Morpho-kinematic analysis of the point-symmetric, bipolar planetary nebulae Hb 5 and K 3-17, a pathway to poly-polarity

The kinematics of the bipolar planetary nebulae Hb~5 and K 3-17 are investigated in detail by means of a comprehensive set of spatially resolved high spectral resolution, long-slit spectra. Both objects share particularly interesting characteristics, such as a complex filamentary, rosette-type nucleus, axial point-symmetry and very fast bipolar outflows. The kinematic information of Hb~5 is combined with {\it HST} imagery to construct a detailed 3D model of the nebula using the code SHAPE. The model shows that the large scale lobes are growing in a non-homologous way. The filamentary loops in the core are proven to actually be secondary lobes emerging from what appears to be a randomly punctured, dense, gaseous core and the material that forms the point symmetric structure flows within the lobes with a distinct kinematic pattern and its interaction with the lobes has had a shaping effect on them. Hb~5 and K~3-17 may represent a class of fast evolving planetary nebulae that will develop poly-polar characteristics once the nebular core evolves and expands.Comment: 19 pages, 8 figures. To appear in The Astrophysical Journa

Variables cinéticas de la batida relacionadas con el rendimiento del salto horizontal a pies juntos

El presente trabajo analiza las variables fuerza-tiempo (f-t), velocidad-tiempo (V-t) y potenciatiempo (P-t) que más se relacionan con la distancia del salto horizontal (SH), y discute sobre la validez de este test como predictor de la fuerza explosiva de las extremidades inferiores. Participaron 144 estudiantes de educación física (96 hombres y 48 mujeres) que realizaron 3 saltos verticales (SV) sobre plataforma de contacto y 3 SH sobre plataforma de fuerzas. Se obtuvieron correlaciones significativas (p<0.05) entre SH y f-t, SH y P-t (relativas al peso corporal) y SH y V-t. Paralelamente, se obtuvieron diferencias significativas (p<0.05) en estas variables entre hombres y mujeres (6-36%). También se obtuvieron altas relaciones (p<0.001) entre SH y SV en hombres y mujeres (r= 0.68 y r= 0.69, respectivamente). En conclusión, el test de SH es válido para evaluar la fuerza explosiva de las extremidades inferiores. Algunos aspectos metodológicos deben tenerse en cuenta para analizar y tratar las variables cinéticas del SH. Futuros trabajos deben seleccionar las variables cinéticas más importantes para corregir la técnica del SH.The present work analyzes the force-time (f-t), speed-time (V-t) and power-time (P-t) variables related with the standing long jump distance (SLJ). Also, this work analyzes the validity of the SLJ in order to predict the lower extremities explosive force. 144 physical education students (96 men and 48 women) participated in this study. The students carried out 3 vertical jumps (VJ) on contact mat, and 3 SLJ on force plate. We have obtained significant correlations (p<0.05) between SLJ and f-t, SLJ and P-t (relative to body weight) and SLJ and V-t variables. Significant differences (p<0.05) between men and women were obtained in these variables (6-36 %). Also, relationships between SLJ and VJ (p< 0.001) were obtained in men and women (r= 0.68 and r= 0.69, respectively). In conclusion, the SLJ test is valid in order to evaluate the lower extremities explosive force. Some methodological aspects are important in order to analyze the SLJ kinetic variables. Future works should select the most important SLJ kinetic variables in order to correct the SLJ technique

Matrix continued fractions associated with lattice paths, resolvents of difference operators, and random polynomials

We begin our analysis with the study of two collections of lattice paths in the plane, denoted $\mathcal{D}_{[n,i,j]}$ and $\mathcal{P}_{[n,i,j]}$. These paths consist of sequences of $n$ steps, where each step allows movement in three directions: upward (with a maximum displacement of $q$ units), rightward (exactly one unit), or downward (with a maximum displacement of $p$ units). The paths start from the point $(0,i)$ and end at the point $(n,j)$. In the collection $\mathcal{D}_{[n,i,j]}$, it is a crucial constraint that paths never go below the $x$-axis, while in the collection $\mathcal{P}_{[n,i,j]}$, paths have no such restriction. We assign weights to each path in both collections and introduce weight polynomials and generating series for them. Our main results demonstrate that certain matrices of size $q\times p$ associated with these generating series can be expressed as matrix continued fractions. These results extend the notable contributions previously made by P. Flajolet and G. Viennot in the scalar case $p=q=1$. The generating series can also be interpreted as resolvents of one-sided or two-sided difference operators of finite order. Additionally, we analyze a class of random banded matrices $H$, which have $p+q+1$ diagonals with entries that are independent and bounded random variables. These random variables have identical distributions along diagonals. We investigate the asymptotic behavior of the expected values of eigenvalue moments for the principal $n\times n$ truncation of $H$ as $n$ tends to infinity.Comment: 48 pages, 3 figure