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d00e8e08bcd25847da17cf071afa572d548033a6
obasi made his lyn debut, in the opening
obasi made his lyn debut, in the opening game of the season, where he played 66 minutes, in a 1–1 draw against fredrikstad. however, obasi struggled to regain a place in the first team and it wasn't until on 25 september 2005 when he scored his first lyn goal, in a 1–0 win over brann. despite this, obasi made five appe...
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87967da7e2ca84b8cb7fe9dfff971339154b4f0a
born in enugu, nigeria, obasi started his football
born in enugu, nigeria, obasi started his football career at river lane youth club enugu and jc raiders in his homeland country. obasi went to norway at the same time as his countryman mikel john obi; both players joined lyn. it was disputed that obasi signed for lyn in 2004, but this was rejected by fifa which ordered...
wikipedia
6e90376cab9a63b158df9cc929d93cd3b28f81d2
pavel jenyš is a czech professional ice hockey
pavel jenyš is a czech professional ice hockey forward currently playing for hc rt torax poruba in the chance liga. jenyš was selected by the minnesota wild in the seventh round at the 2014 nhl entry draft.
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dd21b4e3b7d401d55ebfeffcaa5dfa1a4353dd30
with his entry-level contract completed and as an
with his entry-level contract completed and as an impending free agent from the kings, jenyš opted to return to the czech republic, agreeing to a one-year contract with original club, hc kometa brno, on 5 june 2019.
wikipedia
04da8227f5b04e4895d6e13784ed8482cb30f628
on 5 may 2015, jenyš was signed to
on 5 may 2015, jenyš was signed to a three-year, entry-level contract with the wild. on 21 november 2018, jenyš was traded to the los angeles kings in exchange for stepan falkovsky.
wikipedia
12888f65915d9791d4809b865f6119a839ff334f
jenyš made his czech extraliga debut playing with
jenyš made his czech extraliga debut playing with hc kometa brno debut during the 2013–14 season. after his selection by the minnesota wild in the 2014 nhl entry draft, jenyš moved to north america and played a season of junior hockey with the sudbury wolves of the ontario hockey league (ohl).
wikipedia
a02ae203669b650fc5fa684beb183c4fe96066dc
in mathematics, the pentagram map is a discrete
in mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. the pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. richard schwartz introduced the pent...
wikipedia
5a2b7be1df0a70f24d16576129d364f784cad894
here is a description of the geometric action
here is a description of the geometric action of the boussinesq equation. given a locally convex curve c: r → r 2 {\displaystyle c:r\to r^{2}}, and real numbers x and t, we consider the chord connecting c (x − t) {\displaystyle c(x-t)} to c (x + t) {\displaystyle c(x+t)}. the envelope of all these chords is a new curve...
wikipedia
fa8318f2d2b245d3c7356d466f10d581f34c1f57
the continuous limit of a convex polygon is
the continuous limit of a convex polygon is a parametrized convex curve in the plane. when the time parameter is suitably chosen, the continuous limit of the pentagram map is the classical boussinesq equation. this equation is a classical example of an integrable partial differential equation.
wikipedia
6410d13206fae9eb184862b722697b44064b24fc
to every edge. this rule refers to the
to every edge. this rule refers to the figure at right and is meant to apply to every configuration that is congruent to the two shown. when this labeling is done, the edge-labeling of g satisfies the relations for the pentagram map.
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edc850cb7efef900a511a7b9779b79b5e65fdcd1
alternatively, the following construction relates the octahedral recurrence
alternatively, the following construction relates the octahedral recurrence directly to the pentagram map. let t {\displaystyle t} be the octahedral tiling. let π: t → r 2 {\displaystyle \pi:t\to r^{2}} be the linear projection which maps each octahedron in t {\displaystyle t} to the configuration of 6 points shown in ...
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9bbeec3c8000ff07715a7fab6660be70262d1058
max glick used the cluster algebra formalism to
max glick used the cluster algebra formalism to find formulas for the iterates of the pentagram map in terms of alternating sign matrices. these formulas are similar in spirit to the formulas found by david p. robbins and harold rumsey for the iterates of the octahedral recurrence.
