Choose any functions a: T→R2and b:T→R2such that(2)holds for a and for b.The re?ection of a(t) across b(t)corresponds to the function c(t)=2b(t)?a(t).We bound the velocity of c by
?t1,t2∈T,||c(t1)?c(t2)||=||2[b(t1)?b(t2)]?[a(t1)?a(t2)]||
≤2||b(t1)?b(t2)||+||a(t1)?a(t2)||
≤(2v b+v a)|t1?t2|.
Therefore,the velocity of c is at most2v b+v a.It is straightforward to see that this bound is realized when a and b move in opposite directions.
Bounded-Velocity Approximation of Mobile Euclidean2-Centres9
4.3.Lower Bounds for Re?ection-Based2-Centre Functions
We derive lower bounds on the approximation factor and maximum relative velocity of any re?ection-based2-centre function.
Proposition5.A bounded-approximation re?ection-based2-centre function cannot guarantee relative velocity less than three.
Proof.A re?ection-based2-centre functionΥis de?ned in terms of a re?ection centre F.If the velocity of F is less than the velocity of clients in P,then the clients can coincide at a point away from F and no approximation factor can be guaranteed. Therefore,the relative velocity of F must be at least one.By Proposition4it follows that no re?ection-based2-centre function can guarantee relative velocity less than three.
Proposition6.Any mobile2-centre function for which the position of one facility is set to coincide with the position of a mobile client cannot guarantee an approxi-mation factor less than two.
Proof.Choose any function F:P(R2)→R2.Let P={(?4,0),(?2,0),(4,0)}. Let p0=(?4,0)and choose any q∈R2.LetΥ(P)={p0,q}.Assume there exists aλ<2such thatΥis aλ-approximation of the Euclidean2-centre.Let
min{||p?p0||,||p?q||}.
d=max
p∈P
Observe that the Euclidean2-radius of P is one.Therefore,λ≥d by(4).
Since d must be less than two,point q must lie in the right half-plane;otherwise the distance between client(4,0)and either facility would be at least four.Since ||(?2,0)?p0||=2and||(?2,0)?q||≥2,it follows that d≥2.Therefore,λ≥d≥2, deriving a contradiction.
Consequently,all re?ection-based2-centre functions have maximum relative ve-locity at least three and an approximation factor of at least two.
4.4.Re?ection Across the Euclidean1-Centre
Intuitively,an important criterion in the selection of a re?ection centre F is the degree to which F remains“central”to a set of clients P.When the re?ection centre is the Euclidean1-centre,we refer to the corresponding re?ection-based2-centre function as the Euclidean re?ection2-centre.One might expect the Euclidean re?ection2-centre to have a low approximation factor.Surprisingly,in Sections4.4 through4.7we show that the Euclidean1-centre is not the optimal choice for F, both in terms of approximation factor and maximum velocity.
Theorem1.The Euclidean re?ection2-centre provides a4-approximation of the Euclidean2-centre.This bound is tight.Furthermore,the Euclidean re?ection2-centre cannot guarantee bounded relative velocity.
10Stephane Durocher and David Kirkpatrick
Fig.2.illustration in support of Theorem1:upper bound
Proof.The result on velocity follows from the unbounded velocity of the Euclidean 1-centre shown by Bereg et al.13and Proposition4.
We?rst show that the Euclidean re?ection2-centre provides a4-approximation of the Euclidean2-centre and then demonstrate the bound is tight.
Let P denote any?nite set of clients in R2.Let p0denote a client of P whose position corresponds to the?rst facility,Υ1(P).Let q denote the re?ection of p0 acrossΞ(P).The position of the second facility,Υ2(P)is given by q.Let C denote the minimum enclosing circle of P and let s denote the radius of C.
Let CH(A)denote the convex hull of a set A in R2.LetΞ1(P)andΞ2(P)denote a Euclidean2-centre of P.Let r denote the Euclidean2-radius of P.Let P1and P2denote the partition of P induced byΞ1(P)andΞ2(P)such thatΞ1(P)is the facility closest to any client in P1andΞ2(P)is the facility closest to any client in P2.If any client p in P is equidistant fromΞ1(P)andΞ2(P),then assume p is assigned to either partition arbitrarily.Without loss of generality assume p0∈P1. Therefore,
?p∈P1,||p0?p||≤2r,(5) since p and p0are both contained within the minimum enclosing circle of P1.There-fore,we need only to verify that||q?p||≤4r for all clients p∈P2.
Case1.Assume C is supported by two clients a,b∈P that lie opposite each other on C.Clients a and b must lie in opposite partitions,otherwise the Euclidean2-radius equals the Euclidean1-radius.Without loss of generality assume a∈P1.See Figure2(1).Thus,for all clients p∈P2,||p?b||≤2r since b and p are both contained within the minimum enclosing circle of P2.Observe that||b?q||=||a?p0||. Therefore,by(5),
?p∈P2,||p?q||≤||p?b||+||b?q||≤2r+||b?q||=2r+||a?p0||≤4r.(6) Case2.Assume no two clients in P lie opposite each other on circle C.Let o denote the centre of C.At least three clients a,b,c∈P must support C such that the angles∠aob,∠aoc,and∠boc are all less thanπ.Without loss of generality, assume∠boc corresponds to the minimum of the three angles.Since the angles sum to2π,we get∠boc≤2π/3.Since all angles are less thanπ,we get∠aob≥π/3and ∠aoc≥π/3.Furthermore,at least one of a,b,or c must lie in each partition.
Bounded-Velocity Approximation of Mobile Euclidean 2-Centres 11
Case 2a.Assume a and b lie in the same partition.Therefore,c must lie in the opposite partition.See Figure 2(2A).Since π/3≤∠aob <π,it follows that ||a ?b ||≥s .Consequently,2r ≥s .The distance between any two points contained
within C is at most 2s .Therefore,?p ∈P 2,||p ?q ||≤2s ≤4r.(7)
Case 2b.Assume c,b ∈P 1and a ∈P 2.See Figure 2(2B).Let d denote the point opposite a on circle C .Since ∠aob ,∠aoc ,and ∠boc are all less than π,one of c and b must lie above d and the other must lie below d on circle C .Consequently,d is in the minimum enclosing circle of P 1.Therefore,for all clients p ∈P 1,||p ?d ||≤2r since p is contained within the minimum enclosing circle of P 1.Similarly,since a ∈CH (P 2),for all clients p ∈P 2,||p ?a ||≤2r since p is contained within the minimum enclosing circle of P 2.Since p 0
∈CH (P 1),for all points p in the minimum enclosing circle of P 1,||p ?p 0
||≤2r .In particular,||d ?p 0||≤2r .Observe that
||d ?p 0||=||a ?q ||.Thus,?p ∈P 2,||p ?q ||≤||p ?a ||+||a ?q ||=||p ?a ||+||d ?p 0||≤4r.(8)Case 2c.Assume c,b ∈P 2and a ∈P 1.See Figure 2(2C).Let d denote the point opposite a on circle C .Since ∠aob ,∠aoc ,and ∠boc are all less than π,one of c and b must lie above d and the other must lie below d on circle C .Consequently,d is in the minimum enclosing circle of P 2.Therefore,for all clients p ∈P 2,||p ?d ||≤2r since p is contained within the minimum enclosing circle of P 2.Similarly,since a ∈CH (P 1)for all clients p ∈P 1,||p ?a ||≤2r since p is contained within the minimum enclosing circle of P 1.By (5),||a ?p 0||≤2r .Observe that ||a ?p 0||=||d ?q ||.Thus,
?p ∈P 2,||p ?q ||≤||p ?d ||+||d ?q ||=||p ?d ||+||a ?p 0||≤4r.(9)Case 2d.Assume c,a ∈P 1and b ∈P 2.This case is analogous to Case 2b since we have not made any assumptions to di?erentiate a from b .
Case 2e.Assume c,a ∈P 2and b ∈P 1.This case is analogous to Case 2c since we have not made any assumptions to di?erentiate a from b .
The result follows from (5)through (9).We show this bound is tight with the following example.
Let θ∈(0,π/4).Let P ={p 0,p 1,p 2,p 3
}where p 0=(?cos θ,?sin θ),p 1=(?1,0),p 2=(1,0),and p 3=(cos θ,?sin θ).The Euclidean 1-centre of P lies at the origin.The unique Euclidean 2-centre of P lies at (p 0+p 1)/2and (p 2+p 3)/2.Let the ?rst facility,Υ1(P ),coincide with p 0.Let q denote the re?ection of p 0across Ξ(P ).The position of the second facility,Υ2
(P )is given by q .See Figure 3.The Euclidean 2-radius is 1
2
(1?cos θ)2+sin 2θ=12
2(1?cos θ).The fur-thest client from q is p 2,separated by a distance of 2sin θ.It follows that
λ≥lim θ→0+2sin θ12 2(1?cos θ)=4 lim θ→0+sin 2θ2(1?cos θ)
=4(by L’H?o pital’s rule).
