In joint work with S.-T. Yau, we construct new cohomologies of differential forms and elliptic operators on symplectic manifolds. Their construction can be described simply following a symplectic decomposition of the exterior derivative operator into two first-order differential operators, which are analogous to the Dolbeault operators in complex geometry. These first-order operators lead to ne...

We develop a new decision-making model using the Dempster-Shafer (D-S) belief structure when available information is uncertain and can be assessed with interval numbers. We use a wide range of aggregation operators involving interval numbers such as the uncertain weighted average (UWA), the uncertain ordered weighted average (UOWA), the uncertain generalized weighted average (UGWA) and the unc...

In this paper we study L − L estimates of both extension operators and averaging operators associated with the algebraic variety S = {x ∈ Fdq : Q(x) = 0} where Q(x) is a nondegenerate quadratic form over the finite field Fq. In the case when d ≥ 3 is odd and the surface S contains a (d − 1)/2-dimensional subspace, we obtain the exponent r where the L − L extension estimate is sharp. In particul...

To characterize the influence of decision makers’ psychological factors on the group decision process, this paper develops a new class of aggregation operators based on reference-dependent utility functions (RUs) in multi-attribute group decision analysis. We consider two types of RUs: S-shaped, representing decision makers who are risk-seeking for relative losses, and non-S-shaped, representin...

Using the next-to-leading order low energy effective Hamiltonian for ∆B = 1 transitions, the effects of electroweak penguin operators in some two-body decay modes of B s meson are estimated in the Standard Model (SM). We find that in B s → π+K− and B s → K+K− decay modes, the electroweak penguin effects are small, while in B s → πK̄0, φK̄0, φφ, the electroweak penguin operators enhance or reduce ...

We provide an explicit normal distinguished boundary dilation to a pair of commuting operators (S, P ) having the closed symmetrized bidisc Γ as a spectral set. This is called Sz.-Nagy dilation of (S, P ). The operator pair that dilates (S, P ) is obtained by an application of Stinespring dilation of (S, P ) given by Agler and Young. We further prove that the dilation is minimal and the dilatio...

This remarkable little theorem and related phenomena have been the concern of many authors. Apart from the mysterious appearance of the number 14, the attraction of this theorem is that it is simple to state and can be examined and proved using concepts available after any first encounter with topology. The goal of this article is both to provide an original investigation into variations of the...

The 2–point functions for ∆S = 1 current-current and QCD-penguin operators, as well as for the ∆S = 2 operator, are calculated at the next-to-leading order. The calculation is performed in two different renormalization schemes for γ5, and the compatibility of the results obtained in the two schemes is verified. The scaleand scheme-invariant combinations of spectral 2–point functions and corresp...