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2ab64598eb56f1ed1f9ec693dad63abef9a854b2
here a i {\displaystyle a_{i}} and b i
here a i {\displaystyle a_{i}} and b i {\displaystyle b_{i}} are the labels of antipodal vertices. a common convention is that a 2, b 2, a 3, b 3 {\displaystyle a_{2},b_{2},a_{3},b_{3}} always lie in a central horizontal plane and a_1,b_1 are the top and bottom vertices. the octahedral recurrence is closely related to ...
wikipedia
53f68b8b251a5e2dc2685390e59217ce75d11762
in a 2011 preprint, fedor soloviev showed that
in a 2011 preprint, fedor soloviev showed that the pentagram map has a lax representation with a spectral parameter, and proved its algebraic-geometric integrability. this means that the space of polygons (either twisted or ordinary) is parametrized in terms of a spectral curve with marked points and a divisor. the spe...
wikipedia
cc04b4ff2ae6dc10e542469c9a28c9055e9dee7f
each casimir level set has an iso-monodromy foliation,
each casimir level set has an iso-monodromy foliation, namely, a decomposition into the common level sets of the remaining monodromy functions. the hamiltonian vector fields associated to the remaining monodromy invariants generically span the tangent distribution to the iso-monodromy foliation. the fact that the monod...
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62799e3226fff255b4b9eb7eb5ec6338753e22dc
the monodromy invariants and the invariant bracket combine
the monodromy invariants and the invariant bracket combine to establish arnold–liouville integrability of the pentagram map on the space of twisted n -gons. the situation is easier to describe for n odd. in this case, the two products
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1544724eb1cd6bfa87d63e0cf095a3455bb79a06
the first expression is the directional derivative of
the first expression is the directional derivative of g {\displaystyle g} in the direction of the vector field h (f) {\displaystyle h(f)}. in practical terms, the fact that the monodromy invariants poisson-commute means that the corresponding hamiltonian vector fields define commuting flows.
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119c1c71b25d88d6fde32c9dbc045582f33563b8
a poisson bracket is an anti-symmetric linear operator
a poisson bracket is an anti-symmetric linear operator { ⋅, ⋅ } {\displaystyle \{\cdot,\cdot \}} on the space of functions which satisfies the leibniz identity and the jacobi identity. in a 2010 paper, valentin ovsienko, richard schwartz and sergei tabachnikov produced a poisson bracket on the space of twisted polygons...
wikipedia
012e30635de67fff365df779859b86ce619ae759
whenever p has all its vertices on a
whenever p has all its vertices on a conic section (such as a circle) one has o k (p) = e k (p) {\displaystyle o_{k}(p)=e_{k}(p)} for all k.
wikipedia
ed867eb088ada1cf13f6c3fac00f7aabb45d938c
the monodromy invariants are defined on the space
the monodromy invariants are defined on the space of twisted polygons, and restrict to give invariants on the space of closed polygons. they have the following geometric interpretation. the monodromy m of a twisted polygon is a certain rational function in the corner coordinates. the monodromy invariants are essentiall...
wikipedia
41da2dd260d75d5fe4e6f99ebfd4ffe20ab97bcc
when n is odd, the allowable values of
when n is odd, the allowable values of k are 1, 2,..., (n − 1)/2. when n is even, the allowable values of k are 1, 2,..., n /2. when k = n /2, one recovers the product invariants discussed above. in both cases, the invariants o n {\displaystyle o_{n}} and e n {\displaystyle e_{n}} are counted as monodromy invariants, e...
wikipedia
d10870a2eb621169e5264406d9baa6b408057650
the sign is determined by the parity of
the sign is determined by the parity of the number of single-digit blocks in the sequence. the monodromy invariant o k {\displaystyle o_{k}} is defined as the sum of all monomials coming from odd admissible sequences composed of k blocks. the monodromy invariant e k {\displaystyle e_{k}} is defined the same way, with e...
wikipedia
e3c8d385cc74aec7b187bd2cc83f49cd0778b7c9
with a view towards defining the monodromy invariants,
with a view towards defining the monodromy invariants, say that a block is either a single integer or a triple of consecutive integers, for instance 1 and 567. say that a block is odd if it starts with an odd integer. say that two blocks are well-separated if they have at least 3 integers between them. for instance 123...
wikipedia
ec425eabb8dae727a0f5122ba18d80c106171434
the pentagram map, when acting on the moduli
the pentagram map, when acting on the moduli space x of convex polygons, has an invariant volume form. at the same time, as was already mentioned, the function f = o n e n {\displaystyle f=o_{n}e_{n}} has compact level sets on x. these two properties combine with the poincaré recurrence theorem to imply that the action...