12Stephane Durocher and David Kirkpatrick
Fig.3.illustration in support of Theorem1:lower bound Given the unbounded velocity of the Euclidean re?ection2-centre,bounded-velocity approximations of the Euclidean1-centre provide natural candidates for de?ning the re?ection centre F.The properties of low maximum relative velocity and low approximation factor exhibited by the rectilinear1-centre,the centre of mass,and the Steiner centre11,13,22,25suggest these functions as a natural candi-dates for de?ning the re?ection centre in a re?ection-based2-centre function.As we demonstrate in Sections4.5through4.7,selecting either the rectilinear1-centre or the Steiner centre for the re?ection centre results in a2-centre function with a lower approximation factor than that guaranteed when the re?ection centre is the Euclidean1-centre;selecting the centre of mass for the re?ection centre results in a2-centre function that cannot guarantee any bounded approximation factor.
4.5.Re?ection Across the Centre of Mass
Given a?nite set P in R2,the centre of mass of P is the point
C(P)=
1
|P| p∈P p.(10)
The centre of mass is the unique point that minimizes the sum of the square dis-tances from each clients to its nearest facility.36,40
When the re?ection centre is the centre of mass,we refer to the correspond-ing re?ection-based2-centre function as the mean re?ection2-centre.We now examine its maximum relative velocity and approximation factor.
Theorem2.The mean re?ection2-centre has maximum relative velocity3.This bound is tight.Furthermore,the mean re?ection2-centre cannot guarantee any bounded approximation of the Euclidean2-centre.
Proof.As shown by Bereg et al.,11the centre of mass has at most unit relative velocity.Furthermore,this velocity is realizable.Although the velocity of the centre
Bounded-Velocity Approximation of Mobile Euclidean2-Centres13 of mass is not independent of the velocity of p0,the contribution of p0to the velocity of the centre of mass approaches zero as|P|increases.The result on velocity follows from Proposition4.
Let set P be de?ned by two clients be located at the origin and a single client a located at(1,0).The centre of mass of P lies at C(P)=(1/3,0).The re?ected facility has position either(1/3,0)or(2/3,0),depending on the position of p0.The Euclidean2-radius of P is zero.The distance from client a to the nearest facility is at least1/3.Consequently,noλsatis?es(4).
4.6.Re?ection Across the Rectilinear1-Centre
We now consider the rectilinear1-centre as the re?ection centre.
Given a?nite set P in R2,the rectilinear1-centre of P is the function whose value,R(P),is the point located at the centre of the bounding box of P.That is, R(P)is a point that minimizes
max
p∈P||R(P)?p||∞,(11) where||x||∞denotes the?∞norm of x∈R2.The rectilinear1-centre of P is given by?nding the one-dimensional1-centre of P in each dimension.That is, R(P)i=R(P i)=Ξ(P i),where P i={p i|p∈P}and p i denotes the i-coordinate of a point p in R2for i∈{x,y}.
When the re?ection centre is the rectilinear1-centre,we refer to the correspond-ing re?ection-based2-centre function as the rectilinear re?ection2-centre.We now examine its maximum relative velocity and approximation factor.
We?rst bound the approximation factor of the one-dimensional rectilinear re-?ection2-centre in Lemma1.This result allows us to derive a bound in R2in Theorem3.
Lemma1.Given a set of collinear clients P in R2,the rectilinear re?ection2-centre of P provides a2-approximation of the Euclidean2-centre of P.
Proof.It is straightforward to show that the de?nitions of the rectilinear1-centre, the rectilinear re?ection2-centre,the Euclidean1-centre,and the Euclidean2-centre are consistent across dimensions.Since we only consider collinear sets,we may assume without loss of generality that P is a set of points in R.Let p0denote any client of P.Let the position of the?rst facility,Υ1(P),coincide with p0.Let q denote the re?ection of p0across R(P).Let the position of the second facility,Υ2(P)be given by q.
Let P1and P2denote the partition of P induced by clients positioned respec-tively to the left and right ofΞ(P).If any client p in P coincides withΞ(P),then assume p is assigned to partition P1.There exists a Euclidean2-centre of P,Ξ1(P) andΞ2(P),such thatΞ1(P)is the facility closest to any client in P1andΞ2(P)is the facility closest to any client in P2.Let d denote the maximum of the diameters
14Stephane Durocher and David Kirkpatrick
of P 1and P 2.It follows that d =2r ,where r denotes the Euclidean 2-radius of P .Without loss of generality,assume p 0∈P 1.Therefore,
max p ∈P 1||p ?p 0||≤d and max p ∈P 2||p ?q ||≤d,
?max p ∈P min i ∈{1,2}||p ?Υi (P )||≤2r.
Theorem 3.The rectilinear re?ection 2-centre provides a 2√
2-approximation of
the Euclidean 2-centre and has maximum relative velocity 2√2+1.Both bounds are tight.
Proof.Bereg et al.13show a tight bound of √2on the velocity of the rectilinear 1-centre.The result on velocity follows Proposition 4because the velocity of the rectilinear 1-centre is independent of the velocity of p 0whenever p 0not an extreme point of P .
We ?rst show that the rectilinear re?ection 2-centre provides a 2√2-approximation of the Euclidean 2-centre and then demonstrate the bound is tight.Let P denote any ?nite set of clients in R 2.Let p 0denote a client of P whose position corresponds to ?rst facility,Υ1(P ).Let q denote the re?ection of p 0across R (P ).The position of the second facility,Υ2(P )is given by q .
Since q =2R (P )?p 0,therefore q i =2R (P i )?[p 0]i .Consequently,
max p ∈P min j ∈{1,2}||p ?Υj (P )||=max p ∈P min j ∈{1,2} 2 i =1|p i ?Υj (P )i |2
≤ 2
i =1 max p ∈P min j ∈{1,2}|p i
?Υj (P )i | 2
≤ 2
i =1
(2r i )2,
by Lemma 1,where r i denotes the Euclidean 2-radius of P i ,
≤max
i ∈{1,2} 2(2r i )2
=max i ∈{1,2}
2r i √2
≤2r √2,(12)
where r denotes the Euclidean 2-radius of P .
We show this bound is tight with the following example.Let P ={(?2,0),(?2,?2),(0,2),(2,2)}.Let p 0=(?2,0).The unique Euclidean 2-centre of P has positions (?2,?1)and (1,2).The Euclidean 2-radius of P is 1.The recti-linear 1-centre of P ,R (P ),is located at the origin.The re?ection of p 0across R (P ),
Bounded-Velocity Approximation of Mobile Euclidean2-Centres15
Fig.4.illustration in support of Theorem3
denoted q,is located at(2,0).Client a=(0,2)lies a distance2
√2from both q and p0.See Figure4.
4.7.Re?ection Across the Steiner Centre
Durocher and Kirkpatrick25examine the Steiner centre of P,denotedΓ(P),as a bounded-velocity approximation of the mobile Euclidean1-centre.
Given a?nite set P in R2,the Steiner centre of P is the point
Γ(P)=2
π π0Ξ(Pθ)dθ,(13)
where Pθ={(cosθ,sinθ) p,(cosθ,sinθ) |p∈P}is the projection of P onto the line passing through the origin,parallel to the vector(cosθ,sinθ).See Refs.22 and25for motivation,discussion,and alternate representations of the Steiner centre within the context of continuous motion.
When the re?ection centre is the Steiner centre,we refer to the corresponding re?ection-based2-centre function as the Steiner re?ection2-centre.We now examine its maximum relative velocity and approximation factor.
Theorem4.The Steiner re?ection2-centre has maximum relative velocity8/π+1. This bound is tight.The Steiner re?ection2-centre provides a8/π-approximation but cannot guarantee aλ-approximation of the Euclidean2-centre for anyλless than2 1+1/π2.
Proof.As shown by Durocher and Kirkpatrick,25the Steiner centre has maximum relative velocity4/πand this velocity is realizable.Therefore,the result on velocity follows from Proposition4because the velocity of the Steiner centre is independent of the velocity of p0whenever p0is not an extreme point of P.
We?rst show that the Steiner re?ection2-centre provides a8/π-approximation of the Euclidean2-centre and then demonstrate a lower bound of2 1+1/π2.
Let dφdenote the?∞norm relative to a rotation byφof the reference axis.That is,dφ(x)=||fφ(x)||∞,where fφis a clockwise rotation about the origin byφ.Let Rφ(P)=f?φ(R(fφ(P)))denote the rectilinear1-centre with respect to norm dφ.
16Stephane Durocher and David Kirkpatrick
As shown by Durocher and Kirkpatrick,25the Steiner centre of a set of clients P in R 2can be de?ned as the limit of the convex combinations of the rotated rectilinear 1-centres of P .That is,
Γ(P )=2
π π/20
R θ(P )dθ.(14)
Let P denote any ?nite set of clients in R 2.Let p 0denote a client of P whose position corresponds to the ?rst facility,Υ1(P ).Let q denote the re?ection of p 0across Γ(P ).The position of the second facility,Υ2(P )is given by q .
Let Ξ1(P )and Ξ2(P )denote a Euclidean 2-centre of P .Let r denote the Eu-clidean 2-radius of P .Let P 1and P 2denote the partition of P induced by Ξ1(P )and Ξ2(P )such that Ξ1(P )is the facility closest to any client in P 1and Ξ2(P )is the facility closest to any client in P 2.If any client p in P is equidistant from Ξ1(P )and Ξ2(P ),then assume p is assigned to either partition arbitrarily.Without loss of generality assume p 0∈P 1.Therefore,
?p ∈P 1,||p 0?p ||≤2r,(15)
since p and p 0are both contained within the minimum enclosing circle of P 1.There-fore,we need only to verify that ||q ?p ||≤(8/π)r for all clients p ∈P 2.
