Our main object of study is X ⊂ P5F2 , where X is the degree 5 Fermat hypersurface, which we are looking at in P over F2. X is the zero locus {X 0 +X 1 + ...+X 5 = 0}. The question is, “what kind of rational curves lie on X?” Since F2 only has one invertible element, P(F2) = F 2 \ 0, which suggests that the Fermat quintic has the same zero locus as the linear hypersurface X0 + X1 + ... + X5 = 0...

Spin observables may reveal much deeper properties of non perturbative hadronic physics than unpolarized quantities. We discuss the polarization of hadrons produced in e + e − annihilation at LEP. We show how final state q ¯ q interactions may give origin to non zero values of the off-diagonal element ρ 1,−1 of the helicity density matrix of vector mesons: some predictions are given for K * , φ...

This paper concerns a class of orbital integrals in Lie algebras over p-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on varieties over finite fields. The construction, which is based on motivic integration, works both in characteristic zero and in positive characteristic. As an application, the Fundamental Lemma for this class of integ...

Defining the four vectors n and τ of Abramowicz’s covariant formalism of inertial forces, in terms of the lapse function α, shift vector β, the metric γij and the velocity 3-vector V , we derive the components of centrifugal and Coriolis accelerations acting on a fluid element with four velocity U. We show that while for purely radial flow the centrifugal acceleration component is zero in stati...

The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-φ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of...

Let A be a non-zero abelian variety defined over a number field K and let K be a fixed algebraic closure of K. For each element σ of the absolute Galois group Gal(K/K), let K(σ) be the fixed field in K of σ. We show that the torsion subgroup of A(K(σ)) is infinite for all σ ∈ Gal(K/K) outside of some set of Haar measure zero. This proves the number field case of a conjecture of W.-D. Geyer and ...

We introduce BCI structures which are extensions of 1-sorted structure and are systems 〈 a carrier, an internal complement 〉, where the carrier is a set and the internal complement is a binary operation on the carrier. Let us note that there exists a BCI structure which is non empty and strict. Let A be a BCI structure and let x, y be elements of A. The functor x \ y yielding an element of A is...

We prove necessary and sufficient conditions for the existence of sequences and matrices with elements in given intervals and with prescribed lower and upper bounds on the element sums corresponding to the sets of an orthogonal pair of partitions. We use these conditions to generalize known results on the existence of nonnegative matrices with a given zero pattern and prescribed row and column ...