Mon. Not. R. Astron. Soc. 000, 000–000 (1997) THE MORPHOLOGY OF HII GALAXIES
Mon.Not.R.Astron.Soc.000,000–000(1997)
THE MORPHOLOGY OF HII GALAXIES
Eduardo Telles1,2
Jorge Melnick3
Roberto Terlevich2
1.Institute of Astronomy,Madingley Road,Cambridge CB30HA,U.K.
2.Royal Greenwich Observatory,Madingley Road,Cambridge CB30EZ,U.K.
3.European Southern Observatory,La Silla,Chile
etelles@https://www.wendangku.net/doc/282466524.html,p.br,jmelnick@https://www.wendangku.net/doc/282466524.html,&rjt@https://www.wendangku.net/doc/282466524.html,
accepted January7,1997
ABSTRACT
We present CCD images of a sample of39HII galaxies taken at the Danish1.54m
telescope on La Silla.The images are used to analyse the morphology of these emission
line dwarfs,and the structural properties of the knots of star formation and of the
underlying galaxy.The sizes of the starbursts are measured.We propose a morphological
classi?cation based on the presence or absence of signs of tails,extensions,or distorted
outer isophotes.This criterion segregates the objects into two broad morphological types
with di?erent physical properties:the more disturbed and extended(type I)HII galaxies
having larger luminosities and velocity dispersions than the more compact and regular
(type II)objects.The relative position of HII galaxies and of a sample of dwarf elliptical
galaxies in the[R–σ]diagram support the hypothesis of a possible evolutionary link
between the two types of galaxy.
Key words:HII region–galaxies:dwarf–galaxies:starburst–galaxies:structure.
1INTRODUCTION
HII galaxies are narrow emission line dwarf galaxies under-going violent star formation(Melnick,Terlevich&Eggle-ton1985)whose spectroscopic properties are indistinguish-able from extragalactic giant HII regions in normal late type galaxies(e.g.30Dor in LMC,NGC604in M33)(Sar-gent&Searle1970).Their high rates of star formation and low heavy element abundances imply that the star forma-tion history must be simple and episodic(i.e.few burst of short duration followed by long quiescent periods).A recent review on the global properties of HII galaxies is given by Telles(1995,and references therein).The possi-ble links of HII galaxies with other types of known dwarf galaxies have been discussed by Thuan(1983);Loose& Thuan(1985);Bothun et al.(1986);Kunth,Maurogordato &Vigroux(1988);Davies&Phillipps(1988),Drinkwater& Hardy(1991).However,no conclusive answer has been given to the questions of what these systems will resemble when the present period of violent star formation ends,or what present address:Instituto Astron?o mico e Geof′?sico-USP,Caixa Postal9638,01065-970-S?a o Paulo-BRASIL triggered the burst.It has been suggested that in their qui-escent phase HII galaxies may be related to dwarf irregulars (dI)or dwarf elliptical galaxies(dE).Bothun et al.(1986) made a comparative study of dIs and dEs in the Virgo clus-ter based on the colour distributions and structural proper-ties derived from exponential?ts to the surface brightness pro?les(e.g.scale length and central brightness).They con-clude that dIs are not progenitors of dEs,but they seem to form a parallel sequence of dwarf galaxies.The fading of dIs would make them very di?use and place them below the detection threshold of photographic plates.They propose that Blue Compact Galaxies(BCG’s,of which HII galax-ies are a subset)could probably be gas-rich analog of dEs. Meurer,Mackie&Carignan(1994)have studied the struc-tural properties of the dwarf amorphous galaxy NGC2915 and compared with the properties of NGC1705(Meurer, Freeman&Dopita1992)and NGC5253from the work of and S′e rsic&Donzelli(1992).They?nd that their luminosity pro?les show two components indicating the presence of two distinct stellar populations.The inner component represents the fraction of the galaxy dominated by hydrogen gas pho-toionized by the embedded massive star clusters.Its(B-R) colour pro?le is increasingly bluer inwards.The outer com-ponent has an exponential luminosity(also found for dE’s
2Telles,Melnick&Terlevich
and dIrr’s)and a constant redder colour likely to represent an old stellar population remnant from a previous burst of star formation.Their main conclusion is that these galax-ies are nearby BCG’s that may provide a better insight on the properties of this type of galaxy and their connection with other dwarf galaxies.Kunth,Maurogordato&Vigroux (1988)analysed a small sample of BCG’s to derive surface brightness pro?les by ellipse?tting to di?erent isophotal lev-els.Their results show that the BCG’s present a“mixed bag of morphologies”.They?nd that the outer parts of the galaxies can be best?tted by a power law compared with those of elliptical galaxies.
No de?nitive study has been made on the morphology of HII galaxies(or BCG’s for that matter)up to now.The previous attempts have shown an extensive range of shapes from the most compact and apparently isolated to some clearly revealing di?use extensions,multiple tails,and visu-ally merging systems(Loose&Thuan1985;Melnick1987; Kunth,Maurogordato&Vigroux1988;Salzer,MacAlpine &Boroson1989b).Loose&Thuan(1985)have devised a classi?cation scheme based on the shape and location of the burst in relation with the whole optical structure and the shapes of the outer envelopes.Melnick(1987)describes the systems in terms of being interacting,multiple,or isolated. He has preliminarily reported that50%of the HII galaxies in his sample are star-like and isolated.Salzer,MacAlpine &Boroson(1989b),on the other hand,adopted a more de-tailed classi?cation scheme.Primarily based on the absolute magnitude,size,and morphology,with some spectroscopic information as a secondary indicator,they identi?ed10dif-ferent classes of objects for a sample of emission line objects from the University of Michigan(UM)objective prism sur-vey.Their sample includes some Seyfert galaxies as well as interacting pairs of disk galaxies,starburst nuclei and giant irregulars.Most HII galaxies in our sample are classi?ed as “dwarf HII hot spot galaxies”,“HII hot spot galaxies”or “Sargent&Searle objects”.
We have used surface photometry in order to study the morphology and structural properties of HII galaxies.In Sec-tion2,we?rst present the data sample.In§3,we present our results based on the analysis of the CCD images,as well as structural aspects based on the luminosity pro?les. In§4,we discuss the results,and?nally in§5we present some conclusions.
2THE SAMPLE
The objects in the present study were selected from the sub-sample of the Spectrophotometric Catalogue of HII Galaxies (Terlevich et al.1991,hereafter SCHG)used by Melnick, Terlevich&Moles(1988)in the application of HII galaxies as distance indicators.It consists of39HII galaxies from SCHG brighter than F(Hβ)=5×10?15erg cm2s?1and with Hβequivalent widths,W(Hβ),larger than30?A.The brightness criterion was adopted in order to facilitate the de-termination of emission line pro?les,while objects with large W(Hβ)were selected to minimize age e?ects and contam-ination from an underlying stellar population.Thus,these selection criteria yield a more homogeneous sub-sample of the SCHG,namely,younger starbursts.We have reproduced the relevant data of Melnick,Terlevich&Moles(1988)in
columns1-8in Table1.Columns9-12give the results of our morphological analysis.Column9(prof.)describes the pro-
?le type de?ned in Section3.5.Column10(mult.)describes
whether the object shows a single(single),two(double),or more than two(multiple)knots of star formation.Column
11(ext.)indicates whether the galaxy shows extensions or
signs of distorted outer isophotes which is the primary crite-rion of the morphological classi?cation given in Column12
(type)of Table1,and described in detail in Section3.3.A
colon next to a value in the table indicates that the classi?-cation is uncertain.
2.1CCD images
CCD images through a broad-band V?lter(λ=5480?A,
?λ≈900?A)have been obtained with the Danish1.54-m telescope at the European Southern Observatory(ESO)in
La Silla,Chile.The observations were made in the period
1986-1988.The detector was a thinned RCA CCD512×320 (0.47 per pixel)giving a total?eld of4 ×2.5 .Exposures times were typically1200s.Since our main aim was the
study of the morphology,photometric calibration was not performed.We have nevertheless estimated magnitude zero points when data were available in the literature.Further-more,we have not performed any correction for galactic ex-tinction or reddening.Basic data reduction consisted of bias subtraction and?at?eld division,cosmic rays elimination, and sky subtraction.
3RESULTS
In Figure1we present4panels for each object in the present study.Each page shows these panels for two ob-jects.From top left to bottom right,the?gure shows:1)po-sition,redshift and compiled photometric information from the NASA/IPAC Extragalactic Database(NED)plus ad-ditional photometric information from Salzer,MacAlpine &Boroson(1989a)(indicated in Figure1by?),Mazzarela &Boroson(1993)(indicated by )and Telles&Terlevich (1996)(indicated by?).2)grey scale reproduction of the CCD images.Orientation is shown for each image.The an-gular and physical scales are also shown on each photograph.
3)original illustrative observed spectrum of each star form-ing region from the SCHG.4)circularly averaged surface brightness pro?les centered on the main knot component. The magnitude zero points were determined from di?erential calibration using published photometry,thus they should be taken as an indicative surface brightness level only with an estimated error of at least0.5mag.Error bars in the pro?les are1%sky subtraction errors.
3.1Notes on individual objects
A schematic classi?cation of the morphology of the HII galaxies is given in the last four columns of Table1based on two main criteria:
multiplicity:describes whether the HII galaxy has one(sin-gle)dominant giant HII region,two(double),or more than two main knots of star formation(multiple).
THE MORPHOLOGY OF HII GALAXIES 3
Table 1.Spectroscopic data and the morphological description:(1)name as in SCHG;(2)other name;(3)redshift;(4)line width (σ)
in km s ?1;(5)H β?ux (FH β)in units of 10?13erg cm 2s ?1;(6)extinction coe?cient (CH β);(7)H βequivalent width in ?
A (WH β)and (8)the oxygen abundance in units of 12+log(O/H).Columns (9)-(12)give the morphological description and are discussed in the text.