As shown in the proof of Theorem 3with respect to the rectilinear re?ection 2-centre,if q R =2R (P )?p 0,then
max p ∈P 2|p x ?[q R ]x |≤2r and max p ∈P 2|p y ?[q R ]y |≤2r.
That is,every client in P 2is contained within a box of width and height 4r centred at q R .Let q θ=2R θ(P )?p 0.It follows that every client in P 2is contained within a box of width and height 4r ,whose axis is rotated by θrelative to the x -axis,and whose centre is q θ.Consequently,
max p ∈P 2
|p x ?[q θ]x |≤2√2cos(π/4?θ)r.(16)
We now bound the maximum distance in the x -coordinates from any client in P 2to q .
max p ∈P 2|p x ?q x |=max p ∈P 2|p x ?(2Γ(P )x ?[p 0]x )|
=max p ∈P 2 p x ? 2 2π π/2
0R θ(P )x dθ ?[p 0]x ,by (14),
=max p ∈P 2
2π π/20p x ?(2R θ(P )x ?[p 0]x )dθ
=max p ∈P 2 2π π/20p x ?[q θ]x dθ
Bounded-Velocity Approximation of Mobile Euclidean 2-Centres 17
Fig.5.illustration in support of Theorem 4
≤max p ∈P 22
π π/20|p x ?[q θ]x |dθ
≤2
π π/20max
p ∈P 2|p x ?[q θ]x |dθ
≤2
π π/20
2√2cos(π/4?θ)r dθ,by (16),
=8r
π.
The Steiner re?ection 2-centre is invariant under rotation.Consequently,
max p ∈P 2|p x ?q x |≤8r
π?max p ∈P 2||p ?q ||≤8r π.
We now show that the Steiner re?ection 2-centre cannot
guarantee a λ-approximation of the Euclidean 2-centre for any λless than 2
1+1/π2.Let a continuous arc of clients lie on a unit semicircle centred
at the origin on the positive x -axis.Let two clients lie opposite the arc at a =(?1,1)and b =(1,1).
The unique Euclidean 2-centre of P lies at (0,0)and (?1,0).The corresponding Euclidean 2-radius,r ,is one.The Steiner centre of P lies at (1/π?1/2,0).Let p 0=(0,1)de?ne the position of the ?rst facility,Υ1(P ).Let q denote the re?ection of p 0across Γ(P ).Observe that q =(2/π?1,?1).The position of the second facility,Υ2(P )is given by q .See Figure 5.
The re?ection of q across Γ(P )lies at a distance 2 1+1/π2from client a .
4.8.Kinetic Algorithms for Re?ection-Based 2-Centres
The kinetic maintenance of a re?ection-based 2-centre reduces to the problem of maintaining the corresponding mobile re?ection centre.Kinetic data structures (KDS),introduced by Basch et al.,10allow for e?cient maintenance of various at-tributes of a set of mobile objects under linear (or bounded-degree algebraic)motion.Those related to our discussion of mobile 2-centre functions include the maximum
18Stephane Durocher and David Kirkpatrick
re?ection approximation maximum
centre factor relative velocity
Euclidean 1-centre λ=4v max =∞
centre of mass λ=∞v max =3
rectilinear 1-centre λ=2√2≈2.8284v max =2√2+1≈3.8284Steiner centre 2 1+1/π2≤λ≤8/πv max =8/π+1≈3.5465
?2.0989≤λ≤2.5465bounded approx.factor 3≤v max
any re?ection centre 2≤λ
Table https://www.doczj.com/doc/c15645990.html,paring re?ection-based 2-centre functions in R 2
(in R ),10,30the rectilinear 1-centre,4the Steiner centre,25the convex hull,10,30a (1+?)-approximate Euclidean 1-centre,4and the extent of a set of mobile clients.3,4
5.Conclusion
5.1.Summary of Results
Since continuity and a ?xed upper bound on velocity are natural constraints on mobile problems,the discontinuity of mobile Euclidean 2-centres leads us to consider bounded-velocity approximations.The goal of this paper is to identify 2-centre functions that guarantee a ?xed-degree approximation of a mobile Euclidean 2-centre while maintaining motion whose magnitude of velocity does not exceed a ?xed upper bound.
We established general lower bounds of √2on the approximation factor and 1+√3/2on the maximum relative velocity of any bounded-velocity 2-centre function.We introduced re?ection-based 2-centre functions for which we established stronger lower bounds of 2on the approximation factor and 3on the maximum relative velocity.When the re?ection centre is the Euclidean 1-centre we showed unbounded velocity and a tight bound of 4on the approximation factor.
When the re?ection centre is the rectilinear 1-centre we showed a tight bound of 2√2+1on the relative velocity and a tight bound of 2√2on the approximation factor.When the re?ection centre is the Steiner centre we showed a tight bound of 8/π+1on the relative velocity,an upper bound of 8/πon the approximation factor,and a lower bound of 2
1+1/π2on the approximation factor.Finally,when the re?ection centre is the centre of mass we showed a tight bound of 3on the relative velocity and that no ?xed approximation factor can be guaranteed.These properties are summarized in Table 1.
In conclusion,we have identi?ed two strategies for de?ning a bounded-velocity approximation of the mobile Euclidean 2-centre:the Steiner re?ection 2-centre and the rectilinear re?ection 2-centre.
Bounded-Velocity Approximation of Mobile Euclidean2-Centres19
5.2.Directions for Future Research
The questions explored in this paper have natural extensions into higher dimensions. Preliminary results in three dimensions are discussed in Ref.22.Another possible continuation of this work is to attempt to de?ne a2-centre function without using re?ection.Finally,some of the bounds established here can be improved or shown to be tight,such as the general lower bounds on approximation factors and velocity and the bounds on the approximation factor of the Steiner re?ection2-centre.As mentioned earlier,even in one dimension no bounded-velocity approximation is possible for the mobile Euclidean3-centre.22
Acknowledgements
The authors would like to acknowledge the MITACS project on Facility Loca-tion Optimization headed by Dr.Binay Bhattacharya at Simon Fraser Univer-sity.Our semi-monthly meetings with Dr.Boaz Ben-Moshe,Qiaosheng Shi,and Binay provided stimulating problem-solving sessions,including a discussion of one-dimensional mobile geometric2-centres which seeded the inspiration for re?ection-based2-centre functions.Also,the authors thank the reviewers for their helpful feedback.
