5,105 research outputs found
Volume calculation of the cattle (Bos taurus L.) and the water buffalo (Bos bubalis L.) metapodia with stereologic method
In this study, stereological volume estimations using 26 cattle metapodia (26 metacarpal and 26 metatarsal bones) and 8 water buffalo metapodia (8 metacarpal and 8 metatarsal bones) were made. For this purpose metapodia were parallel sectioned at 1 cm intervals according to Cavalieri principle. Grids with 0.4 cm probe intervals were superimposed on top of these sections and the matching points were counted. All of the bone structures and medullar cavity volumes were calculated with the data obtained from a formulation (V = t Ă a(p) Ă ÎŁP) as a spreadsheet using Microsoft ExcelÂź Windows XP. In addition, percent ratio of this volume to whole bone volume was calculated. The mean ratio of bone marrow space to whole bone structure volume equals 15% in all of the cattle and buffalos. The difference between whole bone volumes of cattle and water buffalo was significant (p < 0.05) while the difference in volume of medullary cavity (cavum medullare) was not significantly different between the two investigated species. The aim of current study is to present a new method that can be used for the volumes calculation of whole bones and medullary cavity in metapodial bones and their percentages.
A New Algebraization of the Lame Equation
We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form.
This yields, in a natural way, an explicit formula for both the Lame
polynomials and the classical non-meromorphic Lame functions in terms of
Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page
Intertwining relations of non-stationary Schr\"odinger operators
General first- and higher-order intertwining relations between non-stationary
one-dimensional Schr\"odinger operators are introduced. For the first-order
case it is shown that the intertwining relations imply some hidden symmetry
which in turn results in a -separation of variables. The Fokker-Planck and
diffusion equation are briefly considered. Second-order intertwining operators
are also discussed within a general approach. However, due to its complicated
structure only particular solutions are given in some detail.Comment: 18 pages, LaTeX20
Quasi-doubly periodic solutions to a generalized Lame equation
We consider the algebraic form of a generalized Lame equation with five free
parameters. By introducing a generalization of Jacobi's elliptic functions we
transform this equation to a 1-dim time-independent Schroedinger equation with
(quasi-doubly) periodic potential. We show that only for a finite set of
integral values for the five parameters quasi-doubly periodic eigenfunctions
expressible in terms of generalized Jacobi functions exist. For this purpose we
also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics
Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential
We present an analytical calculation of periodic orbits in the homogeneous
quartic oscillator potential. Exploiting the properties of the periodic
Lam{\'e} functions that describe the orbits bifurcated from the fundamental
linear orbit in the vicinity of the bifurcation points, we use perturbation
theory to obtain their evolution away from the bifurcation points. As an
application, we derive an analytical semiclassical trace formula for the
density of states in the separable case, using a uniform approximation for the
pitchfork bifurcations occurring there, which allows for full semiclassical
quantization. For the non-integrable situations, we show that the uniform
contribution of the bifurcating period-one orbits to the coarse-grained density
of states competes with that of the shortest isolated orbits, but decreases
with increasing chaoticity parameter .Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear
in J. Phys. A final version 3; error in eq. (33) corrected and note added in
prin
Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems
We investigate cascades of isochronous pitchfork bifurcations of
straight-line librating orbits in some two-dimensional Hamiltonian systems with
mixed phase space. We show that the new bifurcated orbits, which are
responsible for the onset of chaos, are given analytically by the periodic
solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians
with C_ symmetry, they occur alternatingly as Lam\'e functions of period
2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function
appearing in the Lam\'e equation. We also show that the two pairs of orbits
created at period-doubling bifurcations of touch-and-go type are given by two
different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper,
accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of
bifurcations "touch-and-go" replaced by "island-chain
A parallel algorithm for the enumeration of benzenoid hydrocarbons
We present an improved parallel algorithm for the enumeration of fixed
benzenoids B_h containing h hexagonal cells. We can thus extend the enumeration
of B_h from the previous best h=35 up to h=50. Analysis of the associated
generating function confirms to a very high degree of certainty that and we estimate that the growth constant and the amplitude .Comment: 14 pages, 6 figure
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