A Determinantal Formula for Catalan Tableaux and TASEP Probabilities

We present a determinantal formula for the steady state probability of each state of the TASEP (Totally Asymmetric Simple Exclusion Process) with open boundaries, a 1D particle model that has been studied extensively and displays rich combinatorial structure. These steady state probabilities are computed by the enumeration of Catalan tableaux, which are certain Young diagrams filled with $\alpha$'s and $\beta$'s that satisfy some conditions on the rows and columns. We construct a bijection from the Catalan tableaux to weighted lattice paths on a Young diagram, and from this we enumerate the paths with a determinantal formula, building upon a formula of Narayana that counts unweighted lattice paths on a Young diagram. Finally, we provide a formula for the enumeration of Catalan tableaux that satisfy a given condition on the rows, which corresponds to the steady state probability that in the TASEP on a lattice with $n$ sites, precisely $k$ of the sites are occupied by particles. This formula is an $\alpha\ /\ \beta$ generalization of the Narayana numbers.Comment: 19 pages, 12 figure

Research Report: Multiple Case Study Comparison of High School and University Students’ Perceptions of Motivational Factors in Classes with Foreign and Local English Teachers

　　Motivation is one of the major forces in language learning. Teachers’ support, or even more the way students perceive this support is an important factor for increasing Self-Determined motivation and fulfillment of their three basic psychological needs: autonomy, competence and relatedness. Local (LTEs) and foreign teachers of English (FTEs) in Japan are commonly generalized and categorized into two separate groups, and perceived quite differently in the classroom. The present research report reveals that foreign and local teachers’ support of the basic psychological needs is perceived less fulfilling by students of older grades. The drop in satisfaction between younger and older students is bigger for FTEs than for LTEs. Another finding shows that students of different proficiency levels regard their local teachers of English differently. High level students expressed less satisfaction with the competence need support from LTEs, and low level students found them less intrinsically motivating

Classification of integrable quadratic Hamiltonians on e(3)

Linear Poisson brackets on e(3) typical of rigid body dynamics are considered. All quadratic Hamiltonians of Kowalevski type having additional first integral of fourth degree are found. Quantum analogs of these Hamiltonians are listed.Comment: 11 page

Exploring Community Psychology Value Congruence in Academic Setting

Value congruence between employees and their workplace is an important dimension of an individual’s fit with a work environment. The level of congruence between the values of employees and their employing organization and the relation of value congruence to satisfaction, commitment, and willingness to recommend the organization were examined. This study focused on the relationship of value congruence between the individuals who belong to the field of community psychology and their workplace in relation to the aforementioned work-related outcomes in an academic setting. Results show that departments rated higher on community psychology values had a greater number of faculty possessing values similar to those of the field of Community Psychology. In addition, better value fit predicted higher job satisfaction scores and higher organizational commitment scores, as well as a stronger willingness to recommend their department as a good place to work