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27.David Eppstein.Faster construction of planar two-centers.In Proceedings of the Sym-
佳能500D功能操作详解 虽说是入门级的单反相机，但瘦死骆驼比马大，在画面的成像质量和快门速度上还是要远远的强于卡片机。不过话又说回来，即使是入门级的卡片机对于本人这种初级的新手来说还是一个看似不可琢磨的高深玩意，想必不少朋友也有笔者这种情况，对于入门级的单反相机的使用还是存在些问题。而这些问题虽不是很深奥，但对于使用过程中的影响还是很大的，针对这样的情况，笔者就将在初使用单反的过程中遇到的一些问题和解决办法来给大家简单的介绍下。 对于刚刚入门的新手来说来用得比较多的也就是快门、光圈、ISO感光度这三个要素。要很好的应用这三个要素首先就得了解其具体作用是什么，下面笔者抱着和大家一块学习的心态来就这三个要素给大家详细的说说。 一：快门，配合光圈的变化，可以调整快门的速度来实现正确曝光，快门就是曝光时间的长短，比如你的光圈确定为F8，那么快门越快，进来的光亮就越少，快门越慢就进光更多，快速的快门可以把运动瞬间凝结在底片或者CCD上。可以举个形象的比喻，相机的镜头就像人的眼睛，快门就是人的眼皮，快门越快，就是眼睛眨得越快，而眼皮眨得越快相对在两个眨眼之间那个瞬间接收的光线越少，就会觉得很暗；如果眨的越慢，在两个眨眼之间的接收光线越多，而显得光线充足。 不过快门的快慢还会影响到一个方面，就是快门快的话相对就会减少画面糊的情况发生，而快门很慢可能会导致画面很糊，这个道理也很简单，想想卡片机为什么会有那么多的糊的照片就明白了，就是快门速度的原因。所以要寻求一个既可以采集到充足的光线而又不会导致轻微的手动就会影响到画面质量的平衡点。 二：光圈，镜头的通光量有光圈的控制作用，光圈值越大，（既F值越小），通过的光亮就越多，大光圈带来的特点就是能够获得很浅的景深，大光圈的效果对于拍摄人物很适合，能够突出主体。当然，大光圈下面的聚焦一定要保持准确，否则比较浅的景深很容易照成焦点的偏差。光圈越小（既F值越大），通过的光亮就越少，在小光圈下面可以获得比较长的景深，小光圈的设计很适合拍摄风景或是建筑一类的物体。 三：ISO值，它是胶片或CCD感光能力的大小。正常卡片机在白天室内外一般都是用ISO800或是ISO1600这两个值，如果要画面更细腻的话，可以通过降低ISO值来获得，这样的设置适合于拍摄人像或风光静物等场景，层次非常丰富。然而在单反相机中，低感光度带来的影像是造成感光时间加长，不得不使用放大光圈或者放慢快门来补充曝光，以达到正确的画面要求。如果感光度值很高，那么就会带来胶片画面的颗粒感就会增强，画面就有噪点产生，它的好处在于，可以让整个画面更佳的明亮，同时也可以选择更快的快门速度或者更小的光圈。这种方式比较适合抓拍运动场面或者动态景物，合理运用可以产生比较特殊的效果。在比较暗的环境下面，提高感光度值也是一个好办法，不过对于要求画质的效果的朋友来说还是尽量少用提高ISO值的方法。 而在平时的使用过程中笔者发现一般光圈和快门的调节比较多，而且很讲究二者的搭配使用，那么究竟如何搭配这两个应用的值呢。
佳能摄像机说明书 篇一：佳能相机说明书 佳能相机说明书使用 EOS 500D 拍摄短片的简易步骤最近更新 : 15-May-20XX 发行编号 : 820XX98200解决方法本页介绍如何以默认设置拍摄短片。关于如何更改设置拍摄短片，请参阅相关信息。须知拍摄短片时，请使用 SD 速率级别 6 “储卡，短片拍摄和回放可能不正常工作。此外，建议使用大容量的存储卡进行短片拍摄。 1. 将相机电源开关置于。 2. 将镜头对焦模式开关设为。”或更高速的存储卡。如果使用 SD 速率级别较低的存3. 将模式转盘设为。反光镜会发出声音，然后图像会出现在液晶监视器上。 4. 将显示自动对焦点。可以按下将自动对焦点移动到您想要对焦的位置。? 无法移动到图像的边缘。 ? 若要让自动对焦点返回中央，按下按钮。 5. 将自动对焦点对准主体，然后按住按钮。 6. 按下按钮开始拍摄短片。”标记将显示在屏幕的右上方。 7. 再次按下停止拍摄短片。注意短片拍摄期间，请不要把镜头对准太阳。太阳的热量会损坏相机内部部件。注释记录和图像画质? 短片文件格式将为 MOV。 ? 如果单个短片的文件尺寸达到 4GB，短片拍摄将自动停止。若要重新开始短片拍摄，按下按钮。（开始录制新的短片文件。）? 相机的内置麦克风还会录制相机操作音。如果不想录制任何
声音，将声音录制设置为［关］。回放和电视机连接? 如果用 HDMI 电缆将相机连接到电视机并以［1920x1080］或［1280x720］拍摄短片，将以较小的尺寸在电视机上显示所拍摄的短片。然而，实际的短片将以所设置的短片记录尺寸正确录制。? 如果将相机连接到电视机并拍摄短片，在拍摄期间电视机将不会输出任何声音。然而，声音将被正确录制。须知 ? 如果长时间连续拍摄短片，相机的内部温度会升高。这会降低图像画质。不拍摄时，请关闭电源。? 如果在直射阳光或高温条件下进行拍摄，屏幕上可能会出现图标（内部高温警告）。如果在显示警告图标的状态下继续拍摄短片，图像画质可能会降低。应该关闭电源并让相机休息片刻。? 如果在显示图标的状态下继续拍摄短片直到相机的内部温度进一步升高，短片拍摄将会自动停止。如果发生这种情况，相机的内部温度降低前，您将无法再次进行拍摄。关闭电源并让相机休息片刻。 设置白平衡最近更新 : 15-May-20XX 发行编号 : 820XX95000解决方法购买时，佳能数码相机和便携式数码摄像机的白平衡设置为“自动白平衡”。设置通常将获取正确的白平衡。如果用不能获得自然的色彩，可以选择用于不同光源的白平衡设置或通过拍摄白色物体手动设置白平衡。注释在基本拍摄区模式中，将自动设置为。要设置白平衡，请遵循以下步骤。 1. 将电源开关设为。 2. 相机
合格骨健康基本补充剂—绝代双骄之钙剂与维生素D 100分 1.有机酸钙实际吸收率是（A) A.4-30% B.10-30% C.20-30% D.20-50% 2.建议定期监测患者血清钙及12h尿钙浓度，根据其水平调整药物剂量，以避免药物过量所引发的高钙血症或高尿钙的发生。（B) A.正确 B.错误 3.咖啡因摄入过多可增加尿钙的排出，还能轻度减弱（)钙吸收，同时对钙储留有中度影响，并与增加女性镜骨骨折危险性有联系。（C) A.胃 B.骨骼 C.肠
4.补充维生素D时，应首选维生素D3,如果不能得到维生素D3时，可用维生素D2代替。（A) A.正确 B.错误 5.长期使用活性VD治疗的患者，建议在启动治疗后的1、3、6个月分别监测尿钙磷及血钙磷水平，此后建议每年监测两次血钙磷、尿钙磷及肾功能。（A) A.正确 B.错误 6.VD缺乏的矫正非紧迫时，或当补充VD同时口服抗骨吸收药物，或许可以进行维持治疗方案，而无需使用负荷剂量。（A) 。A.正确 B.错误 7.下述给药方法已证明无效，或无效和中毒的风险增加，因此推荐，①采用肌肉注射或口服维生素D的年储备给药方法；②使用活性维生素D制剂（骨化三醇和阿法骨化醇）纠正VD缺乏。（A)
B.错误 多选题：每道题有两个或两个以上的答案，多选漏选均不得分。 1.下列属于骨质疏松的是（ABCD) A.充足的钙和维生素D的摄入对于防治骨质疏松症至关重要 B.充足的钙摄入对获得理想骨峰值，减缓骨丢失，改善骨矿化和维护骨骼健康有益。 C.充足的维生素D可增加肠钙吸收、促进骨骼矿化、保持肌力、改善平衡能力和降低跌倒风险 D.尽可能通过饮食摄入充足的钙，饮食中钙摄入不足时，可给予钙剂补充 2.如何防晒？(ABC) A含氧化锌和二氧化钛等成分的“广诺防晒霜 B.干爽的胜过潮湿的布料 C.限制接触紫外线，太阳最强时戴太阳镜和帽子 D.面部、双上肢和双下肢暴露于阳光5-30min
比亚迪E6纯电动汽车使用磷酸埋钻铁电池，200Ah的超大电池容量使车辆在综合工况下续驶里程超过300km，每100km的能耗在21度（1度=1 kWh）以内，每1 00km的加速时间为10s，最高车速可达160km/h以上。车辆充电比较方便，快充可以使用充电站的380V充电桩充电，慢充可需220V民用交流电源，慢充6～8小时可充满电池。 一、比亚迪E6纯电动汽车动力系统的结构 1．比亚迪E6纯电动汽车动力系统 比亚迪E6纯电动汽车动力系统结构及原理如图1所示，其主要由三大模块组成。
