3,944 research outputs found
Construction of classical superintegrable systems with higher order integrals of motion from ladder operators
We construct integrals of motion for multidimensional classical systems from
ladder operators of one-dimensional systems. This method can be used to obtain
new systems with higher order integrals. We show how these integrals generate a
polynomial Poisson algebra. We consider a one-dimensional system with third
order ladders operators and found a family of superintegrable systems with
higher order integrals of motion. We obtain also the polynomial algebra
generated by these integrals. We calculate numerically the trajectories and
show that all bounded trajectories are closed.Comment: 10 pages, 4 figures, to appear in j.math.phys
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 × a(p) × ΣP) as a spreadsheet using Microsoft Excel® 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.
Sentinel Lymph Node Biopsy in Pure DCIS: Is It Necessary?
Introduction. Sentinel lymph node biopsy (SLNB) in patients with pure ductal carcinoma in situ (DCIS) has been a matter of debate due to very low rate of axillary metastases. We therefore aimed to identify factors in a single institutional series to select patients who may benefit from SLNB.
Material and Methods. Patients, diagnosed with pure DCIS (n = 63) between July 2000 and March 2011, were reviewed. All the sentinel lymph nodes were examined by serial sectioning (50 μm) of the entire lymph node and H&E staining, and by cytokeratin immunostaining in suspicious cases. Results. Median age was 51 (range, 30–79). Of 63 patients, 40 cases (63.5%) with pure DCIS underwent SLN, and 2 of them had a positive SLN (5%). In both 2 cases with SLN metastases, only one sentinel lymph node was involved with tumor cells. Patients who underwent SLNB were more likely to have a tumor size >30 mm or DCIS with intermediate and high nuclear grade or a mastectomy in univariate and multivariate analyses. Conclusion. In our series, we found a slightly higher rate of SLNB positivity in patients with pure DCIS than the large series reported elsewhere. This may either be due to the meticulous examination of SLNs by serial sectioning technique or due to our patient selection criteria or both
Realistic simulations of the AGATA Demonstrator+PRISMA spectrometer
Abstract The performance of the AGATA Demonstrator Array coupled to the PRISMA magnetic spectrometer has been evaluated consistently by using detailed Monte Carlo simulations of the two devices. Results for the multi-nucleon transfer reaction 48Ca+208Pb at 310 MeV beam energy are presented and discussed in this study. The present results suggest that the Doppler correction capabilities of the AGATA+PRISMA setup will be very close to the intrinsic energy resolution of the germanium detectors
Solutions for certain classes of Riccati differential equation
We derive some analytic closed-form solutions for a class of Riccati equation
y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are
C^{\infty}-functions. We show that if \delta_n=\lambda_n
s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}=
\lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and
s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has
a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the
generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also
investigated.Comment: 10 page
On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System
We extend similarity reductions of the coupled (2+1)-dimensional three-wave
resonant interaction system to its Lax pair. Thus we obtain new 3x3 matrix
Fuchs--Garnier pairs for the third and fifth Painleve' equations, together with
the previously known Fuchs--Garnier pair for the fourth and sixth Painleve'
equations. These Fuchs--Garnier pairs have an important feature: they are
linear with respect to the spectral parameter. Therefore we can apply the
Laplace transform to study these pairs. In this way we found reductions of all
pairs to the standard 2x2 matrix Fuchs--Garnier pairs obtained by M. Jimbo and
T. Miwa. As an application of the 3x3 matrix pairs, we found an integral
auto-transformation for the standard Fuchs--Garnier pair for the fifth
Painleve' equation. It generates an Okamoto-like B\"acklund transformation for
the fifth Painleve' equation. Another application is an integral transformation
relating two different 2x2 matrix Fuchs--Garnier pairs for the third Painleve'
equation.Comment: Typos are corrected, journal and DOI references are adde
Nonlocal aspects of -symmetries and ODEs reduction
A reduction method of ODEs not possessing Lie point symmetries makes use of
the so called -symmetries (C. Muriel and J. L. Romero, \emph{IMA J.
Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE
is used here to recover -symmetries of as
nonlocal symmetries. In this framework, by embedding into a
suitable system determined by the function ,
any -symmetry of can be recovered by a local symmetry of
. As a consequence, the reduction method of Muriel and
Romero follows from the standard method of reduction by differential invariants
applied to .Comment: 13 page
Movable algebraic singularities of second-order ordinary differential equations
Any nonlinear equation of the form y''=\sum_{n=0}^N a_n(z)y^n has a
(generally branched) solution with leading order behaviour proportional to
(z-z_0)^{-2/(N-1)} about a point z_0, where the coefficients a_n are analytic
at z_0 and a_N(z_0)\ne 0. We consider the subclass of equations for which each
possible leading order term of this form corresponds to a one-parameter family
of solutions represented near z_0 by a Laurent series in fractional powers of
z-z_0. For this class of equations we show that the only movable singularities
that can be reached by analytic continuation along finite-length curves are of
the algebraic type just described. This work generalizes previous results of S.
Shimomura. The only other possible kind of movable singularity that might occur
is an accumulation point of algebraic singularities that can be reached by
analytic continuation along infinitely long paths ending at a finite point in
the complex plane. This behaviour cannot occur for constant coefficient
equations in the class considered. However, an example of R. A. Smith shows
that such singularities do occur in solutions of a simple autonomous
second-order differential equation outside the class we consider here
Isotropy, shear, symmetry and exact solutions for relativistic fluid spheres
The symmetry method is used to derive solutions of Einstein's equations for
fluid spheres using an isotropic metric and a velocity four vector that is
non-comoving. Initially the Lie, classical approach is used to review and
provide a connecting framework for many comoving and so shear free solutions.
This provides the basis for the derivation of the classical point symmetries
for the more general and mathematicaly less tractable description of Einstein's
equations in the non-comoving frame. Although the range of symmetries is
restrictive, existing and new symmetry solutions with non-zero shear are
derived. The range is then extended using the non-classical direct symmetry
approach of Clarkson and Kruskal and so additional new solutions with non-zero
shear are also presented. The kinematics and pressure, energy density, mass
function of these solutions are determined.Comment: To appear in Classical and Quantum Gravit
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
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