From the Mendeleev periodic table to particle physics and back to the periodic table

We briefly describe in this paper the passage from Mendeleev's chemistry (1869) to atomic physics (in the 1900's), nuclear physics (in the 1932's) and particle physics (from 1953 to 2006). We show how the consideration of symmetries, largely used in physics since the end of the 1920's, gave rise to a new format of the periodic table in the 1970's. More specifically, this paper is concerned with the application of the group SO(4,2)xSU(2) to the periodic table of chemical elements. It is shown how the Madelung rule of the atomic shell model can be used for setting up a periodic table that can be further rationalized via the group SO(4,2)xSU(2) and some of its subgroups. Qualitative results are obtained from this nonstandard table.Comment: 15 pages; accepted for publication in Foundations of Chemistry (special issue to commemorate the one hundredth anniversary of the death of Mendeleev who died in 1907); version 2: 16 pages; some sentences added; acknowledgment and references added; misprints correcte

On the use of the group SO(4,2) in atomic and molecular physics

In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4,2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.Comment: 31 page

A summary of noncyclic difference sets, k < 20

AbstractThis note contains a list of (v, k, λ) difference sets in noncyclic groups, for k < 20

The moral legitimacy of entrepreneurs: An analysis of early-stage entrepreneurship across 26 countries

This article will develop our socio-cultural understanding of entrepreneurship by examining the influence of the moral legitimacy of entrepreneurs in society on an individual’s engagement in early-stage entrepreneurship. A multilevel analysis conducted across 26 countries shows that the higher the perceived degree of moral legitimacy, the more likely an individual is to think about starting a business compared to not thinking about it; to start preparing a business as against just considering it; or to found and run a business as compared to just engaging in preparation activities. We conclude that moral norms in society play an important role in early-stage entrepreneurship and that makes it important to legitimize the understanding of entrepreneurs as moral and beneficial for society as a whole.Peer reviewe

Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator

Cultural Resources Survey of the Leander Rehabilitation Center, Williamson County, Texas

In August-September 1996, personnel from Prewitt and Associates, Inc., conducted a cultural resources survey of ca. 725 acres of the former Leander Rehabilitation Center. The project area lies adjacent to U.S. Highway 183 and FM 620 in southern Williamson County, Texas. The survey resulted in additional documentation of one previously recorded prehistoric archeological site (41 WM452), the identification and recording of four historic archeological sites (41WM892, 41WM893, 41WM896, and 41WM897), and reconnaissance-level documentation of 45 historic buildings and structures. Site 41WM452 is an extensive upland lithic scatter and lithic procurement site which lacks subsurface deposits, features, and datable materials. Site 41WM892 is a wood-chopper camp that contains a number of rock alignments and limited artifact deposits dating to the first decade of the twentieth century. Site 41WM893 is a remnant of a railroad spur used during the 1937-1941 construction of Marshall Ford Dam (now Mansfield Dam). Site 41WM896 contains a small number of features and sparse artifact deposits associated with the 1937-1945 Rhodes farmstead. Site 41WM897 is an isolated historic well with unknown associations. None of these archeological sites contains important information, and it is recommended that they be considered not eligible for listing in the National Register of Historic Places or for designation as State Archeological Landmarks. The 45 buildings and structures, at 36 locations, are associated with the former State Dairy and Hog Farm. This farm was established in 1942, expanded after 1945, and reached its peak years of production as a hog farm between 1950 and the late 1960s, Created to serve the needs of the State Board of Control and the State Hospital, the facility is significant for its success in food production for eleemosynary institutions in Austin and throughout Texas, as well as for its role in the application of modern psychiatric treatment based on the therapeutic value of manual labor. Among the surveyed resources are dwellings, an office and warehouse building, a dormitory, a variety of agricultural buildings and structures, and infrastructural elements, all built between 1943 and 1955. Twenty-one of the 45 surveyed resources are recommended as being eligible for listing in the National Register of Historic Places under Criteria A and C as Contributing resources in a historic district and for designation as State Archeological Landmarks

Archeological Survey Of The Jefferson Street Lift Station Force And Gravity Main Corridors And Louise Hays And Lehmann-Monroe Parks, City Of Kerrville Kerr County, Texas