SCHG other name
redshift σFH βCH βWH βO/H prof.mult.ext.type (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)0341–407
Cam0341–4045E 0.014723.00.440.281408.04dd multiple √I “Cam0341–4045W 0.014723.00.230.3240——Cam0357–39150.074151.10.470.171807.87d single II ——Cam08–28A 0.053749.10.280.77358.40dd multiple √I ——Cam0840+10440.011534.00.100.3955bd single √II:——Cam0840+12010.030536.50.480.521057.88d double √I ——Cam1148–20200.011933.3 1.800.302308.01dd multiple √
I ——Cam12–390.066784.50.24 4.882008.20dd double II 1053+064Fairall 300.003521.8 1.800.22908.01bd single II 1042+097Fairall 2
0.055638.80.270.401008.11
d singl
e I:——Cam1212+11580.022834.20.130.0060d single II 0104–388Tol0104–3880.021149.00.300.3950bd single II 0127–397Tol0127–3970.016033.70.500.5140d single II 0226–390Tol0226–3900.048489.90.570.56908.42bd single √I 0242–387Tol0242–3870.1260134.00.220.79608.23d single √I 0440–381Tol0440–3810.041239.70.300.32358.31d single √I 0513–393Tol0513–3930.050233.20.180.291457.90d single II 0633–415Tol0633–4150.017731.80.450.35908.09dd multiple √I 0645–376Tol0645–3760.026032.10.200.52508.19bd single √I 1004–296
Tol1004–294S 0.003830.6 2.700.69608.23dd double II:“Tol1004–294N 0.003832.3 3.100.77608.281008–287Tol1008–2860.014124.00.300.521258.16bd:multiple √I 1025–284Tol1025–2840.032125.20.300.48608.06dd double √I:1116–326Tol1116–3250.002112.00.430.432758.31d single II 1147–283Tol1147–2830.006418.90.240.47457.90d multiple:II 1214–277Tol1214–2770.025727.60.300.292307.58bd single √I 1324–276Tol1324–2760.006433.40.870.351158.20dd multiple √II:1334–326Tol1334–3260.012516.40.300.222658.00dd multiple √I 1345–421Tol1345–4200.008221.60.380.26708.07d:single II ——Tol1406–1740.033823.90.100.3650d single II 1924–416Tol1924–4160.009329.9 3.830.171007.90dd double √I 2138–405Tol2138–4050.057855.50.330.251207.71dd double √I 2326–405Tol2326–4050.050534.50.140.22808.03bd double √I 0142+046UM1330.009417.20.320.43657.64bd:multiple √II:0131+007UM3360.019716.70.080.0640bd single II 1134+010UM439E 0.003919.70.480.60608.05dd multiple II:1139+006UM4480.018240.8 2.200.79458.36bd double √
I 1147–002UM4550.012420.60.090.26557.84d single II 1148–020UM461A 0.003114.50.700.401557.74dd double II 1150–021
UM462A 0.003118.50.750.38757.98dd double II “UM462B 0.003118.9 1.300.38907.790553+034
IIZw40
0.0028
35.2
1.90
1.00
170
8.13
bd
double
√
I
Figure 1.Basic morphological and spectroscopic illustration for 39HII galaxies in the present sample.Sets of panels for two objects are shown in each page.For each object we show typically 4panels:From top left to bottom right:1)position,redshift and compiled photometric information from NED and references therein.When available,we also include additional photometric information from Salzer,MacAlpine &Boroson (1989a)(indicated in the ?gure by ?),Mazzarela &Boroson (1993)(indicated by )and Telles &Terlevich (1996)(indicated by ?).2)scanned photographs of the CCD images.Orientation is shown for each image.The angular and physical scales are shown on each photograph.3)original observed spectrum of the star forming region from the SCHG.4)circularly averaged surface brightness pro?les,centered on the main knot component.The magnitude zero points were determined from di?erential calibration using published photometry.They have not been derived from absolute calibration of the present work,thus it should be taken as an indicative surface brightness level only,and with an estimated error of at least 0.5mag.No correction for galactic extinction or reddening has been applied.Error bars in the pro?les are 1%sky subtraction errors.
24Telles,Melnick&Terlevich
outer structure:denotes the presence or absence of distorted, irregular extensions,fans or tails beyond the star forming regions.
The results of these two morphological description cri-teria are given in columns10(mult)and11(ext)in Table1, respectively.Some additional notes on individual objects are given below:
SCHG0341–407[Cam0341–4045]Double system;signs of multiplicity can be seen in the West knot of star forma-tion.The faint extension on the NW direction may be all part of the same tail-like structure.This object has signs of extensions and possible merger.
Cam0357–3915Single;very compact;stellar object.
Cam08–28This Markarian object of high luminosity(M V～?22)is in no sense a dwarf system.It has multiple struc-ture and very irregular shape with clear signs of tails of faint surface brightness emanating from the main body to the North and South;one of the extreme examples in this sample of a possible merging system.
Cam0840+1044Faint extension in the E direction but no sign of interaction.This object is2arcminutes South from
a bright foreground SBdm galaxy and close to a bright star
in E.
Cam0840+1200L-shaped outer isophotes;irregular inner structures possibly due to multiple regions of star forma-tion;likely to be product of a merger.
Cam1148–2020Multiple;main burst knot lies in the center surrounded by a ring of3or4other regions;extended outer isophotes.
Cam12–39Compact double system;no signs of extensions. SCHG1053+064[Fairall30]Intrinsically very compact sin-gle system at low redshift with no sign of extensions;very close to bright star to West.
SCHG1042+097[Fairall2]Possible unresolved double sys-tem;indication of outer faint irregular extension to W and
E.It would probably show more disturbed morphology if
it were at a lower redshift.
Cam1212+1158Single;regular isophotes.
SCHG0104–388[Tololo0104–388]Single and compact;close to a foreground spiral galaxy.
SCHG0127–397[Tololo0127–397]Single and compact. SCHG0226–390[Tololo0226–390]Single;faint extensions from the center to the East.
SCHG0242–387[Tololo0242–387]Sign of a possible tail (more visible in the CCD image)to the East at very faint surface brightness level.This object is the highest redshift galaxy in the sample.It is a member of a small group of galaxies at Z=0.126.
SCHG0440–381[Tololo0440–381]Single knot;possibly un-resolved double system;faint blob emanating at the South-East direction.SCHG0513–393[Tololo0513–393]Single object(southern most object in this photograph);regular shape;no sign of interaction.
SCHG0633–415[Tololo0633–415]Spectacular peculiar galaxy at low redshift;very irregular morphology;bright;
streamer westwards;interacting system.Most of the[OIII] emission comes from the main knot in the eastern com-ponent.Very faint line emission is also seen the western component in the narrow band[OIII]image.
SCHG0645–376[Tololo0645–376]The main body is of reg-ular shape with its burst located in the center,but faint extensions are seen to the East and to the West.
SCHG1004–296[Tololo1004–294]Bright low redshift galaxy in cluster;regular outer isophotes;double knots;amor-phous galaxy.
SCHG1008–287[Tololo1008–286]Irregular;interacting sys-tem;two main regions of star formation embedded in com-mon irregular envelope and bridged by faint extensions as revealed in the[OIII]image.
SCHG1025–284[Tololo1025–284]Double system embedded in common envelope.
SCHG1116–326[Tololo1116–325]Very compact object at low redshift.
SCHG1147–283[Tololo1147–283]Single amorphous object at low galactic latitude;knots to the East may be stars superposed on the galaxy image.
SCHG1214–277[Tololo1214–277]Single knot object with extensions along the North-South direction;possible close projected companion at20arcseconds to the South.
SCHG1324–276[Tololo1324–276]Multiple knots at low red-shift;in cluster;signs of faint extension along the main body;foreground bright star superposed on the South-East end.
SCHG1334–326[Tololo1334–326]Multiple system of4 knots at the centre;the most intense knot being the South West condensation;long fan emanating from the main body to the South direction only;object in cluster;bright star≈1arcminute to the North-West direction.Object is at low galactic latitude.
SCHG1345–421[Tololo1345–420]Single object with regular outer isophotes(poor image quality).
Tololo1406–174Single very compact stellar object.
SCHG1924–416[Tololo1924–416]Star on South-East;Mul-tiple knots;almost triangle outer isophotes;The central region of this HII galaxy is irregular and knotty.
SCHG2138–405[Tololo2138–405]Peculiar system in inter-action;two distinct components.The main line emitting region is in the North while the South component has an amorphous structure.The line emitting region(North) seems to be double or of multiple knots.
SCHG2326–405[Tololo2326–405]Extended cometary-like object with the main burst at its“head”at eastern-end of the elongated body;bright star at SE.
THE MORPHOLOGY OF HII GALAXIES25 SCHG0142+046[UM133]Cometary-like or Magellanic-like
object with main burst at the far South end embedded
in a rather regular elongated envelope;possible multiple
knots along the apparent“bar”;no evidence of interac-
tion.This object is at low redshift.It would probably be
characterized as a single object with a fuzz if it were at a
larger distance.
SCHG0131+007[UM336]Single object with regular outer
isophotes.At a moderate redshift this object is not very
compact resembling more objects with amorphous struc-ture.
SCHG0134–010[UM439]Low redshift multiple object.
Main burst is in the South end;faint extensions along the main body;bright star1.5arcminutes to South-East. SCHG1139+006[UM448]High spatial resolution imaging of this object(Telles&Terlevich1996)has shown dou-ble internal structure of spiral-like shape.This is a pecu-liar object with a visible fan,emanating directly from the main burst extending at least2arcminutes to the South-West.
SCHG1147–002[UM455]is an elliptical shape object with the line emission region o?-center.It may be an unresolved double;bright star≈1.5arcminutes to the North-East;in cluster;uncatalogued galaxy at20arcseconds to the East with no line emission.
SCHG1148–020[UM461]Nearby double system.The main knot in the North is of much larger luminosity than the secondary one.At at moderate redshift this object would look very compact.The outer isophotes are regular despite the inner double structure being o?-center.
SCHG1150–021[UM462]Nearby double system.As op-posed to UM461which is a close companion in the group, this object has the inner double structure in the center in relation with the outer regular isophotes.
SCHG0553+034[II Zw40]This is a low redshift object with compact core and fan jets(South)and(South-East).This object has two clear di?erent components which may rep-resent a merging system.At moderate redshift its small linear size would likely hide these features.Despite its very low galactic latitude this HII galaxy has been targeted for various di?erent studies in the literature.Recent work us-ing HST observations by Vacca(1994)reveals that the main burst is split into smaller ionizing regions which are unresolved in ground-based observations.
