英语翻译(e) (0 Fig.3.The zero-crossing points may be of the following types.(a) Ellip-tic.(b) Hyperbolic.(c) Parabolic.The zero-crossing lines may be of the following types.(d) Elliptic umbilic.(e) Hyperbolic umbilic.(f) Para-bolic umbilic.where

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英语翻译(e)(0Fig.3.Thezero-crossingpointsmaybeofthefollowingtypes.(a)Ellip-tic.(b)Hyperbolic.(c)Paraboli

英语翻译(e) (0 Fig.3.The zero-crossing points may be of the following types.(a) Ellip-tic.(b) Hyperbolic.(c) Parabolic.The zero-crossing lines may be of the following types.(d) Elliptic umbilic.(e) Hyperbolic umbilic.(f) Para-bolic umbilic.where
英语翻译
(e) (0 Fig.3.The zero-crossing points may be of the following types.(a) Ellip-tic.(b) Hyperbolic.(c) Parabolic.The zero-crossing lines may be of the
following types.(d) Elliptic umbilic.(e) Hyperbolic umbilic.(f) Para-bolic umbilic.
where the coefficients a,
{3,
j,and 0
are obtained by the Taylor expansion.It is easy to see that the set of points
The ZC lines may be a) an elliptic umbilic,if RA consists of three lines [see Fig.2(d)],b) a hyperbolic.umbilic,ifRA consists of a single real line [see Fig.2(e)] ,c) a parabolic umbilic,if RA consists of three lines,two of which are coincident [see Fig.2(f)],d) a symbolic umbilic,if RA consists of three coin-cident lines.5) If h(x,y) is a smooth function and in P
hex,y) depends on the fourth-order terms,the ZC lines have a complex shape that can be analyzed using results of [42].
Bifurcations of Zero Crossings:The isotopy theorem [50],[1] shows that transversal intersections are structur-ally stable,i.e.,that "transversal zero-crossings" are structurally stable:their topological properties do not change if the size (and thus the scale) of the filter is slightly changed.
If f(x,y) is a Morse function then Sf may meet So non-
elliptic Z.c.
(b) Fig.4.The two types of bifurcations that can occur for incre~sing
and
decreasing a in the case of Morse functions.(a) Left to right.(b) Right to left.
transverally,and these intersections are not structurally stable (observe that Morse functions are structurally sta-ble but not their intersections with So),If f is a Morse function,then Sf may meet So nontransversally at elliptic points and hyperbolic points.These intersections are not structurally stable and may change their topological prop-erties for small perturbations of f.More specifically,we may have two bifurcations:
a) Elliptic ZC:At elliptic ZC,a small perturbation of f may lead to the disappearance of the ZC or to the appearance of a contour of ZC constituted by a closed curve.

英语翻译(e) (0 Fig.3.The zero-crossing points may be of the following types.(a) Ellip-tic.(b) Hyperbolic.(c) Parabolic.The zero-crossing lines may be of the following types.(d) Elliptic umbilic.(e) Hyperbolic umbilic.(f) Para-bolic umbilic.where
(e) (0.3.零相交点也许是以下类型.(a)椭圆.(b)双曲线.(c)抛物面.零相交线也许是以下类型.(d)椭圆umbilic.(e)双曲线中心的.(f)抛物面中心的.那里系数a,{3,j和0由泰勒扩展获得.看套点是容易的 ZC线也许是a)一椭圆中心的,如果镭包括三条线[看见.2 (d)]b) 双曲线的.中心的,ifRA包括一条唯一真正的线[看见.2 (e)] c)一抛物面中心的,如果镭包括三条线,二,其中是一致的[看见.2 (f)]d)一符号中心的,如果镭包括三条一致线.5) 如果h (x,y)是一个光滑的作用和在P不吉利的东西,y)取决于四秩序期限,ZC线有能使用结果被分析的复杂形状[42].零相交的叉路：同位定理[50],[1]表示,横截交叉点结构地是槽枥,即,“横截零相交”结构地是槽枥：他们的拓扑学物产不改变,如果轻微地改变大小(和因而标度)过滤器.如果f (x,y)是莫尔斯作用那么Sf也许遇见那么非椭圆Z.c.(b).4.可能为增加和减少a发生在莫尔斯情况下叉路的二个类型起作用.(a)左到右.(b)右到左.横向地和这些交叉点不结构地是槽枥(观察莫尔斯作用结构地是槽枥,但没有他们的交叉点与如此),如果f是莫尔斯作用,然后Sf也许见面那么非横向地在椭圆点和双曲线点.这些交叉点不结构地是槽枥,并且也许改变他们的拓扑学物产为f.的小扰动.更加具体地,我们也许有二叉路：a) 椭圆ZC ：在椭圆ZC,f的小扰动也许导致ZC的失踪或ZC等高的出现闭合的曲线构成的.

(e)(0图3。这个过零分以下几种可能的。(一)。Ellip-tic。(b)。拟线性双曲型。(c)。抛物线。这个范围可能的线条
下列类型。(d)。umbilic椭圆形。(e)。umbilic双曲型。(f)。Para-bolic umbilic。
一、在系数。
{ 3,
j和0
由泰勒展开。很容易看出点
线条的可能)ZC椭圆um...

