document_title: First appearance

question_text: who came out first batman or spider man

question_tokens: who came out first batman or spider man

text: First appearance

text: Monetary value of first appearance issues[edit]

text: First appearances of popular characters are among the most valuable comic books in existence. Of the "ten most valuable comic books" listed in the spring 2002 issue of The Overstreet Comic Book Price Guide, seven are first appearances of popular superheroes.[1] Another, Marvel Comics #1 (October 1939), is the first appearance of the Golden Age Human Torch but is more noteworthy as the first comic book published by industry giant Marvel Comics.

text: It can take many years for a character to attain sufficient popularity after their first appearance to be considered "iconic." By the point a character reaches that level of popularity, it is common for few copies of their first appearance issues to remain. Furthermore, even fewer of those remaining copies will be in the pristine condition prized by collectors. What few remain can be worth thousands of dollars to interested collectors. For example, in 2004, a copy of Flash Comics #1 (January 1940), the first appearance of The Flash, was auctioned for $42,000[2] and a copy of Captain America Comics #1 (March 1941), the first appearance of Captain America sold for $64,400.[3] In 2010, another copy of Flash Comics #1 sold privately for $450,000.[4]

text: The first appearance of Superman, Action Comics #1 (June 1938), has been regarded as the "holy grail" of comic books, due to its cultural significance and rarity (fewer than one hundred copies are thought to exist).[5] Superman is widely considered to have solidified, if not created, the superhero archetype; therefore, his first appearance is not only important to fans of the character but to fans of superheroes and comic books as a whole.[6] Well-preserved copies of Action Comics #1 have been sold at auction for record-breaking prices. A copy graded at 8.0 ("very fine") on the 10-point scale typically used by collectors was sold at auction for $1,000,000 in 2010.[7] Even a copy graded at a much lower 5.5 ("fine minus") sold for $956,000 in 2016.[5]

text: Shortly after the record-breaking million-dollar sale of Action Comics #1 in 2010, a copy of Detective Comics #27 featuring the first appearance of Batman was sold for $1,075,000 in a Heritage auction.[8]

text: Several factors determine the value of a first appearance. Note: All values are according to ComicsPriceGuide.com and are for editions certified by the Certified Collectibles Group (see below):

text:
The importance of the character(s) that debuted; the first appearance of Spider-Man in very fine condition is listed at $45,150; the first appearance of the less popular Iron Man, in the same condition, is listed at $3,837; and the first appearances of the vast majority of characters are not valued significantly higher than other comics published the same month.
The rarity of comic book itself; comics from the Golden Age are usually more valuable than later comic books because they are older and fewer copies survive. Spider-Man is more popular than The Spectre but Spider-Man’s 1962 first appearance is valued at $45,150 while a copy of The Spectre's 1940 debut, in fine condition, is valued at $54,000. Also, first appearances often lack value if they are relatively recent issues of high-profile, best-selling titles. Except during a 1990s collector’s bubble, the first appearances of several Image Comics characters and newer X-Men have not been as valuable as one may expect for such popular characters because those comics were widely produced.
Other reasons for historical importance; The Fantastic Four (November 1961) #1 is not only the first appearance of the eponymous group but also represents a turning point in the history of Marvel Comics and is the first issue of a long-running series.
Occasionally, a comic book is the first appearance of more than one important character. Usually the characters are related; X-Men #1 (September 1963) introduced the X-Men and their archenemy Magneto.[9] However, rarely a comic book is the first appearance of two unrelated, important characters. More Fun Comics #73 (November 1941) introduced both Green Arrow and Aquaman, who have little relation to one another.[10] This is also the case with Action Comics #1, which contained the first appearances of Zatara and Tex Thomson, as well as Superman.
Occasionally a first appearance will lack the value expected for a character of such stature because the debut was not splashy. Wonder Woman, an immensely popular and historically important hero, debuted in All Star Comics #8 (December 1941) in one of several stories and was not featured on the cover. This issue is valued at $30,000 in fine condition. Comparatively, the first appearances of equally (or even less) important peers Green Lantern and The Flash, boldly introduced on their covers, are worth $131,250 and $69,000, respectively. Arguably, the first appearance of Wonder Woman is worth much less because she did not make a flashy debut that lent the comic book an air of history.
As is the case with all collectibles, condition greatly affects the value of comic books, although considerable wear is expected for decades-old comics. Most comic books are worth more if their condition is certified and they are protectively packaged (or "slabbed") by the Certified Collectibles Group, a professional grading service involved in the sale of most high-value comic books, although some fans accuse the group of inflating the value of comics.[11]

text: Reader interest in first appearances[edit]

text: Collectors value first appearances for their rarity and historical value, while many regular readers are interested in viewing how their favorite characters were originally portrayed. Reprints of first appearances are often published, both as single comic books and in trade paperbacks, usually with other early appearances of the character. Marvel Comics' "Essential" line has become popular by giving readers an affordable glimpse into characters' early history.[12]

text: Historically, first appearances tell the origin story for the character, although some, such as Batman and Green Goblin, remained dubious figures for several issues. Modern writers prefer to tell a character’s origin across an entire story arc or keep a newly introduced character mysterious until a "secret origin" issue. Some fans consider this a gimmick and prefer the older method.[13]

text: The artistic merit of many first appearances is debatable. The events portrayed in most famous first appearances are continuously retconed, rebooted and/or expanded upon by subsequent writers. Like many golden and silver age comics, first appearances often become dated and do not fit the modern portrayal of the character.

text: However, some first appearances are considered classics. 1990s-era Spider-Man writer Howard Mackie said that his favorite story featuring the character was his first appearance and origin story in Amazing Fantasy #15 (August 1962), stating that writer Stan Lee and artist Steve Ditko "gave us everything we needed, I wanted or could ask for in the least possible space. Every single person who retells the origin never improves on the original, they simply expand it."[14]

text: Ambiguity of first appearance[edit]

text: While seemingly a simple concept, determining the first appearance may be complex. The following are instances in which a character’s first appearance may be difficult to determine:

text:
Those unfamiliar to comics may assume that Iron Man’s first appearance is The Invincible Iron Man #1 (May 1968). However, in the golden and early silver ages of comic books, few superheroes debuted in magazines carrying their names. More often a character first appeared in a generically titled anthology series. If the character proved popular, a new series was launched. For example, Iron Man first appeared in Tales of Suspense #39 (March 1963) and appeared regularly in that series for five years before Marvel launched a series properly named Iron Man. Wonder Woman, Spider-Man, The Mighty Thor and many others also first appeared in anthology series.
The first appearance of "all-star" teams is given as the first instance in which that team banded together regardless of whether or not it consists of previously existing characters. The first appearance of The Justice League of America is considered The Brave and the Bold #28 (May 1960), the issue in which they first operated as a group, although none of its members first appeared in that issue. Alternatively, X-Men #1 (September 1963) is both the first appearance of the X-Men and that of each of the team’s original members.
Sometimes a character first appears in the last page of an issue, foreshadowing his or her greater role in the next issue. Arguments can ensue over whether the first appearance is the issue containing the final page cameo or the subsequent issue which more adequately introduced the character. Wolverine was first seen in the last page of The Incredible Hulk #180 (October 1974) but makes a more full appearance in issue #181 (November 1974). Stricter fans may consider The Incredible Hulk #180 Wolverine’s first appearance but most consider it #181. ComicsPriceGuide.com lists a copy of issue #180, rated very fine, at $149 and #181 at $2,075. Comparatively, The Incredible Hulk #179 (September 1974), which has no special importance, is listed at $11, so both types of first appearance add value to a comic book.
Retconning can also complicate first appearances. Initially, Cable was portrayed as a wholly new character, first appearing in The New Mutants #87 (March 1990). However, writers later changed his background, stating that Cable is an adult, time-traveling Nathan Summers, the son of Cyclops and Madelyne Pryor, first seen in Uncanny X-Men #201 (January 1986). Both issues could be given as the first appearance of Cable. Further complicating the matter, Cable was seen in a cameo at the end of The New Mutants #86 (February 1990).
Some superhero identities are used by more than one character. The original Green Lantern first appeared in All-American Comics #16 (April 1940). During the Silver Age, Green Lantern, like many DC heroes, was rebooted with a totally new identity. The second Green Lantern, Hal Jordan, debuted in Showcase #22 (October 1959). All-American Comics #16 is still considered the first appearance of Green Lantern, both of the original title-bearer and the superhero identity itself. To avoid confusion, Showcase #22 is called the first appearance of Hal Jordan, of Green Lantern II or of the Silver Age Green Lantern.
Occasionally, a character will appear in the background of a comic book before fully introduced. Spider-Man’s early love interest Liz Allan is first addressed by name in Amazing Spider-Man #4 (September 1963). However, an unnamed character in Amazing Spider-Man #1 (March 1963) is, based on her appearance and dialogue, probably Allan. Plus, Amazing Fantasy #15 (August 1962), shows an unnamed, unspeaking character who looks exactly like Allan. Thus Allan's first appearance may be given as any of the three.
Some characters appear in more than one continuity. While the first appearance of Nightcrawler is Giant-Size X-Men #1 (May 1975), the first appearance of "Ultimate Nightcrawler" (Nightcrawler in the alternate Ultimate Marvel universe) is Ultimate X-Men #6 (August 2001).
Sometimes new characters are created for television or film adaptations of a franchise and are later added to the comic book continuity. The Batman adversary Harley Quinn debuted in the 1992 Batman: The Animated Series episode "Joker's Favor". Her first appearance in comic format was the graphic novel The Batman Adventures #12, which took place in the continuity of Batman: The Animated Series. Her first appearance in the regular "DC Universe" was the 1999 one-shot Batman: Harley Quinn. Thus her first appearance is technically Joker's Favor, her first appearance in a comic book was The Batman Adventures #12 and her first appearance in the regular DC Comics continuity was Batman: Harley Quinn. Similarly, Firestar first appeared in Spider-Man and His Amazing Friends #1, which adapted the first episode of the TV series. Her first Earth-616 appearance was in The Uncanny X-Men #193.
Rarely, a character debuts in a publisher’s foreign branch and then appears in a domestic series. Psylocke first appeared in Captain Britain #8 (December 1976), an original series of Marvel UK not widely available outside Great Britain. Her debut in an American series was The New Mutants Annual #2 (1986). Her first appearance is sometimes given as either but more correctly it is Captain Britain #8 while The New Mutants Annual #2 is her first US appearance.
Some characters appear first in a normal supporting role before becoming a superhero or villain. For example, Roderick Kingsley first appeared as a minor supporting character in The Spectacular Spider-Man #43 (June 1980). However, he would later take on the villainous role of the Hobgoblin in The Amazing Spider-Man #238 (March 1983), becoming one of Spider-Man's most dangerous foes. The latter issue, featuring his first appearance as the Hobgoblin, is worth quite a bit more than his original debut.

text: First appearances of popular heroes, villains and teams[edit]

text: Note: All values are according to Comics Price Guide. Prices given are for the best available editions. Thus prices of Golden Age comics are for editions in "fine" condition because editions in better condition for such old comics are either extremely rare or have never been confirmed to exist. Prices for Silver Age and subsequent comics are for "very fine" editions. Priced are also for editions graded by the Certified Collectibles Group. Data is correct as of 25 January 2006[update].

text:
Character(s)
First Appearance
Cover Date
Publisher
Estimated Value

Superman
Action Comics #1
June 1938
DC Comics
$2,100,000[1]

Batman
Detective Comics #27
May 1939
DC Comics
$475,000

Sandman (Wesley Dodds)
Adventure Comics #40
July 1939
DC Comics
$60,000

Namor the Sub-Mariner
Marvel Comics #1
October 1939
Timely Comics
$400,000

Jay Garrick/Flash I; Hawkman
Flash Comics #1
January 1940
All-American Pubs.
$95,000

Captain Marvel
Whiz Comics #2
February 1940
Fawcett Comics
$90,000

Robin
Detective Comics #38
May 1940
DC Comics
$75,000

The Spectre
More Fun Comics #52
February 1940
DC Comics
$72,000

Lex Luthor
Action Comics #23
May 1940
DC Comics
$8,025

The Joker; Catwoman
Batman #1
Spring 1940
DC Comics
$160,500[2]

Green Lantern
All-American Comics #16
July 1940
All-American Pubs.
$131,250

Captain America
Captain America Comics #1
March 1941
Timely Comics
$125,250

Aquaman; Green Arrow
More Fun Comics #73
November 1941
DC Comics
$10,050

Wonder Woman
All Star Comics #8
December 1941
All-American Pubs.
$60,000

Barry Allen/Flash II
Showcase #4
October 1956
DC Comics
$48,000[15]

The Justice League of America
The Brave and the Bold #28
May 1960
DC Comics
$8,127

The Fantastic Four
The Fantastic Four #1
November 1961
Marvel Comics
$28,896

The Hulk
The Incredible Hulk #1
May 1962
Marvel Comics
$21,672

Dr. Doom
The Fantastic Four #5
June 1962
Marvel Comics
$4,154

Spider-Man
Amazing Fantasy #15
August 1962
Marvel Comics
$45,150

Iron Man
Tales of Suspense #39
March 1963
Marvel Comics
$3,837

Doctor Strange
Strange Tales #110
July 1963
Marvel Comics
$3,500

X-Men; Magneto
X-Men #1
September 1963
Marvel Comics
$13,545

The Avengers
The Avengers #1
September 1963
Marvel Comics
$5,148

Daredevil
Daredevil #1
April 1964
Marvel Comics
$3,160

Teen Titans
The Brave and the Bold #54
July 1964
DC Comics
$415

The Punisher
The Amazing Spider-Man #129
February 1974
Marvel Comics
$15,000

Wolverine
The Incredible Hulk #181
October 1974
Marvel Comics
$1600

Teenage Mutant Ninja Turtles
Teenage Mutant Ninja Turtles #1
May 1984
Mirage Studios
$2,400


document_title: Reciprocal lattice

question_text: the reciprocal lattice of an fcc crystal is

root

text: Reciprocal lattice

text: Mathematical description[edit]

text: Assuming a two-dimensional Bravais lattice

tag: p

text: Any quantity, e.g. the electronic density in an atomic crystal can be written as a periodic function

text:
Due to the periodicity, it is useful to write

f

{\displaystyle f}

 as a Fourier series

text:
Since

f
(

R

n

+

r

)
=
f

(

R

k

+

r

)

{\displaystyle f(\mathbf {R} _{n}+\mathbf {r} )=f\left(\mathbf {R} _{k}+\mathbf {r} \right)}

 for any

n
,
k
∈

Z

2

{\displaystyle n,k\in \mathbb {Z} ^{2}}

 then the last formula is true for the particular case

R

0

=
0

{\displaystyle \mathbf {R} _{0}=0}

text:
so must be true

e

i

G

m

⋅

R

n

=
1

{\displaystyle e^{i\mathbf {G} _{m}\cdot \mathbf {R} _{n}}=1}

 that means

text:
Mathematically, we can describe the reciprocal lattice as the set of all vectors

G

m

{\displaystyle \mathbf {G} _{m}}

 that satisfy the above identity for all lattice point position vectors R.

text: This reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice, which reveals the Pontryagin duality of their respective vector spaces.

text:
For an infinite two-dimensional lattice, defined by its primitive vectors

(

a

1

,

a

2

)

{\displaystyle \left(\mathbf {a} _{1},\mathbf {a} _{2}\right)}

, its reciprocal lattice can be determined by generating its two reciprocal primitive vectors, through the following formulae,

text: Where,

text:
Here

R

{\displaystyle \mathbf {R} }

 represents a 90 degree rotation matrix.

text:
For an infinite three-dimensional lattice, defined by its primitive vectors

(

a

1

,

a

2

,

a

3

)

{\displaystyle \left(\mathbf {a_{1}} ,\mathbf {a} _{2},\mathbf {a} _{3}\right)}

, its reciprocal lattice can be determined by generating its three reciprocal primitive vectors, through the formulae

text: where

text: Note that the denominator is the scalar triple product. Using column vector representation of (reciprocal) primitive vectors, the formulae above can be rewritten using matrix inversion:

text: This method appeals to the definition, and allows generalization to arbitrary dimensions. The cross product formula dominates introductory materials on crystallography.

text:
The above definition is called the "physics" definition, as the factor of

2
π

{\displaystyle 2\pi }

 comes naturally from the study of periodic structures. An equivalent definition, the "crystallographer's" definition, comes from defining the reciprocal lattice to be

e

2
π
i

K

⋅

R

=
1

{\displaystyle e^{2\pi i\mathbf {K} \cdot \mathbf {R} }=1}

 which changes the definitions of the reciprocal lattice vectors to be

text:
and so on for the other vectors. The crystallographer's definition has the advantage that the definition of

b

1

{\displaystyle \mathbf {b} _{1}}

 is just the reciprocal magnitude of

a

1

{\displaystyle \mathbf {a} _{1}}

 in the direction of

a

2

×

a

3

{\displaystyle \mathbf {a} _{2}\times \mathbf {a} _{3}}

, dropping the factor of

2
π

{\displaystyle 2\pi }

. This can simplify certain mathematical manipulations, and expresses reciprocal lattice dimensions in units of spatial frequency. It is a matter of taste which definition of the lattice is used, as long as the two are not mixed.

text:
Each point

(
h
k
l
)

{\displaystyle (hkl)}

 in the reciprocal lattice corresponds to a set of lattice planes

(
h
k
l
)

{\displaystyle (hkl)}

 in the real space lattice. The direction of the reciprocal lattice vector corresponds to the normal to the real space planes. The magnitude of the reciprocal lattice vector is given in reciprocal length and is equal to the reciprocal of the interplanar spacing of the real space planes.

text: Reciprocal lattices of various crystals[edit]

text: Reciprocal lattices for the cubic crystal system are as follows.

text: Simple cubic lattice[edit]

text:
The simple cubic Bravais lattice, with cubic primitive cell of side

a

{\displaystyle a}

, has for its reciprocal a simple cubic lattice with a cubic primitive cell of side

2
π

a

{\displaystyle \textstyle {\frac {2\pi }{a}}}

 (

1
a

{\displaystyle \textstyle {\frac {1}{a}}}

 in the crystallographer's definition). The cubic lattice is therefore said to be self-dual, having the same symmetry in reciprocal space as in real space.