3.2General notes on morphology
Some additional general remarks can be made about the present sample:
?Objects described to have a single giant HII region usually have their burst at the center(Cam0357-3915, SCHG1053+064,Cam1212+1158,SCHG0104–388, SCHG0226–390,SCHG0242–387,SCHG0513–393, SCHG0645–376,SCHG1116–326,SCHG1345–420, SCHG1406–174,SCHG0131+007).
?A few objects have“pear-like”shapes(Cam 0840+1044,SCHG1042+097,SCHG0440–381,
SCHG Figure2.Redshift Distribution for Type I and Type II HII galax-ies.
1147–002).These have been classi?ed as single systems with burst o?-center.However,they can be double sys-tems where the main knot outshines the secondary.For example,SCHG1147–002(UM461)is a compact object with a double burst which would resemble a“pear-like”
object,had it been located at a larger redshift.
?Systems which appear to be double at a moderate red-shift may split the two main bursts into smaller com-ponents as in the nearby example of SCHG1324–276.
?None of the galaxies in this sample can be classi?ed as
a classical“starburst galaxy”,i.e.a nuclear burst on
an otherwise normal spiral galaxy.Typical HII galaxies do not show spiral structure.
3.3A classi?cation scheme for HII galaxies When studying the morphological properties of HII galaxies, it is important to bear in mind that,although all contain at least one giant region of star formation(whether centered on the nucleus or not),this class presents a wide variety of morphologies.They are,in fact,a very inhomogeneous morphological class of galaxies where the common property is the dominant giant HII region.The results,presented in the last columns of Table1and described in more details in the previous section reveal that the presence of an extended component or possible underlying galaxy is evident in about half of these objects for which CCD images have been ob-tained.We also?nd that some of these objects show possible features of interacting or merging systems(wisps,tidal tails or irregular fuzzy extensions).More than one giant knot of star formation seems to be a common feature,although,this seems unrelated to whether the object is apparently inter-
26Telles,Melnick&Terlevich
acting or isolated.About one third of the galaxies in the sample are actually single stellar-like objects with no evi-dence for extensions or fuzz.
On the basis of the shape of the outer isophotes,HII galaxies can be segregated in two broad groups:
Type I objects have disturbed morphologies and irregular outer isophotes,fuzz or tails.
Type II objects are symmetric and regular objects,regard-less of the multiplicity of the starburst region(i.e.their internal structure).
An indication of the possible existence of these two mor-phological types of HII galaxies was already preliminarily reported in Telles&Terlevich(1994).
Clearly,the perception of the morphology depends on redshift.Individual star-forming regions within the galaxies may only be resolved for nearby brighter objects,while mor-phological details of systems at larger redshifts(z>0.02) may be smeared out rendering the galaxies with a smoother compact appearance.HII galaxies at larger redshift which still show morphological details will be high luminosity sys-tems that may belong to a possibly more disturbed class
of starburst galaxies.These are not dwarfs.On the other hand,although small morphological features would be nat-urally better visible for galaxies at low redshift the distribu-tion of redshifts shown in?gure2shows that these Type II HII galaxies are mostly low redshift galaxies.Therefore,the fact that we do not see faint detailed structures in these low redshift,bright,low luminosity systems is not a resolution e?ect.Objects which are single and compact with no sign of extended envelope or tidal tails at low redshift,such as SCHG1053+064,Cam1212+1158,SCHG0104–388,SCHG 0127–397,SCHG1116–326,SCHG1345–421,Tol1406–174 and SCHG0131+007are of particular interest.They may be truly young galaxies(in the sense of being experienc-ing their?rst major star formation episode)at low redshift. Thus,these objects can provide us with an insight on a era which was marked by the formation and early evolution of the present luminous galaxies.
3.4The burst and galaxy sizes
As mentioned by Djorgovski&Davis(1987)it is di?cult to de?ne a radial scale.In principle we would need a radial scale independent from the magnitude and surface bright-ness calibration,which means that an isophotal radius is not ideal.However,we can use a radial scale derived from the surface brightness pro?les,although we do not know the ex-act form of these pro?les for these bursts of star formation. Therefore,the derived relations may at best be indicative of global rather than central properties of these galaxies.
We have measured the sizes of the star forming regions in the galaxies as well as the half-light radius of HII galaxies from the un-calibrated CCD images in the V band.Seeing measurements(F W HM?)were obtained from Gaussian?ts to the point spread function from stars in each?eld and are listed in column3of Table2.Burst diameters(HII in arcsec-onds)listed in column4of Table2are FWHM of the circular brightness pro?les centered on the peak intensity of the burst region of the galaxy.This method,although rather crude, provides us with a systematic estimate of the total
physical Figure3.Distribution of linear radii of the bursts of star for-mation in HII galaxies(hatched histograms).The thick line his-
tograms show the e?ective radii of the HII galaxies in the V?lter
from their luminosity curves of growth.
size of the ionizing cluster that is adequate to the statistical
approach to study the scaling laws governing the structural properties of HII galaxies(Telles&Terlevich1993).In what
follows,we have applied an approximate seeing correction
to the?nal burst sizes(D20=F W HM2HII?F W HM2?).The results are shown in columns6and7in arcseconds and in
parsec?,respectively.It is important to bear in mind that for barely resolved compact regions with angular sizes of the order of the seeing disk the size estimates may rep-resent upper limits only.This is illustrated in column5 by the ratio of the burst size measurement to the seeing (F W HM HII/F W HM?).E?ective diameters(D ef f in arc-seconds and in parsec)in columns8&9are the true half light diameters of the whole HII galaxy centered on the peak luminosity(main burst)measured directly from the syn-thetic circular aperture luminosity curve of growth for each object obtained from star-free,sky subtracted frames.
Figure3presents the distribution of physical sizes
(burst radii,r b)of the bursts of star formation as shaded histograms and the distribution of e?ective radii(r e?)of HII galaxies.From this,one can see that star forming re-gions have typical sizes of hundreds of parsec and there is a signi?cant cut o?above these values.It is worth noting that these sizes are representative of the total size of the ioniz-ing cluster.True core sizes of the ionizing cluster will be far smaller.If one takes30Doradus,the most spectacular ex-ample of a nearby giant HII region in the LMC,and compare the ratio of sizes of its ionized region to its ionizing cluster resolved by the Hubble Space Telescope(HST)(Walborn
?H
0=50km s
?1Mpc?1is used throughout this paper.
THE MORPHOLOGY OF HII GALAXIES27 1991),one would expect equivalent core sizes of the ionizing
stellar clusters of the gigantic HII regions in galaxies to be
at least100times smaller than their ionized regions,thus
of the order of a few parsec.They will remain completely
unresolved and,if they are like30Dor,most of the ionizing
luminosity will be produced in this small region.
3.5Luminosity Pro?les
We have adopted the simplest procedure of?tting circularly
averaged radial pro?les to represent the light distribution
in the isophotes of HII galaxies.Fitting ellipses to the ir-
regular isophotes of HII galaxies does not produce any addi-
tional information about the true structure of one particular
galaxy.In either case the resulting pro?les are similar.Fig-
ure1shows the derived luminosity pro?les,from star-free
frames,for each HII galaxy in our present sample repre-
sented as surface magnitudeμ(r)plotted against radius r.
In this representation an exponential pro?le is a straight
line.
Figure4shows the three main types of overall light
pro?les found among HII galaxies.The power law pro?le
(solid line)is mostly found in galaxies with long extensions.
These resemble,somewhat,the two-component pro?les such
as bulge+disk pro?les typical of bright early type spi-
ral galaxies.They trace light to larger angular sizes[e.g.
SCHG0633–415,SCHG2326–405,SCHG0553+034(II Zw
40)].Exponential pro?les(dotted lines)typically describe
the more compact,small angular size objects and are heav-
ily a?ected by the point spread function(e.g.Cam0357–
3915,SCHG1042+097,SCHG1116–326).Platform pro-
?les(dashed line)are found for galaxies with more than
one main knot[e.g.SCHG0341–407,SCHG1004–296and
SCHG1134+010(UM439)].
We will label the three typical types of pro?les as fol-
lows:
d A singl
e exponential?t represents well the whole range of
radii of the pro?le.
dd Double pro?le with a“platform”due to the double mor-
phology.An exponential law is well?tted to the outer
regions.
bd a steep bright central region and outer disk-like compo-
nent.No attempt is made to perform a bulge-disk like de-
composition because of the unknown relation of the light
in the burst region with the mass density and the unknown
analytical form of the light pro?le in the inner region.The
exponential?t represents well the outer component only.
The results of this classi?cation scheme for the light pro?les
of HII galaxies are shown in column9of Table1.
A natural further step in the analysis of the luminos-
ity pro?les of HII galaxies is to?t the pro?les with known
scaling laws.The most common scaling laws are:exponen-
tialμ(r)∝r(Freeman1970);μ(r)∝r1/4(de Vaucouleurs
1948);μ(r)∝log(r)(Bahcall1977);I(r)=I0(1+r2
r2
0)?1
(Hubble1930).Although these photometric laws describe the luminosity pro?les of normal galaxies they should actu-ally not be used as morphology descriptors;an exponential pro?le does not imply a disky system unless a disk is clearly seen or there is other indication that this may be the case. Surface photometry alone is helpful but not su?cient to de-
r
d
bd
dd
μ(r)
Figure4.Pro?le types.
termine the spatial structure of a particular dwarf whether it may be spheroidal or disk-like.We have studied which of these common scaling laws best represents the overall shape of each HII galaxy.The main conclusion from this study is that outer parts of all three types of luminosity pro?les of HII galaxies are well described by an exponential scaling law(i.e.exponential?ts have the lowest standard deviation when the outer pro?les are?tted to the same radial range). These?ndings for HII galaxies agree with those of Vader& Chaboyer(1994)who?nd a general predominance of expo-nential pro?les among dwarf of various types although com-posite pro?le and early type r1/4similar to giant ellipticals do occur in some cases.
Therefore,the structural parameters derived from the exponential?ts(i.e.scale length r0and central surface brightnessμ0)to the extensions may well represent the structural properties of the underlying galaxy in HII galax-ies.In Table3we present the results of such exponential ?ts for our present sample.Unfortunately,we do not have absolute calibration and we are able to give approximate central surface brightness values for only～40%of the present sample.We also caution that no reddening correc-tion has been applied.One may wish to compare the results of the structural parameters of HII galaxies directly with the properties of other known types of dwarfs such as dE’s, dIrr’s or other low surface brightness galaxies.A compari-son may help give us some insight on the origin of the HII galaxies and the relation among all dwarf galaxies.However, the large uncertainty in the zero point of the few galaxies for which we have di?erential calibration prevent us from per-forming such comparison until more an better quality data are available.
