To any metric space it is possible to associate the cardinal invariant corresponding to the least number of rectifiable curves in the space whose union is not meagre. It is shown that this invariant can vary with the metric space considered, even when restricted to the class of convex subspaces of separable Banach spaces. As a corollary it is obtained that it is consistent with set theory that ...

Recently, King and Ruskai [1] conjectured that the maximal p–norm of the Werner– Holevo channel is multiplicative for all 1 ≤ p ≤ 2. In this paper we prove this conjecture. Our proof relies on certain convexity and monotonicity properties of the p–norm.

We examine the efficiency of conservation of a renewable resource whose natural productivity is influenced by random environmental disturbances. We allow for non-concave biological production and stock-dependent social welfare. Unlike deterministic models, conservation may be inefficient no matter how productive the resource growth function is. In addition, improvements in the natural productiv...

We consider the impact of job rotation in a directed search model in which …rm sizes are endogenously determined and match quality is initially unknown. A large …rm bene…ts from the opportunity of rotating workers so as to partially overcome loss of mismatch. As a result, in the unique symmetric equilibrium, large …rms have higher labor productivity and lower separation rates. In contrast to th...

This paper considers leisure externalities in a Lucas (1988) type model in which physical and human capital are necessary inputs in both sectors. In spite of a non-concave utility, the balanced growth path is always unique in our model which guarantees global stability for comparative-static exercises. We analyze and quantify the effects of preferences toward leisure on labor supply and welfare...

we have the crisp vector → PQ= (y(1)−x(1),y(2)−x(2), . . . ,y(n)−x(n)) in a pseudo-fuzzy vector space Fn p (1)= {(a(1),a(2), . . . ,a(n))1∀(a(1),a(2), . . . ,a(n))∈Rn}. There is a one-to-one onto mapping P = (x(1),x(2), . . . ,x(n)) ↔ P̃ = (x(1),x(2), . . . , x)1. Therefore, for the crisp vector → PQ, we can define the fuzzy vector → P̃ Q̃= (y(1)− x(1),y(2)−x(2), . . . ,y(n)−x(n))1 = Q̃ P̃ . Let the...

When we regard the plane as a set of points, we can deene various geometric properties of subsets of the plane|connectedness, convexity, area, diameter, etc. It is well known that the plane can also be regarded as a set of lines. This note considers methods of deening sets (or fuzzy sets) of lines in the plane, and of deening (analogs of) \geometric properties" for such sets.

we have the crisp vector → PQ= (y(1)−x(1),y(2)−x(2), . . . ,y(n)−x(n)) in a pseudo-fuzzy vector space Fn p (1)= {(a(1),a(2), . . . ,a(n))1∀(a(1),a(2), . . . ,a(n))∈Rn}. There is a one-to-one onto mapping P = (x(1),x(2), . . . ,x(n)) ↔ P̃ = (x(1),x(2), . . . , x)1. Therefore, for the crisp vector → PQ, we can define the fuzzy vector → P̃ Q̃= (y(1)− x(1),y(2)−x(2), . . . ,y(n)−x(n))1 = Q̃ P̃ . Let the...

This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor α of the generalized ADMM to the infinite interval [F...

We develop a projected Nesterov’s proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov’s momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a convex regularization term. We apply sparse signal regularization where the signa...