For any complex reductive connected Lie group G, many of the structure constants of the ordinary cohomology ring H(G/B;Z) vanish in the Schubert basis, and the rest are strictly positive. We present a combinatorial game, the “root game”, which provides some criteria for determining which of the Schubert intersection numbers vanish. The definition of the root game is manifestly invariant under a...

It is shown that the QCD anomaly may lead to an abnormal mixing behavior of the axial vector mesons similar to the pseudoscalar mesons. These mixing effects, involving a gluonic axial vector state, generate a non-vanishing strange quark component in the nucleon. They reduce the matrix element of the singlet axial vector in comparison to the value obtained in a na¨ıve quark model. The results ar...

In this paper, we derive a simplified formula of electric dipole moments (EDMs) fermion. the Standard Model, it is well-known that non-trivial cancellations between some rainbow-type diagrams induced by $W$ boson exchanges occur in calculation neutron EDM at two-loop level due to gauge symmetry. The fermion self-energy and vertex correction are related through Ward-Takahashi identity, relation ...

It is shown that every set of n integers contains a subset of size Ω(n) in which no element is the average of two or more others. This improves a result of Abbott. It is also proved that for every > 0 and every m > m( ) the following holds. If A1, . . . , Am are m subsets of cardinality at least m each, then there are a1 ∈ A1, . . . , am ∈ Am so that the sum of every nonempty subset of the set ...

Using a reformulation of the Eichler-Selberg trace formula, due to Frechette, Ono and Papanikolas, we consider the problem of the vanishing (resp. non-vanishing) of traces of Hecke operators on spaces of even weight cusp forms with trivial Nebentypus character. For example, we show that for a fixed operator and weight, the set of levels for which the trace vanishes is effectively computable. Al...

This article deals with the approximation of the boundary control of the linear onedimensional wave equation. It is known that the high frequency spurious oscillations that the classical methods of finite difference and finite element introduce lead to nonuniform controllability properties (see [J. A. Infante and E. Zuazua, M2AN Math. Model. Numer. Anal., 33 (1999), pp. 407–438]. A space-discre...

Vanishing and Non-Vanishing Criteria for Branching Schubert Calculus by Kevin Purbhoo Doctor of Philosophy in Mathematics University of California at Berkeley Professor Allen Knutson, Chair We investigate several related vanishing problems in Schubert calculus. First we consider the multiplication problem. For any complex reductive Lie group G, many of the structure constants of the ordinary co...

The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved in [1] under Jensen’s Diamond Principle. In this note, the same is verified using the ZFC axioms alone. In the construction of large indecomposable divisible modules over certain valuation domainsR, the first author used the property thatR satisfied Ext1R(Q,U) 6= 0, where ...