Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

Non-constant discounting in finite horizon: The free terminal time case

This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem.Conditions for the observational equivalence with an associated problem with constantdiscounting are analyzed. Special attention is paid to the case of free terminal time. Strotz¿s model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

Dielectric constant obtained from TDR and volumetric moisture of soils in southern Brazil

Soil moisture is the property which most greatly influences the soil dielectric constant, which is also influenced by soil mineralogy. The aim of this study was to determine mathematical models for soil moisture and the dielectric constant (Ka) for a Hapludalf, two clayey Hapludox and a very clayey Hapludox and test the reliability of universal models, such as those proposed by Topp and Ledieu and their co-workers in the 80's, and specific models to estimate soil moisture with a TDR. Soil samples were collected from the 0 to 0.30 m layer, sieved through a mesh of 0.002 m diameter and packed in PVC cylinders with a 0.1 m diameter and 0.3 m height. Seven samples of each soil class were saturated by capillarity and a probe composed of two rods was inserted in each one of them. Moisture readings began with the saturated soil and concluded when the soil was near permanent wilting point. In each step, the samples were weighed on a precision scale to calculate volumetric moisture. Linear and polynomial models were adjusted for each soil class and for all soils together between soil moisture and the dielectric constant. Accuracy of the models was evaluated by the coefficient of determination, the standard error of estimate and the 1:1 line. The models proposed by Topp and Ledieu and their co-workers were not adequate for estimating the moisture in the soil classes studied. The adjusted linear and polynomial models for the entire set of data of the four soil classes did not have sufficient accuracy for estimating soil moisture. The greater the soil clay and Fe oxide content, the greater the dielectric constant of the medium for a given volumetric moisture. The specific models, θ = 0.40283 - 0.04231 Ka + 0.00194 Ka² - 0.000022 Ka³ (Hapludox) θ = 0.01971 + 0.02902 Ka - 0.00086 Ka² + 0.000012 Ka³ (Hapludox -PF), θ = 0.01692 - 0.00507 Ka (Hapludalf) and θ = 0.08471 + 0.01145 Ka (Hapludox-CA), show greater accuracy and reliability for estimating soil moisture in the soil classes studied.

Effective mass and dielectric constant mismatch effects in spherical multishell quantum dots

The role of effective mass and dielectric mismatches on chemical potentials and addition energies of many-electron multishell quantum dots (QDs) is explored within the framework of a recent extension of the spin density functional theory. It is shown that although the gross electronic density is located in the wells of these multishell QDs, taking position-dependent effective mass and dielectric constant into account can lead to the appearance of relevant differences in chemical potential and addition energies as compared to standard calculations in which the effective mass and the dielectric constant of the well is assumed for the whole multishell structure.

The "image" of the cave and the constant temptation to correct Plato: Benjamin Jowettt as an example

Translations of the first chapters of Book VII of Plato's Republic, in which he introduces the well-known image of the cave, eikón, reveals an astonishing and intriguing variety of interpretations of this image: "allegory", "myth", "fable", "parable", "simile" and "comparison", to cite but a few. Taking as an example the work by Benjamin Jowett, the Victorian translator of Plato, remarkable for its textual accuracy and by means of a close analysis of the terms related to the image, this paper insists on the need to neither interpret nor correct the great ideal philosopher, in this case revealing some evident contradictions that arise when this advice is not followed and pointing out the occasional use of terms extraneous to the Platonic lexicon such as "allegory".

Brane-world creation and black holes

An inflating brane world can be created from ``nothing'' together with its anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap m=(3/2)H, where H is the Hubble rate. We consider the analogue of the Nariai solution and argue that it describes the pair production of ``black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing or the production of AdS black holes in the vicinity of a pre-existing inflating brane world. The Lorentzian evolution of the brane world after creation is briefly discussed. An additional ``integration constant'' in the Friedmann equation-accompanying a term which dilutes like radiation-describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. In general, this could be a 5-dimensional black hole or a ``parallel'' brane world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the AdS/CFT correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.