formulasearchengine - User contributions [en]

Correlation attack

2014-10-05T20:46:59Z

92.225.65.152: /* Example */

After 30 minutes of [http://www.quora.com/What-is-financial-spread-betting learn spread betting] frantic searching, I found my iPhone. Under four inches of standard water. In a pond. Sunken deep in the sandy bottom. Account of how it got there isn't all that interesting - it involves chasing a squealing toddler running toward water's edge - I never even heard the quiet sploosh at the time, when the phone slipped out of my pocket somehow, and into the water. But the horror I felt seeing the shiny little Apple logo glinting in the morning sun beneath the rippling surface region I won't soon forget. My blackberry. Destroyed. Social media is a long game as well as need in order to patient. It requires time create a brand, but as a result of reach of social media, once you have your name out there, it's very difficult to hold back the floodgates! (If put it into practice properly). Give helpful considerations on your niche, interact with normal folks and will certainly go some way to building and establishing your label. You should and must put up at least one video on youtube with a hyperlink back to homepage the brand new opt-in litter box. Tons of people who search online use YouTube to search - indicates that that despite the fact that you're on Google, when search on youtube and must have a video, these people going to discover a you. This really is a free service possibly! Take a backseat together following. Don't get me wrong, leaders need followers. Followers also need leaders that take a stand. I've been ridiculed for chasing the small fish and not the big ones. Allow me to tell that you just little secret; there are lots more little fish than big. I'm taking new people excited by Internet marketing and making them mini-marketers very first. That is one reason so busting fail in the profession. (no marketing skills) I am reversing couple of. "Rico Suave"- Gerardo (1991). The only good this specific song would be a shirtless Gerardo in film. The boy was smokin' sweltering. But the song? Oh my, so bad. So very, very bad. The magic flute can be a Mozart's safari. The Queen of the flute's arias are known to be really harder to sing. Just try to sing it correctly a regarding people will share your video their own friends. After you've determined the businesses that complement with your needs, review their execute. Every video production company must video projects that you view on your website. Analyze their levels.what do you like about their work? Create a list and interview businesses. Ask who'll be your point person for this project. Ask to talk to their prospective buyers. In closing, anyone who thought this particular video is dumb or childish or simply just plain inappropriate, please find it again & think concerning what I've crafted. Look at all of the faces as they dance about the isle. At all of the guests faces that come into focus at their wedding. The time saving benefits they feel just watching it, for some, even if it's just thinking concerning at the time, them to be witnesses on the beginning of their new life - magic that was celebrated with splendor not somberness. Congratulations to the pair. Have a Joyful life together!

Farrell–Jones conjecture

2013-10-05T10:50:19Z

92.225.119.115: /* Inheritances of isomorphism conjectures */

{{refimprove|date=January 2009}}
'''Scanning SQUID microscopy''' is a technique where a [[superconducting quantum interference device]] (SQUID) is used to image surface magnetic field strength with micrometre scale resolution. A tiny SQUID is mounted onto a tip which is then rastered near the surface of the sample to be measured. As the SQUID is the most sensitive detector of magnetic fields available and can be constructed at submicrometre widths via lithography, the scanning SQUID microscope allows magnetic fields to be measured with unparalleled resolution and sensitivity. The first scanning SQUID microscope was built in 1992 by Black ''et al.''.<ref>
{{cite journal
|last = Black
|first = R.C.
|coauthors = A. Mathai, and F. C. Wellstood, E. Dantsker, A. H. Miklich, D. T. Nemeth, J. J. Kingston, and J. Clarke
|title= Magnetic microscopy using a liquid nitrogen cooled YBa2Cu3O7 superconducting quantum interference device
|year = 1993
|journal = Appl. Phys. Lett.
|volume = 62
|pages = 2128–2130
|doi=10.1063/1.109448
|issue = 17|bibcode = 1993ApPhL..62.2128B }}</ref> Since then the technique has been used to confirm [[unconventional superconductor|unconventional superconductity]] in several [[high-temperature superconductors]] including [[YBCO]] and [[BSCCO]] compounds.

==Operating Principles==
[[File:DC_SQUID.svg|thumb|200px|Diagram of a DC SQUID. The current <math>I</math> enters and splits into the two paths, each with currents <math>I_a</math> and <math>I_b</math>. The thin barriers on each path are Josephson junctions, which together separate the two superconducting regions. <math>\Phi</math> represents the magnetic flux entering the inside of the DC SQUID loop.]]