4DISCUSSION
Figure5shows the distributions of the intrinsic properties of HII galaxies segregated in Type I HII galaxies(solid line histograms)and Type II HII galaxies(shaded histograms).
28Telles,Melnick&Terlevich
Table2.Size measurements.F W HM?is the FWHM seeing from a Gaussian?t to a stellar image in the CCD?eld.F W HM HII are the main burst sizes in arcseconds.D0are the burst sizes corrected by the seeing as described in the text.D ef f are the half-total light diameters from the luminosity curves of growth.
D0D ef f
SCHG other name F W HM?F W HM HII F W HM HII
?
(”)(”)(”)(pc)(”)(pc) 0341–407Cam0341–4045E 1.47 2.31 1.57 1.7976418.517915
——Cam0357–3915 1.53 2.03 1.33 1.342886 2.174670
——Cam08–28A 1.28 2.69 2.11 2.373706 6.7810595
——Cam0840+1044 1.32 2.11 1.60 1.655517.162395
——Cam0840+1201 1.26 2.01 1.60 1.571393 5.184597
——Cam1148–2020 1.64 2.75 1.68 2.2076315.645413
——Cam12–39 1.51 1.94 1.29 1.222372 2.454752 1053+064Fairall30 1.64 2.42 1.48 1.78181 6.69681
1042+097Fairall2 1.32 2.18 1.65 1.732799 3.255256——Cam1212+1158 1.36 1.95 1.43 1.40926 2.621737
0104–388Tol0104–388 1.13 2.05 1.82 1.711051 2.751688
0127–397Tol0127–397 1.63 2.62 1.61 2.05955 5.182411
0226–390Tol0226–390 1.13 1.76 1.56 1.351899 2.733846
0242–387Tol0242–387 1.28 2.09 1.63 1.656050 2.308425
0440–381Tol0440–381 1.23 2.92 2.37 2.653178 3.374042
0513–393Tol0513–393 1.39 1.84 1.32 1.201747 2.173164
0633–415Tol0633–415 1.41 2.25 1.59 1.759027.543880
0645–376Tol0645–376 1.34 2.36 1.77 1.951475 6.464888
1004–296Tol1004–294S 1.19 2.14 1.79 1.7819618.372031
1008–287Tol1008–286 1.20 1.85 1.54 1.4057512.064946
1025–284Tol1025–284 1.19 1.89 1.60 1.481378 5.655278
1116–326Tol1116–325 1.43 2.21 1.55 1.69103 2.49152
1147–283Tol1147–283 1.39 3.80 2.73 3.536589.701806
1214–277Tol1214–277 1.14 1.74 1.54 1.32989 2.251683
1324–276Tol1324–276 1.11 2.16 1.94 1.8534413.662543
1334–326Tol1334–326 1.50 2.12 1.42 1.505457.162603
1345–421Tol1345–420 1.58 3.75 2.38 3.4181210.932607
——Tol1406–174 1.41 2.03 1.43 1.451427 2.152112
1924–416Tol1924–416 1.52 4.89 3.22 4.651258 6.031631
2138–405Tol2138–405 1.11 1.98 1.78 1.642761 2.574324
2326–405Tol2326–405 1.13 1.76 1.56 1.351981 2.834151
0142+046UM133 1.62 3.28 2.03 2.8678132.038758
0131+007UM336 1.10 1.98 1.79 1.64941 3.812181
1134+010UM439 1.38 1.96 1.42 1.3915815.641774
1139+006UM448 1.36 4.94 3.64 4.7525159.424987
1147–002UM455 1.75 2.36 1.35 1.59572 5.121845
1148–020UM461A 1.39 3.52 2.53 3.232919.24833
1150–021UM462A 1.497.19 4.837.0463513.801244
0553+034IIZw40 1.45 2.76 1.90 2.3519112.25997
Table4.Statistical results for the distributions of?gure5a-d.The mean and median of the distribution are given for Type I and Type II HII galaxies separately.The last column gives the probability P that the distributions of these spectroscopic properties are drawn from the same distribution function(see text for details).
Type I Type II
Mean Median Mean Median K-S test
log L(Hβ)(erg s?1)41.67±0.6041.41±0.5340.64±0.8440.30±0.48P=0.001
σ(km s?1)40.0±24.232.9±6.628.7±15.623.1±7.3P=0.02
W(Hβ)(?A)112±68100±4094±6465±45P=0.18
12+log(O/H)8.07±0.218.09±0.097.99±0.198.01±0.16P=0.51
THE MORPHOLOGY OF HII GALAXIES
29 Figure5.Histogram of the spectroscopic properties segregated in Type I HII galaxies and Type II HII galaxies.Dotted lines show the
distributions for the whole sample.Solid line histograms are Type I HII galaxies,while short-dashed hatched histograms show Type II
HII galaxies.
Also shown,as dotted lines,are the histograms for all galax-
ies in the sample.Table4summarizes the main statisti-
cal parameters from these distributions.We have checked
the trends shown in?gure5by performing a Kolmogorov-
Smirnov test to the unbinned distributions in order to as-
sess statistically the di?erences of the spectroscopic data for
Type I and Type II HII galaxies.The low values of the sig-
ni?cance level(P≤0.02)disproves that the distributions
of L(Hβ)andσcan be drawn from the same distribution
function.However,the high values of the signi?cance level
(P>0.1)for the distributions of W(Hβ)and O/H indicate
that the data are consistent with them being drawn from
a single distribution function.These results show that HII
galaxies with signs of disturbed morphologies(Type I)tend
to be more luminous than Type II objects.It can also be seen
that Type I also tend to have larger velocity dispersion(σ)in
the line emission regions in agreement with the well known
correlation between L(Hβ)andσ(Terlevich&Melnick1981;
Melnick,Terlevich&Moles1988).The metal abundance and
W(Hβ)distributions seem to overlap for both types of HII
galaxy.However,the morphological disturbances of Type I
HII galaxies do not seem to be of tidal origin.HII galaxies
are not associated with bright companions,they are mostly
isolated and tend to populate low density environments and
are weakly clustered(Telles&Terlevich1995;Vilchez1995;
Rosenberg,Salzer&Moody1994).
It is interesting to point out that other types of dwarf
galaxies have been found to show distinct systematic struc-
tural properties at both ends of the luminosity distribu-
tion(Binggeli&Cameron1991,Binggeli1994,Ferguson&
Binggeli1994).Binggeli&Cameron(1991)have found that
the break in the systematic photometric properties in their
sample of～200early-type dwarfs in the Virgo cluster lies at
M B≈–16to–17.They suggested that this may be caused
by a transition in the internal kinematics of the systems
from disky or rotationally supported systems to spheroidal
systems.They also suspect a connection with the ratio of vis-
ible to dark matter;fainter galaxies being more dark matter
dominated.The question that then arises is whether there is
indeed a real break in physical properties of all dwarf galax-
ies at that luminosity.If so,what is the relation and underly-
ing causes between the break at the photometric properties
for the dwarfs in Virgo and the apparent break in the mor-
phological properties of HII galaxies?In any case,our results
seem to suggest a strong relation between morphology and
luminosity.
30Telles,Melnick&Terlevich
Table3.Structural parameters from exponential?ts:μ0is the extrapolated central surface brightness and r0is the scale length (in arcseconds)of an exponential?t to the extensions of the lu-minosity pro?les.
SCHG other nameμ0r0
0341–407Cam0341–404510.4
——Cam0357–39150.6
——Cam08–28A22.1 4.9
——Cam0840+104423.2 3.4
——Cam0840+1201 1.6
——Cam1148–20207.4
——Cam12–39 1.3
1053+064Fairall30 2.4
1042+097Fairall2 1.0
——Cam1212+115819.8 1.0
0104–388Tol0104–388 1.7
0127–397Tol0127–397 3.1
0226–390Tol0226–390 1.8
0242–387Tol0242–3870.9
0440–381Tol0440–381 1.1
0513–393Tol0513–393 1.0
0633–415Tol0633–41525.215.0
0645–376Tol0645–376 5.6
1004–296Tol1004–29419.97.5
1008–287Tol1008–286 3.8
1025–284Tol1025–284 1.8
1116–326Tol1116–3250.7
1147–283Tol1147–28321.4 4.1
1214–277Tol1214–277 3.4
1324–276Tol1324–27620.2 5.4
1334–326Tol1334–32619.3 2.0
1345–421Tol1345–420 2.2
——Tol1406–1740.5
1924–416Tol1924–41617.3 5.9
2138–405Tol2138–405 1.4
2326–405Tol2326–405 4.9
0142+046UM13323.114.1
0131+007UM33622.6 2.4
1134+010UM43919.5 3.9
1139+006UM44823.714.0
1147–002UM45520.3 1.8
1148–020UM46120.8 3.0
1150–021UM46219.5 3.8
0553+034IIZw4022.210.0 Apart from the photometric evolution of the stellar pop-ulation in HII galaxies,because of the mass loss from stellar winds and supernova ejecta and its short dynamical time scale,dynamical evolution will a?ect the system in less than a Hubble time(Terlevich1994).We can predict the trend of the e?ect of mass loss in the dynamical evolution of the stellar cluster.If the removal is slow compared to the cross-ing time of the system t?,then the system obeys an adia-batic invariant(Dekel&Silk1986,Terlevich1994and ref-erences therein),and the“bloating”of the stellar system will be proportional to the mass loss.For the system to re-main bounded throughout its evolution,the increase in size should be accompanied by a corresponding decrease in ve-locity
dispersion:Figure6.The Radius vs.σrelations for dEs and HII galaxies.R corresponds to R b(D0/2from Table2)for HII galaxies.The big symbols represent the mean locus of the HII galaxies(big solid triangle)and the mean locus of the dwarf elliptical galaxies in the diagram(big open square).
r
r0
=
M0
M=
σ0
σ
where r is the size of the system,M is its total mass and σis the velocity dispersion.During the evolution the total mass lost by a“normal”IMF population is in the range of 20%-40%,considering that all ejecta leave the system.
