With the help of Kirchberg’s and Selberg’s theorems, we prove that the minimal tensor product of B(l2) with itself does not have the WEP (weak expectation property) of Lance.

In a recent Letter [1], Efetov et al. propose an exact mapping of an interacting fermion system onto a new model that is supposed to allow sign-problem-free Monte Carlo simulations. In this Comment, we show that their formalism is equivalent to the standard approach of Blackenbecker, Scalapino, and Sugar (BSS) [2] for fermi-onic systems and has the same sign statistics and minus sign problem. O...

The paper analyses two datasets of elite soccer players (top 1000 professionals and UEFA Under-19 Youth League). In both, we find a Relative Age Effect (RAE) for frequency, but not for value. That is, while there are more players born at the start of the competition year, their transfer values are no higher, nor are they given more game time. We use Poisson regression to derive a transparent in...

with α(x) = f(x)/f0(x), β(x) = f1(x)/f0(x), and γ(x) = f2(x)/f0(x). Let G(x) generate the number sequence {Gn}0 , i.e. G(x) = ∑∞ n=0Gnx . Because G(x) is the generating function for the convolution of the sequence {Gn}0 with itself, i.e. of G (1) n := ∑n k=0GkGn−k, one can use eq. 2 in order to express the convolution numbers G n in terms of {Gk} 0 and the numbers {αk}0 , {βk}0 , and γn, which ...

i=1 t i) k (87) We now comment on how the derivation changes when n = 2 and k 3. The case n 3 and k = 2 follows as well due to the symmetric functional equation (Equation 12). Note that up to Eq. 57 the derivation is valid when n = 2. Furthermore, note that the sum in Eq. 56 consists now of one term where l = j 1 = 1. Thus, Eq. 56 and Eq. 57 yield, using x i = z ij1 y j1 + z in y n (n=2, j 1 = ...

where cs$ rd is the order parameter, e.g., the local magnetization in magnetic systems, or the local density contrast between the two types of monomers in diblock copolymers. t is related to the distance from the order-disorder transition temperature, and the coefficients b, c, u, and y are phenomenological parameters which can be computed from more microscopic models. The last term in Eq. (1) ...

We consider groups G interpretable in a supersimple finite rank theory T such that T eq eliminates ∃∞. It is shown that G has a definable soluble radical. If G has rank 2, then if G is pseudofinite it is soluble-by-finite, and partial results are obtained under weaker hypotheses, such as unimodularity of the theory. A classification is obtained when T is pseudofinite and G has a definable and d...

T original version of Figure 66 is incorrect; the corrected figure is shown below. In addition, the sentence “The experimental data arefit in the fast-exchange limit with a population of the B state of 0.68, yielding an average τm = 5.29 ns and S 2 = 0.13” (p 11126) should read “The experimental data are fit in the fastexchange limit with S = 1 (by construction, eq 21) and a population of the B...