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17 Nov 2023: By. considering other functions of state, such as the free energy F = E TS, derive the. ... this is the original Ginzburg-Landau free energy for a superconductor.). Neglecting interactions, what is the critical dimension dc, such that the coupling.

11 Oct 2023: saddle. Sketch examples, where possible, of flows with a periodic orbit such that the set of fixed points. ... enclosed by it: (a) is empty; (b) contains just one sink; (c) contains just the saddle; (d) contains one sink.

10 Feb 2023: g :(D2,S1. ) (M,B). such that[g|S1. ]6 N. We first explain why the Loop Theorem implies Dehn’s Lemma:. ... g :(D2,S1. ) (M,B). such that[g|S1. ]6= 1. Set c =. [g|S1. ] π1B, and write c = ka b, with. k, Z.

13 Feb 2023: a(tb)Kbk=3[α (k 1)β]. Kbl=1 Γ(n. bl β). Γ(m(b) α)(7). Each segment [ab] S′(T ) contributes such a term.Since this expression ... Equation 9 factorizes into a term for ta and tb. Col-lecting such terms from the branches attached to aninternal node

24 Nov 2023: 45) Show that there is a w such that Ww = {w} and a w such that |Ww| = |w|. ... Show that the following sets arecomputably enumerable:. (a) {w ; there are three distinct words v such that f(w, v)};(b) {w ; there is a word v of even length such

12 Jul 2023: b) Define a sequence of theories {Ti ; i N} and a theory T such that T0 = ZFC ICand (assuming the consistency of all involved theories). ... a) Construct a transitive set M with κ M and |M| = κ such that.

9 Nov 2023: dx = hξdξ hθdθ hφdφ. [5]. (b) Find a suitable form for g(ξ) such that g(0) = 1 and the coordinate system (ξ,θ,φ)is orthogonal. ... b) A function f(x) is constrained such that f(1) = f(1) = 0.

12 Jul 2023: Give an example of a nontrivialopen immersion V Y such that Y is connected and affine and V is also affine. ... Let ϕ : X Y be a morphism ofschemes. Suppose that {Ui} is an open cover of Y such that ϕ1(Ui) Ui is properfor all i.

13 Feb 2023: of algorithms, such that other instances of this family have better statistical properties. ... We explore how such prediction sets impact expert decision-making in human-AI teams.

13 Nov 2023: of office. (b) There may be a Vice-President with such duties as the President and the Vice-President.

2 Aug 2023: b. Now choose a metric such that the line element on the worldsheet is dτ2 dσ2. ... b. Explain why A(m) = A(m), and show that the Jacobi identity fixes.

17 Jul 2023: a) Show that the unique minimizer is x = 0. (b) Find constants 0 < m < M and L > 0 such that m f ′′(x) M and |f ′′′(x)| L for all x. ... Given constants b1, b2 such that b1 eb2 0 use the Lagrangian method to.

9 Nov 2023: Provided Mij is not singular,the matrix inverse (M1)ij is the rank-2 tensor such that Mij(M1)jk = δik. ... The modulooperation k mod r = s means that s is the smallest non-negative integer such thatk s is divisible by r.] [Hint: Rewrite U as a rotation

5 Nov 2023: There were 7 presentations and they covered topics such as Multipath TCP, energy efficiency at different layers on a mobile handset and MANETs. ... b) by enabling opportunistic access to resources available in co-located devices using low power

25 Oct 2023: Then there is a point y / E such. that B(y,r) E 6= whenever r > 0. ... Since Uj1 isopen we can find a δj1 > 0 with δj1 δj/4 such that B(xj1,δj1) Uj1.

27 Jan 2023: Assume that A(r) and B(r) are analytic functionsof r such that both have a simple zero at r = r+ > 0 and are positive for r > r+. ... In lectures we introducedcoordinates (u,,θ,φ) such that I+ is = 0 and the ”unphysical” metric satisfies.

