j=1 vj`j(x). Lagrange multipliers u ∈ R, v ∈ R. Lemma 11.1 At each feasible x, f(x) = supu≥0,v L(x, u, v), and the supremum is taken iff u ≥ 0 satisfying uihi(x) = 0, i = 1, · · · ,m. Proof: At each feasible x, we have hi(x) ≤ 0 and `(x) = 0, thus L(x, u, v) = f(x) + ∑m i=1 uihi(x) + ∑r j=1 vj`j(x) ≤ f(x). The last inequality becomes equality iff uihi(x) = 0, i = 1, · · · ,m. Proposition 11.2 T...

Proof. ‖∇F (δ)‖∞ ≤ guarantees that μ = μ(δ) are -consistent in the sense that |μi(xi) − μc(xi)| ≤ for all c, i ∈ c and xi. Algorithm 1 maps any such -consistent μ to locally consistent marginals μ̃ such that |μi(xi)− μ̃i(xi)| ≤ 3 Nmax, |μc(xc)− μ̃c(xc)| ≤ 2 N max, (3) for all i, xi, c, and xc, where Nmax = max{maxiNi,maxcNc}. In other words, ‖μ− μ̃‖∞ ≤ K . This can be easily derived from the update...

In this talk I will give a overview on the connections between closure operators and choice operators and on related results. An operator on a finite set S is a map defined on the set P(S) of all the subsets of S. A closure operator is an extensive, isotone and idempotent operator. A choice operator c is a contracting operator (c(A) ⊆ A, for every A ⊆ S). Choice operators and their lattices hav...

in this paper, we try to determine the status of the relation between dahr world and matrial world. the conclusion shows the subjective duality and objective unity of dahr and material entities. two interpretations of this duality can be suggested. in the first interpretation, this unity, and the duality supposed, are explained on the basis of different intellectual cognition of immaterial and ...

This research was conducted to study the effect of gender inequality on social participation of women. The method used in this research was Ex-Post Facto and survey method. The statistical population included female students in different fields of faculty of humanities and faculty of training sciences and psychology (Islamic Azad University) Garmsar Branch in 2012-2013. Research instruments inc...

Inrecent years political scientists and economists have spent considerable efforts investigating the impact of income inequality both on political institutions and social conflict (Boix 2003, 2008; Acemoglu and Robinson 2006; Geddes 2007) and on growth and development (Atkinson andBourguignon 2000). In this article I focus on the latter question: I discuss the extent to which (that is, the cond...

While policy makers widely recognise the fact that education serves as an engine for economic growth through the accumulation of human capital, education is also strongly associated with boosting levels of social capital. Indeed, an important justification for the large expenditures on education within many democratic nations is its social, and not just economic, impact – the benefits an educat...

A key prediction of standard models of economic growth is that the output-capital ratio is constant along the economy’s balanced growth path. Using data for 16 OECD countries over 135 years we examine whether the output-capital ratio reverts to a constant in the long run using univariate and panel stationarity tests with structural breaks. Univariate unit root tests with one and two breaks in t...