The [[Scanning SQUID microscope]] is based upon the thin-film [[Direct current|DC]] SQUID. A DC SQUID consists of superconducting electrodes in a ring pattern connected by two weak-link [[Josephson junctions]] (see figure). Above the [[Superconductors#Superconducting_phase_transition|critical current]] of the Josephson junctions, the idealized difference in [[voltage]] between the electrodes is given by<ref name="Boris2004">{{cite book|title=The SQUID Handbook|editor=J. Clarke and A. I. Braginski|publisher=Wiley-VCH|location=Weinheim|year=2004|volume=Vol. I: Fundamentals and Technology of SQUIDs and SQUID Systems|pages=46–48|isbn=3-527-40229-2|author=Boris Chesca, Reinhold Kleiner, Dieter Koelle}}</ref>

:<math>
\begin{align}
V &= \frac{R}{2}\sqrt{I^2 - I_0^2},\\
&= \frac{R}{2}\left(I^2 - \left( 2I_c\cos\left(\pi\frac{\Phi}{\Phi_0}\right)\right)^2 \right)^\frac{1}{2},
\end{align}
</math>

where ''R'' is the [[Electrical resistance|resistance]] between the electrodes, ''I'' is the [[Electric current|current]], ''I''0 is the maximum [[supercurrent]], ''Ic'' is the critical current of the Josephson junctions, Φ is the total [[magnetic flux]] through the ring, and Φ0 is the [[magnetic flux quantum]].

Hence, a DC SQUID can be used as a flux-to-voltage [[transducer]]. However, as noted by the figure, the voltage across the electrodes oscillates [[sine|sinusoidally]] with respect to the amount of magnetic flux passing through the device. As a result, alone a SQUID can only be used to measure the change in magnetic field from some known value, unless the magnetic field or device size is very small such that Φ < Φ0. To use the DC SQUID to measure standard magnetic fields, one must either count the number of oscillations in the voltage as the field is changed, which is very difficult in practice, or use a separate DC bias magnetic field parallel to the device to maintain a constant voltage and consequently constant magnetic flux through the loop. The strength of the field being measured will then be equal to the strength of the bias magnetic field passing through the SQUID.

Although it is possible to read the DC voltage between the two terminals of the SQUID directly, because noise tends to be a problem in DC measurements, an [[alternating current]] technique is used. In addition to the DC bias magnetic field, an AC magnetic field of constant amplitude, with field strength generating Φ << Φ0, is also emitted in the bias coil. This AC field produces an AC voltage with amplitude proportional to the DC component in the SQUID. The advantage of this technique is that the frequency of the voltage signal can be chosen to be far away from that of any potential noise sources. By using a [[lock-in amplifier]] the device can read only the frequency corresponding to the magnetic field, ignoring many other sources of noise.

==Instrumentation==
As the SQUID material must be superconducting, measurements must be performed at low temperatures. Typically, experiments are carried out below [[liquid helium]] temperature (4.2 K) in a [[helium-3 cryostat|helium-3 refrigerator]] or [[dilution refrigerator]]. However, advances in high-temperature superconductor [[thin-film growth]] have allowed relatively inexpensive [[liquid nitrogen]] cooling to instead be used. It is even possible to measure room-temperature samples by only cooling a high ''Tc'' squid and maintaining thermal separation with the sample. In either case, due to the extreme sensitivity of the SQUID probe to stray magnetic fields, in general some form of [[magnetic shielding]] is used. Most common is a shield made of [[mu-metal]], possibly in combination with a superconducting "can" (all superconductors repel magnetic fields via the [[Meissner effect]]).

The actual SQUID probe is generally made via [[thin-film deposition]] with the SQUID area outlined via [[lithography]]. A wide variety of superconducting materials can be used, but the two most common are [[Niobium]], due to its relatively good resistance to damage from [[thermal cycling]], and [[YBCO]], for its high ''Tc'' > 77 K and relative ease of deposition compared to other high ''Tc'' superconductors. In either case, a superconductor with critical temperature higher than that of the [[operating temperature]] should be chosen. The SQUID itself can be used as the pickup coil for measuring the magnetic field, in which case the resolution of the device is proportional to the size of the SQUID. However, currents in or near the SQUID generate magnetic fields which are then registered in the coil and can be a source of noise. To reduce this effect it is also possible to make the size of the SQUID itself very small, but attach the device to a larger external superconducting loop located far from the SQUID. The flux through the loop will then be detected and measured, inducing a voltage in the SQUID.

