Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

Cover inequalities are commonly used cutting planes for the 0–1 knapsack problem. This paper describes a linear-time algorithm (assuming the knapsack is sorted) to simultaneously lift a set of variables into a cover inequality. Conditions for this process to result in valid and facet-defining inequalities are presented. In many instances, the resulting simultaneously lifted cover inequality can...

Maximally entangled states should maximally violate the Bell inequality. In this paper, it is proved that all two-qubit states that maximally violate the Bell-Clauser-Horne-Shimony-Holt inequality are exactly Bell states and the states obtained from them by local unitary transformations. The proof is obtained by using the certain algebraic properties that Pauli’s matrices satisfy. The argument ...

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti, Phys. Rev. Lett. 99, 210405 (2007)10.1103/PhysRevLett.99.210405]. We prove that any n-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our resu...

Let α > 0 and 0 < c = 1 be real numbers. The inequality (Γ(x+ y + c) Γ(x+ y) )1/α < (Γ(x+ c) Γ(x) )1/α + (Γ(y + c) Γ(y) )1/α holds for all positive real numbers x, y if and only if α ≥ max(1, c). The reverse inequality is valid for all x, y > 0 if and only if α ≤ min(1, c).

This note sharpens the smoothing inequality of Giacomin and Toninelli [7], [8] for disordered polymers. This inequality is shown to be valid for any disorder distribution with locally finite exponential moments, and to provide an asymptotically sharp constant for weak disorder. A key tool in the proof is an estimate that compares the effect on the free energy of tilting, respectively, shifting ...

Sutton (1998) has recently proposed a theoretical lower bound to firm size inequality when a market is made of several independent submarkets. His results are valid asymptotically, as the number of submarkets becomes arbitrarily large. We show that, in small samples, his results can be interpreted as a positive relationship between an index of firm size inequality and the number of submarkets. ...

This paper studies the relationship of financial development and income inequality in China over the period of 1978-2013. Using the structural vector auto-regression (SVAR), the empirical results are consistent with the GJ hypothesis of an inverted U-shaped relationship between financial development and income inequality. An economy in its initial stages of financial development would present i...

We develop a nicely packaged form of Talagrand’s inequality that can be applied to prove concentration of measure for functions defined by hereditary properties. We illustrate the framework with several applications from combinatorics and algorithms. We also give an extension of the inequality valid in spaces satisfying a certain negative dependence property and give some applications. 1 Talagr...

When analysing the factors of income inequality, first as many factors as possible have to be included in order to obtain valid results. The present article systematises the factors of income inequality discussed in the pertinent literature into five groups and summarises the hypotheses about the signs of the influences of the discussed factors on income inequality. But additionally the influen...