Angular Momentum on the Lattice: The Case of Non-Zero Linear Momentum

The irreducible representations (IRs) of the double cover of the Euclidean group with parity in three dimensions are subduced to the corresponding cubic space group. The reduction of these representations gives the mapping of continuum angular momentum states to the lattice in the case of non-zero linear momentum. The continuous states correspond to lattice states with the same momentum and continuum rotational quantum numbers decompose into those of the IRs of the little group of the momentum vector on the lattice. The inverse mapping indicates degeneracies that will appear between levels of different lattice IRs in the continuum limit, recovering the continuum angular momentum multiplets. An example of this inverse mapping is given for the case of the ``moving'' isotropic harmonic oscillator.Comment: v3) Little groups for lattice momenta corrected. Includes corrections from erratum submitted to Phys. Rev. D and a more consistent labeling scheme. v2) Minor changes to little groups. (9 pages

The Position of Sgr A∗^* at the Galactic Center

The absolute position of the compact radio source at the dynamical center of the Galaxy, Sgr A$^*$, was known only to an accuracy of $0.2''$ in spite of its accurate location with respect to near-IR stellar sources to within 30 milliarcsecond (mas). To remedy this poor positional accuracy, we have selected 15 high-resolution, high-frequency VLA observations of Sgr A$^*$ carried out in the last 13 years and determined the weighted average position with the average epoch 1992.4 to be at $\alpha$, $\delta$[1950] = $17^{\rm h} 42^{\rm m}$ 29\dsec3076$\pm0.0007$, $-28^\circ 59^\prime 18.484\pm0.014^{\prime\prime}$, or $\alpha$, $\delta$[2000] = $17^{\rm h} 45^{\rm m}$ 40\dsec0383$\pm0.0007$, $-29^\circ 00^\prime 28.069\pm0.014^{\prime\prime}$ which agrees with earlier published values to within the $0.2''$ error bars of the earlier measurements. An accurate absolute position of Sgr A$^*$ can be useful for its identification with sources at other wavelengths, particularly, in soft and hard X-rays with implications for the models of a massive black hole at the Galactic center.Comment: 11 pages, one figure and one table. ApJL (in press

Investigation of Sequential Machine Design Techniques for Implementation of a TRAC Scanning Algorithm

This report will demonstrate the design techniques to translate a given scanning algorithm into a hardwired pre-processor. The language to be pre-processed is TRAC (Text Reckoning and Compiling) devised by Mooers and Deutsch. The major drawback in the current implementation of TRAC is speed. The software overhead required for string manipulations and execution of the input scanning algorithm is the major degrading factor. A TRAC machine consisting of a hardwired pre-processor to scan the input and produce formatted data for a stack oriented evaluator is proposed. The control machine for the input scanning algorithm for the pre-processor is designed using various sequential machine design techniques. The one-hot code and the minimum state variable design represent the two extremes which are presented

Time To Move On: The California Parole Board\u27s Fixation with the Original Crime

In theory, parole is a possibility for tens of thousands of California inmates; in practice, it has been an illusion. California\u27s parole system releases a tiny number of inmates each year, transforming most indeterminate sentences with the possibility of parole into sentences of life-without-parole. As recently as the 1980s, approximately 20% of California inmates with indeterminate life sentences received parole. Since then, the proportion of inmates paroled has decreased dramatically to less than 1%, compounding problems of severe prison overcrowding. Fearing the political consequences of releasing convicted offenders, recent governors have appointed tough on crime parole board members who are unlikely to grant parole. In 2006, the Bureau of Parole Hearings ( parole board or board ) rejected 99.5% of parole applications from eligible inmates. Even when the board approves parole, the Governor can-and frequently does-reverse the decision. Typically, the board and Governor rely on the commitment offense to deny parole, regardless of the offender\u27s rehabilitation and good prison behavior. This Comment explores the due process implications of using the commitment offense as a basis for parole denials. It examines recent California Supreme Court and Ninth Circuit cases and argues that parole decisions should weigh the commitment offense less heavily than rehabilitative progress after the expiration of the minimum sentence term