wikipedia
f20515bfe73f1e3ddf209da238c28347064e8b51
the level sets of the function f =
the level sets of the function f = o n e n {\displaystyle f=o_{n}e_{n}} are compact, when f is restricted to the moduli space of real convex polygons. hence, each orbit of the pentagram map acting on this space has a compact closure.
wikipedia
06a0db965f5d18c4c77195fe41b93bed10762572
are likewise seen, directly from the formula, to
are likewise seen, directly from the formula, to be invariant functions. all these products turn out to be casimir invariants with respect to the invariant poisson bracket discussed below. at the same time, the functions o k {\displaystyle o_{k}} and e k {\displaystyle e_{k}} are the simplest examples of the monodromy ...
wikipedia
6e7858cbd4218ae47b27c4f2b00249a100ebe0c5
these rules are meant to hold for all
these rules are meant to hold for all configurations which are congruent to the ones shown in the figure. in other words, the figures involved in the relations can be in all possible positions and orientations. the labels on the horizontal edges are simply auxiliary variables introduced to make the formulas simpler. on...
wikipedia
4168dd384408b02fe90cd2a225744023a06535f6
the formula for the pentagram map has a
the formula for the pentagram map has a convenient interpretation as a certain compatibility rule for labelings on the edges of triangular grid, as shown in the figure. in this interpretation, the corner invariants of a polygon p label the non-horizontal edges of a single row, and then the non-horizontal edges of subse...
wikipedia
e8a3e368706d59b47c41b8069e9fd0e43d77d03c
(note: the index 2 k + 0 is
(note: the index 2 k + 0 is just 2 k. the 0 is added to align the formulas.) in these coordinates, the pentagram map is a birational mapping of f 2 n {\displaystyle f^{2n}}
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225fb53d6a5a464342574632235c7fd76e2555a2
here is a formula for the pentagram map,
here is a formula for the pentagram map, expressed in corner coordinates. the equations work more gracefully when one considers the second iterate of the pentagram map, thanks to the canonical labelling scheme discussed above. the second iterate of the pentagram map is the composition b ∘ a {\displaystyle b\circ a}. th...
wikipedia
9b49a7e3dc120927d541cbc15e9edee907fd7749
the coordinates a 1, b 1, a 2,
the coordinates a 1, b 1, a 2, b 2, … {\displaystyle a_{1},b_{1},a_{2},b_{2},\ldots } serve as coordinates for the moduli space of twisted n -gons as long as n is not divisible by 3.
wikipedia
9e3e224de99375dd8dd20ae1c7d81c46d504eb90
there is a second set of coordinates for
there is a second set of coordinates for the moduli space of twisted polygons, developed by sergei tabachnikov and valentin ovsienko. one describes a polygon in the projective plane by a sequence of vectors … v 1, v 2, v 3, … {\displaystyle \ldots v_{1},v_{2},v_{3},\ldots } in r 3 {\displaystyle r^{3}} so that each con...
wikipedia
eafd96e99555ddae978a1ea8d5b730ee49246788
the corner invariants make sense on the moduli
the corner invariants make sense on the moduli space of twisted polygons. when one defines the corner invariants of a twisted polygon, one obtains a 2 n -periodic bi-infinite sequence of numbers. taking one period of this sequence identifies a twisted n -gon with a point in f 2 n {\displaystyle f^{2n}} where f is the u...
wikipedia
ca714bf2cfb37a5dd6aae31bd6f5bc444e6abef9
let p be an n -gon, with flags
let p be an n -gon, with flags f 1, …, f 2 n {\displaystyle f_{1},\ldots,f_{2n}} to each flag f, we associate the inverse cross ratio of the points t 1, t 2, t 3, t 4 {\displaystyle t_{1},t_{2},t_{3},t_{4}} shown in the figure at left. in this way, one associates numbers x 1, …, x 2 n {\displaystyle x_{1},\ldots,x_{2n}...
