Analytic Description of the Motion of a Trapped Ion in an Even or Odd Squeezed State

A completely analytic description is given of the motion of a trapped ion which is in either an even or an odd squeezed state. Comparison is made to recent results on the even or odd coherent states, and possible experimental work is discussed.Comment: LaTeX. 9 pages plus 7 figures, include

A Simple Volcano Potential with an Analytic, Zero-Energy, Ground State

We describe a simple volcano potential, which is supersymmetric and has an analytic, zero-energy, ground state. (The KK modes are also analytic.) It is an interior harmonic oscillator potential properly matched to an exterior angular momentum-like tail. Special cases are given to elucidate the physics, which may be intuitively useful in studies of higher-dimensional gravity.Comment: 8 pages, 3 figure

Community-based multicultural counselor preparation as a site of Praxis and social justice

Recent calls in counseling psychology to embrace social justice work and mandates in the field to operationalize multicultural competencies have offered few mature examples of how this work actually looks. This article describes a 35-year-old program in a community-based urban setting which has successfully prepared over 800 counselors while integrating social justice and multicultural competencies into its core curriculum. The authors discuss the impact of the program in terms of multicultural competence, praxis, and social justice agency. The article includes recommendations about challenges that professionals and programs of this nature must negotiate in order to implement a program of this nature effectively

Some Exceptional Cases in Mathematics: Euler Characteristic, Division Algebras, Cross Vector Product and Fano Matroid

We review remarkable results in several mathematical scenarios, including graph theory, division algebras, cross product formalism and matroid theory. Specifically, we mention the following subjects: (1) the Euler relation in graph theory, and its higher-dimensional generalization, (2) the dimensional theorem for division algebras and in particular the Hurwitz theorem for normed division algebras, (3) the vector cross product dimensional possibilities, (4) some theorems for graphs and matroids. Our main goal is to motivate a possible research work in these four topics, putting special interest in their possible links.Comment: 14 pages, Late

Duality, matroids, qubits, twistors and surreal numbers

We show that via the Grassmann-Pl\"ucker relations, the various apparent unrelated concepts, such as duality, matroids, qubits, twistors and surreal numbers are, in fact, deeply connected. Moreover, we conjecture the possibility that these concepts may be considered as underlying mathematical structures in quantum gravity.Comment: 17 pages, published in Frontier in Physic

Division-Alebra/Poncare-Conjecture correspondence

We briefly describe the importance of division algebras and Poincar\'e conjecture in both mathematical and physical scenarios. Mathematically, we argue that using the torsion concept one can combine the formalisms of division algebras and Poincar\'e conjecture. Physically, we show that both formalisms may be the underlying mathematical tools in special relativity and cosmology. Moreover, we explore the possibility that by using the concept of n-qubit system, such conjecture may allow generalization the Hopf maps.Comment: 11 pages, Late