text: Face-centered cubic (FCC) lattice[edit]

text: The reciprocal lattice to an FCC lattice is the body-centered cubic (BCC) lattice.

text: Consider an FCC compound unit cell. Locate a primitive unit cell of the FCC; i.e., a unit cell with one lattice point. Now take one of the vertices of the primitive unit cell as the origin. Give the basis vectors of the real lattice. Then from the known formulae, you can calculate the basis vectors of the reciprocal lattice. These reciprocal lattice vectors of the FCC represent the basis vectors of a BCC real lattice. Note that the basis vectors of a real BCC lattice and the reciprocal lattice of an FCC resemble each other in direction but not in magnitude.

text: Body-centered cubic (BCC) lattice[edit]

text: The reciprocal lattice to a BCC lattice is the FCC lattice.

text:
It can be easily proven that only the Bravais lattices which have 90 degrees between

(

a

1

,

a

2

,

a

3

)

{\displaystyle \left(\mathbf {a} _{1},\mathbf {a} _{2},\mathbf {a} _{3}\right)}

 (cubic, tetragonal, orthorhombic) have

(

b

1

,

b

2

,

b

3

)

{\displaystyle \left(\mathbf {b} _{1},\mathbf {b} _{2},\mathbf {b} _{3}\right)}

 parallel to their real-space vectors.

text: Simple hexagonal lattice[edit]

text:
The reciprocal to a simple hexagonal Bravais lattice with lattice constants c and a is another simple hexagonal lattice with lattice constants

2
π

c

{\displaystyle \textstyle {\frac {2\pi }{c}}}

 and

4
π

a

3

{\displaystyle \textstyle {\frac {4\pi }{a{\sqrt {3}}}}}

 rotated through 30° about the c axis with respect to the direct lattice. The simple hexagonal lattice is therefore said to be self-dual, having the same symmetry in reciprocal space as in real space.

text: Proof that the reciprocal lattice of the reciprocal lattice is the direct lattice[edit]

text: From its definition we know that the vectors of the Bravais lattice must be closed under vector addition and subtraction. Thus it is sufficient to say that if we have

text: and

text:
then the sum and difference

G

1

±

G

2

{\displaystyle \mathbf {G} _{1}\pm \mathbf {G} _{2}}

 satisfy the same.

text: Thus we have shown the reciprocal lattice is closed under vector addition and subtraction. Furthermore, we know that a vector G in the reciprocal lattice can be expressed as a linear combination of its primitive vectors.

text:
From our earlier definition of

b

1

{\displaystyle \mathbf {b} _{1}}

, we can see that:

text:
where

δ

i
j

{\displaystyle \delta _{ij}}

 is the Kronecker delta. We let R be a vector in the direct lattice, which we can express as a linear combination of its primitive vectors.

text: From this we can see that:

text:
From our definition of the reciprocal lattice we have shown that

G

{\displaystyle \mathbf {G} }

 must satisfy the following identity.

text:
For this to hold we must have

G

⋅

R

{\displaystyle \mathbf {G} \cdot \mathbf {R} }

 equal to

2
π

{\displaystyle 2\pi }

 times an integer. This is fulfilled because

n

i

∈

Z

{\displaystyle n_{i}\in \mathbb {Z} }

 and

k

i

∈

Z

{\displaystyle k_{i}\in \mathbb {Z} }

. Therefore, the reciprocal lattice is also a Bravais lattice.

text:
Furthermore, if the vectors

G

{\displaystyle \mathbf {G} }

 construct a reciprocal lattice, it is clear that any vector

K

{\displaystyle \mathbf {K} }

 satisfying the equation:

text:
… is a reciprocal lattice vector of the reciprocal lattice. Due to the definition of

G

{\displaystyle \mathbf {G} }

, when

K

{\displaystyle \mathbf {K} }

 is the direct lattice vector

R

{\displaystyle \mathbf {R} }

, we have the same relationship.

text: And so we can conclude that the reciprocal lattice of the reciprocal lattice is the original direct lattice.

text: Arbitrary collection of atoms[edit]

text: One path to the reciprocal lattice of an arbitrary collection of atoms comes from the idea of scattered waves in the Fraunhofer (long-distance or lens back-focal-plane) limit as a Huygens-style sum of amplitudes from all points of scattering (in this case from each individual atom).[1] This sum is denoted by the complex amplitude F in the equation below, because it is also the Fourier transform (as a function of spatial frequency or reciprocal distance) of an effective scattering potential in direct space:

text: Here g = q/(2π) is the scattering vector q in crystallographer units, N is the number of atoms, fj[g] is the atomic scattering factor for atom j and scattering vector g, while rj is the vector position of atom j. Note that the Fourier phase depends on one's choice of coordinate origin.

text:
For the special case of an infinite periodic crystal, the scattered amplitude F = M Fhkl from M unit cells (as in the cases above) turns out to be non-zero only for integer values of

(
h
k
l
)

{\displaystyle (hkl)}

, where

text: when there are j=1,m atoms inside the unit cell whose fractional lattice indices are respectively {uj, vj, wj}. To consider effects due to finite crystal size, of course, a shape convolution for each point or the equation above for a finite lattice must be used instead.

text: Whether the array of atoms is finite or infinite, one can also imagine an "intensity reciprocal lattice" I[g], which relates to the amplitude lattice F via the usual relation I = F*F where F* is the complex conjugate of F. Since Fourier transformation is reversible, of course, this act of conversion to intensity tosses out "all except 2nd moment" (i.e. the phase) information. For the case of an arbitrary collection of atoms, the intensity reciprocal lattice is therefore:

text: Here rjk is the vector separation between atom j and atom k. One can also use this to predict the effect of nano-crystallite shape, and subtle changes in beam orientation, on detected diffraction peaks even if in some directions the cluster is only one atom thick. On the down side, scattering calculations using the reciprocal lattice basically consider an incident plane wave. Thus after a first look at reciprocal lattice (kinematic scattering) effects, beam broadening and multiple scattering (i.e. dynamical) effects may be important to consider as well.

text: Generalization of a dual lattice[edit]

text: There are actually two versions in mathematics of the abstract dual lattice concept, for a given lattice L in a real vector space V, of finite dimension.

text: The first, which generalises directly the reciprocal lattice construction, uses Fourier analysis. It may be stated simply in terms of Pontryagin duality. The dual group V^ to V is again a real vector space, and its closed subgroup L^ dual to L turns out to be a lattice in V^. Therefore, L^ is the natural candidate for dual lattice, in a different vector space (of the same dimension).

text: The other aspect is seen in the presence of a quadratic form Q on V; if it is non-degenerate it allows an identification of the dual space V* of V with V. The relation of V* to V is not intrinsic; it depends on a choice of Haar measure (volume element) on V. But given an identification of the two, which is in any case well-defined up to a scalar, the presence of Q allows one to speak to the dual lattice to L while staying within V.

text: In mathematics, the dual lattice of a given lattice L in an abelian locally compact topological group G is the subgroup L∗ of the dual group of G consisting of all continuous characters that are equal to one at each point of L.

text: In discrete mathematics, a lattice is a locally discrete set of points described by all integral linear combinations of dim = n linearly independent vectors in Rn. The dual lattice is then defined by all points in the linear span of the original lattice (typically all of R^n) with the property that an integer results from the inner product with all elements of the original lattice. It follows that the dual of the dual lattice is the original lattice.

text: Furthermore, if we allow the matrix B to have columns as the linearly independent vectors that describe the lattice, then the matrix

text:
A
=
B

(

B

T

B

)

−
1

{\displaystyle A=B\left(B^{\mathsf {T}}B\right)^{-1}}

 has columns of vectors that describe the dual lattice.

text: Reciprocal space[edit]

text:
Reciprocal space (also called "k-space") is the space in which the Fourier transform of a spatial function is represented (similarly the frequency domain is the space in which the Fourier transform of a time dependent function is represented). A Fourier transform takes us from "real space" to reciprocal space or vice versa. Reciprocal space comes into play regarding wave-mechanics: As a plane wave can be written by an oscillatory term

e

i
(
k
x
−
ω
t
)

{\displaystyle e^{i(kx-\omega t)}}

 with wave vector

k

{\displaystyle k}

 and angular frequency

ω

{\displaystyle \omega }

, it can be regarded as both a function of

k

{\displaystyle k}

 and

x

{\displaystyle x}

 (and the spectroscopic part as a function of both

ω

{\displaystyle \omega }

 and

t

{\displaystyle t}

). In space, the periodicity oscillates with

k
x
=
2
π

{\displaystyle kx=2\pi }

 - therefore for a given phase,

k

{\displaystyle k}

 and

x

{\displaystyle x}

 are reciprocal to each other:

k
=
2
π

/

x

{\displaystyle k=2\pi /x}

 and

x
=
2
π

/

k

{\displaystyle x=2\pi /k}

.

text:
A reciprocal lattice is a periodic set of points in this space, and contains the

k
→

{\displaystyle {\vec {k}}}

 points that compose the Fourier transform of a periodic spatial lattice. The Brillouin zone is a volume within this space that contains all the unique k-vectors that represent the periodicity of classical or quantum waves allowed in a periodic structure.