13 Feb 2023: o m A a n d ending in B such t h a t each n o d e in t h e sequence is a p a r e n ... o m A a n d e n d i n g in B such t h a t each n o d e in t h e sequence is a

9 Nov 2023: g(x) = x for 1 < x 6 1. [2]. (e) Using your results from parts (c) and (d) above, deduce integers A and B such that. ... a) Find the values of the parameters α,β,γ such that. Ac = b. (†).

12 Feb 2023: Previous research has established that (a) cultural stereotypes andrepresentations of scientists and engineers influence the ability of women toaccess and flourish in STEM fields, (b) such representations in popular mediaare overwhelmingly

14 Aug 2023: For such inducible or repressible devices,the functional response. =. Pa b K. ... Such a promoter isinducible for a > b and repressible for b < a, with no expressionfrom the unbound promoter when b = 0.

13 Feb 2023: Let µ̂X :=. i wik(xi,. ) be an estimator of µX :=. k(x,.) dP(x) such that for some. constants b > 0 and 0 < c 1/2:. ... Let µ̂X :=. i wik(xi,. ) be an estimator of µX :=. k(x,.) dP(x) such that for some. constants b > 0 and 0 < c 1/2:1Adams and

9 Jul 2023: 12. Theorem 4.1 Suppose that F : IRn IRn is an affine mapping such that F(x) = Ax b andA IRnn is positive definite. ... b) Assume α > 0 is chosen such that A AT αI is positive definite.

7 Mar 2023: x = ccoshξ cosη , y = csinhξ sinη , ξ > 0 , 0 6 η < 2π ,. and choose c > 0 such that the boundary of the vortex patch at a particular instantcorresponds to the curve ... b) Determine the effect of a uniform shear flow, u = Sxey, on the shape of an

6 Nov 2023: Thenthere exists a random variable Y such that:. (a) Y is G-measurable;. ... Proof. We will first show that (a) implies (b). If (b) does not hold, then we can findε > 0 such that for all n 1 there exists a set An with

13 Feb 2023: We explore how such prediction sets impact expert decision-making in human-AI teams. ... Despite the capacity to overfit significantly, such large models work better than smaller ones.

9 Jul 2023: b′) > 0 such that for ρ ρ(b′) it is also optimal to buy whenever ĥt = b′. ... There is a function w such that Gw(x) = x on (s,b),w = 12c on [b,), w =. 12c on (,s] and w. ′ = 0 at b and s, where G denotes

27 Jan 2023: LξF = 0) then locally thereexists a scalar potential Φ such that iξF = dΦ. ... The decay happens such that P2 initially has dr/dτ 0. P2 subsequently falls into theblack hole and P3 escapes to r =. Let Ei miEi denote the energy of Pi (which

8 Nov 2023: Dr H. Fawzi. Mathematical Tripos Part II: Michaelmas Term 2023. Numerical Analysis – Lecture 16Theorem 4.10 (The Householder–John theorem) If A and B are real matrices such that both A ... in the Gauss–Seidel method.) By definition of H we have Bw =

13 Feb 2023: We are interested in approaching the analysis of such datasets from a probabilistic perspective. ... In modern GP software libraries such as GPML, GPy, GPflow, and GPyTorch, the kernel is undoubtedly the dominant abstraction.

28 Apr 2023: Xn.(b) Construct a credible set Cn R such that. (i) Π(Cn|X1,. ... Explain your answer. [Throughout, you may use standard facts of stochastic convergence, such as thecentral limit theorem, provided they are clearly stated.].

5 Nov 2023: Each new datatype introduces axioms for constructing values of the datatype, and an elimination axiom (which we call the standard eliminator) for consuming such values. ... Idea: we have A, B, P such that P : A -> B; also A', B' which are isomorphic to A

9 Jul 2023: 2016). In those contributions, it was stressed that the information spreading and imitative pro-cesses are responsible, according to the topology of the social network, of extremeevents on financial markets, such ... Such an approach has been followed,

22 May 2023: Some commentators have already begun to argue that the agencies such as the a ... the_time_101288.html"“FDA should be in Ebola-Mode all the time”/a pointing to cases such as Sanofi’s Lemtrada, a multiple sclerosis drug and Bexsero, a vaccine

