The NumbersWithNames Program

We present the NumbersWithNames program which performs data-mining on the Encyclopedia of Integer Sequences to find interesting conjectures in number theory. The program forms conjectures by finding empirical relationships between a sequence chosen by the user and those in the Encyclopedia. Furthermore, it transforms the chosen sequence into another set of sequences about which conjectures can also be formed. Finally, the program prunes and sorts the conjectures so that themost plausible ones are presented first. We describe here the many improvements to the previous Prolog implementation which have enabled us to provide NumbersWithNames as an online program. We also present some new results from using NumbersWithNames, including details of an automated proof plan of a conjecture NumbersWithNames helped to discover.

Mathematics and fiber arts

Mathematics can be found all over the world, even in what could be considered an unrelated area, like fiber arts. In knitting, crochet, and counted-thread embroidery, we can find concepts of algebra, graph theory, number theory, geometry of transformations, and symmetry, as well as computer science. For example, many fiber art pieces embody notions related with groups of symmetry. In this work, we focus on two areas of Mathematics associated with knitting, crochet, and cross-stitch works – number theory and geometry of transformations.

A practical grammar of the English language : in which the principles established by Lindley Murray, are inculcated, and the theory of modes clearly illustrated by diagrams, representing the number of tenses in each mode, their signs and the manner in which they are formed /

Williamson,

Calculated atomic photoeffect cross sections by modified Stobbe theory for atomic number from Z=2 through Z=50, add photon energies between 0.5 keV and 40.0 keV.

Mode of access: Internet.

A dictionary of chemistry, exhibiting the present state of the theory and practice of that science, its application to natural philosophy, the processes of manufactures, metallurgy, and numerous other arts dependant on the properties and habitudes of bodies, in the mineral, vegetable, and animal kingdoms. With a considerable number of tables, expressing the elective attractions, specific gravities, comparative heats, component parts, combinations, and other affections of the objects of chemical research. Illustrated with engravings.

Paged continuously.

An elementary treatise on astronomy. In two parts. The first containing, a clear and compendious view of the theory; the second, a number of practical problems. To which are added, solar, lunar, and other astronomical tables.

Mode of access: Internet.

A practical grammar of the English language, in which the principles established by Lindley Murray, are inculcated, and his theory of the moods clearly illustrated by diagrams, representing the number of the tenses in each mood--their signs--and the manner in which they are formed.

"Recommendations": prelim. leaves 2-4.

A treatise on surveying : containing the theory and practice : to which is prefixed a perspicuous system of plane trigonometry : the whole clearly demonstrated and illustrated by a large number of appropriate examples, particularly adapted to the use of schools /

With: Mathematical tables / John Gummere. Stereotyped ed., carefully rev. and corrected. Philadelphia : Kimber & Sharpless, 1843.

Design concept evaluation based on rough number and information entropy theory

Concept evaluation at the early phase of product development plays a crucial role in new product development. It determines the direction of the subsequent design activities. However, the evaluation information at this stage mainly comes from experts' judgments, which is subjective and imprecise. How to manage the subjectivity to reduce the evaluation bias is a big challenge in design concept evaluation. This paper proposes a comprehensive evaluation method which combines information entropy theory and rough number. Rough number is first presented to aggregate individual judgments and priorities and to manipulate the vagueness under a group decision-making environment. A rough number based information entropy method is proposed to determine the relative weights of evaluation criteria. The composite performance values based on rough number are then calculated to rank the candidate design concepts. The results from a practical case study on the concept evaluation of an industrial robot design show that the integrated evaluation model can effectively strengthen the objectivity across the decision-making processes.

[the Teaching Of Social Sciences In Health: Between Practice And Theory].

