Doubly stochastic matrices whose squares are idempotent

Formulas for the doubly stochastic square roots of the idempotents are presented. Such square roots must necessarily satisfy per A²≤perA.     

Sharp Trace Hardy–Sobolev-Maz’ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy–Sobolev–Maz’ya inequalities with best Hardy constants for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy–Sobolev–Maz’ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space, our results cover the full range of the exponent ${s \in}$ (0, 1) of the fractional Laplacians. In particular, we give a complete answer in the L ² setting to an open problem raised by Frank and Seiringer (“Sharp fractional Hardy inequalities in half-spaces,” in Around the research of Vladimir Maz’ya. International Mathematical Series, 2010).     

Direct, loss-tolerant characterization of nonclassical photon statistics

We experimentally investigate a method of directly characterizing the photon-number distribution of nonclassical light beams that is tolerant to losses and makes use of only standard binary detectors. This is achieved in a single measurement by calibrating the detector using some small amount of prior information about the source. We demonstrate the technique on a freely propagating heralded two-photon-number state created by conditional detection of a two-mode squeezed state generated by parametric down-conversion.     

The role of polycarboxylic acids in calcium phosphate mineralization

The role of two polyelectrolytes, poly-L-glutamate and poly-L-aspartate, in the growth of calcium phosphate crystal phases, has been investigated at constant supersaturation. Both molecules are strong inhibitors of HAP growth when present in the solution phase but also act as hydroxyapatite and (octacalcium phosphate)-like crystal nucleators when adsorbed on germanium surfaces. The structure of the polymers in solution is presented and various adsorption models are analyzed. A "train-loop" structure of these long, flexible chain polymers on the crystal surface is consistent with all the adsorption (experimental and theoretical), inhibition, and electrophoretic mobility results.     

Doubly stochastic matrices with some equal diagonal sums

Let A be doubly stochastic, and let τ₁,…,τ_m be m mutually disjoint zero diagonals in A, 1?m?n-1. E. T. H. Wang conjectured that if every diagonal in A disjoint from each τ_k (k=1,…,m) has a constant sum, then all entries in A off the m zero diagonals τ_k are equal to (n?m)^-1. Sinkhorn showed the conjecture to be correct. In this paper we generalize this result for arbitrary doubly stochastic zero patterns.     

Generic residual intersections and intersection numbers of movable components

Given a sequence x of elements of a commutative equidimensional noetherian ring R  , cycles _zi(x,R)$z_i(\mathbf{x},R)$ (i∈N$i\in \mathbb{N}$) in the cycle group of polynomial rings over R are defined by generic residual intersections. The study of these cycles gives new insight into the theory for excess intersections in projective space developed by Stückrad and Vogel, in particular concerning the contribution to the intersection cycle of embedded components not defined over the base field.     

Optimization of the design of recuperative heat exchangers in the exhaust nozzle of an aero engine

Today the needs for safer, cleaner and more affordable civil aero engines are found to be of great importance. Five years ago, the EU initiated an action for the design and the construction of efficient and environmentally friendly aero engines (EEFAE). One of the major European gas turbine industries, MTU, has presented a new technology for an advanced aero engine design, which uses an alternative thermodynamic cycle. The basis of this cycle is the adoption of a recuperation part with the use of a system of heat exchangers, installed in the exhaust nozzle of the aircraft engine. Thermal energy in the turbine exhaust is used in the recuperator to pre-heat the compressor outlet air before combustion. The benefits of this technique are focused on reduced pollutants and decreased fuel consumption. In this work, the procedure of the optimization of this installation, by means of the imposed pressure drop downstream the aircraft engine and the balanced mass inflow to the heat exchangers is presented. The optimization is based on experimental measurements in laboratory conditions and preliminary 2D CFD modeling for the flow inside the exhaust duct and through the heat exchangers. It is shown that with a careful approach, a better arrangement of the heat exchangers can be achieved in order to have a minimum pressure drop in the exhaust nozzle which can positively affect the engine’s performance.