（1）电动车的控制模块可分为：电机控制器、DC-DC、动力配电箱、主控ECU、挡位控制器、加速踏板、电池管理单元。 （2）电动车的动力模块有：电动机总成、电池包体总成。
（3）电动车高压辅助模块有：车载慢充、漏电保护器、车载充电口、应急开关。 2．动力控制系统的工作原理 （1）充电过程 充电站的380V高压充电桩通过车辆上的充电口，或者220V市用电源通过车载充电器升压后输电给车上的配电箱，配电箱直接途径应急开关后对Hv电池组充电。在充电过程当中，电源管理器一直监控着HV电池组的温度和电压，如果发现HV电池组内部某单体温度或电压过高，就会切断配电箱给HV电池组的供电。 （2）放电过程 HV电池组在电源管理器和漏电保护器的监控下，通过应急开关输电给配电箱，配电箱根据车辆的实际用电情况分配电量。一部分电量流向电机控制器，另一部分电量流向DC-DC交换器。主控ECU根据驾驶员操作信息（接收加速踏板角度传感器和挡位控制器的信号）控制着电机控制器的工作，电机控制器主要控制流向电机的电量大小，以及控制电机正反转来驱动车辆前进或后退。另一部分从配电箱流向DC-DC交换器的电量，经过DC-DC交换器将高压直流电转化为低压直流电，为车辆电动液压助力转向系统提供42V的电源，同时还为整车用电设备提供12V的电源。 3．动力系统各部件的作用 （1）电机控制器：负责控制电机的前进、倒退、维持电动车的正常运转，关键零部件为IGBT。IGBT实际为大电容，目的是为了控制电流的工作，保证能够按照我们的意愿输出合适的电流参数。 （2）DC-DC：负责将330V高压直流转低压提供给车载低压用电设备，如
补钙为什么要补充维生素d 钙和维生素d是我们人体不可分割的，在当今时代都是这样的。如今的父母都是希望自己的孩子能够茁壮的成长，所以一定要在补钙的时候也是要增加维生素d这样才能更有效的促进人 体的吸收。那么，补钙为什么要补充维生素d？ 1、先了解下钙和维生素D对人体的作用 钙是构成人体的重要组成部分，占人体重量的百分之1.5到百分之2，其中百分之99存在骨骼和牙齿中。钙对维生素神经兴奋性、血液凝固、肌肉收缩和舒张、腺体的分泌有着很总要的作用，并对多种酶有激活作用。钙主要受甲状旁腺素、降钙素与1.25-（OH）D3的共同调节，钙的吸收也需要一定的磷，磷缺乏也会影响钙的吸收。 维生素D主要与甲状旁腺共同作用，维持血钙的水平稳定，它是钙磷代谢重要的调节因子之一，维持着钙和磷的正常水平，
这对正常骨骼的矿化、肌肉收缩、神经传导以及体内所有细胞的功能都是必须的，同时维生素D还具有免疫调节功能，可以改变机体对感染的反应。 2、婴儿时期需要补充钙剂和维生素D吗？ 答案是肯定的，婴儿时期是处于快速生长发育期，对维生素D的需求来那个相对较大，母乳中的维生素D的水平比较低，维生素D既可以由膳食供给，又可以经暴露日光的皮肤合成。如果小婴儿缺乏钙同时也缺乏维生素D，那么就会出现骨质软化症和佝偻病，表现出多汗、易惊生长手足抽搐。久而就会出现骨质软化便会导致乒乓球头颅，肋缘外翻、串珠、手镯、X或者O型腿。 3、每个时期的婴幼儿该如何添加钙剂和维生素D呢？ 一般来说，0-6个月的孩子，纯母乳喂养每天需要钙三百毫克，人工喂养的婴儿考虑到非母乳来源钙吸收率比较低，固定为每天四百毫克。这时候的维生素D的含量为固定的一天一粒，也
数码相机用机宝典是PConline数码相机频道为解决网友用机疑惑的新栏目，帮助初涉摄影的网友逐步掌握摄影技巧，拍摄出好照片。用机宝典每次针对一款机型，从基本的参数设置到进阶使用，还会包括各种相关附件的使用，逐一讲述拍摄技巧和需要注意的要点，力求通过深入浅出的讲解帮助网友进步。本期用机宝典则是围绕相当热门的入门单反佳能500D进行拍摄技巧的讲解，欢迎大家对用机宝典提出自己的见解，帮助我们做得更好。 步骤/方法 1.一、佳能500D简介 2. 佳能500D是佳能门内最新的入门级数码单反，习惯小改小闹 推出升级产品的佳能，这次在500D身上的做法反而十分豪爽，让不少其他门派的粉丝也羡慕不已。佳能500D可谓是一个50D
和5D Mark II（无敌兔）的混合版，它采用了50D身上的1510万像素CMOS、DIGIC 4图像处理引擎、3.0英寸92万像素LCD 和其余的一些特色功能，更拥有在无敌兔身上的1080p高清摄像能力，这样一个混合产品注定出现以下犯上的局面。 3. 不过，作为佳能入门级的机型，在外观设计上仍然是廉价的做法，另外在对焦系统和快么寿命上也有所不同，仍然符合其入门级的定位。这么一次大跃进的升级，使得佳能500D具有了空前丰富的功能，下面我们一起来看看： 4.二、佳能500D基础使用指南 5.1、怎样使用CA模式
6. CA模式也就是创意自动功能，它推出的目的在于照顾入门级的使用者，使得普通用户也可调整图像亮度，或进行背景虚化等。 使用它的时候，只需要把模式转盘转到“CA”模式即可。这时如果不进行任何调节的话，相机基本上会按照P档的情况进行处理。 7. 不过，相机的判断不一定会按照人的意志的，这时则可以通过
佳能500D使用技巧整理 个人整理 使用佳能500D拍摄各种照片 全部内容如下： 1 如何正确暴光 2 光圈快门速度ISO之间的关系 3 如何拍背景虚化的照片 4 镜头焦距的选择 5 如何拍夜景 6 被摄体不在画面中间时如何对焦 7 如何在黑天室外拍人像 8 如何拍摄动态汽车照片 9 如何拍摄鬼影照片 10 如何拍摄剪影照片 11 如何拍摄烟花 12 婚礼上如何拍照 13 台球室拍照 14 如何拍显个，如何拍显瘦，哪个角度最漂亮。。 注意：和我学可学不成大师，很可能还学些凑毛病以后不好改，不过按我说的做能在短期内在外行面前冒充冒充高手。。 现在开始按我的套路来了。。。。。。 1 如何正确暴光 先把相机拍摄模式调到M档，也就是全手动档。。（如果不明白如何调到M档就看一下说明书，以后就不再说明了，看不懂的地方就翻说明书），有人说M档不实用操作麻烦，新手不容易掌握，但我觉得M档更适合新手学习，因为M档需要手动调圈和快门更容易让新手快速的掌握光圈和快门的关系以及对成像的影响。。反正我拍照只要不是很紧急的情况下拍摄都是M档的。。 要想用M档拍照先要知道如何调光圈和快门，从液晶屏上看横排最上方有三个数据，最左边的是快门速度，中间是光劝大小，右边是ISO感光度值。。正常在光线不是很暗的情况下我们拍照都要把ISO值设成一百，如果光线很暗又不想开闪光灯的话可以适当调高。。然后光圈和速度怎么调这个是不固定的，要看你所在的环境光线和你要拍摄的物体。。别急，一步步来…… 说一下M档下如何调快门速度光圈和ISO，直接转动控制转盘就可以调整快门速度，按住液晶屏右上角那Av按钮的同时转动转盘就是调光圈大小，控制转盘边上有个ISO按钮，按一下然后用机背的方向键选择ISO，选好后按方向键中间的SET按钮确定。。 知道怎么调以后我们就要实战演练了，先找个布娃娃或别的差不多的东西或是家里的任意一样摆设，先拿它练起。。这时候你要拿媳妇练估计容易给你媳妇练出拍照恐惧症~正常情况下18-55IS镜头最佳成像光圈是8。。先把光圈设成8再说。。这时候的设置是光圈8，ISO100。。设置好后把眼睛贴近取景窗，然后瞄准被摄体，半按快门，听到嘀一声响表示对焦完成就可以拍摄了， 在取景器里我们能看到下方有这样一排发绿光的数字和标尺，先说一下这分别是什么意思，最左边的是
考试成绩100分，考试通过 骨健康基本补充剂—绝代双骄之钙剂与维生素D 单选题：每道题只有一个答案。 1.长期使用活性VD治疗的患者，建议在启动治疗后的1、3、6个月分别监测尿钙磷及血钙磷水平，此后建议每年监测两次血钙磷、尿钙磷及肾功能。（） A.正确 B.错误 2.建议定期监测患者血清钙及12h尿钙浓度，根据其水平调整药物剂量，以避免药物过量所引发的高钙血症或高尿钙的发生。（） A.正确 B.错误 3.下述给药方法已证明无效，或无效和中毒的风险增加，因此推荐，①采用肌肉注射或口服维生素D 的年储备给药方法；②使用活性维生素D 制剂(骨化三醇和阿法骨化醇)纠正VD 缺乏。（） A.正确 B.错误 4.咖啡因摄入过多可增加尿钙的排出，还能轻度减弱（）钙吸收，同时对钙储留有中度影响，并与增加女性髋骨骨折危险性有联系。 A.胃 B.骨骼 C.肠 D.血液 5.有机酸钙实际吸收率是（）