The resolution and sensitivity of the device are both proportional to the size of the SQUID. A smaller device will have greater resolution but less sensitivity. The change in voltage induced is proportional to the [[inductance]] of the device, and limitations in the control of the bias magnetic field as well as electronics issues prevent a perfectly constant voltage from being maintained at all times. However, in practice, the sensitivity in most scanning SQUID microscopes is sufficient for almost any SQUID size for many applications, and therefore the tendency is to make the SQUID as small as possible to enhance resolution. Via [[e-beam lithography]] techniques it is possible to fabricate devices with total area of 1–10 μm2, although devices in the tens to hundreds of square micrometres are more common.

The SQUID itself is mounted onto a [[cantilever]] and operated either in direct contact with or just above the sample surface. The position of the SQUID is usually controlled by some form of electric [[stepping motor]]. Depending on the particular application, different levels of precision may be required in the height of the apparatus. Operating at lower-tip sample distances increases the sensitivity and resolution of the device, but requires more advanced mechanisms in controlling the height of the probe. In addition such devices require extensive [[vibration]] dampening if precise height control is to be maintained.

==Operation==
Operation of a scanning SQUID microscope consists of simply cooling down the probe and sample, and [[rasterisation|raster]]ing the tip across the area where measurements are desired. As the change in voltage corresponding to the measured magnetic field is quite rapid, the strength of the bias magnetic field is typically controlled by feedback electronics. This field strength is then recorded by a computer system that also keeps track of the position of the probe. An optical camera can also be used to track the position of the SQUID with respect to the sample.

==Applications==
The [[Scanning SQUID microscope]] was originally developed for an experiment to test the pairing symmetry of the high-temperature cuprate superconductor YBCO. Standard superconductors are [[isotropic]] with respect to their superconducting properties, that is, for any direction of electron momentum '''k''' in the superconductor, the magnitude of the [[order parameter]] and consequently the superconducting [[energy gap]] will be the same. However, in the high-temperature cuprate superconductors, the order parameter instead follows the equation
Δ('''k''') = Δ0(cos(''kxa'')-cos(''kya'')), meaning that when crossing over any of the [110] directions in momentum space one will observe a sign change in the order parameter. The form of this function is equal to that of the ''l'' = 2 [[spherical harmonic]] function, giving it the name d-wave superconductivity. As the superconducting electrons are described by a single coherent wavefunction, proportional to exp(-''i''φ), where φ is known as the [[phase (waves)|phase]] of the wavefunction, this property can be also interpreted as a phase shift of π under a 90 degree rotation.

This property was exploited by Tsuei ''et al.''.<ref>
{{cite journal
|last = Tsuei
|first = C.C.
|coauthors = J. R. Kirtley, C. C. Chi, Lock See Yu-Jahnes, A. Gupta, T. Shaw, J. Z. Sun, and M. B. Ketchen
|title=Pairing Symmetry and Flux Quantization in a Tricrystal Superconducting Ring of YBa2Cu3O7−δ
|year = 1994
|journal = Phys. Rev. Lett.
|volume = 73
|pages = 593–596
|doi=10.1103/PhysRevLett.73.593
|bibcode=1994PhRvL..73..593T
|issue = 4}}</ref> by manufacturing a series of YBCO ring Josephson junctions which crossed [110] [[Bragg plane]]s of a single YBCO crystal (figure). In a Josephson junction ring the superconducting electrons form a coherent wave function, just as in a superconductor. As the wavefunction must have only one value at each point, the overall phase factor obtained after traversing the entire Josephson circuit must be an integer multiple of 2π, as otherwise, one would obtain a different value of the probability density depending on the number of times one traversed the ring.