Figure6shows the[R–σ]relation for our sample of HII galaxies(solid triangles)and compares it with sample of dwarf elliptical galaxies(open squares)from Peterson& Caldwell(1993,and references therein).The big symbols represent the mean locus of the HII galaxies(big solid tri-angle)and the mean locus of the dwarf elliptical galaxies in the diagram(big open square).The arrow connecting the big symbols is the observed shift from the HII galaxies to the dwarf elliptical galaxies.This trend,namely that dwarf ellipticals are typically slightly larger and with lower ve-locity dispersion than HII galaxies,is compatible with the expectation if the stellar population in HII galaxies evolve dynamically into dwarf elliptical galaxies.In addition,the magnitude of the observed shift is in good agreement with the estimated dynamical evolution due to mass loss by a “normal”IMF population(?M/M ～20%?40%),repre-sented in the?gure by the arrows in the right lower corner. The similarity of the parametric relations of“aged”HII galaxies with those of other dwarf galaxies(Telles&Ter-levich1993),together with the indication of a possible dy-namical evolution of HII galaxies into dwarf ellipticals,may be suggestive of a close kinship among these dwarfs.
THE MORPHOLOGY OF HII GALAXIES31
5CONCLUSIONS
The morphological and structural properties of HII galaxies are studied in this paper.The main conclusions of this study are:
?HII galaxies can be classi?ed within two broad morpho-logical types:
Type I irregular systems with signs of distorted outer isophotes,tails,wisps,fans,etc.
Type II regular and compact systems with symmetric morphology.
Type I’s were found to have higher luminosities and ve-locity dispersions than Type II’s,while the equivalent widths of Hβand oxygen abundances of the two types are roughly similar.This seems to indicate that the star-bursts may have been triggered by di?erent mechanisms in the two classes of objects.
?We?nd three main types of light pro?les in HII galax-ies.The pro?le types qualitatively relate to the overall morphology of the galaxies.The outer parts of the lu-minosity pro?les of HII galaxies are well represented by an exponential scaling law.This will allow a direct com-parison of the structural parameters(scale length and central surface brightness)with other types of dwarf galaxies and will lead us to derive important structural properties of the underlying systems once calibrated im-ages are obtained.
?While the burst sizes of HII galaxies are of the order of hundreds of parsec,the“true”core radii of HII galaxies are basically unresolved and probably only few parsecs across.Yet,most of the ionizing luminosity produced may be coming from these very small regions.
?The similar trends of dynamically“aged”HII galax-ies,and their relative positions in the[R–σ]diagram support the hypothesis of a possible evolutionary link between the two types of galaxy.If this is the case,dEs could be the descendants of HII galaxies.
Acknowledgments
ET acknowledges his grant from CNPq/Brazil.We espe-cially thank Richard Sword for his art work in this paper.
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应用离散数学-集合与关系
集合与关系《应用离散数学》 第3章 21世纪高等教育计算机规划教材
目录 3.1 集合及其运算 3.2 二元关系及其运算3.3 二元关系的性质与闭包3.4 等价关系与划分 3.5 偏序关系与拓扑排序3.6 函 数 3.7 集合的等势与基数3.8 多元关系及其应用
集合是现代数学中最重要的基本概念之一，数学概念的建立由于使用了集合而变得完善并且统一起来。集合论已成为现代各个数学分支的基础，同时还渗透到各个科学技术领域，成为不可缺少的数学工具和表达语言。对于计算机科学工作者来说，集合论也是必备的基础知识，它在开关理论、形式语言、编译原理等领域中有着广泛的应用。 本章首先介绍集合及其运算，然后介绍二元关系及其关系矩阵和关系图，二元关系的运算、二元关系的性质、二元关系的闭包，等价关系与划分、函数，最后介绍多元关系及其在数据库中的应用等。
3.1 集合及其运算 3.1.1 基本概念 集合是数学中最基本的概念之一，如同几何中的点、线、面等概念一样，是不能用其他概念精确定义的原始概念。集合是什么呢？直观地说，把一些东西汇集到一起组成一个整体就叫做集合，而这些东西就是这个集合的元素或叫成员。 例3.1 （1）一个班级里的全体学生构成一个集合。 （2）平面上的所有点构成一个集合。 （3）方程 的实数解构成一个集合。 （4）自然数的全体（包含0）构成一个集合，用N表示。 （5）整数的全体构成一个集合，用Z表示。 （6）有理数的全体构成一个集合，用Q表示。 （7）实数的全体构成一个集合，用R表示。
（8）复数的全体构成一个集合，用C表示。 （9）正整数集合Z+，正有理数集合Q+，正实数集合R+。（10）非零整数集合Z*，非零有理数集合Q*，非零实数集合R*。（11）所有n 阶(n≥2)实矩阵构成一个集合，用M n(R)表示，即
嵌入式系统的低功耗设计
第27卷第6期增刊 2006年6月 仪 器 仪 表 学 报 Chinese Journal of Scientific Instrument Vol.27No.6 J une.2006 嵌入式系统的低功耗设计 3 杨天池 金 梁 王天鹏 (解放军信息工程大学 郑州 450002) 摘 要 嵌入式系统的电源管理是系统设计中关键部分,合理的电源管理方案可以减少系统的功耗并提高整体性能。本文提出了一种层次化的电源管理结构,分别为硬件层、驱动层、操作系统层、电源管理层和应用层。本文同时引入了动态的电源管理方法来解决电源功耗的动态管理问题。通过在实际的系统中的测试表明,该电源管理机制的有效性。关键词 嵌入式系统 低功耗设计 动态电源管理 PXA255 Low pow er design in embedded system Yang Tianchi Jin Liang Wang Tianpeng (Universit y of I nf ormation Engineering ,Zhengz hou 450002,China ) Abstract Proper power management mechanism is important when designing embedded system.It is helpful to reduce power consumption and improve performance.This low power model adopt s five 2layer architecture ,which are hardware platform ,driver layer ,operating system ,power manage mechanism and application program.Dynamic power management (DPM )technology is also introduced to solve the problem of power consumption.The experiment on embedded system demonstrates t hat this power management mechanism is feasible.K ey w ords embedded system low power design dynamic power management PXA255 3基金项目:河南人才创新基金(0421000100) 1 引 言 随着嵌入式系统的发展以及应用面的不断扩展,功耗控制是系统设计中必不可少的组成部分。