document_title: Ceiba speciosa

question_text: south african tree with thorns on the trunk

text: Ceiba speciosa

text: Description[edit]

text: The natural habitat of the silk floss tree is the north-east of Argentina, east of Bolivia, Paraguay, Uruguay and southern Brazil. It is resistant to drought and moderate cold. It grows fast in spurts when water is abundant, and sometimes reaches more than 25 metres (82 ft) in height. Its trunk is bottle-shaped, generally bulging in its lower third, measuring up to 2 metres (7 ft) in girth. The trunk is also studded with thick, sharp conical prickles which deter wild animals from climbing the trees. In younger trees, the trunk is green due to its high chlorophyll content, which makes it capable of performing photosynthesis when leaves are absent; with age it turns to gray.[3]

text: Leaves, stems, and flowers[edit]

text: The branches tend to be horizontal and are also covered with prickles. The leaves are composed of five to seven long leaflets. The flowers are creamy-whitish in the center and pink towards the tips of their five petals. They measure 10 to 15 centimetres (4 to 6 in) in diameter and their shape is superficially similar to hibiscus flowers. Their nectar is known to attract insect pollinators, as well as hummingbirds.[4] C. speciosa flowers are in bloom between February and May (in its native Southern Hemisphere), but can also bloom at other times of the year. The flowers of the related C. chodatii are similar in form and size, but their color goes from creamy white centers to yellow tips.[3] As a deciduous tree, it is completely bare of leaves and flowers during the winter months, especially when growing outside of its native South America habitat.

text: Fruits[edit]

text: The fruits are lignous ovoid capsules, 20 centimetres (8 in) long, which contain bean-sized black seeds surrounded by a mass of fibrous, fluffy matter reminiscent of cotton or silk.[3]

text: Uses[edit]

text: The cotton inside the capsules, although not of as good quality as that of the kapok tree, has been used as stuffing f(density = 0.27 g/cm³). The wood can be used to make canoes, as wood pulp, and to make paper. The bark has been used to make ropes. From the seeds it is possible to obtain vegetable oil (both edible and industrially useful).

text: The silk floss tree is cultivated mostly for ornamental purposes. Outside of private gardens around the world, it is often planted along urban streets in subtropical areas such as in Spain, South Africa, Australia, northern New Zealand and the southern USA, although its prickled trunks and limbs require safety buffer zones, especially around the trunks, in order to protect people and domesticated animals from its prickles. Ceiba speciosa is added to some versions of the hallucinogenic drink Ayahuasca.

text: Gallery[edit]

text:
Flower.

Flowered pink specimen, in a road at Mogi-Mirim, near São Paulo, Brazil.

An open fruit pod, displaying the silk-like fibers that give the tree its name, Silk Floss Tree.

Detail of the thorny trunk.

Swollen trunk.

Cultivated mature specimen at Huntington Library and Botanical Garden.

tag: ul


document_title: UCLA–USC rivalry

question_text: where is the ucla usc game being played

question_tokens: where is the ucla usc game being played

text: UCLA–USC rivalry

text: Background[edit]

text: USC is recognized as consistently being one of the top football programs in the nation, while UCLA is recognized as consistently being one of the top basketball programs in the nation. However, a somewhat rare confluence of events occurred in 1954, which began with USC in their last of only two Final Four appearance in the 1954 NCAA Men's Division I Basketball Tournament and ended with UCLA winning their only Football National Championship.

text: Both schools also are successful in many "non-revenue" or "olympic" sports. Both have had success in track and field, water polo, tennis, volleyball, and golf. USC has won 26 NCAA Championships in Men's Outdoor Track and Field, 21 in Men's Tennis, and 12 in Baseball, the most of any school in each respective sport. Likewise, UCLA has won 19 NCAA Championships in Men's Volleyball, 11 in Softball, and 7 in Women's Water Polo, also the most of any school in those sports.

text: UCLA ranks second overall in NCAA teamp championships, with 114, behind Stanford, with 115. They also rank second in men's NCAA team championships with 72, and second (behind Stanford) in women's NCAA team championships with 39. USC ranks higher than UCLA and first in the nation in men's NCAA team championships with 84; it is 3rd overall with 104 NCAA titles (behind UCLA and Stanford) .[1] Both school also have several non-NCAA Championships, including AIAW and pre-NCAA championships.

text: Gauntlet[edit]

text: The Lexus Gauntlet is the name given to a competition between UCLA and USC in the 18 varsity sports that both compete in head-to-head; in 2003, 2005, and 2007 UCLA won the Lexus Gauntlet Trophy, while USC won the trophy in 2002, 2004, 2006, 2008, and 2009 (the first back-to-back win). After the 2009 season, Lexus stopped sponsoring the award, and the winner has been tracked less formally. Since the end of the Lexus sponsorship, USC has won in 2010 and 2011. UCLA won in 2012, 2013, and 2014.[2][3][4][5][6]

text: Football rivalry[edit]

text: Quite often, the winner of the football game has won or shared the Pac-12 Conference (Pac-12) title in football. A berth in the Rose Bowl game has been on the line many times as well for both schools. Since the 1916 formation of the Pacific Coast Conference, which the Pac-12 claims as part of its history, USC has won or shared 37 conference titles and UCLA has won or shared 17 titles.[7] Washington is third in overall conference titles with 15.[7] Since the 1959 season, when the Pac-12 was formed as the Athletic Association of Western Universities, through the 2007 season, the schools have won or shared 33 of the 48 conference titles.[7] USC has won 17 championships outright, shared eight and gone to the Rose Bowl or BCS bowl 21 times.[7] UCLA has won six championships outright, shared five and gone to the Rose Bowl eight times.[7] The schools have thrice shared the championship.[7] In 2011, UCLA became the first Pac-12 South Division champion while USC held the better of the two records; the Trojans were ineligible for postseason play that year due to NCAA sanctions. Both teams have spoiled conference and national championship runs for the other.

text: USC was a somewhat established national football power under Howard Jones and had begun a major rivalry with Notre Dame when UCLA joined the Pacific Coast Conference in 1928.[8] Los Angeles Times sportswriter Braven Dyer predicted on the day of the first football meeting on September 28, 1929, "In years to come, this game will probably be one of the football spectacles of the West" [9] USC dominated the early games (so much so, that after the first two games, the series was suspended for five years and they did not play each other from 1931 to 1935) until UCLA established itself.

text: By the late 1930s, star players such as Kenny Washington, Jackie Robinson, and Bob Waterfield enabled UCLA to be competitive. With the hiring of Hall of Fame Coach Henry "Red" Sanders, UCLA became the more dominant program in the 1950s with their one and only National Championship in 1954. A famous quote was attributed to Sanders regarding the rivalry, "Beating 'SC is not a matter of life or death, it's more important than that." [10][11]

text: But Sanders died suddenly of a heart attack, and shortly thereafter, one of the greatest colleges football coaches in NCAA history took over the struggling USC program. Upon the arrival of their new head coach John McKay (1960–1975), USC entered a new golden age in their storied history. During McKay's tenure, the Trojans won 8 conference titles, 5 Rose Bowls, produced two Heisman Trophy winners (Mike Garrett and O. J. Simpson) and won three National Championships (1962, 1967, and 1972) and shared one (1974). Against UCLA, McKay was tough to beat, posting a 10–5–1 record against the Bruins between 1960 and 1975.

text: For most seasons from the mid-1960s to the end of the 1970s, the two schools were the top powers on the West Coast with USC usually holding the top spot. In the 15 Rose Bowls played from 1966 to 1980, USC or UCLA played in 12 of them. Even with the rise of Don James' Washington Huskies in the 1980s and early 90s, UCLA or USC still went to the Rose Bowl seven times between 1981 and 1995. In the 1990s, UCLA enjoyed an eight-game winning streak against USC.

text: The Bruins' unbeaten string ended in 1999 when the Trojans began their longest win streak, 7, against the Bruins, though two of those wins (2004 and 2005) are now vacated, cutting the USC streak to five. This unprecedented dominance was the direct result of the hiring of Pete Carroll by USC in 2000.[citation needed] During Carroll's tenure (2001–2009 seasons), USC was virtually unbeatable against its two most heated rivals, UCLA and Notre Dame. The only game that UCLA beat a Pete Carroll-coached team was the 13–9 win in 2006 at the Rose Bowl that kept USC out of the BCS Championship game and allowed the Bruins to keep the record for consecutive wins (8) in the rivalry.

text: Title of the game[edit]

text: A number of titles have been applied to the football game such as: "The Los Angeles City Championship", "The Crosstown Showdown", "The Battle of L.A.", or simply the "crosstown rivalry".[citation needed] But none really have gained traction. Most often the game is referred to as the USC-UCLA (or UCLA-USC) football game by the media.[12] Fans of a particular team refer to it as the USC game or UCLA game, using the name of the opposing school.

text: Activities before the game[edit]

text: At UCLA, the week before the game is known as "Beat 'SC Week" (officially dubbed "Blue and Gold Week"). At USC, the week before the game is known as "Troy Week" or, more popularly, "Conquest".[citation needed]

text: Both schools host a number of activities on their respective campuses during the week to promote school spirit. Activities include parades, bonfires, rallies, and live entertainment.

