Froissart Bound on Total Cross-section without Unknown Constants

We determine the scale of the logarithm in the Froissart bound on total cross-sections using absolute bounds on the D-wave below threshold for $\pi\pi$ scattering. E.g. for $\pi^0 \pi^0$ scattering we show that for c.m. energy $\sqrt{s}\rightarrow \infty$, $\bar{\sigma}_{tot}(s,\infty)\equiv s\int_{s} ^{\infty} ds'\sigma_{tot}(s')/s'^2 \leq \pi (m_{\pi})^{-2} [\ln (s/s_0)+(1/2)\ln \ln (s/s_0) +1]^2$ where $m_\pi^2/s_0= 17\pi \sqrt{\pi/2}$ .Comment: 6 page

Froissart Bound on Inelastic Cross Section Without Unknown Constants

Assuming that axiomatic local field theory results hold for hadron scattering, Andr\'e Martin and S. M. Roy recently obtained absolute bounds on the D-wave below threshold for pion-pion scattering and thereby determined the scale of the logarithm in the Froissart bound on total cross sections in terms of pion mass only. Previously, Martin proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ which is one-fourth of the corresponding upper bound on $\sigma_{tot}$, and Wu, Martin,Roy and Singh improved the bound by adding the constraint of a given $\sigma_{tot}$. Here we use unitarity and analyticity to determine, without any high energy approximation, upper bounds on energy averaged inelastic cross sections in terms of low energy data in the crossed channel. These are Froissart-type bounds without any unknown coefficient or unknown scale factors and can be tested experimentally. Alternatively, their asymptotic forms,together with the Martin-Roy absolute bounds on pion-pion D-waves below threshold, yield absolute bounds on energy-averaged inelastic cross sections. E.g. for $\pi^0 \pi^0$ scattering, defining $\sigma_{inel}=\sigma_{tot} -\big (\sigma^{\pi^0 \pi^0 \rightarrow \pi^0 \pi^0} + \sigma^{\pi^0 \pi^0 \rightarrow \pi^+ \pi^-} \big )$,we show that for c.m. energy $\sqrt{s}\rightarrow \infty$, $\bar{\sigma}_{inel }(s,\infty)\equiv s\int_{s} ^{\infty } ds'\sigma_{inel }(s')/s'^2 \leq (\pi /4) (m_{\pi })^{-2} [\ln (s/s_1)+(1/2)\ln \ln (s/s_1) +1]^2$ where $1/s_1= 34\pi \sqrt{2\pi }\>m_{\pi }^{-2}$ . This bound is asymptotically one-fourth of the corresponding Martin-Roy bound on the total cross section, and the scale factor $s_1$ is one-fourth of the scale factor in the total cross section bound. The average over the interval (s,2s) of the inelastic $\pi^0 \pi^0$cross section has a bound of the same form with $1/s_1$ replaced by $1/s_2=2/s_1$.Comment: 9 pages. Submitted to Physical Review

Juvenile Probation Officer Workload and Caseload Study: Alaska Division of Juvenile Justice

This report describes results of a study to measure and analyze the workload and caseload of Juvenile Probation Officers (JPOs) within the Alaska Division of Juvenile Justice. More specifically, this study assessed the resources needed in both rural and urban Alaska to adequately meet minimum probation standards, to continue the development and enhancement of system improvements, and to fully implement the restorative justice field probation service delivery model.Bureau of Justice Assistance Grant No. 2008-IC-BX-K001Section I – Juvenile Probation Officer Workload and Caseload Study Table 1. Total Time Available by Office Figure 1. Referrals for New Offenses, by Depth of Processing Table 2. Average Caseloads by Office: FY06-08 Table 3. Summary Estimates for Hours Required per Type of Case Table 4. Final Results Table 5. Workload Burdens / Section II – Workload Elements Table 6. Total Time Available by Office Figure 2. Referrals for New Offenses, by Depth of Processing Table 7. Average Caseloads for Ultimate Probation Officers: FY06-08 Table 8. Average Caseloads for Immediate Probation Officers: FY06-08 Table 9. Summary Estimates for Hours Required per Type of Case / Section III – Workload Calculations Table 10. Total Hours Needed by Office Table 11. Total Hours Needed and Available by Office Table 12. Positions Needed by Office Table 13. Workload Burdens by Office Table 14. Summary of Final Results Table 15. Final Results with Average Times Required per Case Table 16. Final Results with Average Case Dispositions Table 17. Final Results with Average Times Required per Case and Case Dispositions Table 18. Summary of Final Results Table 19. Time Study Comparisons / Appendix A – Time Available Table A.1. Number of Positions by Region and Location Table A.2. Average Hours per Week Required for Other Activities Table A.3. Total Hours Available per Year by Position and Office / Appendix B – Number of Cases Figure B.1. Referrals for New Offenses, by Depth of Processing Table B.1. Average Caseloads for Ultimate Probation Officers: FY06-08 Table B.2. Average Caseloads for Immediate Probation Officers: FY06-08 / Appendix C – Time Required Table C.1. Summary Estimates for Hours Required per Type of Case Table C.2. Average Estimates (in Minutes) per Type of Case and Activity Table C.3. Detailed Estimates (in Minutes) for Time Required per Dismissed Case Table C.4. Detailed Estimates (in Minutes) for Time Required per Case Adjusted Without a Referral Table C.5. Detailed Estimates (in Minutes) for Time Required per Case Adjusted With a Referral Table C.6. Detailed Estimates (in Minutes) for Time Required per Informal Probation Case Table C.7. Detailed Estimates (in Minutes) for Time Required per Petitioned Cas

