In this note, we provide detailed characterization of operators in terms norm-attainability and norm estimates Banach algebras. particular, establish the necessary sufficient conditions for derivations also give their bounds norm-attainable classes.

A nonlinear controlled system of differential equations has been constructed to describe the process of production and sales of a consumer good. This model can be controlled either by the rate of production or by the price of the good. The attainable sets of corresponding controlled systems are studied. It is shown that in both cases the boundaries of these sets are the unions of two two-parame...

We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called attainable by a player if there is a finite horizon T such that the player can guarantee that after time T the distance between the set and the cumulative payoff is arbitrarily small, regardless of the strategy Player 2 is using. We provide a necessary and s...

Abstract We quantify the role of geography and land quality for agricultural productivity differences across countries using high-resolution micro-geography data a spatial accounting framework. The rich provide each cell covering entire globe, potential yield 18 crops, which measures maximum attainable crop output given soil quality, climate conditions, terrain topography, level cultivation inp...

Biexciton properties strongly affect the usability of a light emitter in quantum photon sources and lasers but are difficult to measure for single fluorophores at room temperature due to luminescence intermittency and bleaching at the high excitation fluences usually required. Here, we observe the biexciton (BX) to exciton (X) to ground photoluminescence cascade of single colloidal semiconducto...

Abstract-The asymptotic stability regions for the patterned steady-state solution in a two-particle catalytic CSTR, established by Arce and Ramkrishna (1991, A.IC1I.E. J. 37,98-l lo), are constructed using two approaches, Liapunov’s direct method and the construction of a trapping region. In addition, the trapping regions are also constructed for uniform steady-state solutions. Stability region...