22 May 2023: Some commentators have already begun to argue that the agencies such as the a ... the_time_101288.html"“FDA should be in Ebola-Mode all the time”/a pointing to cases such as Sanofi’s Lemtrada, a multiple sclerosis drug and Bexsero, a vaccine

23 Jan 2023: Suppose there exists a class [b] B(G,{µ}) such that ν[b] = µ(such a class is necessarily unique if it exists by the above remark). ... When G is quasi-split,this class is just [b]µ. However if G is not quasi-split, there may be no [b] B(G,{µ})such

28 Apr 2023: Be as precise as. possible when describing a distribution.]. (d) Let ψ : Θ R be a continuously differentiable function, and θ̃n another estimatorof θ0 such that |θ̂n θ̃n| 6 1/n ... What is the distribution of θ̂n? (b) For α (0,1), construct a

28 Apr 2023: Assuming that the criterion () holds also for observations which are not discrete, showthat it is not possible to find (C(X),S(X)) sufficient for (a,b) such that S is ... ancillarywhen b is regarded as a nuisance parameter, and a is the parameter of

7 Jul 2023: Prove that for every positive integer d there exist integers a and b such that4a2 9b2 1 is divisible by d. ... radially such that its moment of inertia is γMa2 for some constant γ.

23 Oct 2023: Show that:. (a) There is a nondeterministic automaton N with n 1 states such that L(N) = Ln and(b) if D is a deterministic automaton with fewer than 2n states, ... Prove that there is a proper excerpt e of v such that xey L.

21 Nov 2023: Let a,b K such that the polynomials f = Xm a, g = Xm b are irreducible. ... Use asuitable Lagrange resolvent to find a Q(ζ3) such that K = Q(ζ3, 3.

25 Aug 2023: Dr Dan Hodson https://www.stemcells.cam.ac.uk/people/pi/hodson djh1002@cam.ac.uk Jeffrey Cheah Biomedical Centre Aggressive B cell lymphomas such as Burkitt and diffuse large B ... However, newer sequencing technologies such as ribosome foot printing

19 Jan 2023: A sesquilinear form θ is bounded if there is aconstant C > 0 such that. | ... 1.6 Adjoints For T B(H) there is a unique map T : H H such that〈Tx,y〉 = 〈x,Ty〉 for all x,y H.

27 Apr 2023: Prove directly from the definition thatAX has an m-variate normal distribution AX Nm(Aµ,AΣAT ). 2. Let X and Y be N(0, 1) random variables such that ... a random set C(Y ) such that Pβ,σ2 (b C(Y )) = 1 α for all β,σ2.

29 Sep 2023: The discriminant = (a, b)=16(4a327b2)is non-zero. Conversely, for any pair (a, b) O2K such that (a, b) , 0, the equation(2.1) defines an elliptic curve. ... ap bp = cp. to the Fermat equation in exponent p; thus a, b, c Z are coprime non-zero

5 Nov 2023: This system also uses sensors such as accelerometer and gyro-based image detection. ... b) by enabling opportunistic access to resources available in co-located devices using low power interfaces such as bluetooth.

24 Jul 2023: 3. ‘There was no such thing as the Scientific Revolution.’ (SHAPIN). ... such currency in Victorian Britain? 3. How did the ideal of disinterested scientific research become established in.

11 Jul 2023: Sidgwick Avenue, Cambridge, and of carrying on and developing its work under such. ... the University of Cambridge. (b) To do all such other things as are incidental or conducive to advancing.

13 Feb 2023: obtainedfrom an existing set of attribute classifiers, such as [1]. Our goal is to augment aiwith a non-semantic bi B, forming a hybrid [ai,bi] AB, where [] denotes theconcatenation of ... Such casescan be seen in Figure 3 at dimension m = 20, and at

16 Aug 2023: Such constitutive laws are required to predictfracture in events such as the first bite. ... which is closely related to textural attributes such asfood hardness, crumbliness and grittiness.

21 Jul 2023: Antibodies bind to antigens, fragments or proteins from infectious agents such as viruses and bacteria. ... Such cells can be grown in vitro in massive cultures to provide specific antibody.