function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...

In this paper we consider superconvergence and supercloseness in the least-squares mixed finite element method for elliptic problems. The supercloseness is with respect to the standard and mixed finite element approximations of the same elliptic problem, and does not depend on the properties of the mesh. As an application, we will derive more precise a priori bounds for the least squares mixed ...

We study the three positivity constraints among the eight structure functions of virtual photon, derived from the Cauchy-Schwarz inequality and hence, which are model independent. The photon structure functions obtained from the simple parton model show quite different behaviors either in a massive quark case or in a massless one, but they satisfy, in both cases, the three positivity constraint...

Huang [ Journal of Statistics and Management Systems, Vol. 6 (2003), No. 2, pp. 171-180 ] studied the EOQ (Economic Order Quantity) and EPQ (Economic Production Quantity) models with backlogging and defective items using the algebraic approach. He assumed 100% inspection policy and the known proportion of defective items was removed prior to storage or use after the screening process. In this p...

A FAMILY of inequalities concerning inner products of vectors and functions began with Cauchy. The extensions and generalizations later led to the inequalities of Schwarz, Minkowski and Holder. The well known Holder inequality involves the inner product of vectors measured by Minkowski norms. In this paper, another step of extension is taken so that a Holder type inequality may apply to general...

In this paper, we study the Schrödinger-Robertson uncertainty relations as corollaries of equalities in a scalar product space. Moreover, we give a number of characterizations in the case where the associated inequalities are in fact equalities. Our presentation is based exclusively on an algebraic observation on the standard Cauchy-Schwarz inequality and could presumably provide a clear and ex...

Classes of an equivalence relation on a module $V$ over supertropical semiring, called rays, carry the underlying structure 'supertropical trigonometry' and thereby version convex geometry which is compatible with quasilinearity. In this theory, traditional Cauchy-Schwarz inequality replaced by CS-ratio, gives rise to special characteristic functions, CS-functions. These functions partite ray s...