Equivalence Between the Lagrangian and Hamiltonian Formalisms for Constrained Systems

The equivalence between the Lagrangian and Hamiltonian formalism is studied for constraint systems. A procedure to construct the Lagrangian constraints from the Hamiltonian constraints is given. Those Hamiltonian constraints that are first class with respect to the Hamiltonian constraints produce Lagrangian constraints that are FL-projectable.

Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

Dirac and reduced quantization: A Lagrangian approach and Application to Coset Spaces

A Lagrangian treatment of the quantization of first class Hamiltonian systems with constraints and Hamiltonian linear and quadratic in the momenta, respectively, is performed. The first reduce and then quantize and the first quantize and then reduce (Diracs) methods are compared. A source of ambiguities in this latter approach is pointed out and its relevance on issues concerning self-consistency and equivalence with the first reduce method is emphasized. One of the main results is the relation between the propagator obtained la Dirac and the propagator in the full space. As an application of the formalism developed, quantization on coset spaces of compact Lie groups is presented. In this case it is shown that a natural selection of a Dirac quantization allows for full self-consistency and equivalence. Finally, the specific case of the propagator on a two-dimensional sphere S2 viewed as the coset space SU(2)/U(1) is worked out. 1995 American Institute of Physics.

Putting the Special Case in Its Place: Switzerland and Small-N Comparison in Policy Research

This research note presents a set of strategies to conduct small-N comparisons in policy research including the Swiss case. Even though every country can be considered "special" to some extent, the Swiss political system is often viewed as a particularly difficult case for comparison because of the impact of its idiosyncratic institutional features (most notably direct democracy). In order to deal with this problem, our note sets out two possible strategies - the use of functional equivalents and of counterfactual reasoning - and explains how to implement them empirically through process tracing and the establishment of causal chains. As an illustration, these strategies are used for a comparison of the process of electricity market liberalisation in Switzerland and Belgium.

Relationships between anthropometric measures and athletic performance, with special reference to repeated-sprint ability, in the Qatar national soccer team.

The aim of this study was to determine potential relationships between anthropometric parameters and athletic performance with special consideration to repeated-sprint ability (RSA). Sixteen players of the senior male Qatar national soccer team performed a series of anthropometric and physical tests including countermovement jumps without (CMJ) and with free arms (CMJwA), straight-line 20 m sprint, RSA (6 × 35 m with 10 s recovery) and incremental field test. Significant (P < 0.05) relationships occurred between muscle-to-bone ratio and both CMJs height (r ranging from 0.56 to 0.69) as well as with all RSA-related variables (r < -0.53 for sprinting times and r = 0.54 for maximal sprinting speed) with the exception of the sprint decrement score (Sdec). The sum of six skinfolds and adipose mass index were largely correlated with Sdec (r = 0.68, P < 0.01 and r = 0.55, P < 0.05, respectively) but not with total time (TT, r = 0.44 and 0.33, P > 0.05, respectively) or any standard athletic tests. Multiple regression analyses indicated that muscular cross-sectional area for mid-thigh, adipose index, straight-line 20 m time, maximal sprinting speed and CMJwA are the strongest predictors of Sdec (r(2) = 0.89) and TT (r(2) = 0.95) during our RSA test. In the Qatar national soccer team, players' power-related qualities and RSA are associated with a high muscular profile and a low adiposity. This supports the relevance of explosive power for the soccer players and the larger importance of neuromuscular qualities determining the RSA.

Report on a special investigation of the City of Dexter for the period July 1, 2004 through August 31, 2010

Report on a special investigation of the City of Dexter for the period July 1, 2004 through August 31, 2010

A reduction of order two for infinite-order Lagrangians

Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.

Report on a special investigation of the Burlington Community School District and the Parent Teacher Organization at Grimes Elementary School for the period August 1, 2009 through June 30, 2011

Report on a special investigation of the Burlington Community School District and the Parent Teacher Organization at Grimes Elementary School for the period August 1, 2009 through June 30, 2011

Report on a special investigation of the Department of Natural Resources’ Honey Creek Resort for the period October 1, 2010 through October 20, 2011

Report on a special investigation of the Department of Natural Resources’ Honey Creek Resort for the period October 1, 2010 through October 20, 2011

Report on a special investigation of the Sunrise Sunset Daycare of the Southeast Warren Community School District for the period September 1, 2010 through September 26, 2011

Report on a special investigation of the Sunrise Sunset Daycare of the Southeast Warren Community School District for the period September 1, 2010 through September 26, 2011

Report on a special investigation of the Starmont Community School District for the period July 1, 1993 through November 30, 2010

Report on a special investigation of the Starmont Community School District for the period July 1, 1993 through November 30, 2010

CJJP Forecasts Increase in Special Sentence Sex Offenders Caseloads, Data Download, Iowa Department of Corrections, December 2011

The Iowa Sex Offender Research Council recently released a report to the Iowa General Assembly focusing on sex offender registration and the special sentence for sex offenders. Regarding the latter, the Council (staffed by the state’s Division of Criminal & Juvenile Justice Planning) projected a steady increase in community-based corrections’ special sentence caseloads from 619 offenders in 2011 to 2,651 offenders in 2021:

Special Sentence Revocations High, Data Download, Iowa Department of Corrections, May 2010

In addition to their original sentence, persons convicted of sexual abuse, incest or sexual exploitation of a minor also receive a “special sentence” of ten years, or in some cases, life. In its prison population forecast, the Iowa Division of Criminal and Juvenile Justice Planning noted “an unexpectedly high rate of revocation among those released to the special sentence, particularly given past research that has shown Iowa sex offenders having very low rates of re-arrest and/or return to prison.”

Special Sentence Sex Offender Caseloads Adding Up, Data Downloads, Iowa Department of Corrections, December 2008

Several years ago the General Assembly increased the penalties for certain sex offenses by an additional ten years of community-based supervision, and in some case lifetime supervision. The Division of Criminal and Juvenile Justice Planning (CJJP) studied the effect the new law would have on CBC supervision caseloads: