Some remarks on Huisken's monotonicity formula for mean curvature flow

We discuss a monotone quantity related to Huisken's monotonicity formula and some technical consequences for mean curvature flow.Comment: in "Singularities in nonlinear evolution phenomena and applications", 157-169, CRM Series, 9, Ed. Sc. Norm. Pisa, 200

Making sense of the local Galactic escape speed estimates in direct dark matter searches

Direct detection (DD) of dark matter (DM) candidates in the $\lesssim$10 GeV mass range is very sensitive to the tail of their velocity distribution. The important quantity is the maximum WIMP speed in the observer's rest frame, i.e. in average the sum of the local Galactic escape speed $v_{\rm esc}$ and of the circular velocity of the Sun $v_c$. While the latter has been receiving continuous attention, the former is more difficult to constrain. The RAVE Collaboration has just released a new estimate of $v_{\rm esc}$ (Piffl {\em et al.}, 2014 --- P14) that supersedes the previous one (Smith {\em et al.}, 2007), which is of interest in the perspective of reducing the astrophysical uncertainties in DD. Nevertheless, these new estimates cannot be used blindly as they rely on assumptions in the dark halo modeling which induce tight correlations between the escape speed and other local astrophysical parameters. We make a self-consistent study of the implications of the RAVE results on DD assuming isotropic DM velocity distributions, both Maxwellian and ergodic. Taking as references the experimental sensitivities currently achieved by LUX, CRESST-II, and SuperCDMS, we show that: (i) the exclusion curves associated with the best-fit points of P14 may be more constraining by up to $\sim 40$% with respect to standard limits, because the underlying astrophysical correlations induce a larger local DM density; (ii) the corresponding relative uncertainties inferred in the low WIMP mass region may be moderate, down to 10-15% below 10 GeV. We finally discuss the level of consistency of these results with other independent astrophysical constraints. This analysis is complementary to others based on rotation curves.Comment: 18 pages, 7 figures. V2: improved version that matches to the published on

A note on non lower semicontinuous perimeter functionals on partitions

We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in $\mathbb{R}^n$. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity

Rating and ranking firms with fuzzy expert systems: the case of Camuzzi

In this paper we present a real-life application of a fuzzy expert system aimed at rating and ranking firms. Unlike standard DCF models, it integrates financial, strategic and business determinants and processes both quantitative and qualitative variables. Twenty-one value drivers are defined, concerning the target firm (strategic assets in place and expected financial performance), the acquisition (synergies, quality of management) and the sector (intensity of competition, entry barriers). Their combination via “if-then” rules leads to the definition of an output represented by a real number in the interval [0,1]. Such a number expresses the value-generating power of the target firm inclusive of synergies with the bidder (Strategic Enterprise Value). The system may be used for rating and ranking firms operating in the same sector. A regression analysis using hostile takeovers multiples may be employed to translate the score into price. The real-life case refers to Camuzzi (a natural gas distributor), acquired by Enel, the Italian ex monopolist of electric energy.Corporate finance, firm, rating, ranking, expert system, fuzzy, evaluation

Project valuation and investment decisions: CAPM versus arbitrage

This paper shows that (i) project valuation via disequilibrium NPV+CAPM contradicts valuation via arbitrage pricing, (ii) standard CAPM-minded decision makers may fail to profit from arbitrage opportunities, (iii) standard CAPM-based valuation violates value additivity. As a consequence, the standard use of CAPM for project valuation and decision making should be reconsidered.Investment, valuation, CAPM, arbitrage, disequilibrium NPV

Systemic Value Added, Residual Income and Decomposition of a Cash Flow Stream

The problem of decomposing a cash flow has been treated in recent years by Gronchi (1986, 1987), Peccati (1987, 1991, 1992), Stewart (1991), Pressacco and Stucchi (1997). After showing that the Economic Value Added introduced by Stewart bears a strong resemblance to (and in some conditions coincides with) the periodic Net Present (or Final) Value in Peccati's model and that Pressacco-Stucchi's model can be seen as a formal generalization of Stewart's model, this paper proposes a different decomposition model introducing the Systemic Value Added, which lends itself to a disaggregation in periodic shares whose uncompounded sum coincides with Peccati's and Pressacco-Stucchi's Net Final Value. The model proposed offers the opportunity to dwell on the notion of residual income, showing that the interpretation given by the three previous models fails to explain the correct evolution of the investor's financial system. The evaluation process is then reshaped by introducing the concept of shadow project, by means of which Peccati's and Stewart's model can be retrieved. Pressacco-Stucchi's model can also be retrieved and generalized and some of its assumptions are relaxed. The formal results in the last section provide sufficient and necessary conditions for integrating all models in the systemic framework here adopted. Finally, some hints shows that the results Pressacco and Stucchi obtain can be proved by using the systemic approach here suggested.Residual income, cash flow, Net Final Value, Systemic Value Added

A Sum&Discount method for appraising firms:An illustrative example

This paper presents a new way of valuing firms and measuring residual income. The method, originally introduced in Magni (2000a, 2000b, 2000c, 2001), is here renamed lost-capital paradigm. In order to enhance comprehension the presentation relies on a very simple numerical example which shows that the new paradigm of residual income enjoys a property of abnormal earnings aggregation, according to which the NPV (and therefore the market value) of the firm does not change if each residual income changes, as long as the (uncapitalized) sum of all residual incomes do not change. While radically different from the standard residual income, the difference between the two notions is equal to the interest accrued on the past cumulated standard residual incomes, which has interesting implications for incentive compensation.Firm valuation, residual income, lost capital, Discount&Sum, Sum&Discount, incentive compensation

Project selection and equivalent CAPM-based investment criteria

This article shows that the Capital Asset Pricing Model-based capital budgeting criteria proposed by Tuttle and Litzenberger (1968), Mossin (1969), Hamada (1969), Stapleton (1971), Rubinstein (1973), Bierman and Hass (1973) and Bogue and Roll (1974) are equivalent. They all state that a project is profitable if its internal rate of return is greater than the riskadjusted cost of capital, where the latter is given by the sum of the risk-free rate and a risk-premium which is a function of the systematic risk of the project, itself a function of the project cost.Capital budgeting, investment decisions, capital asset pricing model, equivalence