text: Also, both schools take steps to prevent vandalism of two major landmarks on campus: USC wraps its Trojan Shrine (better known as "Tommy Trojan") in bubble wrap and duct tape, while UCLA covers its Bruin Bear statue with tarp stating "THE BRUIN BEAR IS HIBERNATING. BEAT 'SC.", and more recently a $5000 wooden puzzle box. Groups of UCLA students known as "Bruin Bear Security Force" also camp out in Bruin Plaza, ostensibly to protect the Bruin Bear in the event of a prank, while the USC Trojan Knights hold a week-long vigil guarding Tommy Trojan with the sign "Don't Bruin your life". This has come as a response to students painting the statues in the rival schools' colors before the game. On November 12, 2012, a photo was circulating an entrance sign at UCLA was defaced with a "S" painted between the letters U and C on Microsoft Paint.[citation needed]

text: There are a number of inter-campus competitions between various groups before the game.

text:
ROTC "Blood Bowl" – The football rivalry extends to the military training units at both schools. The Naval and Army Officers Training Corps midshipmen and cadets at both universities compete in the annual "Blood Bowl" flag football game against each other, usually held the Friday before the official game, as a parallel to the varsity match. The name stems from the often rough and passionate play by the midshipmen and cadets representing school pride. After a 25–12 victory on December 3, 2010, by the Army Battalion, UCLA continues to lead the series all time versus USC 15–11. As for Navy ROTC, the UCLA Bruin Battalion has soundly defeated the USC Trojan Battalion the past two years and three times over the past four years.
Daily Bruin vs. Daily Trojan "Blood Bowl" – Staff of the Daily Bruin and Daily Trojan have competed in a flag football contest that is also called the "Blood Bowl". This tradition has existed since at least 1950.
The Band Bowl – From the 1950s until 2000 the UCLA Marching Band and the USC Marching Band played in a flag football contest called the "Band Bowl". While parked on the USC campus for the 2000 game, UCLA band's equipment truck was broken into with many instruments and gear being stolen.[13] The incident ended the Band Bowl between the two schools.
UCLA vs. USC Football Manager's Bowl – UCLA and USC football equipment managers compete in a flag football contest the week leading up to the actual football game.[14] The series was suspended in 2007 after several participants required hospital emergency-room treatment in 2006 because of injuries[15] In 2011, the UCLA managers beat the USC managers in triple overtime.[16] The UCLA managers have won the previous 4 match-ups.
UCLA vs. USC Kickoff Golf Challenge – UCLA teams compete against USC teams in a two-person best ball scramble.
UCLA vs. USC Men's Ice Hockey – UCLA and USC have teams that compete in ACHA Division II club-level Ice hockey. They begin their series for the Crosstown cup.
UCLA vs. USC Men's Rugby – UCLA and USC compete every year on the day after the football game.
We Run the City 5K – A 5 km rivalry run held the Sunday before the football game that benefits Special Olympics Southern California. Runners pledge their allegiance to their team upon registration. Registration is open to all fans, students, alumni, staff, and the community. This is a family friendly run/walk managed by Special Olympics Southern California with USC and UCLA serve as the title sponsors since its inception in 2012.[17]

text: Activities during the game[edit]

text: Starting with the 2008 season, the winners of a blood drive competition were announced during halftime, with the winners donating more blood to the American Red Cross. UCLA won in 2008,[18] 2009, 2010 and 2011.

text: On November 13, 2012, UCLA served notice to the USC Marching Band that its drum major would not be allowed to stab a sword into the Bruins logo before the game in the Rose Bowl on November 17, 2012.[19]

text: Sharing the Los Angeles Coliseum[edit]

text: For a number of years, the schools shared the Los Angeles Memorial Coliseum as their home stadium until UCLA moved to the Rose Bowl for the 1982 season. Each school alternated as the "home" team for the game, with home fans on the north side of the Coliseum and visiting fans on the south (press box) side. Until 1983, players on both teams wore their home football jerseys for the game. Since the 1984 season, when the game was played at the Rose Bowl for the second time, the visiting fans sit in the visitor section of each respective stadium, and the visiting team wears their white jerseys. Because UCLA called the Coliseum home and USC won a number of Rose Bowl games, each school has a lifetime winning record in the others' current home stadium.

text: Starting in 2006, the coaches at the time, USC coach Pete Carroll and UCLA coach Karl Dorrell, expressed an interest in restarting the tradition of both teams wearing primary colored home jerseys. At the time, the NCAA football rules Article 3. a. stated, "Players of opposing teams shall wear jerseys of contrasting colors, and the visiting team shall wear white jerseys."[20] USC coach Pete Carroll said he would be willing to lose two timeouts during the game so that the USC team could wear their cardinal jerseys for the UCLA-USC football game on December 6, 2008.[21] It was determined before the 2008 game that the visiting school would only lose one timeout for incorrect equipment. Carroll agreed to forfeit a timeout to satisfy the ruling and Coach Rick Neuheisel agreed to forfeit one, in return (even though, as the coach of the home team, he was not required to do so by the ruling) to get back this tradition, and it was renewed in the 2008 game.[22] In the wake of the coaches' decisions, the NCAA decided to amend their rules regarding away teams' uniforms (which were originally put into place to provide more contrast for black-and-white photography and television broadcasts), changing the rule to state that the teams must agree on the decision for both teams to wear their colored jerseys before the game and that the uniforms must be of easily contrasted colors.[23] Since the home team is already required to wear its colored home jerseys and would not be in violation of any equipment rules, this essentially leaves the decision up to them as to whether or not to allow the visiting team is to wear their home uniforms.

text: Victory Bell[edit]

text: When the football teams from these schools compete against each other, the victor is awarded the Victory Bell. The Victory Bell was originally from an old Southern Pacific railroad locomotive. It was given to the UCLA student body by the UCLA Alumni Association in 1939.

text: It was UCLA's symbol of victory until it was stolen by a USC organization called the Trojan Knights in 1941. After being hidden in various locations for over a year before resurfacing in a USC student magazine (known as the Wampus), a prank war between the two universities ensued until 1942, when the student body presidents of the two schools agreed that the bell would be the trophy awarded the winner of the annual UCLA-USC football game.

text: The bell itself is brass, and the metal mounting around it is painted blue or cardinal by the school that won the football game and earned its possession. When UCLA possesses it, the UCLA Rally Committee is responsible for its protection and care. While it is in USC's possession, the Trojan Knights are responsible for hiding, protecting, and showcasing the bell (including ringing the bell during home football games). USC currently has the victory bell.

text: Rose Bowl[edit]

text: Until the Rose Bowl Game became part of the Bowl Championship Series (BCS) and later the College Football Playoff (CFP), a berth in the Rose Bowl to face the Big Ten Conference champion was the ultimate goal that was awarded to the then-Pacific-10 conference champion. Through the 2016 season, USC has appeared in the Rose Bowl 34 times and UCLA has appeared 12 times. During the BCS era (1998–2013), the Rose Bowl was the destination for the first-place Big Ten and Pac-12 teams, should either fail to qualify for the BCS championship game. Since the establishment of the CFP in 2014, the Rose Bowl is one of six bowls that rotates as host of a CFP semifinal game; in years in which the Rose Bowl does not host a CFP semifinal, the Rose Bowl Game is assured of hosting the first-place teams from the two conferences should they fail to be selected for the CFP semifinals.

text: UCLA was the first Pac-10 team to appear in a BCS bowl, the 1999 Rose Bowl, their last conference championship year. USC has appeared in six BCS bowl games, winning the BCS championship in 2005. With the Rose Bowl stadium being the home field for UCLA, the UCLA–USC rivalry football game has been played there to a sellout crowd during even numbered years since 1982.

text: Before the Pac-10 expanded in 2011 and became the Pac-12, the Rose Bowl and conference championship were on the line for both teams 20 times and at least one team 37 times. Following expansion and the division of the conference into two football divisions, with UCLA and USC both in the South Division, the division title and a berth in the Pac-12 Championship Game have been on the line for at least one team twice. Both teams have either won the championship or spoiled it for the other at one time or another.