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0a3f38c6614a3ebc4618f6e3fbce97d6341ce7cd
the corner invariants are basic coordinates on the
the corner invariants are basic coordinates on the space of twisted polygons. suppose that p is a polygon. a flag of p is a pair (p, l), where p is a vertex of p and l is an adjacent line of p. each vertex of p is involved in two flags, and likewise each edge of p is involved in two flags. the flags of p are ordered ac...
wikipedia
db57a9fabb47f58103985c3a74141ae1fc1aac2f
in the slightly more general set-up below, the
in the slightly more general set-up below, the cross ratio makes sense for any four collinear points in projective space one just identifies the line containing the points with the projective line by a suitable projective transformation and then uses the formula above. the result is independent of any choices made in t...
wikipedia
243a88effbeb579924adf2f16a828303f57307d2
most authors consider 1/ x to be the
most authors consider 1/ x to be the cross-ratio, and that is why x is called the inverse cross ratio. the inverse cross ratio is invariant under projective transformations and thus makes sense for points in the projective line. however, the formula above only makes sense for points in the affine line.
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743e6a63f22258cc7b3e10300a229c979e1b71bb
given the four points t 1, t 2,
given the four points t 1, t 2, t 3, t 4 {\displaystyle t_{1},t_{2},t_{3},t_{4}} in the affine line one defines the (inverse) cross ratio
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f9f19a06f38fcb2f511e507a8bd505366f9b72f6
when the field underlying all the constructions is
when the field underlying all the constructions is f, the affine line is just a copy of f. the affine line is a subset of the projective line. any finite list of points in the projective line can be moved into the affine line by a suitable projective transformation.
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1d164c281e5c29b3396c3d7f6c5647426694d4c8
the tori are invisible subsets of the moduli
the tori are invisible subsets of the moduli space. they are only revealed when one does the pentagram map and watches a point move round and round, filling up one of the tori. roughly speaking, when dynamical systems have these invariant tori, they are called integrable systems. most of the results in this article hav...
wikipedia
ea65f79a0a73efb18d32d2a09b32b5b6acd79ad9
one can do experiments with the pentagram map,
one can do experiments with the pentagram map, where one looks at how this mapping acts on the moduli space of polygons. one starts with a point and just traces what happens to it as the map is applied over and over again. one sees a surprising thing: these points seem to line up along multi-dimensional tori. these inv...
wikipedia
6045902fa656ed894718ea8d75d76a197b1be125
to explain how the pentagram map acts on
to explain how the pentagram map acts on the moduli space, one must say a few words about the torus. one way to roughly define the torus is to say that it is the surface of an idealized donut. another way is that it is the playing field for the asteroids video game. yet another way to describe the torus is to say that ...
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68ed997fc2f03933c689bddb6cef0a38945edc60
the reason for considering what the pentagram map
the reason for considering what the pentagram map does to the moduli space is that it gives more salient features of the map. if you just watch, geometrically, what happens to an individual polygon, say a convex polygon, then repeated application shrinks the polygon to a point. to see things more clearly, you might dil...
wikipedia
e44c4e72895913ab761b8e30989aaf013ec3e947
the pentagram map is fruitfully considered as a
the pentagram map is fruitfully considered as a mapping on the moduli space of polygons. a moduli space is an auxiliary space whose points index other objects. for example, in euclidean geometry, the sum of the angles of a triangle is always 180 degrees. you can specify a triangle (up to scale) by giving 3 positive num...
wikipedia
29634673760dba9189f66b139d3cce9f5d7b293c
this section is meant to give a non-technical
this section is meant to give a non-technical overview for much of the remainder of the article. the context for the pentagram map is projective geometry. projective geometry is the geometry of our vision. when one looks at the top of a glass, which is a circle, one typically sees an ellipse. when one looks at a rectan...
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927d1dd08e6bf417b7b36ae33d1391aee8e8d4de
the iterates of the pentagram map shrink any
the iterates of the pentagram map shrink any convex polygon exponentially fast to a point. this is to say that the diameter of the nth iterate of a convex polygon is less than k a n {\displaystyle ka^{n}} for constants k > 0 {\displaystyle k>0} and 0 < a < 1 {\displaystyle 0<a<1} which depend on the initial polygon. he...
wikipedia
b71a26aa9aa17b69f117b9046be0823d0fd0b65d
the map t 2 {\displaystyle t^{2}} is the
the map t 2 {\displaystyle t^{2}} is the identity on the space of labeled hexagons. here t is the second iterate of the pentagram map, which acts naturally on labeled hexagons, as described above. this is to say that the hexagons h {\displaystyle h} and t 2 (h) {\displaystyle t^{2}(h)} are equivalent by a label-preserv...
wikipedia
eaa322cb9589d8f44bfb3bb6436915a3d3b007e5
two twisted n -gons are equivalent if a
two twisted n -gons are equivalent if a projective transformation carries one to the other. the moduli space of twisted n -gons is the set of equivalence classes of twisted n -gons. the space of twisted n -gons contains the space of ordinary n -gons as a sub-variety of co-dimension 8.
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df0d1cb5c1ab31afb8740f8adb7da7c8599094b0
a twisted n -gon is a bi-infinite sequence
a twisted n -gon is a bi-infinite sequence of points in the projective plane that is n -periodic modulo a projective transformation that is, some projective transformation m carries p k {\displaystyle p_{k}} to p n + k {\displaystyle p_{n+k}} for all k. the map m is called the monodromy of the twisted n -gon. when m is...
wikipedia
aa21b56a874b9434dd32358cc75e5436cc3444e4
there is a perfectly natural way to label
there is a perfectly natural way to label the vertices of the second iterate of the pentagram map by consecutive integers. for this reason, the second iterate of the pentagram map is more naturally considered as an iteration defined on labeled polygons. see the figure.
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3ad9c45718737a7be4d19588a299fb3887893278
the map p → q {\displaystyle p\to q}
the map p → q {\displaystyle p\to q} is slightly problematic, in the sense that the indices of the p -vertices are naturally odd integers whereas the indices of q -vertices are naturally even integers. a more conventional approach to the labeling would be to label the vertices of p and q by integers of the same parity....
wikipedia
5b6b969f09f95e4430dab237a48c8fa02c38a045
on a basic level, one can think of
on a basic level, one can think of the pentagram map as an operation defined on convex polygons in the plane. from a more sophisticated point of view, the pentagram map is defined for a polygon contained in the projective plane over a field provided that the vertices are in sufficiently general position. the pentagram ...
wikipedia
5529bff249bc50807420a0498da0cde7ea652f3f
suppose that the vertices of the polygon p
suppose that the vertices of the polygon p are given by p 1, p 3, p 5, … {\displaystyle p_{1},p_{3},p_{5},\ldots } the image of p under the pentagram map is the polygon q with vertices q 2, q 4, q 6, … {\displaystyle q_{2},q_{4},q_{6},\ldots } as shown in the figure. here q 4 {\displaystyle q_{4}} is the intersection o...
wikipedia
a02ae203669b650fc5fa684beb183c4fe96066dc
in mathematics, the pentagram map is a discrete
in mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. the pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. richard schwartz introduced the pent...
wikipedia
20619eed617d6ff6cc525eea81265b4add425868
max denmark mh is a hong kong rugby
max denmark mh is a hong kong rugby union player. denmark was educated at island school in hong kong and millfield school in england. denmark plays for the hong kong national rugby sevens team and hong kong rugby union team. he captained the hong kong u19 team to victory at the asian rugby u19 championships in 2018. he...
wikipedia
f9f271cf970a6f335b3b5729d71bf3a7ab939d1b
denmark became the 297th player for hong kong
denmark became the 297th player for hong kong when he made his debut for the hong kong rugby union team on 18th november 2017, in an 40-30 win over kenya at hong kong football club.
wikipedia
ca7b91984344ca7f38e569fbe7082d8f4bfc78a6
denmark plays for the hong kong national rugby
denmark plays for the hong kong national rugby sevens team and hong kong rugby union team. he captained the hong kong u19 team to victory at the asian rugby u19 championships in 2018. he competed for hong kong at the 2022 rugby world cup sevens in cape town.
wikipedia
bc3916453baba8896c4756e9a4ddd9e1bef615cc
hans-peter kohler is a german-american demographer and sociologist.
hans-peter kohler is a german-american demographer and sociologist. he is the frederick j. warren professor of demography, professor of sociology, and co-director of the population aging research center at the university of pennsylvania. in 2005, he received the clifford c. clogg award for early career achievement from...
wikipedia
374dafe7b2d2626b27f688bfd2ca28779868d049
hans-peter kohler is a german-american demographer and sociologist.
hans-peter kohler is a german-american demographer and sociologist. he is the frederick j. warren professor of demography, professor of sociology, and co-director of the population aging research center at the university of pennsylvania. in 2005, he received the clifford c. clogg award for early career achievement from...