如何最大限度的降低系统功耗、减少不必要的能源损失、延长电池使用时间已经成为嵌入式系统特别是便携式系统设计中研究的热点问题。系统的低功耗设计,并非是某一方面、某一角度的解决方案,而应当从系统级的设计考虑功耗的节省,是一个硬件设计与软件控制相互结合的协调过程。 2 低功耗电路模型 低功耗设计对于无线设备、PDA 等便携式设备的实际应用具有重要的意义。低功耗元件的发展和系统设计的进步使得通用计算技术可以用到表、无线电话、 PDA 和桌面计算机中。在这些系统中的电源管理技 术传统上集中在休眠模式和设备能源管理这2个方面上[1]。但是,这样的电源管理缺乏直观性和灵活性,而且功耗的降低,并非单独软件、硬件单方面可以解决的[2],因此设计并建立如图1所示的系统低功耗设计模型。整个模型由硬件平台,驱动层,操作系统层,电源管理机制层和应用程序五个部分组成。 2.1 硬件平台 几乎所有系统功耗都集中于硬件平台,因此降低硬件平台的功耗是实现低功耗的基本所在。公式(1)为系统功耗的表达式: P ∞CV 2 f (1) 式中:C 是负载电容,V 是器件电压,f 是工作频率[3]。系统功耗同负载电容、器件电压平方以及工作频率成正比。因此,硬件平台设计多选用低电压,电压、频率可调器件,以及采用SOC 设计来进一步降低功耗[4,5]。另外,模式可控器件在空闲状态消耗的能量为运行状
ARM低功耗设计_全面OK
嵌入式系统中的低功耗设计 2008-12-31 18:19:55 作者：电子之都来源：电子之都浏览次数：59 网友评论 0 条 经过近几年的快速发展，嵌入式系统（Embedded system）已经成为电子信息产业中最具增长力的一个分支。随着手机、PDA、GPS、机顶盒等新兴产品的大量应用，嵌入式系统的市场正在以每年30%的速度递增（IDC预测），嵌入式系统的设计也成为软硬件工程师越来越关心的话题。 在嵌入式系统的设计中，低功耗设计（Low-Power Design）是许多设计人员必须面对的问题，其原因在于嵌入式系统被广泛应用于便携式和移动性较强的产品中去，而这些产品不是一直都有充足的电源供应，往往是靠电池来供电，所以设计人员从每一个细节来考虑降低功率消耗，从而尽可能地延长电池使用时间。事实上，从全局来考虑低功耗设计已经成为了一个越来越迫切的问题。 那么,我们应该从哪些方面来考虑低功耗设计呢？笔者认为应从以下几方面综合考虑： 1.处理器的选择 2.接口驱动电路设计 3.动态电源管理 4.电源供给电路的选择 下面我们分别进行讨论： 一、处理器的选择 我们对一个嵌入式系统的选型往往是从其CPU和操作系统（OS）开始的，一旦这两者选定，整个大的系统框架便选定了。我们在选择一个CPU的时候，一般更注意其性能的优劣（比如时钟频率等）及所提供的接口和功能的多少，往往忽视其功耗特性。但是因为CPU 是嵌入式系统功率消耗的主要来源---对于手持设备来讲，它几乎占据了除显示屏以外的整
个系统功耗的一半以上（视系统具体情况而定），所以选择合适的CPU对于最后的系统功耗大小有举足轻重的影响。 一般的情况下，我们是在CPU的性能（Performance）和功耗（Power Consumption）方面进行比较和选择。通常可以采用每执行1M次指令所消耗的能量来进行衡量，即Watt/M IPS。但是，这仅仅是一个参考指标，实际上各个CPU的体系结构相差很大，衡量性能的方式也不尽相同，所以，我们还应该进一步分析一些细节。 我们把CPU的功率消耗分为两大部分：内核消耗功率PCORE和外部接口控制器消耗功率PI/O，总的功率等于两者之和，即P=PCORE+PI/O。对于PCORE，关键在于其供电电压和时钟频率的高低；对于PI/O来讲，除了留意各个专门I/O控制器的功耗外，还必须关注地址和数据总线宽度。下面对两者分别进行讨论： 1、CPU供电电压和时钟频率 我们知道，在数字集成电路设计中，CMOS电路的静态功耗很低，与其动态功耗相比基本可以忽略不计，故暂不考虑。其动态功耗计算公式为： Pd=CTV2f 式中，Pd---CMOS芯片的动态功耗 CT----CMOS芯片的负载电容 V----CMOS芯片的工作电压 f-----CMOS芯片的工作频率 由上式可知，CMOS电路中的功率消耗是与电路的开关频率呈线性关系，与供电电压呈二次平方关系。对于一颗CPU来讲，Vcore电压越高，时钟频率越快，则功率消耗越大。所以，在能够满足功能正常的前提下，尽可能选择低电压工作的CPU能够在总体功耗方面得到
基于MSP430的极低功耗系统设计
基于MSP430的极低功耗系统设计 摘要：MSP430是TI公司出品的一款强大的16位单片机，其显著特点是具有极低的功耗。本文对构造以MSP430为基础极低功耗系统作为有益的探讨，对于设计各种便携式设备都具有较高的参考价值。 对于一个数字系统而言，其功耗大致满足以下公式：P=CV2f，其中C为系统的负载电容，V为电源电压，f为系统工作频率。由此可见，功耗与电源电压的平方成正比，因此电源电压对系统的功耗影响最大，其次是工作频率，再就是负载电容。负载电容对设计人员而言，一般是不可控的，因此设计一个低功耗系统，应该考虑到不影响系统性能前提下，尽可能地降低电源的电压和使用低频率的时钟。下面对TI公司新出MSP430来具体探讨这个问题。 MSP430具有工业级16位RISC，其I/O和CPU可以运行在不的时钟下。CPU功耗可以通过开关状态寄存器的控制位来控制：正常运行时电流160μA,备用时为0.1μA，功耗低，为设计低功耗系统提供了有利的条件。 图1是我们设计的以MSP430为CPU的“精密温度测试仪”（下面简称测试仪）。该产品使用电池供电，体积小巧，携带方便。 在使用时应该尽可能地选择最低的电源电压。对于MSP430而言，可用的最低电压是很低的，最低可达1.8V。我们使用TI公司推荐使用的3V。通常的电源只提供5V电压，因此，需要将5V电压由一个3V的稳压管降压后给CPU供电，也可以直接锂电池供电。3V不是标准的TTL电平，因此，在使用时需要用接口电路使CPU的非TTL标准电平能与TTL标准电平的器件连接。这些接口电路应该也是低功耗的，否则会造成一方面使用低电压降低了功耗，另一个方面使用额外的接口电路又增加了系统的功耗。或者直接使用支持3V电压的外围芯片。图1 （2）时钟频率 从低功耗的角度看，需要较低的频率，但是在实时应用中为了快速响应外部事件
离散数学知识点总结
离散数学知识点总结 一、各章复习要求与重点 第一章 集 合 [复习知识点] 1、集合、元素、集合的表示方法、子集、空集、全集、集合的包含、相等、幂集 2、集合的交、并、差、补等运算及其运算律（交换律、结合律、分配律、吸收律、 De Morgan 律等），文氏（V enn ）图 3、序偶与迪卡尔积 本章重点内容：集合的概念、集合的运算性质、集合恒等式的证明 [复习要求] 1、理解集合、元素、子集、空集、全集、集合的包含、相等、幂集等基本概念。 2、掌握集合的表示法和集合的交、并、差、补等基本运算。 3、掌握集合运算基本规律，证明集合等式的方法。 4、了解序偶与迪卡尔积的概念，掌握迪卡尔积的运算。 [本章重点习题] P5~6，4、6； P14~15，3、6、7； P20，5、7。 [疑难解析] 1、集合的概念 因为集合的概念学生在中学阶段已经学过，这里只多了一个幂集概念，重点对幂集加以掌握，一是掌握幂集的构成，一是掌握幂集元数为2n 。 2、集合恒等式的证明 通过对集合恒等式证明的练习，既可以加深对集合性质的理解与掌握；又可以为第三章命题逻辑中公式的基本等价式的应用打下良好的基础。实际上，本章做题是一种基本功训练，尤其要求学生重视吸收律和重要等价式在B A B A ~?=-证明中的特殊作用。 [例题分析] 例1 设A ，B 是两个集合，A={1，2，3}，B={1，2}，则=-)()(B A ρρ 。 解 }}3,2,1{},3,2{},3,1{},2,1{},3{},2{},1{,{)(φρ=A }}2,1{},2{},1{,{)(φρ=B 于是}}3,2,1{},3,2{},3,1{},3{{)()(=-B A ρρ
离散数学关系性质的C++或C语言判断实验报告
1.【实验目的】 对称： 通过算法设计并编程实现对给定集合上的关系是否为对称关系的判断，加深学生对关系性质的理解，掌握用矩阵来判断关系性质的方法 自反： 通过算法设计并编程实现对给定集合上的关系是否为自反关系的判断，加深学生对关系性质的理解，掌握用矩阵来判断关系性质的方法。 2.【实验内容】 已知关系R 由关系矩阵M 给出，要求判断由M 表示的这个关系是否为对称关 系。假定R 的关系矩阵为：?????? ? ??=1234210330124321M 3.【实验要求】 C 语言编程实现 4.【算法描述】 对称： 从给定的关系矩阵来判断关系R 是否为对称是很容易的。若M （R 的关系矩阵）为对称矩阵，则R 是对称关系；若M 为反对称矩阵，则R 是反对称关系。因为R 为对称的是等价关系的必要条件，所以，本算法可以作为判等价关系算法的子程序给出。 算法实现： （1） 输入关系矩阵M （M 为n 阶方阵）； （2） 判断对称性，对于i=2，3，….，n ；j=1，2,……，i-1，若存在m ij =m ji ， 则R 是对称的； （3） 判断反对称性； （4） 判断既是对称的又是反对称的； （5） 判断既不是对称的又不是反对称的； （6） 输出判断结果。
自反： 从给定的关系矩阵来断判关系R是否为自反是很容易的。若M（R的关系矩阵）的主对角线元素均为1，则R是自反关系；若M（R的关系矩阵）的主对角线元素均为0，则R是反自反关系；若M（R的关系矩阵）的主对角线元素既有1又有0，则R既不是自反关系也不是反自反关系。本算法可以作为判等价关系算法的子程序给出。 算法实现 （1）输入关系矩阵M（M为n阶方阵）。 （2）判断自反性，对于i=1，2，….，n；若存在m =0，则R不是自反 ii =1，则R是自反的；否则R既不是自反关系也不是的；若存在m ii 反自反关系。 （3）输出判断结果。 源代码 #include
单片机MSP430的极低功耗系统设计
单片机MSP430的极低功耗系统设计
超低功耗系统设计
超低功耗系统设计 学院： 学号： 姓名：