In April 2013, personnel with Prewitt and Associates, Inc., performed an archeological survey for proposed sewer and water main improvements and park improvements in the City of Kerrville, Texas. The work was done for Freese and Nichols, Inc., and the City of Kerrville, under Texas Antiquities Permit No. 6508. Three contiguous project areas totaling 96 acres were surveyed: the Jefferson Street lift station force main corridor, the Jefferson Street gravity main and water line corridor, and Louise Hays and Lehmann-Monroe Parks. In total, 62 shovel tests and 4 backhoe trenches were excavated. No new archeological sites were found. Two previously recorded sites (41KR105 and 41KR677) were shovel tested and evaluated. Both are disturbed, sparse lithic scatters and lack important information; they are considered ineligible for listing in the National Register of Historic Places or designation as State Archeological Landmarks. Survey determined that the modern Guadalupe River floodplain at Kerrville consists of extensive gravel deposits that appear to be the result of recent high-energy deposition associated with periodic scouring of the river valley. Given its age and the depositional/erosional context, this floodplain is very unlikely to contain intact archeological sites. The south end of the Jefferson Street lift station force main, ca. 80 percent of Louise Hays and Lehmann-Monroe Parks, and all of the gravity main and water line corridor are in this floodplain setting; no further archeological work is warranted in any of these areas. The west edge of the park area and the north part of the force main corridor are on higher terraces with a greater potential for archeological sites, but survey indicates that both areas are substantially disturbed and do not contain intact archeological sites. Hence, no further archeological work is recommended in either area

Archeological Survey For The Canadian River Municipal Water Authority (CRMWA) II Water Pipeline, Carson, Gray, Potter, And Roberts Counties, Texas

An archeological survey was conducted between March 8 and June 17, 2016, for the Canadian River Municipal Water Authority (CRMWA) II pipeline in Carson, Gray, Potter, and Roberts Counties, Texas. The proposed pipeline will transport water from wells located 27 km (17 miles) northeast of Pampa, Texas, to Amarillo, Texas. The total length of the pipeline, including a lateral line to the City of Pampa, is 108 km (68 miles). The pipeline will occupy a right of way that is 120 ft (36.6 m) wide, resulting in an Area of Potential Effects (APE) totaling 985 acres. The average depth of the proposed line will be between 4 and 6 ft (1.2–1.8 m). The pedestrian survey examined the full length and width of the APE only in areas with a moderate to high potential for archeological sites, consisting of playas and stream channels emptying into playas on the Southern High Plains surface and the Canadian Breaks environment. These settings account for about 47 km (29 miles) of the pipeline route and encompass about 430 acres. The remainder of the route, with a low potential for sites, was not examined by pedestrian survey. The survey recorded four archeological sites: 41CZ86, 41CZ87, 41CZ88, and 41PT514. Sites 41CZ87, 41CZ88, and 41PT514 are small prehistoric sites of unknown ages; 41CZ86 consists of a surface scatter of early-twentieth-century artifacts. All four sites lack the capacity to contribute important information and are considered ineligible for listing in the National Register of Historic Places and designation as State Antiquities Landmarks because of the disturbed and surficial nature of the cultural deposits, the lack of buried intact cultural deposits, and the paucity of interpretable artifacts and features. It is recommended that the project be allowed to proceed without any additional archeological investigations

The Prehistoric Components at the Rubin Hancock Farmstead, 41TV875, Travis County, Texas

From 1984 to 1987, a series of archeological projects was undertaken by the Texas State Department of Highways and Public Transportation (SDHPT, now the Texas Department of Transportation, TxDOT) at site 41TV875 in Travis County, Texas. The work focused on the historic component, representing the late-nineteenth- to early twentieth-century farmstead of the African American Rubin Hancock family, but many prehistoric artifacts were recovered as well. In 1998, TxDOT contracted with Prewitt and Associates, Inc., to complete the analysis, report production, and curation requirements for the mitigation work on both the prehistoric and historic components.This volume discusses the prehistoric component. Study of the prehistoric materials had five primary goals. The first was to produce an inventory of the artifacts. The second was to conduct a typological analysis of the projectile points to gain an understanding of the chronology of the site. The third was to couple the chronological information with an examination of the horizontal and vertical distributions of the cultural materials to determine whether components can be isolated. The fourth was to identify those parts of the collection that have the potential to yield important information and hence warrant curation. And the fifth was to analyze the materials from a concentration of lithic debitage to determine if they represent a cache. Analysis revealed that the site was occupied sporadically beginning at the late end of the Paleoindian period and continuing into the early part of the Late Prehistoric period. Most of the deposits were mixed, but it appears that a reasonably discrete early component may have been present in one part of the site. These early materials have the greatest interpretive potential. Analysis of the materials in the lithic debitage concentration indicates that they are not particularly homogeneous but, instead, they consist of a wide range of flake types and sizes representing various reduction strategies and stages. There is little evidence that the materials were being prepared for further tool manufacture. This concentration can be interpreted best as a discard pile