wikipedia
e61da51a940ddf4cba606edded38ba5551d4b9ae
007: quantum of solace is a 2008 shooter
007: quantum of solace is a 2008 shooter video game published by activision. based on the james bond films casino royale (2006) and quantum of solace (2008), it was developed by treyarch for playstation 3 (ps3) and xbox 360 and by beenox for microsoft windows and wii, and is mostly played as a first-person shooter, wit...
wikipedia
d63ac7a09ea8a81e22077fd7b88f15b331bc432f
the ds version was praised for its gameplay
the ds version was praised for its gameplay ideas, although critics found the execution to be poor. the touchscreen-based controls were considered difficult and unreliable in their accuracy, with hand-to-hand combat receiving particular criticism. some critics also considered the isometric view too zoomed-in, making it...
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041396f341993f5195e28f689080cc7a37805f22
the wii version was criticized for its difficult
the wii version was criticized for its difficult motion controls, as well as poor graphics and frame rate, the latter contributing further to the game's difficulty. mark bozon of ign considered the wii version a "wreck" because of its numerous issues, calling the frame rate "unreliable at best, and broken entirely in s...
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b9ccb777b0091b7b522806a5a8e2c256311a37eb
natalie romano of gamezone found the ps2 version
natalie romano of gamezone found the ps2 version an adequate alternative to the ps3/xbox 360 version, while ahearn considered it more enjoyable thanks to its third-person perspective. however, the ps2 version did receive criticism for its lack of multiplayer.
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acac3c8e3e58c320d5b05d4ee3d8a917a559deaa
alex sassoon coby, writing for gamespot, found that
alex sassoon coby, writing for gamespot, found that the casino royale portion occupied too much of the game and felt out of place in the storyline. constantino wrote, "the majority of your time is spent recapping the events of casino royale, with only a few brief opening and closing sections taken from the game’s names...
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ffddac15a68ccfa8b2153830e199c4902e4d0762
criticism went towards the combination of both film
criticism went towards the combination of both film storylines in a single game. andrew reiner of game informer criticized the lack of chronological order: "the result is a plot that bounces chaotically like a super ball in a stairwell. it’s impossible to comprehend what is going on in this game unless you have seen bo...
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83b4edabd0c63dd537509749f2dc4be37b871c2a
critics generally believed that quantum of solace, like
critics generally believed that quantum of solace, like previous bond games, failed to live up to the standards set by goldeneye. conversely, roy kimber of videogamer.com called it "goldeneye for a new generation and by far the best bond game we've had in years", stating, "praise really doesn't come much higher than th...
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7b5d9c7daeed1b63f23fb462991ff9184e759247
travis moses of gamepro concluded that the game
travis moses of gamepro concluded that the game "can't stand up to the properties it was based on, hampered by bland and repetitive gameplay". ben fritz of variety found the game to play "more like a series of new 'call of duty' levels", criticizing the decision to develop a spy game with an engine used for a military ...
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e94aca8ea0f6941986b842836623105e8665f0ae
the gameplay was a source of criticism, generally
the gameplay was a source of criticism, generally viewed as repetitive and lacking in variety. seth schiesel of the new york times was critical of the excessive shooting gameplay and lack of driving levels. bryan stratton of gamespy also found the gameplay repetitive: "there's no real hand-to-hand combat, no puzzle-sol...
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e4bfdf20be9085d8972e38145d15d5a300121717
across all platforms, quantum of solace received "mixed
across all platforms, quantum of solace received "mixed or average reviews" according to metacritic. criticism went to the game's short length and lack of replay value, as well as poor ai. the graphics received a mixed response, with praise going towards the character models, while criticism went to the environments. p...
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484870d210a8bc73dc4621fb9fe0e5abb165bcde
the game features a different theme song from
the game features a different theme song from that of the film. titled "when nobody loves you", it was written by richard fortus and kerli, and performed by them along with david maurice, who produced and arranged it. the song plays over an opening title sequence that is proprietary to the game, but based on the film's...
wikipedia
4aaf0dcb30a3e01a1d8e65fd10994903cf10e778
the game's score was recorded in two locations,
the game's score was recorded in two locations, with strings and winds handled in bratislava, followed by brass and percussion recording with members of the hollywood studio symphony at capitol studios in hollywood. according to lennertz, "the brass is especially integral to the sound of any bond music and i felt that ...