Quantitative Analysis of Disparities in Juvenile Delinquency Referrals

Minority youths in Anchorage are referred to the Alaska Division of Juvenile Justice (DJJ) for delinquent behavior at rates much higher than white youths. This report, presenting the first findings from an extended examination of extended examination of race, ethnicity, and juvenile justice in Anchorage, provides a broad overview of the level of disproportionate minority contact in the Alaska juvenile justice system and examines whether disproportionate minority contact occurs (1) for all minority youth, (2) for both males and females, (3) for both youth referred for new crimes and youth referred for conduct or probation violations, and (4) throughout the Municipality of Anchorage or in specific geographical areas within the Municipality of Anchorage. By developing a detailed understanding of the scope of disproportionate minority contact, we become much better prepared to identify its causes and to develop promising evidence-based solutions. The sample in this analysis includes 1,936 youths who resided in Anchorage and were referred to DJJ in Anchorage during fiscal year 2005 for new crimes, probation violations, or conduct violations.National Institute of Justice Grant No. 2005-IJ-CX-0013Table and Figures / Acknowledgments / Executive Summary / Quantitative Analysis of Disparities in Juvenile Delinquency Referrals / Sample and Data / Geographic Data / Census Data / Juvenile Justice Data / Analysis / Results / Racial, Ethnic, and Gender Composition of Referred Youth / Disproportionate Minority Contact in Anchorage / Rates of Referral by Census Tract / Disproportionate Minority Contact by Census Tract / Disproportionate Minority Contact by Census Tract, for All Minority Youth / Disproportionate Minority Contact by Census Tract, for Black Youth / Disproportionate Minority Contact by Census Tract, for Native Youth / Disproportionate Minority Contact by Census Tract, for Asian Youth / Disproportionate Minority Contact by Census Tract, for Pacific Youth / Disproportionate Minority Contact by Census Tract, for Other Minority Youth / Disproportionate Minority Contact by Census Tract, for Multiracial Youth / Disproportionate Minority Contact by Census Tract, for Hispanic Youth / Summary of DMC Analyses by Census Tract / Summary and Conclusion / Appendices A. Technical Notes on Relative Rate Indices B. Technical Notes on Relative EB Rate Indices C. Type of Analysis by Census Trac

Case Attrition of Sexual Violence Offenses: Empirical Findings

Originally published in the Alaska Justice Forum 25(1–2): 1, 18–20 (Spring 2008-Summer 2008).This report examined the legal resolutions for 1,184 contact sexual violence cases reported to Alaska State Troopers in 2003 and 2004, and excluded results from other law enforcement agencies. We determined whether cases were founded with an identifiable suspect, were referred to the Alaska Department of Law for prosecution, were accepted for prosecution, and if the case resulted in a conviction. We only examined whether any conviction on any charge was obtained. In some cases, the conviction may be for a non-sexual offense. * Seventy-five percent of cases were founded with at least one identifiable suspect, 51% of founded cases were referred to the Alaska Department of Law for prosecution, 60% of referred cases were accepted for prosecution, and 80% of accepted cases resulted in a conviction on at least one charge. The greatest point of attrition was from the founding to the referral decision. * For the most part, cases of Alaska Native victims were as likely, or even more likely, to be processed by the criminal justice system relative to the cases of non-Native victims. * Cases of sexual violence in the most rural portions of Alaska had an equal or greater chance of being subject to legal sanction when compared with cases from Alaska's less rural areas, and were as likely or more likely to receive full enforcement and prosecution. Unfortunately, the percentage of founded cases that resulted in a conviction never exceeded 30%

ADS modules

We study the class of ADS rings and modules introduced by Fuchs. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R is ADS as a right R-module must be either right self-injective or indecomposable as a right R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.Comment: 7 page

A Periodicity Theorem for the Octahedron Recurrence

We investigate a variant of the octahedron recurrence which lives in a 3-dimensional lattice contained in [0,n] x [0,m] x R. Generalizing results of David Speyer math.CO/0402452, we give an explicit non-recursive formula for the values of this recurrence in terms of perfect matchings. We then use it to prove that the octahedron recurrence is periodic of period n+m. This result is reminiscent of Fomin and Zelevinsky's theorem about the periodicity of Y-systems.Comment: 22 pages, (a few pictures added, section 3 has been reorganized