Valadier-like formulas for the supremum function II: The compactly indexed case

We generalize and improve the original characterization given by Valadier [20, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdifferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to Valadier formula. Our starting result is the characterization given in [10, Theorem 4], which uses the epsilon-subdiferential at the reference point.Comment: 23 page

Valadier-like formulas for the supremum function I

We generalize and improve the original characterization given by Valadier [18, Theorem 1] of the subdifferential of the pointwise supremum of convex functions, involving the subdifferentials of the data functions at nearby points. We remove the continuity assumption made in that work and obtain a general formula for such a subdiferential. In particular, when the supremum is continuous at some point of its domain, but not necessarily at the reference point, we get a simpler version which gives rise to the Valadier formula. Our starting result is the characterization given in [11, Theorem 4], which uses the epsilon-subdifferential at the reference point.Comment: 27 page

One-dimensional relativistic dissipative system with constant force and its quantization

For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization of the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.Comment: 11 pages, no figure

On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

Genetic study in patients operated dentally and anesthetized with articaine-epinephrine

Aims: In this study we wanted to figure out if there was a correlation between OPRM1 N40D, TRPV1 I316M, TRPV1 I585V, NOS3 −786T>C and IL6 −174C>G polymorphisms and the response to locally applied articaine-epinephrine anesthetic. Methods: In this observational study, 114 oral cell samples of patients anesthetized with articaine-epinephrine (54 from men 60 from women), were collected from dental centers in Madrid (Spain). High molecular weight DNA was obtained from oral mucosa cells. The analysis of OPRM1 N40D (rs1799971), TRPV1 I316M (rs222747), TRPV1 I585V (rs8065080) and IL6 −174C>G polymorphism was performed through real-time PCR allelic discrimination using TaqMan probes. Polymorphism NOS3 −786T> C (rs2070744) was analyzed using RFLP-PCR. Results: The studied polymorphisms are involved neither in the response to the anesthetic, nor in the intensity of perceived dental pain. However, in a subset of female patients we found that TRPV1 I316M was associated with a delayed onset of anesthesia. Conclusions: There is no association among these polymorphisms and the time elapsed between the application of the anesthetic and the onset of its effect

Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigonometric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in particular cases and in general, to give insight into the properties of the solution of the spectral problem. As examples, the analytical index and the eigenvalues of the Dirac operator on the torus and on the sphere are obtained and as an application of this technique, the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page

Anatomical pathways for auditory memory II: information from rostral superior temporal gyrus to dorsolateral temporal pole and medial temporal cortex

Auditory recognition memory in non-human primates differs from recognition memory in other sensory systems. Monkeys learn the rule for visual and tactile delayed matching-to-sample within a few sessions, and then show one-trial recognition memory lasting 10–20 min. In contrast, monkeys require hundreds of sessions to master the rule for auditory recognition, and then show retention lasting no longer than 30–40 s. Moreover, unlike the severe effects of rhinal lesions on visual memory, such lesions have no effect on the monkeys' auditory memory performance. The anatomical pathways for auditory memory may differ from those in vision. Long-term visual recognition memory requires anatomical connections from the visual association area TE with areas 35 and 36 of the perirhinal cortex (PRC). We examined whether there is a similar anatomical route for auditory processing, or that poor auditory recognition memory may reflect the lack of such a pathway. Our hypothesis is that an auditory pathway for recognition memory originates in the higher order processing areas of the rostral superior temporal gyrus (rSTG), and then connects via the dorsolateral temporal pole to access the rhinal cortex of the medial temporal lobe. To test this, we placed retrograde (3% FB and 2% DY) and anterograde (10% BDA 10,000 mW) tracer injections in rSTG and the dorsolateral area 38DL of the temporal pole. Results showed that area 38DL receives dense projections from auditory association areas Ts1, TAa, TPO of the rSTG, from the rostral parabelt and, to a lesser extent, from areas Ts2-3 and PGa. In turn, area 38DL projects densely to area 35 of PRC, entorhinal cortex (EC), and to areas TH/TF of the posterior parahippocampal cortex. Significantly, this projection avoids most of area 36r/c of PRC. This anatomical arrangement may contribute to our understanding of the poor auditory memory of rhesus monkeys

The effect of vacancy-induced magnetism on electronic transport in armchair carbon nanotubes

The influence of local magnetic moment formation around three kinds of vacancies on the electron conduction through metallic single-wall carbon nanotubes is studied by use of the Landauer formalism within the coherent regime. The method is based on the single-band tight-binding Hamiltonian, a surface Green's function calculation, and the mean-field Hubbard model. The numerical results show that the electronic transport is spin-polarized due to the localized magnetic moments and it is strongly dependent on the geometry of the vacancies. For all kinds of vacancies, by including the effects of local magnetic moments, the electron scattering increases with respect to the nonmagnetic vacancies case and hence, the current-voltage characteristic of the system changes. In addition, a high value for the electron-spin polarization can be obtained by applying a suitable gate voltage.Comment: 6 pages, 6 figure