Nuclear level densities in the constant-spacing model

A new method to calculate level densities for non-interacting Fermions within the constant-spacing model with a finite number of states is developed. We show that asymptotically (for large numbers of particles or holes) the densities have Gaussian form. We improve on the Gaussian distribution by using analytical expressions for moments higher than the second. Comparison with numerical results shows that the resulting sixth-moment approximation is excellent except near the boundaries of the spectra and works globally for all particle/hole numbers and all excitation energies.     

On isocline lines for functions and convex stratifications of two variables

Let the isoclines of a function u be the level lines of the function θ = arg(Du). Formulas for the curvature and the length of isocline lines in terms of the curvatures k, j of the level curves and of the steepest descent lines of u are given. The special case when all isoclines are straight lines is studied: in this case the steepest descent lines bend proportionally to the level lines; the support function of the level lines is linear function on the isoclines parameterized by the level values, possibly changing them. This characterization gives a new proof of a property of the developable surfaces found in [A. Fialkow, Geometric characterization of invariant partial differential equations, Amer. J. Math. 59(4) (1937), pp. 833–844]. When u is in the class of quasi convex functions, the L _p norm of the length function I _θ of the isoclines has minimizers with isoclines straight lines; the same occurs for other functionals on u depending on k, j. For a strictly regular quasi convex function isoclines may have arbitrarily large length and arbitrarily large L ₁ norm of I _θ.     

Mutually nearest and farthest points of sets and the Drop Theorem in geodesic spaces

Let A and X be nonempty, bounded and closed subsets of a geodesic metric space (E, d). The minimization (resp. maximization) problem denoted by min(A, X) (resp. max(A, X)) consists in finding ${(a_0,x_0) \in A \times X}$ such that ${d(a_0,x_0) = \inf\left\{d(a,x) : a \in A, x \in X\right\}}$ (resp. ${d(a_0,x_0) = \sup\left\{d(a,x) : a \in A, x \in X\right\}}$ ). We give generic results on the well-posedness of these problems in different geodesic spaces and under different conditions considering the set A fixed. Besides, we analyze the situations when one set or both sets are compact and prove some specific results for CAT(0) spaces. We also prove a variant of the Drop Theorem in Busemann convex geodesic spaces and apply it to obtain an optimization result for convex functions.     

k-Domination and k-Independence in Graphs: A Survey

In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating if every vertex of V − S is adjacent to at least k vertices in S. The subset S is k-independent if the maximum degree of the subgraph induced by the vertices of S is less or equal to k − 1. In this paper we survey results on k-domination and k-independence.     

Chemical composition, antifungal and herbicidal effects of essential oil isolated from Chersodoma Argentina (Asteraceae)

Analysis of the hydrodistilled essential oil of the aerial parts of Chersodoma argentina Cabrera by GC-MS and NMR spectroscopy revealed that over 80% consisted of monoterpene hydrocarbons such as alpha-thujene, alpha-pinene and beta-pinene. Contact and headspace volatile exposure assays of the essential oil demonstrated antifungal activity against Sclerotinia sclerotiorum, Sclerotium rolfsii and Rhizoctonia solani with the contact assay showing greater activity than the headspace assay. Herbicidal activity was shown by reduced root growth of Allium porrum, Solanum lycopersicon and Sorghum halepense in both assays.     

Identification of adequate vehicles to carry nerve regeneration inducers using tubulisation

ABSTRACT: BACKGROUND: Axonal regeneration depends on many factors, such as the type of injury and repair, age, distance from the cell body and distance of the denervated muscle, loss of surrounding tissue and the type of injured nerve. Experimental models use tubulisation with a silicone tube to research regenerative factors and substances to induce regeneration. Agarose, collagen and DMEM (Dulbecco's modified Eagle's medium) can be used as vehicles. In this study, we compared the ability of these vehicles to induce rat sciatic nerve regeneration with the intent of finding the least active or inert substance. The experiment used 47 female Wistar rats, which were divided into four experimental groups (agarose 4%, agarose 0.4%, collagen, DMEM) and one normal control group. The right sciatic nerve was exposed, and an incision was made that created a 10 mm gap between the distal and proximal stumps. A silicone tube was grafted onto each stump, and the tubes were filled with the respective media. After 70 days, the sciatic nerve was removed. We evaluated the formation of a regeneration cable, nerve fibre growth, and the functional viability of the regenerated fibres. RESULTS: Comparison among the three vehicles showed that 0.4% agarose gels had almost no effect on provoking the regeneration of peripheral nerves and that 4% agarose gels completely prevented fibre growth. The others substances were associated with profuse nerve fibre growth. CONCLUSIONS: In the appropriate concentration, agarose gel may be an important vehicle for testing factors that induce regeneration without interfering with nerve growth.