In YBCO, upon crossing the [110] planes in momentum (and real) space, the wavefunction will undergo a phase shift of π. Hence if one forms a Josephson ring device where this plane is crossed (2''n''+1), number of times, a phase difference of (2''n''+1)π will be observed between the two junctions. For 2''n'', or even number of crossings, as in B, C, and D, a phase difference of (2''n'')π will be observed. Compared to the case of standard s-wave junctions, where no phase shift is observed, no anomalous effects were expected in the B,C, and D cases, as the single valued property is conserved, but for device A, the system must do something to for the φ=2''n''π condition to be maintained. In the same property behind the scanning SQUID microscope, the phase of the wavefunction is also altered by the amount of magnetic flux passing through the junction, following the relationship Δφ=π(Φ0). As was predicted by Sigrist and Rice,<ref>
{{cite journal
|last = Sigrist
|first = Manfred
|coauthors = T. M. Rice
|title = Paramagnetic Effect in High T c Superconductors -A Hint for d-Wave Superconductivity
|year = 1992
|journal = J. Phys. Soc. Jpn.
|volume = 61
|pages = 4283
|doi=10.1143/JPSJ.61.4283
|issue = 12|bibcode = 1992JPSJ...61.4283S }}</ref> the phase condition can then be maintained in the junction by a spontaneous flux in the junction of value Φ0/2.

Tsuei ''et al.''. used a scanning SQUID microscope to measure the local magnetic field at each of the devices in the figure, and observed a field in ring A approximately equal in magnitude Φ0/2''A'', where ''A'' was the area of the ring. The device observed zero field at B, C, and D. The results provided one of the earliest and most direct experimental confirmations of d-wave pairing in YBCO.

==See also==
* [[Josephson Effect]]
* [[BCS theory]]
* [[Cryogenics|Low-Temperature Physics]]
* [[Scanning SQUID microscope]]

==References==
{{reflist}}

==External links==
* [http://www.kirtleyscientific.com/ John Kirtley], one of the pioneers in scanning SQUID microscopy.
* [http://www.neiu.edu/~pjdolan/Link5/ Design and applications of a scanning SQUID microscope]
* [http://www.csr.umd.edu/csrpage/research/scanningprobe/index.htm Center for Superconductivity Research, University of Maryland]
* [http://www.neocera.com/ Neocera LLC]

[[Category:Measuring instruments]]
[[Category:Superconductivity]]
[[Category:Josephson effect]]
[[Category:Microscopes]]
[[Category:Scanning probe microscopy]]

Hilbert symbol

2013-07-23T01:46:18Z

92.225.79.85:

{{Refimprove|date=March 2013}}
The '''slant height''' of a [[right circular cone]] is the distance from any point on the [[circle]] to the apex of the cone.

The slant height of a cone is given by the formula <math>\sqrt{r^2+h^2}</math>, where <math>r</math> is the [[radius]] of the circle and <math>h</math> is the height of a square

If the [[line segment]] from the center of the circle to its radius is taken as one leg of a [[right triangle]] inscribed within the cone, and the second leg of the triangle runs from the apex of the cone to the center of the circle, then one leg will have length <math>r</math>, another leg will have length <math>h</math>, and by the [[Pythagorean theorem]], <math>r^2+h^2=d^2</math>, and <math>d=\sqrt{r^2+h^2}</math> gives the length of the circle to the apex of the cone. This application is primarily useful in determining the slant height of a cone when given other information regarding the radius or height.

The variety of geometric implications of the slant height has made it a commonly seen factor in the mathematical community for 3-d geometric study.

A cone is defined primarily by three central aspects, with which one can determine any one factor given the other two. They are as follows:
*The vertical height (or altitude) which is the perpendicular distance from the top down to the base.
*The radius of the circular base
*The slant height which is the distance from the top, down the side, to a point on the base circumference.

==References==
*[http://www.mathopenref.com/coneslantheight.html Slant height of a right cone] at Math Open Reference

[[Category:Geometric measurement]]

{{elementary-geometry-stub}}

Grothendieck inequality

2012-05-21T19:08:03Z

92.225.94.222:

Claude is her title and she completely digs that name. The job he's been occupying for many years is a messenger. The favorite pastime for him and his kids is to generate and now he is attempting to make money with it. Arizona has always been my living location but my wife desires us to move. Here is my page; extended car warranty ([http://Xn--H1aecfj6f.Xn--P1ai/content/auto-repair-tips-youll-wish-youd-read-sooner Learn Alot more])