In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

Modeling in ecol ogy or epidemiol ogy gener all y opposes tw o classes of models, Equa tion Based Models and Agent Based Models. Mathema tical models all ow predicting the longterm dynamics of the studied systems. How ever, the variability betw een individ uals is difficul t to represen t, wha t makes these more suitable models for larg e and homog eneous popula tions. Mul ti-agent models all o...

The Problem: Modeling highly articulated objects such as people is an extremely difficult problem in computer vision. This work investigates an alternative to the two extremes of using explicit models and using “exemplars.” Rather than fitting an articulated model to a silhouette or treating the silhouettes holistically, this work explains how to derive a sparse basis to represent the observed ...

In the discounted expected utility model, risk aversion is fully determined by deterministic intertemporal choice. General recursive preferences like KrepsPorteus and Epstein-Zin-Weil preferences resolve this short-coming. These preferences are widely used in finance because they capture the spread between safe and risky returns significantly better than the discounted expected utility model (e...

The typological literature generally assumes that semantic maps and the underlying conceptual spaces have mental reality, that is, they correspond to a universal arrangement of the relevant conceptual situations in a speaker's mind, based on perceived relations of similarity between these conceptual situations (Croft 2001 and 2003, Haspelmath 2003, among others). Croft (2003) goes far as arguin...

Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g, we have the Cauchy-Schwarz inequality: 0.1 THEOREM (Cauchy-Schwarz inequality). Let (Ω, M, µ) be a measure space. Then for any two complex valued measurable functions f and g such that

We prove two new reverse Cauchy–Schwarz inequalities of additive and multiplicative types in a space equipped with a positive sesquilinear form with values in a C *-algebra. We apply our results to get some norm and integral inequalities. As a consequence, we improve a celebrated reverse Cauchy–Schwarz inequality due to G. Pólya and G. Szegö.