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(e)(0图3。这个过零分以下几种可能的。(一)。Ellip-tic。(b)。拟线性双曲型。(c)。抛物线。这个范围可能的线条
下列类型。(d)。umbilic椭圆形。(e)。umbilic双曲型。(f)。Para-bolic umbilic。
一、在系数。
{ 3,
j和0
由泰勒展开。很容易看出点
线条的可能)ZC椭圆umbilic,如果RA由三行(见图2(d)],b),ifRA hyperbolic.umbilic由单一的实际线路(见图2(e)],c)抛物面umbilic,如果RA由三部分,其中两线(见图相;2(f)],d)一个象征性的umbilic,如果RA由三个coin-cident线。五)。如果h(x,y)是平滑函数,在P
十六进制,y)取决于阶条件,有ZC复杂形状,可以用分析结果的[42]。
分支的通道:isotopy定理为零(约50]、[1]表明断面的structur-ally交叉口是稳定的,即“横向zero-crossings”是其拓扑结构的稳定:如果不改变,因此规模(略)滤波器的改变。
如果f(x,y)是一种功能就可以满足莫尔和非如此科幻小说
Z.c椭圆形。
(b)图4。这两种类型的分支,就会对财产重估增值~唱歌
,
减少了在电码功能。(一)。从左到右。(b)。从右到左。
transverally,这些交叉口是不稳定的结构功能(观察sta-ble莫尔而不是他们的十字路口上如此),如果是,那么一莫尔功能可能遇到这样nontransversally科幻小说在椭圆积分和双曲线分。这些交叉口是不稳定的,可以改变他们结构拓扑prop-erties为小的动摇。更确切地说,我们可以有两个分支。
一)椭圆形ZC:在椭圆ZC型,一个小扰动的f可能导致的消失或外观ZC轮廓所组成的一个封闭曲线ZC。

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英语翻译(e) (0 Fig.3.The zero-crossing points may be of the following types.(a) Ellip-tic.(b) Hyperbolic.(c) Parabolic.The zero-crossing lines may be of the following types.(d) Elliptic umbilic.(e) Hyperbolic umbilic.(f) Para-bolic umbilic.where 英语翻译The thermal stability tests for stainless steel support after anodic oxidation process is reported in Fig.3.The microphotographs in Fig.3 show an obvious difference as compared with in Fig.2.It is worth noting,the abnormity and multiangul 英语翻译the average length of the dispersed clay particles,andhence the aspect ratio.Fig.81 represents thedependence of the tensile modulus E measured at120 8C for exfoliated N6 nanocomposites with variousclay content,obtained by the in situ inte 英语翻译Unpacking(models WMN 642M)1.remove back panel screws and lift panel clear(Fig.A)2.Remove fixing screws from the four brackets to cross bearing (Fig.B) and remove brackets.3.Fix back panel with 3 screws previously removed (Fig.C)4.Close th 英语翻译FIG.2 illustrates a crosssectional view of the packaged IC of FIG.1 at a stage in processing inaccordance with one embodiment of the present disclosure. 英语翻译in fig .1-7c all voltages are marked in the -to+sense in going clockwise around the loop.the voltmeters are connected as shown in fig.1-7d to measure voltages u'1,u'2and u'3.nothing that the voltmeter readings are the same as the variable 英语翻译3.Results and discussion3.1.Water uptake and diffusion coefficientsGravimetric results are presented in Fig.1 were the frac-tional amount of water is plotted against t1/2.In Fig.2,the water content measured by FT-NIR for the different sam 英语翻译Fig.11a shows the velocity profiles of the plane parallel to thejet axis (x–y plane) at z = 0 between streamwise distance,x of 0.1and 1.3 m with an increment of every 0.1 m.Fig.11a shows theevolution of the jet velocity profile and its 问一句英语翻译：the data from two-class categories with a Gaussian distribution are shown in Fig.1 the healing garden ORGANICS FIG $LAVENDER 是什么 英语翻译Experimental results for the magnetic coupling can be seenin Fig.10 where both the load disturbance and torsion angleerrors are corrected for a load-side set-point position-referenced system.Although the results shown in Fig.10 show fast 英语翻译The adsorption of RB21 was independent on the interaction of RR195 in binary solution 50,100 and 150mgL−1 of RR195,as shown in Fig.3. 英语翻译The development of pig embryos originatingfrom enucleolated oocytes arrested after afew cleavages (Table 1 and Fig.3A).In contrast,embryos from sham-operated oocytesdeveloped to blastocysts with detectable nucleoli(fig.S8,Pig).The cleavag 英语翻译The result of DME combustionwithout catalyst is shown inFig.S1 (Supplementary data,Fig.S1),whichindicates that thehomogeneous oxidation startsafter 200 °C and the temperaturefor complete conversion is higherthan 525 °C.Fig.1 and Table 1 英语翻译Both figures show that the system can effectively analyze water quality.Fig.5 shows that the measured water quality remained well below the warning line (i.e.,the COD level at which additional water must be released to maintain water qual 英语翻译Fig.3.Spectral response of microfiber coupler:Transmission spectra of the MFC at (a) output port3 and (b) port4 for different MFC outer diameters during a single taper fabrication process.Both higher-order modes filtering effect [refer to 英语翻译A typical passenger car of today contains more than 15000separate,individual parts that must work together.These parts can be grouped into four into major categories:engine ,body,chassis and electrical equipment,rederredto Fig.1-3.The eng 英语翻译2.2.Test schemeTwo types of strengthened beams,i.e.a single layer strengthening and a double layer strengthening,and three lengths of CFRP,i.e.0.6,1.2 and 1.6 m are considered.Fibres are used at the bottom of beams and are shown in Fig.3(