基于MSP430单片机的开关稳压电源设计 MSP430系列单片机是美国TI公司生产的新一代16位单片机，是一种超低功耗的混合信号处理器(MixedSignal Processor)，它具有低电压、超低功耗、强大的处理能力、系统工作稳定、丰富的片内外设、方便开发等优点，具有很高的性价比，在工程控制等领域有着极其广泛的应用范围。开关Boost稳压电源利用开关器件控制、无源磁性元件及电容元件的能量存储特性，从输入电压源获取分离的能量，暂时把能量以磁场的形式存储在电感器中，或以电场的形式存储在电容器中，然后将能量转换到负载。对DC—DC主回路采用Boost升压斩波电路。 2 系统结构和总设计方案 本开关稳压电源是以MSP430F449为主控制器件，它是TI公司生产的16位超低功耗特性的功能强大的单片机，其低功耗的优点有利于系统效率高的要求，且其ADCl2是高精度的12位A／D转换模块，有高速、通用的特点。这里使用MSP430完成电压反馈的PI调节；PWM波产生，基准电压设定；电压电流显示；过电流保护等。 系统框图如图1所示。 3 硬件电路设计 3．1 DC／DC转换电路设计 系统主硬件电路由电源部分、整流滤波电路、DC／DC转换电路、驱动电
路、MSP430单片机等部分组成。交流输入电压经整流滤波电路后经过DC／DC变换器，采用Boost升压斩波电路DC／DC变换，如图2所示： 根据升压斩波电路的工作原理一个周期内电感L积蓄的能量与释放的能量相等，即： 式(1)中I1为输出电流，电感储能的大小通过的电流与电感值有关。在实际电路中电感的参数则与选取开关频率与输入／输出电压要求，根据实际电路的要求选用合适的电感值，且要注意其内阻不应过大，以免其损耗过大减小效率采样电路。对于电容的计算，在指定纹波电压限制下，它的大小的选取主要依据式(2)： 式(2)中：C为电容的值；D1为占空比；TS为MOSFET的开关周期；I0为负载电流；V’为输出电压纹波。 3．2 采样电路 采样电路为电压采集与电流采集电路，采样电路如图3所示。其中P6．O，P6．1为MSP430芯片的采样通道，P6．O为电压采集，P6．1为电流采集。 电压采集因为采样信号要输入单片机MSP430内部，其内部采样基准电压选为2．5 V，因此要将输入的采样电压限制在2．5 V之下，考虑安全裕量则将输入电压限制在2 V以下，当输入电压为36 V时，采样电压为：12／ (12+200)×36=2．04 V，符合要求。 电流采集采用康铜丝进行采集。首先考虑效率问题，康铜丝不能选择过大，同时MSP430基准电压为2．5 V，且所需康铜丝需自制。考虑以上方面在康铜丝阻值选取上约为O．1Ω。 3．3 PWM驱动电路的设计 电力MOSFET驱动功率小，采用三极管驱动即可满足要求，驱动电路如图
离散数学 集合与关系 函数 习题 测验
一、已知A、B、C是三个集合，证明(A∪B)－C＝(A－C)∪(B－C) 证明：因为 x∈(A∪B)－C?x∈(A∪B)－C ?x∈(A∪B)∧x?C ?(x∈A∨x∈B)∧x?C ?(x∈A∧x?C)∨(x∈B∧x?C) ?x∈(A－C)∨x∈(B－C) ?x∈(A－C)∪(B－C) 所以，(A∪B)－C＝(A－C)∪(B－C)。 二、设R={<2，1>，<2，5>，<2，4>，<3，4>，<4，4>，<5，2>}，求r(R)、s(R)和t(R)，并作出它们及R的关系图。 解：r(R)={<2，1>，<2，5>，<2，4>，<3，4>，<4，4>，<5，2>，<1，1>，<2，2>，<3，3>，<4，4>，<5，5>} s(R)={<2，1>，<2，5>，<2，4>，<3，4>，<4，4>，<5，2>，<1，2>，<4，2>，<4，3>} R2=R5={<2，2>，<2，4>，<3，4>，<4，4>，<5，1>，<5，5>，<5，4>} R3={<2，1>，<2，5>，<2，4>，<3，4>，<4，4>，<5，2>，<5，4>} R4={<2，2>，<2，4>，<3，4>，<4，4>，<5，1>，<5，5>，<5，4>} t(R)={<2，1>，<2，5>，<2，4>，<3，4>，<4，4>，<5，2>，<2，2>，<5，1>，<5，4>， <5，5>} 三、证明等价关系 设R是集合A上的一个具有传递和自反性质的关系，T是A上的关系，使得
DSP电源系统的低功耗设计
DSP电源系统的低功耗设计 自从美国TI公司推出通用可编程DSP芯片以来，DSP技术得到了突飞猛进的发展。DSP电源设计是DSP应用系统设计的一个重要组成部分，低功耗是DSP电源系统设计的发展方向。由于DSP一般在系统中要承担大量的实时数据计算，在CPU内部，频繁的部件转换会使系统功耗大大增加，降低DSP内部CPU供电的核电压是降低系统功耗的有效方法，因此TI公司的DSP大多采用低电压供电方式。 从一定程度上说，选择什么样的DSP就决定系统处于什么样的功耗层次。在实际应用中，电源系统直接决定了DSP能否在高性能低功耗的情况下工作，因此，一个稳定而可靠的电源系统是至关重要的。 TI公司最新推出的TPS6229X系列开关电源芯片有两种工作模式：PWM 模式和节能模式。在额定负载电流下，芯片处于PWM模式，高效稳定的为DSP 供电，当负载电流降低时，芯片自动转入节能模式，以减小系统功耗，适宜于DSP系统的低功耗设计，本文主要介绍了该芯片的特点，并给出了基于此芯片的DSP电源电路。 l DSP电源特点 1．1电源要求 TI公司的DSP需要给CPU、FLASH、ADC及I／O等提供双电源供电，分别为1．8V或2．5V核电源和3．3V的I／O电源，每种电源又分为数字电源和模拟电源，即数字1．8V(2．5V)、模拟1．8V(2．5V)，数字3．3V，模拟3．3V。
相对与模拟电源和数字电源，也要求有模拟地和数字地。数字电源与模拟电源单独供电，数字地与模拟地分开，单点连接。 DSP大多采用数字电源供电，可以通过数字电源来获得模拟电源，主要有两种方式：(1)数字电源与模拟电源、数字地与模拟地之间加电感或铁氧体磁珠构成无源滤波网络。铁氧体磁珠在低频时阻抗很低，在高频时很高，可以抑制高频干扰，从而消除数字电路的噪声。(2)采用多路稳压器。方法(1)结构简单，能满足一般的应用要求，方法(2)有更好的去耦效果，但电路复杂成本高。 1．2 供电次序 TI公司DSP采用双电源供电，因此，需要考虑上电、掉电顺序。大部分DSP 芯片要求内核电压先上电，I／O电压后上电。因为如果只有CPU内核获得供电，周边I／O没有供电，对芯片不会产生损害，只是没有输入输出能力而已；如果周边I／O获得供电而CPU内核没有加电，那么DSP缓冲驱动部分的三极管处于未知状态下工作，这是很危险的。但是也有要求I／O电压先上电，内核电压后上电，如TMS320F2812。 在设计不同DSP芯片的电源系统时，要根据其不同的电源特点，否则可能造成整个电源系统的损坏。 2 TPS62290芯片介绍 2．1 芯片特点 TPS62290是TI公司最新推出的高效率同步降压DC／DC转换器，应用于手机、掌上电脑、便携式媒体播放器以及低功耗DSP电源设计中，其主要有以下特点： 输出电流高达1000mA
单片机低功耗设计
单片机系统的低功耗设计策略 摘要：嵌入式系统的低功耗设计需要全面分析各方面因素，统筹规划。在设计之初，各个因素往往是相互制约、相互影响的，一个降低系统功耗的措施有时会带来其他方面的“负效应”。因此，降低系统整体功耗，需要仔细分析和计算。本文从硬件和应用软件设计两个方面，阐述一个以单片机为核心的嵌入式系统低功耗设计时所需考虑的一些问题。 关键词：低功耗设计硬件设计应用软件设计低功耗模式 在嵌入式应用中，系统的功耗越来越受到人们的重视，这一点对于需要电池供电的便携式系统尤其明显。降低系统功耗，延长电池的寿命，就是降低系统的运行成本。对于以单片机为核心的嵌入式应用，系统功耗的最小化需要从软、硬件设计两方面入手。 随着越来越多的嵌入式应用使用了实时操作系统，如何在操作系统层面上降低系统功耗也成为一个值得关注的问题。限于篇幅，本文仅从硬件设计和应用软件设计两个方面讨论。 1 硬件设计 选用具有低功耗特性的单片机可以大大降低系统功耗。可以从供电电压、单片机内部结构设计、系统时钟设计和低功耗模式等几方面考察一款单片机的低功耗特性。 1.1 选用尽量简单的CPU内核 在选择CPU内核时切忌一味追求性能。8位机够用，就没有必要选用16位机，选择的原则应该是“够用就好”。现在单片机的运行速度越来越快，但性能的提升往往带来功耗的增加。一个复杂的CPU集成度高、功能强，但片内晶体管多，总漏电流大，即使进入STOP 状态，漏电流也变得不可忽视；而简单的CPU内核不仅功耗低，成本也低。 1.2 选择低电压供电的系统 降低单片机的供电电压可以有效地降低其功耗。当前，单片机从与TTL兼容的5 V供电降低到3.3 V、3 V、2 V乃至1.8 V供电。供电电压降下来，要归功于半导体工艺的发展。从原来的3 μm工艺到现在的0.25、0.18、0.13 μm工艺，CMOS电路的门限电平阈值不断降低。低电压供电可以大大降低系统的工作电流，但是由于晶体管的尺寸不断减小，管子的漏电流有增大的趋势，这也是对降低功耗不利的一个方面。 目前，单片机系统的电源电压仍以5 V为主，而过去5年中，3 V供电的单片机系统数量增加了1倍，2 V供电的系统也在不断增加。再过五年，低电压供电的单片机数量可能会超过5 V电压供电的单片机。如此看来，供电电压降低将是未来单片机发展的一个重要趋势。 1.3 选择带有低功耗模式的系统 低功耗模式指的是系统的等待和停止模式。处于这类模式下的单片机功耗将大大小于运行模式下的功耗。过去传统的单片机，在运行模式下有wait和stop两条指令，可以使单片机进入等待或停止状态，以达到省电的目的。 等待模式下，CPU停止工作，但系统时钟并不停止，单片机的外围I/O模块也不停止工作；系统功耗一般降低有限，相当于工作模式的50%～70%。 停止模式下，系统时钟也将停止，由外部事件中断重新启动时钟系统时钟，进而唤醒CPU继续工作，CPU消耗电流可降到μA级。在停止模式下，CPU本身实际上已经不消耗什么电流，要想进一步减小系统功耗，就要尽量将单片机的各个I/O模块关掉。随着I/O模块的逐个关闭，系统的功耗越来越小，进入停止模式的深度也越来越深。进入深度停止模式无异于关机，这时的单片机耗电可以小于20 nA。其中特别要提示的是，片内RAM停止供电后，RAM中存储的数据会丢失，也就是说，唤醒CPU后要重新对系统作初始化。因此在让系统进入深度停止状态前，要将重要系统参数保存在非易失性存储器中，如EEPROM中。深度停止模式关掉了所有的I/O，可能的唤醒方式也很有限，一般只能是复位或IRQ中断等。 保留的I/O模块越多，系统允许的唤醒中断源也就越多。单片机的功耗将根据保留唤醒方式的不同，降至1μA至几十μA之间。例如，用户可以保留外部键盘中断，保留异步串行
SoC系统的低功耗设计
SoC系统的低功耗设计 摘要：功耗问题正日益变成VLSI系统实现的一个限制因素。对便携式应用来说，其主要原因在于电池寿命，对固定应用则在于最高工作温度。由于电子系统设计的复杂度在日益提高，导致系统的功耗得到其主要功耗成分。其次，以该主要功耗成分数学表达式为依据，突出实现SoC低功耗设计的各种级别层次的不同方法。 关键词：VLSI SoC CMOS集成电路低功耗设计 引言 从20世纪80年代初到90年代初的10年里，微电子领域的很多研究工作都集中到了数 字系统速度的提高上，现如今的技术拥有的计算能力能够使强大的个人工作站、复杂实时语音和图像识别的多媒体计算机的实现 成为可能。高速的计算能力对于百姓大众来说是触指可及的，不像早些年代那样只为少数人服务。另外，用户希望在任何地方都能
