This paper consists of two parts. In the first we present a general theory of Euler systems. The main results (see §§3 and 4) show that an Euler system for a p-adic representation T gives a bound on the Selmer group associated to the dual module Hom(T, μp∞). These theorems, which generalize work of Kolyvagin [Ko], have been obtained independently by Kato [Ka1], Perrin-Riou [PR2], and the author...

I am pleased to contribute to this volume in memory of Yuri Golfand. His name will be remembered by future generations of physicists for his 1971 paper with Likhtman, which introduced the four-dimensional super-Poincaré algebra for the first time. Recognizing that such a symmetry algebra is a consistent mathematical possibility was certainly a remarkable achievement. It is a curious coincidence...

To appear in G.S. Maddala and C.R. Rao ed., Handbook of Statistics: Statistical Methods in Finance, NorthHolland. In some financial studies the dependent variable is a count, taking nonnegative integer values. Examples include the number of takeover bids received by a target firm, the number of unpaid credit installments (useful in credit scoring), the number of accidents or accident claims (us...

In this paper the author generalizes the E and N -type resolutions used by Martin-Deschamps and Perrin [10] to subschemes of pure codimension in projective space, and shows that these resolutions are interchanged by the mapping cone procedure under a simple linkage. Via these resolutions, Rao’s correspondence is extended to give a bijection between even linkage classes of subschemes of pure cod...

Singular defects with fractional topological charge in σ models and gauge theories. Abstract A novel class of self-dual solutions in σ models and gauge theories is considered. The contribution of the corresponding fluctuations to the chiral condensate is calculated. We discuss the few tightly connected problems, such as the U (1) problem, the θ dependence and the chiral symmetry breaking within...

We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve at least 3/16 of supersymmetries. In a wide subspace of the extended ADHM data, we show that the integer k which appears in the extended ADHM construction s...

We consider generalizations of parity polytopes whose variables, in addition to a parity constraint, satisfy certain ordering constraints. More precisely, the variable domain is partitioned into k contiguous groups, and within each group, we require xi ≥ xi+1 for all relevant i. Such constraints are used to break symmetry after replacing an integer variable by a sum of binary variables, so-call...

Let λ be a simple eigenvalue of an n-by-n matrix A. Let y and x be left and right eigenvectors of A corresponding to λ, respectively. Then, for the spectral norm, the condition number cond(λ,A) := ‖x‖2 ‖y‖2/|yx| measures the sensitivity of λ to small perturbations in A and plays an important role in the accuracy assessment of computed eigenvalues. R. A. Smith [Numer. Math., 10(1967), pp.232-240...

objectives: the aim of this study was to identify the role of attentional process in postural control using choice reaction time task while changing the visual and proprioceptive cues under difficult balance task (standing on one-leg). methods: this cross-sectional study was conducted by participating 20 young people (22.75±2.29). each subject performed one-leg standing as balance task for each...

In noncommutative spaces it is unknown whether the Pontrjagin class gives integer, as well as, the relation between the instanton number and Pontrjagin class is not clear. Where we define “Instanton number” by the size of Bα in the ADHM construction. We show the analytical derivation of the noncommuatative U(1) instanton number as an integral of Pontrjagin class (instanton charge) in the Fock s...