Algebraic independence is a fundamental notion in commutative algebra that generalizes independence of linear polynomials. Polynomials {f1, . . . , fm} ⊂ K[x1, . . . , xn] (over a field K) are called algebraically independent if there is no non-zero polynomial F such that F (f1, . . . , fm) = 0. The transcendence degree, trdeg{f1, . . . , fm}, is the maximal number r of algebraically independen...

Introduction. Let G be a reductive Lie group with maximal compact subgroup K and let Γ be a cocompact discrete subgroup of G. We consider the induced representation IndΓ (C), which is the canonical representation on the space L2(Γ\G). The duality theorem of Gelfand [6] states that there is a Frobenius reciprocity as follows: for any irreducible unitary representation π of G it holds HomG,cont(I...

We show that a C *-algebra A is nuclear iff there is a number α < 3 and a constant K such that, for any bounded homomorphism u : A → B(H), there is an isomorphism ξ : H → H satisfying ξ −1 ξ ≤ Ku α and such that ξ −1 u(.)ξ is a *-homomorphism. In other words, an infinite dimensional A is nuclear iff its length (in the sense of our previous work on the Kadison similarity problem) is equal to 2. ...

In the simplest type-I seesaw leptogenesis scenario right-handed neutrino annihilation processes are absent. However, in the presence of new interactions these processes are possible and can affect the resulting B − L asymmetry in an important way. A prominent example is provided by models with spontaneous lepton number violation, where the existence of new dynamical degrees of freedom can play...

What is the relation between (a) “full” or “outright” belief and (b) the various levels of confidence that agents can have in the propositions that concern them? This paper argues for a new answer to this question. Decision theory implies that in making decisions, rational agents must treat certain propositions as though they were completely certain; but on most forms of decision theory, these ...

In a recent paper [12] Gang Yu stated the following conjecture: Let {pi}i=1 be an arbitrary sequence of polynomials with increasing degrees and all coefficients in {0, 1}. If we denote by (#pi) the number of non-zero coefficients of pi, and let M(pi ) be the maximal coefficient of pi , then Q := lim inf i→∞ deg(pi) M(pi ) (#pi) ≥ 1, (∗) as long as (#pi) = o(deg pi), as i → ∞. We give an explici...

In our earlier paper [7], we presented an algorithm for computing explicitly the coset representatives and the action of the Hecke operators on Siegel modular forms for arbitrary degree. The action was expressed in terms of the effect on the lattice-Fourier coefficients of the form (see the introduction for a definition of this term). This expression involved combinatorial terms that count loca...

The high-level contributions of this paper are as follows: We modify an existing branch-andbound based exact algorithm (for maximum clique size of an entire graph) to determine the maximal clique size that the individual vertices in the graph are part of. We then run this algorithm on six real-world network graphs (ranging from random networks to scale-free networks) and analyze the distributio...

We study bifix codes in factorial sets of words. We generalize most properties of ordinary maximal bifix codes to bifix codes maximal in a recurrent set F of words (F -maximal bifix codes). In the case of bifix codes contained in Sturmian sets of words, we obtain several new results. Let F be a Sturmian set of words. Our results express the fact that an F -maximal bifix code of degree d behaves...