A.4-30% B.10-30% C.20-30% D.20-50% 6.补充维生素D时，应首选维生素D3，如果不能得到维生素D3时，可用维生素D2代替。（） A.正确 B.错误 7.VD缺乏的矫正非紧迫时，或当补充VD同时口服抗骨吸收药物，或许可以进行维持治疗方案，而无需使用负荷剂量。（） A.正确 B.错误 多选题：每道题有两个或两个以上的答案，多选漏选均不得分。 1.如何防晒？（） A.含氧化锌和二氧化钛等成分的“广谱”防晒霜 B.干爽的胜过潮湿的布料 C.限制 接触紫外线，太阳最强时戴太阳镜和帽子 D.面部、双上肢和双下肢暴露于阳光5-30 min 2.普通维生素D是否需要常规监测（） A.普通VD安全剂量范围宽 B.没必要常规监测血清25OHD C.通过血清25OHD 判断是否中毒 D.有维生素D缺乏症状、吸收不良、怀疑用药效果不佳等，可能需要监 测血清25OHD 3.下列属于骨质疏松的是（）
用佳能5d2单反摄像技巧及注意事项——很详细5d2在电影领域中的应用电影《终结者2018》的摄影指导 shanehurlbertasc美国电影摄影家协会会员他用5d2拍的短片《最后三分钟》在摄影界引起了轩然大波单反视频早已成为广大发烧友和专业影视从业人员热捧的新鲜事物了。5d2的变革就在于用低廉的价格能让普通大众拥有最好的甚至超越35mm电影摄影机的动态画质a:硬件和配套设备部分1三角架极其重要。照相机的架子本身不是为移动拍摄的所以最好找摄像机脚架这样才可以平稳拍摄摇画面也才能保证长焦拍摄的画面稳定。例如曼富图利拍libec的摄像机专业架。唯一小问题是摄像机托板装在照相机上使用时间长后照相机下面会有难看的挤压痕迹。2镜头选择。一般来说最常用的是超广角和长焦中焦段一定要大光圈定焦。因为5d2是全画幅所以可以按照电影头来选择。建议配置如下10mm或12mm--24mm超广角24--105mm光圈大一点好比如 2.824-70的佳能红圈120-500600mm炮筒50mmf1.2这个强烈推荐人像专用。3聚焦问题。目前来说如果没有合适的跟焦器配套用5d2来拍摄动态需要跟焦的画面是相当麻烦。照相机镜头的对焦阻尼是很涩的手感不好。当然了偶尔用用问题不大。但是小液晶屏幕看对焦只能看个大概。5d2有hdmi接口可以带一个720p的带hdmi的监视器这样现场显示就会比较靠谱。当然如果是专业跟焦员他看刻度的那种也行。 不过佳能镜头的刻度都在镜头的。上面非常的不方便。4电池问题。5d2的原装电池一般可以断续拍摄1张8g卡大概12分钟建议用大容量的储存卡。广告上说的可以连续拍摄2小时是直接打开机器拍的理论最大值大部分时间你还需要取景、找焦点、找画面感觉所以不可能用到这么长时间。所以电池极其重要至少要准备3快电池才能保证不会出问题。5如果经常拍摄城市宣传片或者风光片的朋友肯定会常用到定格拍摄比如日出日落夜景。这些镜头用5d2拍简直爽到极点了。一来分辨率超爽后期可以调整的空间巨大。另一点快门时间可以放的很慢夜景尤其是车流的效果非常出色。慢门能大幅度降低画面躁点画面显得特别的干净漂亮。这里特别要推荐买一个定时快门手柄可以设置间隔时间自动拍摄。6准备足够的滤色片。nduv必不可少保护镜头必须灰片也要带足因为正午阳光下iso100光圈要收到8-11而视频又不能过多加快快门速度会造成缺少运动模糊导致播放有抖动感你想要得浅景深效果就没了。nd0.30.60.91.2最好都备上。常用的可能就是0.6和0.9.7取景器超低和超高机位的大广角如果没有外置取景器那是要命的。5d2套件概念简介5d2套件通常是指用于佳能5dmark2单反相机的摄像承托系统套组设备。随着数码科技的日新月异发展canon等公司最新出品的全尺寸ccd专业单反相机 5d2.7d.50d.60d.70d.500d都拥有了高清hd1920x1080p摄 像功能.其摄影能力已经远远超越了传统磁带摄像机。拍摄视频画面质量也在逐渐接近电影摄影机。并凭借其强大的镜头兼容性和广泛的镜头源.完全可以满足宣传篇片.电视广告片.电影短片的拍摄任务。但单反照相机拍摄高清视频的缺点也暴漏出来了。虽然拍摄的画面可以和电影摄影机和摄像机有一比。相机机身设计造成了拍摄视频的不方便机身小不能肩扛通过手持又不能保持很好的画面平衡针对这一点让广大单反视频摄像爱好者对5d2等机型是又爱又恨.爱的是拍摄视频画质好更换镜头方便恨的是拍摄不方便固定镜头画面还好说可以放在三角架上拍摄.但运动起来就麻烦了总不能用手端着拍吧。就算端着拍短时间可以但长时间实在承受不了。还有就是单反相机相机的遮光罩太小在拍摄特定场景时。光线总是斜射入镜头内。让原本漂亮的画面曝光过度。还有就是专业单反拍视频时无法进行手动对焦。必定没有类似为摄像机而设计的电动伺服器。对于以上缺点遗憾不在机器本身.5d2等机器能拍摄出足够干掉广播级别摄像机的画面已经足够对得起我们了。必定5d2等机器才1万元左右.而同级别的redone.arri等专业摄影机也都在30万到400万不等.即使拍摄画面不如5d2等机器的sonyax200e190p250p松下103等高清机也价格都在2万元以上并且还都不可更欢镜头。看
佳能500d使用说明书 佳能500d使用说明书 佳能500d使用说明书 篇一: 佳能500D PAS佳能500D PAS-C数码单反详细参数，如下: 主要性能发布日期机身特性操作方式传感器类型 201X年03月 APS-C规格数码单反全手动支持 CMS 长宽比: 3:2 传感器件尺寸 2 2.3×1 4.9mm 传感器描述有效像素数影像处理器最高分辨率除尘功能: 自动，手动，添加除尘数据 1510万 DIGIC 4 4752×3168 大: 约1510万像素(4752×3168) 中: 约800万像素(3456×2304) 图像分辨率小: 约370万像素(2352×1568) RA: 约1510万像素(4752×3168) 全高清(1080P) 高清摄像镜头特点佳能EF系列镜头(包括EF-S系列镜头)(35mm换算焦距约为镜头焦距的 1.6 镜头说明倍) 类型: TTL辅助影像重合，相位检测自动对焦点: 9个自动对焦点测光范围: EV -0.5-18(23?，73?，IS 100) 对焦方式对焦模式: 单次自动对焦，人工智能伺服自动对焦，人工智能自动对焦，手动对焦(MF) 自动对焦辅助光: 由内置闪光灯发出的短促连续闪光 9点变焦环 3英寸类型:
TFT彩色液晶监视器(可分7级调节亮度) 监视器尺寸和点数: 3英寸，约92万点(VGA) 对焦点数变焦方式显示功能显示屏尺寸像素及类型视野率: 约100% 界面语言: 25种(含简体中文) 可旋转液晶屏否触摸屏是否双屏取景器不支持 否光学类型: 眼平五面镜视野率: 垂直/水平方向约95% 放大倍率: 约0.87倍(-1m-1，使用50mm镜头对无限远处对焦) 眼点: 约19mm(自目镜透镜中央起-1m-1) 取景器描述内置屈光度调节: - 3.0-+ 1.0m-1(dpt) 对焦屏: 固定式，精确磨砂反光镜: 快回型景深预视快门性能快门类型快门速度闪光灯闪光类型外接闪光灯(热靴) 电子控制纵走式焦平面快门 1/60-1/4000秒(全自动模式)，闪光同步速度1/200秒 30-1/4000，B快门(总快门速度范围。可用范围随拍摄模式各异。) 外接支持外接闪光灯: EX系列闪光灯(能用相机设置功能) 闪光模式闪光测光: E-TTL II自动闪光闪光曝光补偿: ?2级间以1/3或1/2级为单位调节闪光曝光锁闪光范围闪光指数闪光灯回电时间曝光控制 17mm镜头视角 13/43(IS 100，以米/英尺为单位) 约3秒程序自动曝光P(全自动，人像，风光，微距，运动，夜景人像，闪光灯关闭，创意自
骨健康基本补充剂绝代双骄之钙剂与维生素D 一、单选题 1、有机酸钙实际吸收率是（A）。A、4-30% 2、咖啡因摄入过多可增加尿钙的排出，还能轻度减弱（C）钙吸收，同时对钙储留有中度影响，并与增加女性髋骨危险性有联系。C、肠 3、补充维生素D时，应首选维生素D3，如果不能得到维生素D3时，可用维生素D2代替。（A）A、正确 4、下述给药方法已证明无效，或无效和中毒的风险增加，因此推荐，①采用肌肉注射或口服维生素D的年储备给药方法；②使用活性维生素D制剂（骨化三醇和阿法骨化醇）纠正VD缺乏。（B）B、错误 5、VD缺乏的矫正非紧迫时，或当补充VD同时口服抗骨吸收药物，或许可以进行维持治疗方案，而无需使用负荷剂量。（A）A、正确 6、建议定期监测患者血清钙及12h尿钙浓度，根据其水平调整药物剂量，以避免药物过量所引发的高钙血症或高尿钙的发生。（B）B、错误 7、长期使用活性VD治疗的患者，建议在启动治疗后的1、3、6个月分别监测尿钙磷及血钙磷水平，此后建议每年监测两次血钙磷、尿钙磷及肾功能。（A）A、正确 二、多选题 1、如何防嗮？（ABCD） A、含氯化锌和二氧化钛等成分的“广谱”防嗮霜 B、干爽的胜过潮湿的布料 C、限制接触紫外线，太阳最强时戴太阳镜和帽子 D、面部、双上肢和双下肢暴露于阳光5-30min 2、下列属于骨质疏松的是（ABCD）。 A、充足的钙和维生素D的摄入对于防治骨质疏松症至关重要 B、充足的钙摄入对获得理想骨峰值，减缓骨丢失，改善骨矿化和维护骨骼健康有益 C、充足的维生素D可增加肠钙吸收、促进骨骼矿化、保持肌力、改善平衡能力和降低跌倒风险 D、尽可能通过饮食摄入充足的钙，饮食中钙摄入不足时，可给予钙剂补充 3、普通维生素D是否需要常规监测（ABCD）。