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bf5041b2c0b504e28d4333cdb74ec6e9659fec3e
the music was composed by christopher lennertz, who
the music was composed by christopher lennertz, who previously scored the 2005 bond game from russia with love. lennertz began working on the score in early 2008, while parts of the game were still in a conceptual stage. to maintain a classic bond sound, lennertz rewatched casino royale and also listened to previous bo...
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in japan, square enix published the game for
in japan, square enix published the game for home consoles on 26 march 2009, two months after the film's release there. quantum of solace and other bond games by activision were removed from the company's website and steam in january 2013, reportedly due to expiration of the game rights licence.
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the game was released in europe on 31
the game was released in europe on 31 october 2008, followed by the u.s. debut on 4 november. the release coincided with the film's theatrical debut, making it the first film-based bond game to release concurrently with its source material. a collector's edition of the ps3 and xbox 360 versions was released in the u.k....
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craig provided his likeness and voice for the
craig provided his likeness and voice for the game, along with other cast members from the two films, including judi dench as m, eva green as vesper lynd, mads mikkelsen as le chiffre, olga kurylenko as camille montes, and mathieu amalric as dominic greene. craig's likeness was created using three-dimensional scans and...
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executive producer garrett young said that craig's version
executive producer garrett young said that craig's version of bond "isn't quite as reliant on gadgets as previous bonds, but with the ok from the filmmakers, we added the gadgets we felt would be fun and that would help gameplay, yet still fit within the world of the new, more realistic james bond". the hacking feature...
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quantum of solace marked the first bond video
quantum of solace marked the first bond video game for actor daniel craig, who played the character in the films. craig was reluctant to be involved in a bond game: "when i started signing contracts for bond i said, 'i'm not doing the computer game' and they said, 'tough, you are'. i said to the people making the bond ...
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the treyarch team played previous bond games, including
the treyarch team played previous bond games, including the acclaimed 1997 instalment goldeneye 007, which provided the biggest source of inspiration. the game lacks driving levels, a common element in past games, as treyarch sought to avoid taking on more than it could handle. the company also wanted the game to focus...
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because the film quantum of solace (2008) is
because the film quantum of solace (2008) is a direct sequel to casino royale (2006), the decision was made for the former's game adaptation to cover both films. the development team visited the sets of both instalments and observed some filming, while taking reference photos to help recreate the environments for the g...
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in may 2006, activision reached a deal to
in may 2006, activision reached a deal to acquire the publishing rights to james bond video games. the company reportedly paid $70 million for the licence, which had been held by electronic arts since the late 1990s. activision's deal took effect in september 2007, and quantum of solace would mark its first bond game. ...
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quantum of solace, with the exception of the
quantum of solace, with the exception of the ps2 and ds versions, includes a multiplayer option with several game modes. players are split between mi6 and quantum. online multiplayer is available for up to 4 players on the wii game, and up to 16 players on the other versions. the wii version also offers an offline spli...
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the ds version follows an altered storyline compared
the ds version follows an altered storyline compared with the other games. the character of camille is cut altogether, the opening mission at white's estate is replaced by a training simulation at mi6 headquarters and, after fighting street gangs in bolivia, the final mission and boss fights against greene and mr. whit...
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scattered throughout each level are various items, including
scattered throughout each level are various items, including casino chips and cards, which can be used to upgrade abilities. cards can be equipped in different orders to enhance abilities with varying effects, depending on what poker hands are formed. chips are used to purchase upgrades such as better aiming.
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the ds game is viewed from a third-person
the ds game is viewed from a third-person isometric perspective, but switches to an over-the-shoulder view during melee attacks. gameplay is mostly controlled with the console's touchscreen, which is used to guide bond around, as well as to aim and shoot at enemies. bond can jump at predetermined sections in the game.
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the various versions are generally the same, though
the various versions are generally the same, though with minor changes to suit the technological capabilities of each platform. the ps2 version excludes the missions set at the miami airport, on the train, and in venice. it adds a new mission set in the docks, and all levels feature slightly different designs. the wii ...
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the player can hold up to three weapons
the player can hold up to three weapons and can pick up fallen weapons left behind by dead enemies. the player is also given a map of each level and can use hacking to unlock doors and disable security cameras. stealth can be used and is sometimes necessary to proceed. examples of this include the use of silenced weapo...
