We study future constraints on dark energy parameters determined from several combinations of cosmic microwave background experiments, supernova data, and cosmic shear surveys with and without tomography. In this analysis, we look in particular for combinations of experiments that will bring the uncertainties to a level of precision tight enough (a few percent) to answer decisively some of the ...

In the representation approach to computable analysis (TTE) [Grz55, KW85, Wei00], abstract data like rational numbers, real numbers, compact sets or continuous real functions are represented by finite or infinite sequences (Σ∗, Σ) of symbols, which serve as concrete names. A function on abstract data is called computable, if it can be realized by a computable function on names. It is the purpos...

In this section, we motivate the construction of variance and covariance processes for continuous local martingales, which is crucial in the construction of stochastic integrals w.r.t. continuous local martingales as we shall see. In this section, unless otherwise specified, we fix a Brownian motion Bt and a filtration {Ft} such that: 1. For each t, Bt is Ft-measurable. 2. For and s ≤ t, the ra...

We prove that the following statement follows from the Open Colouring Axiom (OCA): if X is locally compact σ-compact but not compact and if itš Cech-Stone remainder X * is a continuous image of ω * then X is the union of ω and a compact set. It follows that the remainders of familiar spaces like the real line or the sum of countably many Cantor sets need not be continuous images of ω * .

ABSTRACT This paper presents an efficient method to design cascaded Σ∆ modulators implemented with continuous-time circuits. Instead of using a discrete-to-continuous time transformation, the proposed methodology is based on the direct synthesis of the whole cascaded architecture. This leads to more efficient topologies in terms of circuit complexity, power consumption and robustness with respe...

12. Considering discrete-time channels, sketch a chart showing the following plots: (a) Continuous-valued AWGN channel capacity (bits/symbol) as a function of SNR (b) Maximal conveyed information as a function of SNR for the following alphabets: 2-PSK, 4-PSK, 16-QAM, 64-QAM The characteristic shapes of the curves and asymptotic behaviors are essential. 13. The capacity per symbol for a continuo...

Hammett constants (σ) can be important factor to understanding substitution and position effects on benzoic acid. This report describes a computational study of ∆G◦ and σ for six substituted benzoic acid (X= F,Cl ,OH ,NH2 ,CN,NO2 )and phenylacetic acid substituted (X=OH ,NH2 ) at para and meta positions ingas and aqueousphases by DFT method and comparesit to available experimental and theoretic...