访问到这种计算能力，而不是被一个有线的物理网络所束缚。便携能力对产品的尺寸、重量和功耗加上严格的要求。由于传统的镍铬电池每磅仅能提供的能量，因而功耗就变得尤为重要。电池技术正在改进，每5年最大能将电池的性能提高30%，然而其不可能在短期内显着地解决现在正遇到的功耗问题。 虽然传统可便携数字应用的支柱技术已经 成功地用于低功耗、低性能的产品上，诸如电子手表、袖珍计算器等等，但是有很多低功耗、高性能可便携的应用一直在增长。例如，笔记本计算机就代表了计算机工业里增长最快的部分。它们要求与桌上计算机一样具有同样的计算能力。同样的要求在个人通信领域也正在迅速地发展，如采用了复杂语音编解码算法和无线电调制解调器的带袖 珍通信终端的新一代数字蜂窝网。已提出的未来个人通信服务PCS应用对这些要求尤其明显，通用可便携多媒体服务是要支持完整的数字语音和图像辨别处理的。在这些应用中，不仅语音，而且数据也要能在无线链路
离散数学作业1_集合与关系答案
离散数学作业1_集合与关系 1. 设A、B、C为任意三个集合，判断下列命题的真与假。如命题为真，则证明之；否则，举反例说明。 （1）若A?C=B?C，则A=B(假命题) （2）若A?C=B?C ，则A=B(假命题) （3）若A?C=B?C 且A?C=B?C ，则A=B (真命题,参考ppt 1.2节例8) 2.证明A-B=A∩~B. 证明思路：任取x∈A-B?……? x∈A∩~B 证明：任取x∈A-B?x∈A且x/∈B（根据相对补的定义） ? x∈A且x∈~B(根据绝对补的定义) ? x∈A∩~B 3. 设A={1，2，3，4，5，6},下面各式定义的R都是A上的二元关系。试分别以序偶、关系矩阵、关系图三种形式分别写出R。 (1) R={
>,<6,1>,<6,2>,<6,3>,<6,6>} (3) R={<1,2>,<1,3>,<2,1>,<2,3>,<2,4>,<3,2>,<3,4>,<3,1>,<3,5>,<4,3 >,<4,5>,<4,2>,<4,6>,<5,4>,<5,6>,<5,3>,<6,5>,<6,4>} (4) 质数又称素数。指在一个大于1的自然数中，除了1和此整数自身外，不能被其他自然数整除的数。 100以内的质数有2，3，5，7，11，13，17，19，23，29，31，37，41，43，47，53，59，61，67，71，73，79，83，89，97，在100内共有25个质数。 注：1既不是质数也不是合数。因为它的约数有且只有1这一个约数。 R={<2,1>,<3,1>,<4,2>,<5,1>,<6,2>,<6,3>} 4. 设R是A到B的二元关系，证明：对于A的任意子集A1和A2, R(A1∩A2) = R(A1)∩R(A2)当且仅当? a∈A,b∈A,且a≠b有R(a)∩R(b) = Φ. 证明(1)先证充分性（由后推前）即已知 ? a∈A， b∈A ，有R(a)∩R(b) = Φ， 目的是证明对于A的任意子集A1和A2, 有 R(A1∩A2) = R(A1)∩R(A2) （下面通过证明R(A1∩A2) ?R(A1)∩R(A2)，以及R(A1)∩R(A2) ? R(A1∩A2)）
MSP430低功耗设计大作业
MSP430低功耗设计大作业
MSP430低功耗设计 1.MSP430单片机有几种工作模式，在中断子程序中如何设置，可以使系统从LPM4 模式进入活动模式。 答：五种低功耗功耗模式，分别为LPM0~LPM4；cpu的活动状态成为AM. LPM0模式：关闭CPU；LPM1、LPM2模式：通过开启、关闭不同时钟源控制系统功耗；LPM3模式：时钟开启时的最低功耗模式，仅低频时钟处于运行状态。Lpm4模式工作时只保存RAM区数据，CPU只能通过I／O口外部中断唤醒。在主函数中进入休眠模式并打开总中断，然后在中断程序里面执行你想要的操作就可以了。 2看门狗用于看门狗监测的原理是什么？ 答：工作原理是在系统运行以后也就启动了看门狗的计数器，看门狗就开始自动计数，如果到了一定的时间还不去清看门狗，那么看门狗计数器就会溢出从而引起看门狗中断，造成系统复位。所以，在使用有看门狗的芯片时要注意清看门狗。在由单片机构成的微型计算机系统中,由于单片机的工作常常会受到来自外界电磁场的干扰,造成程序的跑飞,而陷入死循环,程序的正常运行被打断,由单片机控制的系统无法继续工作,会造成整个系统的陷入停滞状态,发生不可预料的后果,所以出于对单片机运行状态进行实时监测的考虑,便产生了一种专门用于监测单片机程序运行状态的芯片,俗称"看门狗"看门狗电路的应用,使单片机可以在无人状态下实现连续工作,其工作原理是:看门狗芯片和单片机的一个I/O引脚相连,该I/O引脚通过程序控制它定时地往看门狗的这个引脚上送入高电平(或低电平),这一程序语句是分散地放在单片机其他控制语句中间的，一旦单片机由于干扰造成程序跑飞后而陷入某一程序段不进入死循环状态时,写看门狗引脚的程序便不能被执行,这个时候,看门狗电路就会由于得不到单片机送来的信号,便在它和单片机复位引脚相连的引脚上送出一个复位信号,使单片机发生复位,即程序从程序存储器的起始位置开始执行,这样便实现了单片机的自动复位。 3.捕获/比较寄存器CCR0有什么特殊性？ 答：用做捕获时：捕获的同时TAR的值会传给CCRx，用来测算周期是很好的方法，一般捕获用法时无须设置参数。 用作比较时：CCR0一般用来设置输出电平的转换时机，就是TAR计数到CCR0时输出电平发生相应的变化（输出方式可以设置）；也可以将CCR0设置为最大值，此时CCRx（x：1或2）用来设置输出电平转换的时机，即TAR计数到CCRx 时输出电平转换，计数到CCR0时重新开始计数。 4.定时器A工作于捕获，比较，定时方式时，中断标志在什么情况下置位？ 捕捉：看你如何设定的控制寄存器，上一个上升沿捕捉还是一个下降沿捕捉还是多个上升沿捕捉，捕捉到了中断标志置位。 比较：当定时器的值（随系统运行在不断的加1）和比较寄存器的值相同的时候，中断标志置位 定时：定时器值溢出（从全1变成全0）的时候中断标志置位。
离散数学作业2_集合与关系答案
离散数学作业2_集合与关系 1. 设A={1,2,3,4,5}，R是集合A上的二元关系，aRb当且仅当a
2. 设A={a,b,c}, R={
系统低功耗设计
系统低功耗设计 论文关键词：集成电路低功耗设计SoC 论文摘要：功耗问题正日益变成VLSI系统实现的一个限制因素。对 便携式应用来说，其主要原因在于电池寿命，对固定应用则在于最高 工作温度。因为电子系统设计的复杂度在日益提升，导致系统的功耗 得到其主要功耗成分。其次，以该主要功耗成分数学表达式为依据， 突出实现SoC低功耗设计的各种级别层次的不同方法。 引言 从20世纪80年代初到90年代初的10年里，微电子领域的很多研究 工作都集中到了数字系统速度的提升上，现如今的技术拥有的计算水 平能够使强大的个人工作站、复杂实时语音和图像识别的多媒体计算 机的实现成为可能。高速的计算水平对于百姓大众来说是触指可及的，不像早些年代那样只为少数人服务。另外，用户希望在任何地方都能 访问到这种计算水平，而不是被一个有线的物理网络所束缚。便携水 平对产品的尺寸、重量和功耗加上严格的要求。因为传统的镍铬电池 每磅仅能提供20W.h的能量，因而功耗就变得尤为重要。电池技术正 在改进，每5年最大能将电池的性能提升30%，不过其不可能在短期内显著地解决现在正遇到的功耗问题。 虽然传统可便携数字应用的支柱技术已经成功地用于低功耗、低性能 的产品上，诸如电子手表、袖珍计算器等等，但是有很多低功耗、高 性能可便携的应用一直在增长。例如，笔记本计算机就代表了计算机 工业里增长最快的部分。它们要求与桌上计算机一样具有同样的计算 水平。同样的要求在个人通信领域也正在迅速地发展，如采用了复杂 语音编解码算法和无线电调制解调器的带袖珍通信终端的新一代数字 蜂窝网。已提出的未来个人通信服务PCS （PersonalCommunicationServices）应用对这些要求尤其明显，通用 可便携多媒体服务是要支持完整的数字语音和图像辨别处理的。在这 些应用中，不但语音，而且数据也要能在无线链路上传输。这就为实
离散数学作业6_集合与关系答案
离散数学作业 作业6 ——等价关系 1. 设R和S均为A上的等价关系，确定下列各式，哪些是A上的等价关系？如果是，证明之；否则，举反例说明。 （1）R∩S （2）R∪S （3）r (R-S) （4）R- S （5）R?S （6）R2 解：(1),(6)正确，其余错误。 2. R是集合A上的二元关系， a,b,c ,若aRb,且bRc,有cRb,则称R是循环关系。证明R是自反和循环的，当且仅当R是一等价关系。 分析: 需要证明两部分: (1)已知R是自反和循环的，证明:R是一等价关系 (2)已知R是一等价关系, 证明R是自反和循环的. 证明：（1）先证必要性。只需要证明R是对陈的和传递的。 任取(x,y)∈R。因为R是自反的，所以(y,y)∈R。由R是循环的可得(y,x)∈R，即R是对陈的。 任取(x,y)，(y,z)∈R。因R是循环的，所以(z,x)∈R。由R对称性得(x,z)∈R，即R是传递的。 （2）证充分性。只需要证明R是循环的。任取(x,y)，(y,z)∈R，下证(z,x)∈R。由于R是传递的，所以(x,z)∈R。又由R是对称的得(z,x)∈R。所以R是循环的。 3. 设|A|=n，在A上可以确定多少个不同的等价关系？ 解：2n!/((n+1)n!n!)
4. 给定集合S={ 1 , 2 , 3, 4, 5 }，找出S 上的等价关系R ，此关系R 能够产生划分{{1，2}，{3}，{4，5}}，并画出关系图。 解：{(1,2),(2,1),(4,5),(5,4)}S R I =? 5. 设A={1，2，3，4，5}。R 是集合A 上的二元关系，其关系矩阵如下图所示。求包含R 的最小等价关系和该等价关系所确定的划分。 ????????????????=0010001000 000000101000001R M 分析: 可以证明tsr(R)是包含R 的最小等价关系. 解：包含R 的最小等价关系的矩阵表示如下： 100000 1010001010 101000101?? ? ? ? ? ? ??? 上述等价关系确定的划分为{{1},{2,4},{3,5}}. 6. 自学华氏(WalShall)算法，写出算法的基本概念、基本步骤和一个 求解传递闭包的具体实例，并可清晰讲解算法整体实现过程。 7. （选做题）设R 与S 是A 上的等价关系，证明： （1）R S 是A 上的等价关系，iff R S=S R ； （2）R ∪S 是A 上的等价关系，if R S ?S 且 S R ?R. 分析: iff 是if and only if 的缩写, 是当且仅当的意思. 证明：（1）先证必要性。任取(x,z)∈R S ，则存在y 使得xRy,ySz 。因为R 与S 是A 上的等价关系，所以R 与S 是对陈的，即yRx,zSy,所以