text: Football series record[edit]

text: As of the 2017 season[update], USC leads 49–31–7 (record includes 2 USC wins vacated due to NCAA penalty for violation of NCAA rules).[24][25] There has been one overtime game in the series in 1996. Many[clarification needed] of the games of this rivalry have ultimately determined the Pac-10 Rose Bowl representative and often a chance to play for the national championship. USC was forced to vacate both its wins from the 2004 and 2005 seasons due to NCAA violations.[24][26]

text:
UCLA victories
USC victories
Ties
Forfeits / Vacated wins

tag: table

text:
No.
Date
Location
Winner
Score

1
September 28, 1929
USC
USC
76–0

2
September 27, 1930
UCLA
USC
52–0

3
November 26, 1936
USC
Tie
7–7

4
December 4, 1937
USC
USC
19–13

5
November 24, 1938
USC
#14 USC
42–7

6
December 9, 1939
UCLA
Tie
0–0

7
November 30, 1940
USC
USC
28–12

8
December 6, 1941
UCLA
Tie
7–7

9
December 12, 1942
USC
#13 UCLA
17–14

10
September 23, 1943
UCLA
USC
20–0

11
November 27, 1943
USC
USC
26–13

12
September 23, 1944
USC
Tie
13–13

13
November 25, 1944
UCLA
#8 USC
40–13

14
September 21, 1945
UCLA
USC
13–6

15
December 1, 1945
USC
USC
26–15

16
November 23, 1946
UCLA
#4 UCLA
16–13

17
November 22, 1947
USC
#4 USC
6–0

18
November 20, 1948
UCLA
USC
20–13

19
November 19, 1949
USC
USC
21–7

20
November 25, 1950
UCLA
UCLA
39–0

21
November 24, 1951
USC
#18 UCLA
21–7

22
November 22, 1952
UCLA
#4 USC
14–12

23
November 21, 1953
USC
#5 UCLA
13–0

24
November 20, 1954
UCLA
#2 UCLA
34–0

25
November 19, 1955
USC
#5 UCLA
17–7

26
November 25, 1956
UCLA
USC
10–7

27
November 23, 1957
USC
UCLA
20–9

28
November 22, 1958
UCLA
Tie
15–15

29
November 21, 1959
USC
UCLA
10–3

30
November 26, 1960
UCLA
USC
17–6

31
November 25, 1961
USC
UCLA
10–7

32
November 24, 1962
UCLA
#1 USC
14–3

33
November 30, 1963
USC
USC
26–6

34
November 21, 1964
UCLA
USC
34–13

35
November 20, 1965
USC
#7 UCLA
20–16

36
November 19, 1966
UCLA
#8 UCLA
14–7

37
November 18, 1967
USC
#8 USC
21–20

38
November 23, 1968
UCLA
#1 USC
28–16

39
November 22, 1969
USC
#5 USC
14–12

40
November 21, 1970
UCLA
UCLA
45–20

41
November 20, 1971
USC
Tie
7–7

42
November 18, 1972
UCLA
#1 USC
24–7

43
November 24, 1973
USC
#9 USC
23–13

44
November 23, 1974
UCLA
#8 USC
34–9

45
November 28, 1975
USC
#14 UCLA
25–22

No.
Date
Location
Winner
Score

46
November 20, 1976
UCLA
#13 USC
24–14

47
November 25, 1977
USC
USC
29–27

48
November 18, 1978
UCLA
#5 USC
17–10

49
November 24, 1979
USC
#4 USC
49–14

50
November 22, 1980
UCLA
#18 UCLA
20–17

51
November 21, 1981
USC
#10 USC
22–21

52
November 20, 1982
Rose Bowl
#11 UCLA
20–19

53
November 19, 1983
Coliseum
UCLA
27–17

54
November 17, 1984
Rose Bowl
#7 UCLA
29–10

55
November 23, 1985
Coliseum
USC
17–13

56
November 22, 1986
Rose Bowl
#18 UCLA
45–25

57
November 21, 1987
Coliseum
USC
17–13

58
November 19, 1988
Rose Bowl
#2 USC
31–22

59
November 18, 1989
Coliseum
Tie
10–10

60
November 17, 1990
Rose Bowl
#19 USC
45–42

61
November 23, 1991
Coliseum
#25 UCLA
24–21

62
November 21, 1992
Rose Bowl
UCLA
38–37

63
November 20, 1993
Coliseum
#16 UCLA
27–21

64
November 19, 1994
Rose Bowl
UCLA
31–19

65
November 18, 1995
Coliseum
UCLA
24–20

66
November 23, 1996
Rose Bowl
UCLA
48–41(2 OT)

67
November 22, 1997
Coliseum
#7 UCLA
31–24

68
November 21, 1998
Rose Bowl
#3 UCLA
34–17

69
November 20, 1999
Coliseum
USC
17–7

70
November 18, 2000
Rose Bowl
USC
38–35

71
November 17, 2001
Coliseum
USC
27–0

72
November 23, 2002
Rose Bowl
#7 USC
52–21

73
November 22, 2003
Coliseum
#2 USC
47–22

74
December 4, 2004
Rose Bowl
#1 USC†
29–24

75
December 3, 2005
Coliseum
#1 USC†
66–19

76
December 2, 2006
Rose Bowl
UCLA
13–9

77
December 1, 2007
Coliseum
#8 USC
24–7

78
December 6, 2008
Rose Bowl
#5 USC
28–7

79
November 28, 2009
Coliseum
#24 USC
28–7

80
December 4, 2010
Rose Bowl
USC
28–14

81
November 26, 2011
Coliseum
#10 USC
50–0

82
November 17, 2012
Rose Bowl
#17 UCLA
38–28

83
November 30, 2013
Coliseum
#22 UCLA
35–14

84
November 22, 2014
Rose Bowl
#11 UCLA
38–20

85
November 28, 2015
Coliseum
USC
40–21

86
November 19, 2016
Rose Bowl
#13 USC
36–14

87
November 18, 2017
Coliseum
#11 USC
28–23

Series: USC leads 47–31–7

† USC was forced to vacate victories.
Vacated wins and ties have previous winner retaining trophy.

text: Winning streaks in the series[edit]

text: UCLA holds the longest winning streak in the series, as UCLA won eight straight games from 1991 to 1998. USC's longest streak was for seven wins from 1999 to 2005. But the 7 game winning streak is not recognized because multiple years have vacated wins.

text: The 1967 "Game of the Century"[edit]

text: The 1967 USC vs. UCLA football game was one of the historically significant football games of the 20th century. It matched No. 4 USC with O.J. Simpson against No. 1 UCLA with Gary Beban for the Conference Championship, National Championship, and Heisman Trophy on the line for Beban or Simpson. USC won 21–20 and went on to defeat Indiana in the Rose Bowl and win the national championship. Despite Simpson's sensational performance in this game and accumulating 1,543 rushing yards for the season, Beban won the Heisman Trophy. Simpson won the trophy the following year.

text: Other notable games[edit]

text:
In the 1929 season, UCLA would play football in the Pacific Coast Conference for the first time. USC had just come off an undefeated National Championship season under the legendary Howard Jones. In the opening game of the season, the USC "Thundering Herd" defeated UCLA 76–0, which stands as the most lopsided score of the series.[27]
1939 season – This was the first year where the Rose Bowl was on the line for both teams, and the first time both teams were ranked. The game ended in a scoreless tie, and USC went to the 1940 Rose Bowl.[28]
1952 season – UCLA was ranked #3 and USC was ranked #4. Both teams were undefeated and untied. USC would win on 14–12. USC would later go on to lose to Notre Dame but win the 1953 Rose Bowl.
1963 season - The game, scheduled for November 23, was postponed on account of the assassination of John F. Kennedy, which occurred on Friday, November 22. It was played on November 30, with USC prevailing 26–6.[29]
1965 season #7 UCLA met #6 USC for the AAWU (Pac-8) title and the right to meet undefeated and #1 Michigan State in the 1966 Rose Bowl. The 1965 "Gutty Little Bruins" team won 20–16 with a score at 2:39 left to play.[30]
1969 season – Undefeated #6 UCLA (8–0–1) met undefeated #5 USC (8–0–1) with the 1970 Rose Bowl on the line. USC would prevail with a score in the final two minutes to win 14–12.
1976 season – This was one of the biggest games of the 1976 season. Undefeated #2 UCLA (9–0–1) vs. #3 ranked USC (8–1) met to determine the 1977 Rose Bowl representative, and an outside shot at the National Championship should #1 ranked Pittsburgh lose. USC won 24–14 in the first rivalry game for both John Robinson and Terry Donahue.
1986 season – Just before halftime, UCLA is up 24–0 over USC. A fake kneel down followed by a hail mary into the end zone put UCLA up 31–0 over USC at halftime. This play was known as "Hail Mary, and In Your Face". UCLA won the game 45–25.
1988 season – Undefeated second-ranked USC (9–0) and quarterback Rodney Peete met 9–1, sixth-ranked UCLA and quarterback Troy Aikman with the 1989 Rose Bowl on the line. UCLA had been ranked #1 before losing to Washington State. A possible Heisman trophy for Peete or Aikman was on the line. The attendance set a regular season Rose Bowl record of 100,741. Rodney Peete was stricken with measles the week before the game and had been to the hospital. But he managed to lead the Trojans over the Bruins 31–22. It would set up the classic #1 Notre Dame vs #2 USC matchup the following week. Peete and Aikman would finish 2nd and 3rd in the Heisman balloting behind Barry Sanders.
1999 season – USC won 17–7 to break the Bruins' streak of eight straight.
2005 season – USC had been ranked #1 all season and faced a one-loss eleventh ranked UCLA (9–1) team as its last obstacle to the dream 2006 Rose Bowl BCS Championship matchup with #2 Texas. USC featured Heisman trophy winner Matt Leinart and eventual winner Reggie Bush. USC defeated UCLA 66–19 in one of the most lopsided games of the series since the first matchup in 1929.[31] The win was later vacated for NCAA infractions.

