Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems

The problem considered in this paper is that of finding a point which iscommon to almost all the members of a measurable family of closed convexsubsets of R₊₊ ⁿ , provided that such a point exists.The main results show that this problem can be solved by an iterative methodessentially based on averaging at each step the Bregman projections withrespect to f(x)=_i=1 ⁿx_i· ln x_i ofthe current iterate onto the given sets.     

Silicon–air batteries

A new “metal”–air battery based on silicon–oxygen couple is described. Silicon–air battery employing EMI·2.3HF·F room temperature ionic liquid (RTIL) as an electrolyte and highly-doped silicon wafers as anodes (fuels) has an undetectable self-discharge rate and high tolerance to the environment (extreme moisture/dry conditions). Such a battery yields an effectively infinite shelf life with an average working voltage of 1–1.2 V. Silicon–air battery can support relatively high current densities (up to 0.3 mA/cm²) drawn from flat polished silicon wafers anodes. Such batteries may find immediate applications, as they can provide an internal, built-in autonomous and self sustained energy source.     

Convex feasibility modeling and projection methods for sparse signal recovery

A computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS), is presented. The theory of CS usually leads to a constrained convex minimization problem. In this work, an alternative outlook is proposed. Instead of solving the CS problem as an optimization problem, it is suggested to transform the optimization problem into a convex feasibility problem (CFP), and solve it using feasibility-seeking sequential and simultaneous subgradient projection methods, which are iterative, fast, robust and convergent schemes for solving CFPs. As opposed to some of the commonly-used CS algorithms, such as Bayesian CS and Gradient Projections for sparse reconstruction, which become inefficient as the problem dimension and sparseness degree increase, the proposed methods exhibit robustness with respect to these parameters. Moreover, it is shown that the CFP-based projection methods are superior to some of the state-of-the-art methods in recovering the signal’s support. Numerical experiments show that the CFP-based projection methods are viable for solving large-scale CS problems with compressible signals.     

Cyclic subgradient projections

A cyclically controlled method of subgradient projections (CSP) for the convex feasibility problem of solving convex inequalities is presented. The features of this method make it an efficient tool in handling huge and sparse problems. A particular application to an image reconstruction problem of emission computerized tomography is mentioned.Research supported by National Institute of Health Grant HL 28438-01.     

Magidor–Malitz reflection

In this paper we investigate the consistency and consequences of the downward Löwenheim–Skolem–Tarski theorem for extension of the first order logic by the Magidor–Malitz quantifier. We derive some combinatorial results and improve the known upper bound for the consistency of Chang’s conjecture at successor of singular cardinals.     

Conducting polyfurans by electropolymerization of oligofurans

Polyfurans have never been established as useful conjugated polymers, as previously they were considered to be inherently unstable and poorly conductive. Here, we show the preparation of stable and conducting polyfuran films by electropolymerization of a series of oligofurans of different chain lengths substituted with alkyl groups. The polyfuran films show good conductivity in the order of 1 S cm^–1, good environmental and electrochemical stabilities, very smooth morphologies (roughness 1–5 nm), long effective conjugation lengths, well-defined spectroelectrochemistry and electro-optical switching (in the Vis-NIR region), and have optical band-gaps in the range of 2.2–2.3 eV. A low oxidation potential needed for polymerization of oligofurans (compared to furan) is a key factor in achievement of improved properties of polyfurans reported in this work. DFT calculations and experiments show that polyfurans are much more rigid than polythiophenes, and alkyl substitution does not disturb backbone planarity and conjugation. The obtained properties of polyfuran films are similar or superior to the properties of electrochemically prepared poly(oligothiophene)s under similar conditions.