Measurement of the thorium-228 activity in solutions cavitated by ultrasonic sound

We show that cavitation of a solution of thorium-228 in water does not induce its transformation at a faster rate than the natural radioactive decay. We measured the activity of a thorium-228 solution in water before, and after, it was subjected to a cavitation at 44 kHz and $250$W for 90 minutes in order to observe any change in the thorium half-life. The results were compared to the original activity of the sample and we observed no change. Our results and conclusions conflict with those in a recent paper by F. Cardone et. al. [Phys. Lett. A 373 (2009) 1956-1958].Comment: 6 pages, 1 figure, 2 tables, v1 submitted to Physics Letters A. v2: minor corrections, change caption for tables (include comment for counter efficiency with uncertainty) and symbols for beta-alph

Neumann spectral problem in a domain with very corrugated boundary

Let $\Omega\subset\mathbb{R}^n$ be a bounded domain. We perturb it to a domain $\Omega^\varepsilon$ attaching a family of small protuberances with "room-and-passage"-like geometry ($\varepsilon>0$ is a small parameter). Peculiar spectral properties of Neumann problems in so perturbed domains were observed for the first time by R. Courant and D. Hilbert. We study the case, when the number of protuberances tends to infinity as $\varepsilon\to 0$ and they are $\varepsilon$-periodically distributed along a part of $\partial\Omega$. Our goal is to describe the behaviour of the spectrum of the operator $\mathcal{A}^\varepsilon=-(\rho^\varepsilon)^{-1}\Delta_{\Omega^\varepsilon}$, where $\Delta_{\Omega^\varepsilon}$ is the Neumann Laplacian in $\Omega^\varepsilon$, and the positive function $\rho^\varepsilon$ is equal to $1$ in $\Omega$. We prove that the spectrum of $\mathcal{A}^\varepsilon$ converges as $\varepsilon\to 0$ to the "spectrum" of a certain boundary value problem for the Neumann Laplacian in $\Omega$ with boundary conditions containing the spectral parameter in a nonlinear manner. Its eigenvalues may accumulate to a finite point.Comment: 29 pages, 3 figure

Bingham flow in porous media with obstacles of different size

By using the unfolding operators for periodic homogenization, we give a general compactness result for a class of functions defined on bounded domains presenting perforations of two different size. Then we apply this result to the homogenization of the flow of a Bingham fluid in a porous medium with solid obstacles of different size. Next we give the interpretation of the limit problem in term of a non linear Darcy law.Comment: 19 pages, 2 figure

The assessment of credit guarantee schemes for SME's: valuation and cost

Small and medium enterprises (SME' s) have important limitations from the financial viewpoint. Their reduced capability to generate resources (self-financing) and their high financial costs as compared to the profitability of investments, makes them highly dependent of short-term bank financing. Among the different mechanisms used to solve these financial problems we find credit guarantee schemes as the Loan Guarantee Associations (LGA). These (mutual or government granted) credit insurance systems were set to facilitate the access of SME ' s to the credit market covering part of the loss incurred when borrowers default on a loan. In spite of some legal differences, LGA in most European Union countries function in a fairly similar way, making therefore easier to compare their operational cost and impact on business. This study provides a model for the valuation of the costs and implicit benefits associated with the loan guarantee programs. Empirical results indicate that the use of LGA is likely to differ among SME' s depending on company size and debt financial cost. The relatively high cost of the loan guarantee, is not always fully compensated with a similar reduction of the interest rates of the financing entity, hindering, in many cases, the full development of the schemes

Simplifying Wireless Social Caching

Social groups give the opportunity for a new form of caching. In this paper, we investigate how a social group of users can jointly optimize bandwidth usage, by each caching parts of the data demand, and then opportunistically share these parts among themselves upon meeting. We formulate this problem as a Linear Program (LP) with exponential complexity. Based on the optimal solution, we propose a simple heuristic inspired by the bipartite set-cover problem that operates in polynomial time. Furthermore, we prove a worst case gap between the heuristic and the LP solutions. Finally, we assess the performance of our algorithm using real-world mobility traces from the MIT Reality Mining project dataset and two mobility traces that were synthesized using the SWIM model. Our heuristic performs closely to the optimal in most cases, showing a better performance with respect to alternative solutions.Comment: Parts of this work were accepted for publication in ISIT 2016. A complete version is submitted to Transactions on Mobile Computin

The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks

In ISIT'12 Brahma, \"{O}zg\"{u}r and Fragouli conjectured that in a half-duplex diamond relay network (a Gaussian noise network without a direct source-destination link and with $N$ non-interfering relays) an approximately optimal relay scheduling (achieving the cut-set upper bound to within a constant gap uniformly over all channel gains) exists with at most $N+1$ active states (only $N+1$ out of the $2^N$ possible relay listen-transmit configurations have a strictly positive probability). Such relay scheduling policies are said to be simple. In ITW'13 we conjectured that simple relay policies are optimal for any half-duplex Gaussian multi-relay network, that is, simple schedules are not a consequence of the diamond network's sparse topology. In this paper we formally prove the conjecture beyond Gaussian networks. In particular, for any memoryless half-duplex $N$-relay network with independent noises and for which independent inputs are approximately optimal in the cut-set upper bound, an optimal schedule exists with at most $N+1$ active states. The key step of our proof is to write the minimum of a submodular function by means of its Lov\'{a}sz extension and use the greedy algorithm for submodular polyhedra to highlight structural properties of the optimal solution. This, together with the saddle-point property of min-max problems and the existence of optimal basic feasible solutions in linear programs, proves the claim.Comment: Submitted to IEEE Information Theory Workshop (ITW) 201