text:
2006 season – "13–9"; on December 2, 2006, UCLA defeated the Trojans, 13–9. In doing so, the Bruins not only ended No. 2-ranked USC's 63-game streak of scoring 20-plus points per game, but also eliminated the Trojans' from competing in their fourth-consecutive national title game (after winning the 2003 and 2004 AP National Championships and narrowly losing to Texas in the 2005 BCS National Championship game), which would have pitted the No. 2 Trojans against No. 1 ranked Ohio State in the 2006 BCS National Championship game. This was only the second USC loss to a major rival (UCLA or Notre Dame) in the Pete Carroll era.
2011 season – "50–0"; on November 26, 2011, USC routed UCLA 50–0, which is the largest margin of victory in the rivalry since the 1930 matchup. Quarterback Matt Barkley set the record for passing yards (423) and touchdowns (6) in the history of the rivalry, while wide receiver Marqise Lee set the record for receiving yards (224). The game marked USC's 12th victory in 13 years against UCLA.[32]

text: Rivalry glory years[edit]

text: Between 1965 and 1978, the conference championship and Rose Bowl berth were on the line for both teams nine times.

text:
1965 #7 UCLA uses two late touchdowns sandwiched around an on-side kick to beat #6 USC, 20–16.
1966 #8 UCLA, playing without injured star QB Gary Beban, beats #7 USC, 14–7.
1967 #2 USC, led by O.J. Simpson's 64-yard TD run and three blocked kicks, beats #1 UCLA, 21–20.
1969 #5 USC, after a penalty on a 4th & 10 incompletion, scores a controversial late TD to beat #6 UCLA, 14–12.
1972 #1 USC pulls away in the 2nd half to beat #14 UCLA, 24–7.
1973 #9 USC, taking advantage of numerous turnovers, beats #8 UCLA, 23–13.
1974 #8 USC wins easily over an injury riddled unranked UCLA squad, 34–9.
1976 #3 USC, behind the scrambling and passing of QB Vince Evans, beats #2 UCLA, 24–14.
1978 #5 USC runs out the last 6½ minutes of the clock to hold off #14 UCLA, 17–10.

text: In two other years (1975 and 1977) between 1965 and 1978, the Rose Bowl berth was on the line for UCLA only.

text:
1975 #14 UCLA overcomes 8 lost fumbles and holds off unranked USC, 25–22 and goes on to upset #1 Ohio State in the Rose Bowl
1977 #17 UCLA loses on a last-second USC field goal, 29–27; thus, Washington goes to the Rose Bowl and upsets Michigan.

text: The USC coaches during this time were John McKay and John Robinson, while UCLA was coached by Tommy Prothro, Pepper Rodgers, Dick Vermeil, and Terry Donahue.

text: Basketball[edit]

text: Men's[edit]

text: UCLA has 31 conference championships and USC has seven. When John Wooden became the coach, UCLA turned into a national basketball powerhouse. UCLA has won 11 NCAA Men's Division I Basketball Tournaments and has dominated the conference, winning two games for every one that USC won. As of the 2013–2014 season, UCLA has won or shared the conference title 31 times, and USC has won or shared the title 9 times.[33] There have been some notable games in the rivalry.

text:
The first official meeting between the two schools as they are now known took place in February 1928 after UCLA was invited to join the Pacific Coast Conference. UCLA won two of a three-game basketball series to inaugurate the basketball rivalry.
USC had a 41-game winning streak against UCLA from 1932 to 1943, a national record that stood until UCLA eventually beat it in 1980 with a 42nd consecutive win against Cal, on the way to a 52-game winning streak, the current NCAA record of one opponent over another.[34] UCLA Defeated USC 42–37 in the first of the two final home games in the 1943 season to break the streak.[35] This is still the third-longest streak of one Division 1 opponent against another.
In the 1960–1961 season, USC and UCLA met for the third time on March 3, 1961 in the game that would ultimately decide the AAWU champion and 2nd place. The teams had split the two previous games. USC beat UCLA 86–85 in overtime, and later advanced to the NCAA tournament.
In the 1968–1969 season, USC took UCLA, led by Lew Alcindor, to two overtimes before losing 61–55 at the Los Angeles Sports Arena. On the second game, one night later on March 8, 1969, USC would finally defeat UCLA 46–44, marking the Bruins' first loss in Pauley Pavilion.
In the 1970–1971 basketball season, UCLA and USC were ranked #1 and #2 for much of the season. #2 ranked USC coached by Bob Boyd suffered its first loss against #3 ranked UCLA, blowing a 9-point second half lead. In the rematch in the final game of the season, UCLA jumped out to a big early lead and went on to win 72–63. USC would finish the season 24–2 and ranked #2, but only the conference champion, UCLA, could be invited to the 1971 NCAA Men's Division I Basketball Tournament, as there were no at-large slots in the bracket. This would be one of the cases for expanding the bracket to 32 teams for the 1975 NCAA Men's Division I Basketball Tournament.
In the 1973–1974 basketball season, the two teams were tied for first in the Pac-8 going into the last game of the season. With the conference championship and berth in the 1974 NCAA Men's Division I Basketball Tournament on the line, Bill Walton led UCLA to a lopsided victory. Notably, UCLA would be the national semi-finalist in the NCAA tournament, while USC would be the semi-finalist in the Collegiate Coaches' Association Tournament, a tournament that invited second-place conference teams.
In the 1984–1985 season, UCLA and USC would meet for the game that would decide first place in the Pacific-10. USC already had beat UCLA 78–77 in double overtime at the Los Angeles Memorial Sports Arena. The second game at Pauley Pavilion on February 28, 1985 was finally decided in quadruple overtime with USC winning 80–78. USC would be invited to the 1985 NCAA Men's Division I Basketball Tournament, while UCLA was invited to and won the National Invitation Tournament.
In the 2007–2008 season, UCLA and USC met in the 2008 Pacific-10 Conference Men's Basketball Tournament, for the first time in 225 games in post-season play. The teams had split in the regular season with the Trojans winning at Pauley Pavilion and the Bruins winning at Galen Center. In their third game, a capacity crowd of 18,997 at the Staples Center saw UCLA beat USC 57–54 in the semi finals.[36] Both teams had highly regarded freshmen: Kevin Love and O. J. Mayo. USC later had to vacate the win when it was found that Mayo had accepted gifts from agents while still in high school, which made him ineligible for NCAA play.

text: Women's[edit]

text: In Women's basketball, UCLA has one AIAW championship and USC has two NCAA Women's Division I Basketball Championships. Ironically, USC won its second title, in 1984, at UCLA's Pauley Pavilion. The Bruins and the Women of Troy have faced each other twice in the second round of the AIAW championships with UCLA winning in 1979 and USC winning in 1981.

text: Other notable sports rivalries[edit]

text: Because of the geographical proximity and conference affiliation, UCLA and USC compete in other NCAA sanctioned sports, such as Basketball, Track and Field, Volleyball, and Water Polo. UCLA and USC are #1 and #3 respectively in terms of the most NCAA championships won in Division I as of 2007.[37] They have faced each other for the national title in several sports including Men's Volleyball and Women's water polo. Although basketball and football tend to get the most attention, the rivalry between the two schools is intense in every sport.

text: Baseball[edit]

text: The athletic rivalry began in 1920 when the University of California, Southern Branch Cubs defeated USC in spring baseball 7–6.[38] USC has gone on to be the premier team in college baseball with 21 appearances in the College World Series and 12 titles, the most of any school and double the next closest school, Texas, who has six titles in 34 appearances. UCLA has appeared in the College World Series five times. UCLA won its first NCAA Baseball title in 2013.

text: As of the end of the 2014 season, USC leads UCLA in the series 256–130.[39] Since 2010, UCLA and USC have met in the second game of a college baseball doubleheader at Dodger Stadium called the Dodgertown classic as well as a three-game conference series.[40]

text: Fencing[edit]

text: Both the USC Fencing Club and UCLA fencing club are in the Intercollegeiate Fencing Conference of Southern California (IFCSC). They compete against NCAA fencing teams as well, such as UCSD, Caltech, and ASU.[41][42][43]

text: Soccer[edit]

text: UCLA women's soccer team has dominated the Women of Troy, 22–5–1. But at the 2007 NCAA College Cup, USC won in the semi-finals, ended UCLA's 8 straight victories over the Trojans. USC went on to be the first Pac-10 (as it was called at the time) school to win the NCAA Women's Soccer Championship. In the 2008 regular season game, a pair of goals by Kristina Larsen gave UCLA a 2–1 win over USC in the Los Angeles Coliseum before a record crowd of 7,804 fans.

text: To advance to the NCAA Championship quarterfinals, the Bruins defeated the Women of Troy (1–0) in the round of 16 on Saturday, November 22, 2008 at Drake Stadium. It was also a battle between UCLA's Lauren Cheney and Kara Lang and USC's Amy Rodriguez, all of whom participated in the Beijing Olympic Games—Cheney and Rodriguez for the USA and Lang for Canada. Cheney and Rodriguez would win gold medals with Team USA, defeating Lang's Canada team in the quarterfinals. UCLA won the NCAA Division I Women's Soccer Championship in 2013, defeating Florida State 1–0 in overtime.

text: Tennis[edit]

text: As of the 2014 season, USC has won 21 NCAA Men's Tennis Championships and UCLA has won 16. USC has won 5 of the last 6 (2009–2012, 2014), while UCLA's most recent Championship was in 2005. There was a run from 1960 to 1971 where either UCLA or USC was the champion. In twelve of the tournaments, one team has been runner-up to the other who won the championship, with an even split of six championships for both UCLA and USC.

