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We present a number of new physical systems that may be addressed using methods of time dependent transformation. A recap of results available for two-state systems is given, with particular emphasis on the AC stark effect. We give some results that are not well known, including the full solution for a two state system in a static electric field with arbitrary direction. Connection with established theorems in time optimal quantum control is given, and a full discussion outlines some advanced results in matrix calculus. In particular, we derive a set of matrix gates relevant to quantum information theory and computation using time optimal unitary operators, and define the hyperbolic equivalent of the quantum brachistochrone problem., Comment: 11 pages

An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal quantum state control. We establish compact mechanisms for achieving time dependent unitary evolution, and present new calculation methods for time-ordered exponential operators. A powerful modification of the brachistochrone technique is presented that allows solution of a class of problems via matrix decomposition of the Hamiltonian. These techniques allow us to arrive at a series of solutions for quantum systems that have readily accessible physical realisations. We contrast the output of the theory when constrained to a relativistic space-time to that of other physical systems of lower dimensionality. Some comment is given regarding hypercomplex numbers and their application in quantum mechanics., Comment: 10 pages, 51 equations

We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic curves and periodic orbits on higher dimensional non-commutative geometries., Comment: 34 pages, 581 equations

The Academic Senate of the California Community Colleges created this document in 2001. Its goal is to measure the degree of use, effectiveness, and acceptance of the Intersegmental General Education Transfer Curriculum (IGETC). The study was completed through three different questionnaires: (1) one was distributed to recent community college transfer students preparing to graduate; (2) another was distributed to professional guidance faculty in the California Community College System; and (3) the last one was given to the chief student services administrators at each of the California Community Colleges. The study had a 10% response rate. The study concluded that the IGETC pattern of lower-division general education requirements is well known to community college transfer students and it would become even more popular with an extended effort at community colleges and four-year colleges and universities to inform students of their about the program. If more students knew of the benefits that they would gain IGETC pattern then it would increase the number of students that utilized it and benefited from it. Those students that knew of the IGETC pattern viewed it as a flexible alternative that maximizes the student's options more than any other available program. (MZ)

The Intersegmental Committee of Academic Senates (ICAS) for the California Community Colleges undertook this study to assess the degree of use, effectiveness, and awareness of Intersegmental General Education Transfer Curriculum (IGETC). IGETC was adopted in 1991 by the University of California (UC), the California State University (CSU), and the California Community Colleges (CCC) systems. IGETC identifies a set course of requirements that will satisfy lower-division general education requirements for the student to transfer to any UC or CSU if a student completes the requirements at any community college. Two questionnaires were delivered (via mail and Internet), one to CSU and UC upper-division students who had transferred from a community college, and one to counseling faculty in the CCC. The total available student population was approximately 30,700 (22,700 from CSU and 8,000 from UC). A total of 2,082 students completed and submitted the survey. Surveys were also submitted by 332 community college counseling faculty (estimated to represent one-third of the statewide total of counselors). Key findings include: 82% of UC transfer students and 48% of CSU transfer students used IGETC. In addition, 54% of students who used IGETC reported using it in order to assure completion of general education requirements, 39% used it to transfer to CSU, and 37% used it to transfer to UC. The appendixes, containing the student survey; the counseling faculty survey; and an extensive number of data tables from the study comprise the majority of the document's contents. (NB)

This paper considers the distinctive issues demographers face when they must forecast enrollments in a context of court-ordered desegregation. Specifically, it examines whether magnet schools strengthen a district's overall attractiveness to enrollees from outside, or whether they only siphon students away from other nonmagnet schools within the district, achieving no net effect districtwide. This issue can be clarified by examining patterns of change in grade progression rates as magnet schools are phased in. Methodology involved the analysis of student enrollment and retention for the years 1986-90 in the Kansas City, Missouri School District (KCMSD), a large urban district being transformed by the implementation of a comprehensive magnet school plan. Findings indicate that the magnet schools had enhanced the district's overall retention at most grades but did not produce actual increases at most grades, having merely slowed the overall weakening of districtwide retention. The data provide a "reality check" on the necessary judgment for crafting appropriate forecasting assumptions. Six tables and two figures are included. (LMI)