纯电动汽车及动力电池发展现状调研 一、纯电动汽车发展现状 所谓纯电动汽车，是指完全由可充电电池作为动力源、以驱动电机及其控制系统驱动行驶的汽车。纯电动汽车（Battery Electric Vehicle，BEV）与混合动力汽车（Hybrid Electric Vehicle，HEV）和燃料电池汽车（Fuel Cell Electric Vehicle，FEV）是目前主要的新能源汽车类型。 1.1 发展纯电动汽车的必要性 （1）促进节能减排。与传统汽车相比，纯电动汽车具有更高的能源利用效率，同时也具有二氧化碳减排的潜力。机动车污染排放是城市空气污染的主要来源之一，2013年春季北京出现多次大面积雾霾天气，机动车尾气是主要原因之一。在上海，中心城区的主要大气污染物可吸入颗粒物、氮氧化物、挥发性有机物分别有66%、90%和26%来自机动车尾气。大力推广纯电动汽车是交通领域实现低碳的最佳方案，纯电动汽车行驶过程中不产生二氧化碳，即使考虑到中国目前电力生产过程中的二氧化碳排放，纯电动汽车仍然具有13%~68%的减排能力。随着我国能源结构和电力生产方式的转变，纯电动汽车必将在未来发挥更大的减排作用。 图1.1 传统汽车与纯电动汽车综合能量效率比较（单位：%）（2）降低石油对外依存度。汽车保有量的迅速增加为我国能源安全带来严峻挑战。我国汽车保有量与原油对外依存度变化趋势见图1.2。最新数据显示，截止到2012年底，中国汽车保有量已达2.4亿辆，与此相对应的是2012年中国原油对外依存度达到56.4%，创下历史新高。如果不采取措施，“十二五”中将原油依存度控制在61%的计划将很难实现。在此背景下，如何满足未来汽车的能源需求，是关系到我国能源安全的关键问题。电动汽车由于其电力来源多样化，不仅更加适合中国以煤炭为主的资源禀赋，而且能够与中国大力发展可再生能源
执业药师继续教育合格骨健康基本补充剂—绝代双 骄之钙剂与维生素D LELE was finally revised on the morning of December 16, 2020
合格骨健康基本补充剂—绝代双骄之钙剂与维生素D 100分 1.有机酸钙实际吸收率是（A) A.4-30% B.10-30% C.20-30% D.20-50% 2.建议定期监测患者血清钙及12h尿钙浓度，根据其水平调整药物剂量，以避免药物过量所引发的高钙血症或高尿钙的发生。（B) A.正确 B.错误 3.咖啡因摄入过多可增加尿钙的排出，还能轻度减弱（)钙吸收，同时对钙储留有中度影响，并与增加女性镜骨骨折危险性有联系。（C) A.胃 B.骨骼 C.肠 D.血液 4.补充维生素D时，应首选维生素D3,如果不能得到维生素D3时，可用维生素D2代替。（A) A.正确
B.错误 5.长期使用活性VD治疗的患者，建议在启动治疗后的1、3、6个月分别监测尿钙磷及血钙磷水平，此后建议每年监测两次血钙磷、尿钙磷及肾功能。（A) A.正确 B.错误 6.VD缺乏的矫正非紧迫时，或当补充VD同时口服抗骨吸收药物，或许可以进行维持治疗方案，而无需使用负荷剂量。（A) 。A.正确 B.错误 7.下述给药方法已证明无效，或无效和中毒的风险增加，因此推荐，①采用肌肉注射或口服维生素D的年储备给药方法；②使用活性维生素D制剂（骨化三醇和阿法骨化醇）纠正VD缺乏。（A) A.正确 B.错误 多选题：每道题有两个或两个以上的答案，多选漏选均不得分。 1.下列属于骨质疏松的是（ABCD) A.充足的钙和维生素D的摄入对于防治骨质疏松症至关重要
纯电动汽车动力系统及驱动技术 一、电动汽车简介及现状 电动汽车是指以车载电源为动力，用电机驱动车轮行驶，符合道路交通、安全法规各项要求的车辆，电动汽车可分为三种:蓄电池式纯电动车、燃料电池电动汽车和混合动力电动汽车。电动汽车历史悠久，世界上的第一辆电动汽车于1834年诞生，比1886年问世的世界上第一辆内燃机汽车还要早半个世纪。 大力发展新能源汽车从而实现世界交通及能源结构的转型已经成为当代汽车行业实现可持续发展的重要趋势。和传统燃油汽车相比，电动汽车尽管目前技术不太成熟，但凭借其能源效率高、环境污染小、能源多样化的优点已经成为汽车行业发展的必然选择，其发展也得到世界各国政府的重视与支持。 国内电动汽车发展现状 我国的电动汽车研究大约开始于上个世纪60年代，自“八五”以来，通过大量人力、物力和财力在纯电动汽车研究上的投入，正式把电动汽车的研究列入攻关计划，并在在北京、杭州等城市开展了不同形式的小规模示范运行。 2001年我国正式启动了“十五”国家高新技术研究发展计划(863)，电动汽车被列入其中并投资数亿，确立了以燃料电池汽车、混合动力汽车和纯电动汽车为“三纵”，以多能源动力总成、驱动电机和动力蓄电池共性关键技术为“三横”的“三纵三横”研发布局川，具体分工如下:承担电动大客车项目的有北方车辆厂和北京理工大学，承担纯电动轿车研发的是上海汽车、上海交通大学、天津汽车集团等。 自2009年以来，国家陆续出台《汽车产业调整振兴规划》、电动汽车“十城千辆”项目，这表明在低碳经济的政策背景下，国家对于纯电动汽车的扶持力度正在不断加大。 国外电动汽车发展现状 在电动汽车的发展进程中，各国和各地区都依据自己的国情和特点择了不同的技术路线，而处在技术领先位置的仍然是日本、美国和欧洲，他们在电动汽车的车速、续驶里程、加速性能、动力蓄电池、基础设施等方面都有较大的优势。纯电动汽车已经在欧洲各国中拥有大量的用户，特别是在当地政府部门。但是由于没有成功地解决电动汽车续驶里程问题，商业化进程缓慢。各大汽车厂商发展电动汽车的热情明显不如日本和美国，所以其注意力更多地转向了其它清洁能源车的开发。下表是国外几种电动汽车的技术指标。
佳能500D入门教材（浅显易懂、菜鸟必看哦） 如何使用佳能500D拍摄各种照片 前几天帮朋友买了个500D，他没接触过单反一时不知从何下手，所以给他写个简易教程，也同时请熟悉单反熟悉500D的色友给予指正，因为我拍照也是瞎拍，所以有时候说的难免有错误或不科学的地方，大家发现问题一定要及时给予究正。 买来新相机无论是老手还是新手都应当仔细阅读一遍说明书，然后再拿起相机亲自操作拍摄几天，然后回过头来再看一遍说明书，然后再拍几天，再看一遍说明书，一般至少要看三遍吧。。。反正我是第五次看说明书的时候还能从中学到新东西。因为说明书里有些容在你没有实际拍摄经验的情况下是看不懂的，所以说明书一定要多看，说明书是最好的教材。 全部容如下： 1 如何正确曝光 2 光圈快门速度ISO之间的关系 3 如何拍背景虚化的照片 4 镜头焦距的选择 5 如何拍夜景 6 被摄体不在画面中间时如何对焦
7 如何在黑天室外拍人像 8 如何拍摄动态汽车照片 9 如何拍摄鬼影照片 10 如何拍摄剪影照片 11 如何拍摄烟花 12 婚礼上如何拍照 13 台球室拍照 14 如何拍显个，如何拍显瘦，哪个角度最漂亮。 注意：和我学可学不成大师，很可能还学些凑毛病以后不好改，不过按我说的做能在短期在外行面前冒充冒充高手 现在开始按我的套路来了。。。 1 如何正确曝光 先把相机拍摄模式调到M档，也就是全手动档。（如果不明白如何调到M档就看一下说明书，以后就不再说明了，看不懂的地方就翻说明书），有人说M档不实用操作麻烦，新手不容易掌握，但我觉得M档更适合新手学习，因为M档需要手动调圈和快门更容易让新手快速的掌握光圈和快门的关系以及对成像的影响。反正我拍照只要不是很紧急的情况下拍摄都是M档的。 要想用M档拍照先要知道如何调光圈和快门，从液晶屏上看横排最上方有三个数据，最左边的是快门速度，中间是光劝大小，右边是ISO感光度值。正常在光线不是很暗的情况下我们拍照都要把
