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30 Nov 2018: FIG. 4. Bifurcation behavior of the lips. Diagrams in (, E ) space of some solution branches for (a) k = 4.0 > k and (b) k = 2.5 < k.Roman numerals label branches. ... The recent observation that inver-sion in the genus Pleodorina features nonuniform

16 Jun 2022: Pij(t) = |⟨j| exp(itĤ)|i⟩|2 (34). where |i⟩ are the normalized eigenvectors of some observable, e.g. ... Ĥ =ˆS B =. i. ŜiBi , (62). where B is some constant vector.

4 Dec 2017: Hence. supp(RN ) supp(ϕ) B|h|. Choose |h| small enough1 so that the left hand side is contained in some compact subset of X. ... Compactness of supp(ϕ) implies d(x) δ for some δ > 0, sotaking |h| < 1.

13 Dec 2023: b)Algae and bacteria as observed through the brightfield and fluorescent channels, respectively. ... In a simple approximation, theextent of the turbulent transport is proportional to thebacterial concentration, giving a contribution to the algalflux J =

13 Dec 2018: Unless [A, B] = 0, in which case (5) is exact, some subtlety is needed in characterizing [A, B] as “small.” The natural measure for bounded operators, [[[A, B]11/(211All /B[]), ... 2) lml reaches a maximum at every point on St with respect to some

22 Jan 2018: EA(x,t) = cAtn/2 exp(x Bx/4t). and zero elsewhere, for some B Matn(C) and constant cA, both of which will obviously depend on A.For EA to ... Hence. sing supp F {. (t,x) : x p|p|. t = 0 for some p 6= 0}. =

13 Dec 2018: where the superscript denotes an X derivative of some de-gree, and h is any function. ... If we assume that the solution is of order a, then ak- a X(2kAo)a, where X is some constant that will vary withrealizations.

9 Nov 2019: Note that the commutator[A, B] is in some sense small, and so the accuracy of equation ( 6) is better in practicethan is suggested by the quantity (AZ) 2 (see [8]). ... Some features of these may be compared with the numerical solution, but they arenot

19 Sep 2022: 3(b)]. From these distributions, we estimate, for both models,the probabilities of extinction of some species for systems. ... We confirm some of these numerical results byderiving exact results for simplified models in Appendix B.These exact results

26 Jun 2024: strong nuclear interactions, and we will consider this specific theory in some detail in. ... b $ c) (b $ d)i. Momentum conservation, pa pb = pc pd, ensures that some of these terms cancel.

21 Jun 2007: B 0 = 0, and so ABA 0 B 0 = FAB A 0 B 0 for some FAB. ... ÁA 0 B 0 = Á A 0 B 0 for some function Á.

11 Jun 2022: B. Organisation. In Section II we review some background material onsemidefinite programming and sums of squares. ... 15] K. G. Murty and S. N. Kabadi, “Some NP-complete problems inquadratic and nonlinear programming,” Mathematical Programming,vol.

20 Sep 2011: B′ εA′B′ρAB = 0. (where Pab = (1/2)Rab (1/12)Rgab) for some ρ Λ2(M).Differentiate and commute derivatives:. ... Γ̂kij = Γkij δi. kωj δjkωi, i,j,k = 1, 2 for some ω = ωidxi.

1 Dec 2023: Simple one-dimensionalmodels are developed to describe some of the observed features of the relationshipNu(). ... a) Dimensionalvariables. (b) Dimensionless variables. system that capture some of the observed features of the relationship Nu(), and

2 Mar 2004: Given that the particle’s trajectoryis r = a sin θ for some constant a, deduce that (up to an arbitrary additive constant)V r4. ... 7 If µ(r) = |f(r)| for some function f, show that B.

19 Jan 2012: considered. Some astrophysical discs are non-self-gravitating, meaning that the internal. contribution can be neglected relative to that of external masses, most importantly the. ... mass does not vanish in general. However, some new topological

7 Apr 2021: It is called the magnetic length. lB =. sqB. To give you some sense for this, in a magnetic field of B = 1 Tesla, the magnetic length. ... At certain, very special values of B, we will find some number of Landau levels that.

22 Mar 2012: z‖b = maxt[0,T ]. ebt ‖z(t)‖,. for some b > 0, so that for sufficiently large b and any element z(t) of the space it istrue that ‖z(t)‖ ... Indeed,. ‖y[ν] y‖b γ ‖y[ν1] y‖b, for some 0 γ < 1 and b > 0.

2 May 2024: For this lecture, we consider a simple class of ODEs: consider x 2 Rand some (unknown) function y : R! ... the end point and h is the step size% returns 2 column vectors, estimates of x and y(x) at n points % the "round" function gives the closest

13 Jan 2021: 2(b)].Some comments are in order. Although free MTs have a. complex dynamics of growth and decay, recent evidence[29] for “superstable” cortically bound MTs in stagesdisplaying unidirectional streaming justifies ... Results ofcomputations at ρ 4.65:

4 May 2023: ai 2i. for some integers (n, a0, a1, a2,. , an), with ai 2 {0, 1}. ... The numberpA2 b is likely not representable. we have to approximate it by some representable number C<latexit

25 Jan 2007: To some extent the converse holds, if the ThirdLaw did not hold these conservation laws would not necessarily hold. ... The last astronauts to visit left behind some cornerreflectors, i.e. three plane mirrors meeting mutually at right angles.

1 Dec 2023: Although in some situations (such as classical poroelasticity), the porous matrix provides anelastic solid stress and deformations are recoverable, many complex suspensions can exhibit asignificant plastic stress, owing to rearrangements,

26 Jul 2013: The force-displacement relation, Eqs. 2c and 2d can then be linear-ized, and after some straightforward algebra, we obtain. ... 2c and2d, and after some tedious but straightforward algebra weobtain locomotion and relative motion at speeds V , V2. =

27 Apr 2024: by bit, looking at situations where only some of the equations are important. ... charge Q. Next the dipole moment p which contains some basic information about.

