Numerical treatment of a generalized Vandermonde system of equations

AbstractA stable method is proposed for the numerical solution of a linear system of equations having a generalized Vandermonde matrix. The method is based on Gaussian elimination and establishes explicit expressions for the elements of the resulting upper triangular matrix. These elements can be computed by means of sums of exclusively positive terms. In an important special case these sums can be reduced to simple recursions. Finally the method is retraced for the case of a confluent type of generalized Vandermonde matrix

A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates

We have established the exact expression for the gravitational potential of a homogeneous polar cell - an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any opening angle and radial extension of the cell. It is valid at any point in space, i.e. in the plane of the distribution (inside and outside) as well as off-plane, thereby generalizing the results reported by Durand (1953) for the circular disc. The three components of the gravitational acceleration are given. The mathematical demonstration proceeds from the "incomplete version of Durand's formula" for the potential (based on complete elliptic integrals). We determine first the potential due to the circular sector (i.e. a pie-slice sheet), and then deduce that of the polar cell (from convenient radial scaling and subtraction). As a by-product, we generate an integral theorem stating that "the angular average of the potential of any circular sector along its tangent circle is 2/PI times the value at the corner". A few examples are presented. For numerical resolutions and cell shapes commonly used in disc simulations, we quantify the importance of curvature effects by performing a direct comparison between the potential of the polar cell and that of the Cartesian (i.e. rectangular) cell having the same mass. Edge values are found to deviate roughly like 2E-3 x N/256 in relative (N is the number of grid points in the radial direction), while the agreement is typically four orders of magnitude better for values at the cell's center. We also produce a reliable approximation for the potential, valid in the cell's plane, inside and close to the cell. Its remarkable accuracy, about 5E-4 x N/256 in relative, is sufficient to estimate the cell's self-acceleration.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

Theories with the independence property

A first-order theory T has the Independence Property provided T ⊢ (Q)(Φ⇒

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

beta-decay study of Cu-77

A beta-decay study of Cu-77 has been performed at the ISOLDE mass separator with the aim to deduce its beta-decay properties and to obtain spectroscopic information on Zn-77. Neutron-rich copper isotopes were produced by means of proton- or neutron-induced fission reactions on U-238. After the production, Cu-77 was selectively laser ionized, mass separated and sent to different detection systems where beta-gamma and beta-n coincidence data were collected. We report on the deduced half-live, decay scheme, and possible spin assignment of 77Cu

A Unifying View on Recombination Spaces and Abstract Convex Evolutionary Search

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.Proceedings of EvoCOP 2019 - 19th European Conference on Evolutionary Computation, 24-26 April 2019, Leipzig, GermanyPrevious work proposed to unify an algebraic theory of fitness landscapes and a geometric framework of evolutionary algorithms (EAs). One of the main goals behind this unification is to develop an analytical method that verifies if a problem's landscape belongs to certain abstract convex landscapes classes, where certain recombination-based EAs (without mutation) have polynomial runtime performance. This paper advances such unification by showing that: (a) crossovers can be formally classified according to geometric or algebraic axiomatic properties; and (b) the population behaviour induced by certain crossovers in recombination-based EAs can be formalised in the geometric and algebraic theories. These results make a significant contribution to the basis of an integrated geometric-algebraic framework with which analyse recombination spaces and recombination-based EAs

On-line yields obtained with the ISOLDE RILIS

The ISOLDE resonance ionization laser ion source (RILIS) allows to ionize efficiently and selectively many metallic elements. In recent yield surveys and on-line experiments with the ISOLDE RILIS we observed $^{23-34}$Mg , $^{26-34}\!$Al , $^{98-132}$Cd , $^{149}$Tb , $^{155-177}\!$Yb , $^{179-200}$Tl , $^{183-215}$Pb and $^{188-218}$Bi. The obtained yields are presented together with measured release parameters which allow to extrapolate the release efficiency towards more exotic (short-lived) nuclides of the same elements

Ventricular beat detection in single channel electrocardiograms

BACKGROUND: Detection of QRS complexes and other types of ventricular beats is a basic component of ECG analysis. Many algorithms have been proposed and used because of the waves' shape diversity. Detection in a single channel ECG is important for several applications, such as in defibrillators and specialized monitors. METHODS: The developed heuristic algorithm for ventricular beat detection includes two main criteria. The first of them is based on steep edges and sharp peaks evaluation and classifies normal QRS complexes in real time. The second criterion identifies ectopic beats by occurrence of biphasic wave. It is modified to work with a delay of one RR interval in case of long RR intervals. Other algorithm branches classify already detected QRS complexes as ectopic beats if a set of wave parameters is encountered or the ratio of latest two RR intervals RR(i-1)/RR(i )is less than 1:2.5. RESULTS: The algorithm was tested with the AHA and MIT-BIH databases. A sensitivity of 99.04% and a specificity of 99.62% were obtained in detection of 542014 beats. CONCLUSION: The algorithm copes successfully with different complicated cases of single channel ventricular beat detection. It is aimed to simulate to some extent the experience of the cardiologist, rather than to rely on mathematical approaches adopted from the theory of signal analysis. The algorithm is open to improvement, especially in the part concerning the discrimination between normal QRS complexes and ectopic beats