基于某款纯电动汽车动力系统计算与仿真分析 摘要动力系统参数的选择与匹配对电动汽车的动 力性和经济性会产生很大的影响。文章在理论计算和系统分析的基础上，对电机、电池以及传动系传动比进行了参数匹配，分析了纯电动汽车动力系统参数的选择对电动汽车性能的影响。GT-suite 仿真结果表明，所选动力总成部件与整车匹配后能够满足纯电动轿车动力性的要求。为纯电动汽车动力系统参数选择与匹配提供了参考。 关键词电动汽车动力系统参数匹配动力性仿真 中图分类号：U463. 23 文献标识码：A 电动汽车是解决当前能源短缺和环境污染问题可行的 技术之一。电动汽车是由车载动力电池作为能量源的零排放汽车。近些年来，电动汽车的研制热潮在全世界范围内兴起，尤其是在我国，逐步向小批量商业化生产的方向发展。电动汽车技术的发展依赖于多学科技术的进步，尤其需要解决的问题是进一步提高动力性能，增加续驶里程，降低成本。考虑开发经费和开发周期，建立计算机仿真模型对电动汽车的性能进行仿真分析是很有意义的。 1电动汽车动力系统参数要求电动汽车的动力性主要取决于动力及传动系统参数匹配，包括动力电池、驱动电机及传动系统控制器等部 件。 根据设计要求，本电动汽车设计参数为：最高车速 150km/h，最大爬坡度》30%，续驶里程》180km。0100km/h 的时间为： < 15s。相关的车辆参数为：汽车整备质量: 1600kg ;迎风面积：2.19m2;长？卓？赘呤滴？631?? 790?? 470 m m ；轴距为：2650；滚动阻力为：0.0015；风阻系数： 0.296 。 2电机参数匹配电机作为电动汽车主要动力源，电机的匹配对电动汽车
佳能400D操作说明书 数码相机用机宝典是PConline数码相机频道为解决网友用机疑惑的新栏目，帮助初涉摄影的网友逐步掌握摄影技巧，拍摄出好照片。用机宝典每次针对一款机型，从基本的参数设置到进阶使用，还会包括各种相关附件的使用，逐一讲述拍摄技巧和需要注意的要点，力求通过深入浅出的讲解帮助网友进步。第六期购机宝典则是围绕佳能元老级数码单反400D进行拍摄技巧的讲解，欢迎大家对本栏目提出自己的见解以及希望获得的讯息，帮助我们做得更好。 佳能400D简介 佳能EOS 400D(Rebel XTi)(配18-55mm镜头套机
佳能400D是佳能上一代入门数码单反相机的代表作，相比较更为低端的350D有较大的改进，有不错的实用性能，并能使用佳能全部镜头。但由于定位低端，机身采用塑料材质，握持手感仍显得不够舒适。从上市开始到退市仍不能摆脱塑料拖鞋的称号，自推出佳能450D之后，400D逐步退出市场，但发行两年的时间里，销售量巨大，至今仍有相当大的保有量。 佳能400D装备1010万像素APS-C格式CMOS，有超声波除尘功能，可明显减少自行清洁的次数。9点宽区自动对焦，使用的DIGIC II 芯片图像处理，画质上仍有不错的表现。使用2.5英寸LCD显示屏，启动速度是0.2秒，连拍速度最快3张/秒，一次最多拍摄27张JPEG 或10张RAW照片，快门速度的范围是1/4000-30秒，最高闪光同步速度为1/200秒。在市场上混了两年的佳能400D早已成为单反用户耳熟能详的一个型号。 一、佳能400D使用常识 佳能400D作为一台上市售卖两年的入门级单反，没有太多的辅助功能，所以在使用上没有太多的操作难点，相较其升级版本450D，按键排布在显示屏左边一排，各项功能也较易操实现。这里主要讲解一下刚接触单反、还不了解相关操作的买家容易忽视的问题，内容通俗易懂，相信大家一看就懂。另外，说一下数码单反维护的一些方法。 1、模式切换转盘与拨轮的使用方法
第一章绪论 1.1课题的目的意义： 1.1.1 纯电动汽车的背景 当前，我国电动汽车发展已经进入关键时期，既面临重大的发展机遇，也面临着严峻的挑战。我国电动汽车发展中还存在很多需要解决的问题，如核心技术还不具备竞争力，企业投入不足，政府的统筹协调能力还没有充分发挥等。总体上看来，我国电动汽车产业，起步不晚，发展不慢，但是由于传统汽车及相关产业基础相对薄弱、投入不足，差距仍然存在，中高端技术竞争压力越来越大，因此，必须加大攻坚力度，推动我国汽车产业向创新驱动转型，提高核心技术竞争力，确保我国汽车行业的可持续发展。 纯电动汽车使用电动机作为传动系统的动力源，缓解了能源紧缺的压力，实现了人们长期以来对汽车零尾气排放的期盼，传动系统作为汽车的核心组成部分，其技术创新是纯电动汽车发展的必经之路。 1.1.2纯电动汽车的意义 近年来，关于纯电动汽车的研究主要集中在能量存储系统、电驱动系统和控制策略的开发研究三方面。 能量存储系统相当于纯电动汽车的发动机，是纯电动汽车电动机所需电能的提供者。目前，铅酸蓄电池是使用最为广泛的，但其充电速度较慢，使用寿命短，节能环保差。随着电动汽车技术的发展，其他电池正在渐渐取代着铅酸蓄电池。目前发展的新电源有纳硫电池、锂电池、镍镉电池、飞轮电池、燃料电池等，尽管这些新电源投入应用，但是短时间内还是无法解决纯电动汽车电源充电缓慢，电量存储低续航里程短的问题。 纯电动汽车整车控制策略的开发研究一直在紧锣密鼓的进行着，整车控制系统是纯电动汽车实现整车控制和管理的关键，是实现和提高整车控制功能和性能水平的一个重要技术保证。其核心技术主要体现在整车控制软件的架构设计、转矩控制策略以及对整车和各系统得能量管理上。尽管控制策略的开发研究一直没有间断，但是，系统开发较为复杂，进度较慢。 1.2近年来国内外研究现状： 1.2.1国内发展现状： 我国正式对电动汽车的研制始于1981年，当时全球对电动汽车的宣传和需求并不强烈，对电动汽车的研究也相当零散，投入很少。近年来，我国电动汽车的研究、开发进入了有组织。有领导的全面发展阶段，国家在电动汽车研制开发方面也采取了积极有效的宏观引导措施。
佳能500D入门教你如何正确曝光 前几天帮朋友买了个500D，他没接触过单反一时不知从何下手，所以给他写个简易教程，也同时请熟悉单反熟悉500D的色友给予指正，因为我拍照也是瞎拍，所以有时候说的难免有错误或不科学的地方，大家发现问题一定要及时给予究正。 买来新相机无论是老手还是新手都应当仔细阅读一遍说明书，然后再拿起相机亲自操作拍摄几天，然后回过头来再看一遍说明书，然后再拍几天，再看一遍说明书，一般至少要看三遍吧。。。反正我是第五次看说明书的时候还能从中学到新东西。因为说明书里有些内容在你没有实际拍摄经验的情况下是看不懂的，所以说明书一定要多看，说明书是最好的教材。 如何正确曝光 先把相机拍摄模式调到M档，也就是全手动档。（如果不明白如何调到M档就看一下说明书，以后就不再说明了，看不懂的地方就翻说明书），有人说M档不实用操作麻烦，新手不容易掌握，但我觉得M档更适合新手学习，因为M档需要手动调圈和快门更容易让新手快速的掌握光圈和快门的关系以及对成像的影响。反正我拍照只要不是很紧急的情况下拍摄都是M档的。 要想用M档拍照先要知道如何调光圈和快门，从液晶屏上看横排最上方有三个数据，最左边的是快门速度，中间是光劝大小，右边是ISO感光度值。正常在光线不是很暗的情况下我们拍照都要把ISO值设成一百，如果光线很暗又不想开闪光灯的话可以适当调高。然后光圈和速度怎么调这个是不固定的，要看你所在的环境光线和你要拍摄的物体。别急，一步步来…… 说一下M档下如何调快门速度光圈和ISO，直接转动控制转盘就可以调整快门速度，按住液晶屏右上角那Av按钮的同时转动转盘就是调光圈大小，控制转盘边上有个ISO 按钮，按一下然后用机背的方向键选择ISO，选好后按方向键中间的SET按钮确定。 知道怎么调以后我们就要实战演练了，先找个布娃娃或别的差不多的东西或是家里的任意一样摆设，先拿它练起。这时候你要拿媳妇练估计容易给你媳妇练出拍照恐惧症~正常情况下18-55IS镜头最佳成像光圈是8。先把光圈设成8再说。这时候的设置是光圈8，ISO100。设置好后把眼睛贴近取景窗，然后瞄准被摄体，半按快门，听到嘀一声响表示对焦完成就可以拍摄了， 在取景器里我们能看到下方有这样一排发绿光的数字和标尺，先说一下这分别是什么意思，最左边的是速度，画面中是1/125秒，第二个是光圈8，中间的标尺就是测试暴光度的，右边的是ISO100，我们注意观察这个暴光度标尺下面有一个小竖条，这个条的位置有时候偏左，有时候偏右，有时候在中间。偏左说明暴光不足，这时候拍出来的照片会发黑，偏右说明暴光过度，这时候拍出来的照片会发亮，只有在正中间的时候拍摄才是最合适的，但这也不是绝对的，这只是个参考，因为测光模式不同和你的对焦点都会对这有一定影响，但咱先不管它。这时候如果你的测光尺的浮标正好在中间那么你就可以直接拍摄了，如果在右边那么你就需要把速度调快，调成1/160 1/200 1/250 1/320 1/400直到标尺到正中间为止，但需要注意的是别太快了，如果你是拍静止不动的物体（包括风景静止的人物体）那就别调太快，如果到了1/500还是偏右那说明你现在正在一个阳光充足光线非常良好的环境下拍摄，这时候你就把速度停在1/500秒这然后去调整光圈把光圈调小些，把光圈调小就是指把光圈的数值调大的意思。然后一直缩小直至测光尺浮标到中间为止，如果你光圈调到22了还是偏右那么你还是再继续调速度吧。。。另外问下你是不是在拍太阳？？？那可不好，