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the pc, ps3, wii, and xbox 360 versions
the pc, ps3, wii, and xbox 360 versions are primarily a first-person shooter, but perspective switches to third-person whenever bond takes cover from enemy fire. the ps2 version is played solely from a third-person perspective. health is automatically regenerated when not taking damage.
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bond and camille soon arrive at a hotel
bond and camille soon arrive at a hotel in the middle of the bolivian desert. there, greene and medrano are discussing the land that greene wants to buy; greene will fund medrano's attempt to overthrow the government in exchange for the land that he wants. bond and camille break up the meeting; camille kills medrano wh...
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the game jumps forward to bond crashlanding in
the game jumps forward to bond crashlanding in bolivia, where greene is trying to buy land. by this time, bond has met camille montes, who is seeking vengeance against general medrano, who is trying to overthrow the bolivian government. bond learns that medrano killed camille's family, and this is why she wants revenge...
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the game begins with mi6 agent james bond
the game begins with mi6 agent james bond kidnapping mr. white, a member of the previously unknown criminal-terrorist organization quantum. while he and m interrogate white, they are attacked by the traitorous mi6 agent craig mitchell, who is killed by bond while white escapes. later, bond spies on a meeting of quantum...
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quantum of solace, according to metacritic, received "mixed
quantum of solace, according to metacritic, received "mixed or average reviews" across all platforms. critics generally believed that the game failed to live up to the standards set by goldeneye due to its repetitive gameplay and short length, although they praised the multiplayer options, voice acting and music.
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quantum of solace marked activision's first james bond
quantum of solace marked activision's first james bond video game, following a deal the company reached in 2006 to acquire the game rights, previously held by electronic arts. the developers referred to previous bond games, with the acclaimed goldeneye 007 providing the biggest source of inspiration. they also visited ...
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007: quantum of solace is a 2008 shooter
007: quantum of solace is a 2008 shooter video game published by activision. based on the james bond films casino royale (2006) and quantum of solace (2008), it was developed by treyarch for playstation 3 (ps3) and xbox 360 and by beenox for microsoft windows and wii, and is mostly played as a first-person shooter, wit...
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6e509b4d8a6c784d64254f698d53b3945f0b4b31
the director circle of an ellipse is a
the director circle of an ellipse is a special case of this more general construction with two points p and p at the foci of the ellipse, weights w = w = 1, and c equal to the square of the major axis of the ellipse. the apollonius circle, the locus of points x such that the ratio of distances of x to two foci p and p ...
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more generally, for any collection of points p,
more generally, for any collection of points p, weights w, and constant c, one can define a circle as the locus of points x such that ∑ i w i d (x, p i) 2 = c. {\displaystyle \sum _{i}w_{i}\,d(x,p_{i})^{2}=c.}
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907c540bdf57c62b022ac01fa9779544b4994e34
the director circle of a hyperbola has radius
the director circle of a hyperbola has radius a 2 − b 2 {\textstyle {\sqrt {a^{2}-b^{2}}}}, and so, may not exist in the euclidean plane, but could be a circle with imaginary radius in the complex plane.
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the director circle of an ellipse circumscribes the
the director circle of an ellipse circumscribes the minimum bounding box of the ellipse. it has the same center as the ellipse, with radius a 2 + b 2 {\textstyle {\sqrt {a^{2}+b^{2}}}}, where a {\displaystyle a} and b {\displaystyle b} are the semi-major axis and semi-minor axis of the ellipse. additionally, it has the...
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84a977a572e05075750436018e1d3e7c454ffbf4
in geometry, the director circle of an ellipse
in geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or fermat–apollonius circle) is a circle consisting of all points where two perpendicular tangent lines to the ellipse or hyperbola cross each other.
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gallium(iii) chloride is an inorganic chemical compound with
gallium(iii) chloride is an inorganic chemical compound with the formula gacl3 which forms a monohydrate, gacl3·h2o. solid gallium(iii) chloride is a deliquescent white solid and exists as a dimer with the formula ga2cl6. it is colourless and soluble in virtually all solvents, even alkanes, which is truly unusual for a...
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110 tons of gallium(iii) chloride aqueous solution was
110 tons of gallium(iii) chloride aqueous solution was used in the gallex and gno experiments performed at laboratori nazionali del gran sasso in italy to detect solar neutrinos. in these experiments, germanium -71 was produced by neutrino interactions with the isotope gallium-71 (which has a natural abundance of 40%),...
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