text: UCLA has won two NCAA Division I Women's Tennis Championships, most recently in 2014. USC won in 1983 and 1985.

text: Volleyball[edit]

text: UCLA has dominated men's volleyball under the coaching of Al Scates. As of 2013, UCLA has won 19 NCAA Men's Volleyball Championships. The next closest school is Pepperdine with five NCAA titles. USC has won four NCAA titles. UCLA and USC have faced each other in the championship game of the NCAA Men's Volleyball Championship four times.

text:
1979 UCLA 3–1 USC
1980 USC 3–1 UCLA
1981 UCLA 3–2 USC
1987 UCLA 3–0 USC

text: In women's volleyball, UCLA won the 2011 national Championship. UCLA now has won four and USC has won three NCAA Women's Volleyball Championships in Division I. In addition, USC and UCLA have won three AIAW Women's volleyball championships.

text: In 1981 USC defeated UCLA three games to two in the first NCAA Women's Volleyball Championship game. In 1976 USC defeated UCLA to win the AIAW volleyball championship.

text: Water polo[edit]

text: The two schools compete in water polo. In men's, UCLA carries a slight lead over USC in the all-time series of 80–76–1. In the NCAA Men's Water Polo Championship, the two school are tied with 9 championships apiece. UCLA won the most recent championship in 2014, with USC winning the prior 6 titles dating back to 2008. Due to the low number of schools participating in the sport and the State of California's dominance (no team from outside of California has ever played in the championship match), title game matches between the two teams are relatively common, occurring in 1996, 2009, 2012, and 2012. In title game matches, USC holds a 3–2 advantage. UCLA won 8–7 in 1996, and 9-8 in 2014, while USC won 7–6 in 2009, 7-4 in 2011, and 11-10 in 2012.

text: In women's water polo, UCLA has a commanding 46-22 lead over USC in the all-time series. In the NCAA Women's Water Polo Championship, UCLA dominated early on, winning 7 of the first 9 NCAA Championships, including the first tournament in 2001. USC has won 4, most recently in 2016. The two teams have faced each other in the women's title game 3 times, in 2006, 2008, and 2009. UCLA won all 3 matches by scores of 9–8, 6–3,[44] and 5–4, respectively. All three wins were part of UCLA's streak of 5 consecutive championships.

text: Head-to-head records by sport[edit]

text: As of December 18, 2014[update], USC leads the all-time all-sport record 967–922–10.[45]

text: Men's

text:
Baseball: USC 256–130
Basketball: UCLA 138–105
Football: USC 46–31–7
Tennis: UCLA 105–90
Track & Field: USC 42–39
Volleyball: UCLA 90–41
Water Polo: UCLA 80–76–1
Gymnastics: UCLA 9–7
Soccer: UCLA 13–3
Swimming: USC 67–13

text: Women's

text:
Basketball: USC 47–39
Cross Country: UCLA 1–0
Rowing: USC 13–0
Sand Volleyball: USC 3–0
Soccer: UCLA 22–5–1
Swimming: USC 24–16
Tennis: UCLA 50–47
Track & Field: UCLA 22–9
Volleyball: UCLA 60–56
Water Polo: UCLA 46–22
Gymnastics: UCLA 16–10–1

text: Italic sports are inactive due to one of both schools discontinuing the sport

text: Note: This record includes all games played in active sports, but does not include every inactive sport.

text: Olympic athletes[edit]

text: Both UCLA and USC send many athletes to the Olympic Games. As of the last games, USC athletes account for 258 medals and UCLA athletes account for 241. A USC Trojan has been a Gold medal winner in every summer Olympics since 1912. As of the 2008 Summer Olympics, UCLA and USC athletes combined account for nearly one fifth of all medals won by the United States of America and their 499 combined medals would rank 9th on the country list.[46] [47] [48] [49]

text: Rivalry outside sports competition[edit]

text:
College Comparison (2013)

Category
USC
UCLA

Location
Los Angeles, CA
Los Angeles, CA

Ownership
Private university
Public university

Founded
1880
1919

Students
40,000 [50]
42,163 [51]

School colors
Cardinal and gold
True Blue and gold

Nickname
Trojans
Bruins

Football stadium
LA Coliseum
Rose Bowl

Basketball arena
Galen Center
Pauley Pavilion

Annual tuition
$52,283 [52]
$12,692 Calif Resident
$35,570 (non-resident)[53]

text: The UCLA–USC rivalry is like few other college or university rivalries. Both universities are in the same city. Both universities are at the top in the nation not only for their sports achievements, but also for academic standing. While UCLA historically has been viewed as the more selective institution, USC has made great strides in improving its position in university rankings. Graduate schools at both universities are among the top in their fields. Furthermore, graduates from both universities work together all across Southern California. It is not uncommon for married couples or family members to consist of graduates from each school. Undergraduates of one school can be found attending graduate school and/or professional school across town. High schools in Southern California send some of their top graduates to both schools every year, as do community colleges around Los Angeles. Students from each school, including athletes, even can be found rooming together in the same house or apartment in Los Angeles.

text: The rivalry is also a microcosm of a geopolitical rivalry based upon the locations of the schools, the cost of attending each school, and the founding and growth patterns of the schools.

text: Geographic location[edit]

text: UCLA is located on the Westside of Los Angeles and is nestled between many several of the most affluent and desirable communities in southern California: Brentwood, Bel-Air, Beverly Hills and Westwood. Although this area was relatively remote and unsettled at the time of UCLA's founding, decades of growth in the area around campus means that UCLA is hardly the suburban location it once was.

text: In 2012, Bruins football coach Jim Mora said he sold recruits on the safety of UCLA's campus location. "I mean, we don't have murders one block off our campus," said Mora. He denied he was making a reference to USC, which months earlier had two of their students killed near campus.[54]

text: USC, by contrast, is located on the Southern fringe of downtown Los Angeles by Exposition Park. In the early years of the city, it was a fashionable area, but it began to be rundown as wealthier residents migrated towards other suburban neighborhoods, following the national trend. USC was an isolated enclave for a number of years and the surrounding neighborhood had a bad reputation. Lately, with newer downtown construction, the area is becoming connected with downtown again, although the neighborhood remains marginal. Most of the major LA area public sports facilities are located near campus, including the Los Angeles Coliseum and Staples Center.

text: Funding and cost of attendance[edit]

text: The University of California is a public university, while the University of Southern California is a private university. As a public university, UCLA offers discounted attendance rates for California residents. For 2009–10 the estimated cost of attendance (tuition, fees, room, board, books, etc.) at UCLA is approximately $30,476 for in-state students living on campus, compared to $53,354 for out-of-state students, also living on campus.[55]

text: At USC, no differentiation in fees is made between California residents and those coming from out-of-state. USC estimates the cost of attendance for all students living on campus for the 2009–10 school year at about $60,801 [56]

text: The University of California System has raised fees on all its campuses, including at UCLA, over the years to account for declines in state support and to keep pace with inflation.[57]

text: Costs of attendance at both UCLA and USC may be off-set by financial aid, in the form of loans or grants based on merit or need or both. This includes athletic scholarships.

text: Founding[edit]

text: USC was established in 1880 and UCLA was founded in 1919 when California Gov. William D. Stephens signed California Assembly Bill 626, establishing the Southern Branch of the University of California. UCLA moved to its current location in 1927 when it was renamed the University of California at Los Angeles. USC had been playing football since 1888 and joined the Pacific Coast Conference in 1922. UCLA started playing football in 1919 and joined the PCC in 1928.

text: UCLA-USC rivalry in popular culture[edit]

text:
On the Jack Benny NBC radio program from November 26, 1950 (the Sunday after that season's UCLA – USC game), the episode was about Jack trying to go to the game with Mary Livingstone and Dennis Day.[58] Jack also had the USC and UCLA coaches as guests on his television show.
The Sports Illustrated Swimsuit Issue in 1989 is the magazine's top-selling issue of all-time.[59] On page 225 is a photo of a UCLA student posing in a bikini in her bedroom, while in the background are a Bruin bear wearing a button with a four-letter expletive directed at USC, "Fuck SC", and a poster underneath that says "My Two Favorite Teams are the BRUINS and Whoever Is Playing USC."[60][61][62] The St. Petersburg Times brought the picture to the magazine's attention. Sports Illustrated managing editor Mark Mulvoy responded, "You're the first person to tell me this. Twenty million people have read that issue and no one noticed it. We did not do it on purpose. This was not an attempt to sneak the word into Sports Illustrated. I regret it."[60] The Register-Guard wrote that the magazine was accustomed to criticism for Swimsuit Issue photos being too revealing. The newspaper published an accompanying photo of the magazine cover with the caption, "The SI cover was OK, but page 225 wasn't".[63]
In a 2005 ESPN commercial, a man wearing a UCLA sweatshirt opens his door on Halloween to find a young Trick-or-treater dressed in a Trojan outfit. He closes his door in disgust without handing out any candy. (The commercial's comedy lies in the fact that UCLA and USC fans retain a lifetime rivalry with each other, while still living side-by-side.)
In a 2006 episode of The New Adventures of Old Christine, Old Christine's ex-husband, Richard, takes their son Richie to the UCLA-USC game at the Coliseum.