The Cultural Development of Negroes in Limestone County Since 1860

The problem of this study is the past and present status of Negro culture in Limestone County, Texas. Growing out of this major problem are the following questions which this study proposes to answer: 1. What were the causes of the Negroes\u27 presence in Limestone County, Texas? 2. What were the living conditions of Negroes during the period of involuntary servitude from 1860 until their emancipation (June 19, 1865 in the State of Texas)? 3. What were the chances of cultural development during this period of involuntary servitude? 4. What opportunities did Negroes of Limestone County, Texas have to develop themselves culturally immediately after the Emancipation? 5. What out-of-state agencies made contributions to the Negroes of Limestone County as well as to Texas and the south, to set up a public school system? 6. What attitude did the white people of Limestone County take toward persons who sought to enlighten the freedmen? 7. What progress was made culturally during the period of reconstruction? 8. What part did the church play in the cultural development of Negroes in Limestone County, Texas? 9. what are some of the out-standing changes that have been made in the public schools of Limestone County within the past decade? 10. What are the tendencies which indicate the possibilities of further cultural developments in Limestone County? This study has been made to present the past and present status of the cultural development of the Negroes of Limestone County, Texas, from I860 to 1951, and it is the aim of the writer to present a fair word-picture of the progress that has been made within these years. On the other hand, this study attempts to show the progress and improvements that are yet to be made in the development of a greater number of intelligent, wage earning Negro citizens of Limestone County, Texas. It is true that for the past twenty-five years the greatest number of people of this county have migrated to the manufacturing centers of the states in the north and west, yet the fact remains that the majority of those remaining still live in rural areas. In fifteen southern states it was found that 67.4% of the Negro population were rural dwellers.1 For the last fifteen or twenty years there has been a steady migration of Negroes from Limestone County to larger cities within the state of Texas, and to many sections of the United States. There are several reasons for this migration which has caused the problem of overcrowded living and working conditions in toe cities where this group has moved. One of the main causes for this migration is the limited educational opportunities for Negro children. Charles S. Johnson made an extensive survey of various comparative studies of the two races, Negro and White, and concluded that inefficiency of Negro pupils is at least a function of a poor educational system and an inferior background, as an inferior inherited mental constitution.1 Another cause can be traced to World War II, when a call for workers for the war effort regardless of race and color, sent men and women to many sections of the United States. 1 Ambrose Caliver, Secondary Education for Negroes , National Survey of Secondary Education. Bulletin No. 17, 1932, Government Printing Office, Office of Education, Washington, D. C. 1 Charles S. Johnson, The Negro in American Civilization, Henry Holt and Company, New York, 1930. pp. 273-4

Alien Registration- Clarke, F. Robin (Holden, Penobscot County)

https://digitalmaine.com/alien_docs/8197/thumbnail.jp

PT-symmetry broken by point-group symmetry

We discuss a PT-symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schr\"{o}dinger equation for a particle in a square box with the PT-symmetric potential $V(x,y)=iaxy$. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of $|a|$. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schr\"odinger equation with the potential $V(x,y)=iaxy^{2}$ exhibits real eigenvalues for sufficiently small values of $|a|$. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one

Radio Continuum Observations of the Galactic Center: Photoevaporative Proplyd-like Objects near Sgr A*

We present radio images within 30$''$ of Sgr A* based on recent VLA observations at 34 GHz with 7.8 microJy sensitivity and resolution $\sim88\times46$ milliarcseconds (mas). We report 44 partially resolved compact sources clustered in two regions in the E arm of ionized gas that orbits Sgr A*. These sources have size scales ranging between ~50 and 200 mas (400 to 1600 AUs), and a bow-shock appearance facing the direction of Sgr A*. Unlike the bow-shock sources previously identified in the near-IR but associated with massive stars, these 34 GHz sources do not appear to have near-IR counterparts at 3.8 $\mu$m. We interpret these sources as a candidate population of photoevaporative protoplanetary disks (proplyds) that are associated with newly formed low mass stars with mass loss rates ~10^{-7} - 10^{-6} solar mass per year and are located at the edge of a molecular cloud outlined by ionized gas. The disks are externally illuminated by strong Lyman continuum radiation from the ~100 OB and WR massive stars distributed within 10'' of Sgr A*. The presence of proplyds implies current in-situ star formation activity near Sgr A* and opens a window for the first time to study low mass star, planetary and brown dwarf formations near a supermassive black hole.Comment: 13 pages, 4 figures, ApJL (in press