17 Nov 2008: Therefore the integral curves of (3.1) are geodesics of some projective structure (anequivalence class of torsion-free connections sharing the same unparametrized geodesics). ... 3a3 ka c. where b and c are some constants. The pure dust case considered

1 Dec 2023: In some experiments,we also measure the internal deformation through the mediumby tracking a representative sample of individual particles. ... ρgHf2,. (25a,b,c). respectively, for some dimensionless functions f1(,H ρgH /σ ) and f2(,H).

4 Feb 2022: Ideally with error control. 2/34. Some common techniques. Domain truncation and absorbing boundary conditions: B. ... Philosophy of the new approach. Previous approaches: A is discretised to A Cnn and we use some sort offinite-dimensional solver –

5 Oct 2020: 2 for some a, b and c. The infor-mation contained in this Hilbert space is not carried by any local degree of freedom. ... We first fuse a and b together and,. of all the possibilities allowed by the fusion rules, we get some specific anyon i.

12 Jun 2021: In the Vector Calculus course, you will spend some time computing quantities such. ... m. g. et/m b. To determine this second integration constant, we need some further information about.

2 Feb 2020: Some care should be taken in examining? P and its dependence on step-size. ... g=B’(Z,)h(B(Z,,),.,B(Z,), u)>. where the superscript denotes an X-derivative of some degree and h is any function.

10 Jan 2017: 8 F. CONTATTO AND M. DUNAJSKI. diagonal, i.e. takes the form (1.3) for some λa(X b) and can be linearized by a hodograph transformationinterchanging dependent (X 1, X ... An affine connection is metrizable iff it shares its unparameterizedgeodesic with

21 Aug 2019: Want tocompute spectra of a class B(l 2(N)). What attributes should an “algorithm” Γn(A) possess? ... Call this class1. Some notation:. If z / Sp(A) write. R (z, A) := (A zI )1 B(l 2(N)).

8 Mar 2004: Let y(x) be a function of x in some interval a < x < b, and consider the definite integral. ... What shape must. the wire have for the bead to reach some lower point B in the shortest time?

30 Jan 2020: for some |f〉 Hn,F. (3.52). Thus any state |b〉 Hn,B with energy En > 0 is necessarily the Q̄-transformation of somestate |f〉 Hn,F. ... A similar argument shows that any state in Hn,F with n > 0 is theQ-transformation of some state in Hn,B.

1 Sep 2011: n k, for some f Mk(a, b). Also, if lj = k for some j, then f. ... Thus, we can assume that Z = [c, d] for some [c, d] [a, b].

16 Jun 2009: UV degrees of freedom which comprise the (2, 0) theory. Let’s look at some circumstantial evidence for this proposal. ... partons. For example, here’s some plots showing the single lump in CP2.

19 Jul 2019: It is called the magnetic length. lB =. sqB. To give you some sense for this, in a magnetic field of B = 1 Tesla, the magnetic length. ... At certain, very special values of B, we will find some number of Landau levels that.

30 Sep 2008: where ψ̃ is the normalised wavefunction corresponding to ψ(x, t). After some algebra,. ... The corresponding particle fluxis,. j = |B|2 k. m. In our scattering problem we have incident particles from the left and also expect some.

13 Oct 2013: On Being the Right SizeJ. B. S. Haldane. The most obvious differences between different animals are differences of size, but for some reason the zoologists have paid singularly little attention to ... But it is time that we pass to some of the advantages

1 Dec 2023: Fx(δ, n, Bi) Bifx(|δ|) sgn(δ) Fz(δ, n, Bi) Bifz(|δ|) sgn(cos δ), (3.6a,b)for some functions fx and fz. ... decreasedfurther, however, because Ws vanishes at some non-zero amplitude in the viscoplastic case.

25 Aug 2021: Let’s look at some properties of this. First, consider the action of 2,. ... for some choice of phase m which, as the notation shows, can depend on m. –

9 Oct 2017: Bz vEy/c2. . (3.31)Since we want to demonstrate that for some β = v/c with |β| < 1, we can set E′ andB′ parallel, consider E′ B′ (which lies ... µTµν = some 4-vector linear in the field strength tensor and current 4-vector.

26 Nov 2016: So altogether,. we are free to specify Cauchy data along some other curve B R2 that is transverse to allthe characteristic curves, meaning that the tangent vector to B is nowhere ... Thus, if J = 0 then the family of integral curves of uare

11 Mar 2024: dwlog G(w). (S24). Integrating, we obtain G(x) = bexp(cx) for some b. ... Λ(E) =. E. λ(x)dx (S67). for some function λ : K R+.

24 Aug 2023: so that, for example, if some section of the endomorphism bundle has componentsAi. ... and plugging in some X 2 H yields2p. n p 1d(X, )|H d|H.

16 Sep 2023: we see immediately that probability is conserved, meaning that ifRd3x P = 1 at some. ... some position in between. And we sum up the probabilities for each position.

1 Dec 2021: Ideally with error control. 2/34. Some common techniques. Domain truncation and absorbing boundary conditions: B. ... Philosophy of the new approach. Previous approaches: A is discretised to A Cnn and we use some sort offinite-dimensional solver –

10 Jun 2016: b(h)| = o(h), for n some unit vector. ... they are not connected. This allows for some useful constructions, for example (these.

31 Dec 2018: satisfies this equation is. (vx) = AeBv2x. for some constants A and B. ... taken up by the particles. It is worth pointing out where some quizzical factors of two come from in b = 2r30/3.