Pioneers of logic, among them J.R. Büchi, M.O. Rabin, S. Shelah, and Y. Gurevich, have shown that monadic second-order logic offers a rich landscape of interesting decidable theories. Prominent examples are the monadic theory of the successor structure S1 = (N,+1) of the natural numbers and the monadic theory of the binary tree, i.e., of the two-successor structure S2 = ({0, 1} ∗, ·0, ·1). We c...

Let S = {S1,S2, . . .} represent a collection of nonempty sets of nonnegative integers in which each member contains the integer 0. Then S is called a complementing system of subsets for X ⊆ {0,1, . . .} if every x ∈ X can be uniquely represented as x = s1 + s2 + ··· with si ∈ Si. We will also write X = S1 ⊕ S2 ⊕ ··· and, when necessary, refer to X as the direct sum of the Si. We will denote th...

The objective of this problem is to derive a learning bound for cross-validation comparing its performance to that of SRM. Let (Hk)k∈N be a countable sequence of hypothesis sets with increasing complexities. The cross-validation (CV) solution is obtained as follows. Suppose the learner receives an i.i.d. sample S of size m ≥ 1. He randomly divides S into a sample S1 of size (1−α)m and a sample ...

We observe the weak S0 → S2 transitions of the T-shaped benzene dimers (Bz)2 and (Bz-d6)2 about 250 cm(-1) and 220 cm(-1) above their respective S0 → S1 electronic origins using two-color resonant two-photon ionization spectroscopy. Spin-component scaled (SCS) second-order approximate coupled-cluster (CC2) calculations predict that for the tipped T-shaped geometry, the S0 → S2 electronic oscill...

A double-loop digraph G=G(N ; s1; s2), with gcd(N; s1; s2)=1, has the set of vertices V =ZN and the adjacencies are given by u → u + si (mod N ) i = 1; 2. The diameter of G, denoted by D(N ; s1; s2), is known to be lower bounded by lb(N ) with D(N ) = min 16s1¡s2¡N; gcd(N;s1 ; s2)=1 D(N ; s1; s2)¿ ⌈√ 3N ⌉ − 2 = lb(N ): This lower bound is known to be sharp. For a 0xed N ∈N, some algorithms to 0...

Let S1 and S2 be Γ-semigroups. In this note, we determine when S1 and S2 are isomorphic if the power semigroup of S1 and the power semigroup of S2 are o-isomorphic.

OBJECTIVE Ovarian inhibins (INH) are hormones participating in the regulation of gametogenesis. We monitored inhibin A and B levels in serum (S) and follicular fluids (FF), depending on the type of fertility failure and treatment outcome. MATERIAL AND METHODS We examined INHA and B levels in S and FF of 72 women undergoing ovarian stimulation for in vitro fertilization, including embryo trans...