The optimal dividend barrier in the Gamma-Omega model

In the traditional actuarial risk model, if the surplus is negative, the company is ruined and has to go out of business. In this paper we distinguish between ruin (negative surplus) and bankruptcy (going out of business), where the probability of bankruptcy is a function of the level of negative surplus. The idea for this notion of bankruptcy comes from the observation that in some industries, companies can continue doing business even though they are technically ruined. Assuming that dividends can only be paid with a certain probability at each point of time, we derive closed-form formulas for the expected discounted dividends until bankruptcy under a barrier strategy. Subsequently, the optimal barrier is determined, and several explicit identities for the optimal value are found. The surplus process of the company is modeled by a Wiener process (Brownian motion).

Mammalian target of rapamycin complex 1 orchestrates invariant NKT cell differentiation and effector function.

Invariant NKT (iNKT) cells play critical roles in bridging innate and adaptive immunity. The Raptor containing mTOR complex 1 (mTORC1) has been well documented to control peripheral CD4 or CD8 T cell effector or memory differentiation. However, the role of mTORC1 in iNKT cell development and function remains largely unknown. By using mice with T cell-restricted deletion of Raptor, we show that mTORC1 is selectively required for iNKT but not for conventional T cell development. Indeed, Raptor-deficient iNKT cells are mostly blocked at thymic stage 1-2, resulting in a dramatic decrease of terminal differentiation into stage 3 and severe reduction of peripheral iNKT cells. Moreover, residual iNKT cells in Raptor knockout mice are impaired in their rapid cytokine production upon αGalcer challenge. Bone marrow chimera studies demonstrate that mTORC1 controls iNKT differentiation in a cell-intrinsic manner. Collectively, our data provide the genetic evidence that iNKT cell development and effector functions are under the control of mTORC1 signaling.

Derivation of the gauge-invariant action for open and closed free bosonic string field theories

The gauge-invariant actions for open and closed free bosonic string field theories are obtained from the string field equations in the conformal gauge using the cohomology operations of Banks and Peskin. For the closed-string theory no restrictions are imposed on the gauge parameters.

BRST-invariant path integral for a spinning relativistic particle

The propagator of a relativistic spinning particle is calculated using the Becchi-Rouet-Stora-Tyutin-(BRST)-invariant path-integral formalism of Fradkin and Vilkovisky. The spinless case is considered as an introduction to the formalism.

Renormalization of gauge-invariant operators and the axial anomaly

The renormalization properties of gauge-invariant composite operators that vanish when the classical equations of motion are used (class II^a operators) and which lead to diagrams where the Adler-Bell-Jackiw anomaly occurs are discussed. It is shown that gauge-invariant operators of this kind do need, in general, nonvanishing gauge-invariant (class I) counterterms.

Gauge-invariant actions from constraint Hamiltonian dynamics

Dirac's constraint Hamiltonian formalism is used to construct a gauge-invariant action for the massive spin-one and -two fields.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Poincar-Cartan integral invariant and canonical transformation for singular lagrangians

In this work we develop the canonical formalism for constrained systems with a finite number of degrees of freedom by making use of the PoincarCartan integral invariant method. A set of variables suitable for the reduction to the physical ones can be obtained by means of a canonical transformation. From the invariance of the PoincarCartan integral under canonical transformations we get the form of the equations of motion for the physical variables of the system.

Poincar-Cartan intregral invariant and canonical trasformation for singular Lagrangians: an addendum

The results of a previous work, concerning a method for performing the canonical formalism for constrained systems, are extended when the canonical transformation proposed in that paper is explicitly time dependent.

Invariant decomposition of the retarded electromagnetic field.

The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor J. These field equations are an algebraic differential first-order system of oneforms, which verifies automatically the integrability conditions.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.

Determinants of the omega-3 index in a Mediterranean population at increased risk for CHD.

The omega-3 index, defined as the sum of EPA and DHA in erythrocyte membranes expressed as a percentage of total fatty acids, has been proposed as both a risk marker and risk factor for CHD death. A major determinant of the omega-3 index is EPA þ DHA intake, but the impact of other dietary fatty acids has not been investigated. In a cross-sectional study on 198 subjects (102 men and 96 women, mean age 66 years) at high cardiovascular risk living in Spain, the country with low rates of cardiac death despite a high prevalence of cardiovascular risk factors, dietary data were acquired from FFQ and blood cell membrane fatty acid composition was measured by GC. The average consumption of EPA þ DHA was 0·9 g/d and the mean omega-3 index was 7·1%. In multivariate models, EPA þ DHA intake was the main predictor of the omega-3 index but explained only 12% of its variability (P,0·001). No associations with other dietary fatty acids were observed. Although the single most influential determinant of the omega-3 index measured here was the intake of EPA þ DHA, it explained little of the former"s variability; hence, the effects of other factors (genetic, dietary and lifestyle) remain to be determined. Nevertheless, the high omega-3 index could at least partially explain the paradox of low rates of fatal CHD in Spain despite a high background prevalence of cardiovascular risk factors.