The models of teaching social sciences and clinical practice are insufficient for the needs of practical-reflective teaching of social sciences applied to health. The scope of this article is to reflect on the challenges and perspectives of social science education for health professionals. In the 1950s the important movement bringing together social sciences and the field of health began, however weak credentials still prevail. This is due to the low professional status of social scientists in health and the ill-defined position of the social sciences professionals in the health field. It is also due to the scant importance attributed by students to the social sciences, the small number of professionals and the colonization of the social sciences by the biomedical culture in the health field. Thus, the professionals of social sciences applied to health are also faced with the need to build an identity, even after six decades of their presence in the field of health. This is because their ambivalent status has established them as a partial, incomplete and virtual presence, requiring a complex survival strategy in the nebulous area between social sciences and health.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

The number of reproductive workers in highly eusocial Hymenoptera: monogyny and monandry

Haplodiploidy results in relatedness asymmetries between colony members of highly eusocial Hymenoptera. As a consequence, queen and reproductive workers are more related to their own sons than to each other's male offspring. Kin selection theory predicts multiple optima in male parentage: either the queen or the workers should produce all the males. Nevertheless, shared male parentage is common in highly eusocial hymenopterans. An inclusive fitness model was used to analyze the effect of the number of reproductive workers on male parentage shared by the queen and laying workers by isolating the male component from an inclusive fitness equation using the equal fitness through male condition for each pairwise combination of the three female classes comprised of the queen, laying workers and non-laying workers. The main result of the theoretical analyses showed that the fraction of males produced by workers increases asymptotically with the number of laying workers at an increasingly diminishing rate, tending to an asymptotic value of 0.67. In addition, as the number of laying workers increases, the share of male parentage converges to that of non-laying workers. The diminishing return effect on male parentage share depending on the number of reproductive workers leads us to expect the number of reproductive workers to be relatively small in a stingless bee colony, even in the absence of productivity costs. The available data confirms this hypothesis, as there is an unusually small number of reproductive workers in stingless bee colonies.

Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters

The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of 3d, 4d, and 5d metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the 3d, 4d, and 5d metal (30 elements) clusters containing 13 atoms, M(13). First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first- principles molecular-dynamics simulation, structure crossover, and the selection of five well-known M(13) structures. Several new lower energy configurations were identified, e. g., Pd(13), W(13), Pt(13), etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large d states occupation. (ii) For Au(13), we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the d states and hence, most of the properties can be explained by the chemistry picture of occupation of the bonding and antibonding states.

Theory of nitride oxide adsorption on transition metal (111) surfaces: a first-principles investigation

In this work, we report a density functional theory study of nitric oxide (NO) adsorption on close-packed transition metal (TM) Rh(111), Ir(111), Pd(111) and Pt(111) surfaces in terms of adsorption sites, binding mechanism and charge transfer at a coverage of Theta(NO) = 0.25, 0.50, 0.75 monolayer (ML). Based on our study, an unified picture for the interaction between NO and TM(111) and site preference is established, and valuable insights are obtained. At low coverage (0.25 ML), we find that the interaction of NO/TM(111) is determined by an electron donation and back-donation process via the interplay between NO 5 sigma/2 pi* and TM d-bands. The extent of the donation and back-donation depends critically on the coordination number (adsorption sites) and TM d-band filling, and plays an essential role for NO adsorption on TM surfaces. DFT calculations shows that for TMs with high d-band filling such as Pd and Pt, hollow-site NO is energetically the most favorable, and top-site NO prefers to tilt away from the normal direction. While for TMs with low d-band filling (Rh and Ir), top-site NO perpendicular to the surfaces is energetically most favorable. Electronic structure analysis show that irrespective of the TM and adsorption site, there is a net charge transfer from the substrate to the adsorbate due to overwhelming back-donation from the TM substrate to the adsorbed NO molecules. The adsorption-induced change of the work function with respect to bare surfaces and dipole moment is however site dependent, and the work function increases for hollow-site NO, but decreases for top-site NO, because of differences in the charge redistribution. The interplay between the energetics, lateral interaction and charge transfer, which is element dependent, rationalizes the structural evolution of NO adsorption on TM(111) surfaces in the submonolayer regime.