Feynman-Jackson integrals

We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.Comment: Final versio

qq-Trinomial identities

We obtain connection coefficients between $q$-binomial and $q$-trinomial coefficients. Using these, one can transform $q$-binomial identities into a $q$-trinomial identities and back again. To demonstrate the usefulness of this procedure we rederive some known trinomial identities related to partition theory and prove many of the conjectures of Berkovich, McCoy and Pearce, which have recently arisen in their study of the $\phi_{2,1}$ and $\phi_{1,5}$ perturbations of minimal conformal field theory.Comment: 21 pages, AMSLate

The measurement of the velocities of particles in an air-solid flow

Theoretical investigations of two-phase flows have not so far produced a useful model since the interdependence of the many variables has been difficult to predict. Progress towards such a model is dependent on accurate experimental work on two-phase flows. Particle velocity is an especially important property, but most available techniques either disturb the flow or are slow or inaccurate. The laser-Doppler velocity meter, LDV, was developed for measurements in single-phase flows, but it has been demonstrated by a few authors to be practical for particle velocity measurements in air-solid flows. The aim of the investigation was to find the range for which the LDV was suitable, and also to make useful measurements in a pipe conveying a dilute suspension of solids pneumatically. Air and solid velocity distributions across the diameter of a vertically upward flowing air-solid suspension in a 50 mm diameter pipe were made using an LDV. The solids conveyed were spherical glass balls, mean diameter 455 um, and sand, mean diameters 176 um and 366 um. The maximum ratio of solids to air mass flow rate was 2.5 and the maximum mean air velocity was 50 ms. Significant slip between the phases was found. Some of the correlations postulated between the particle velocity and other flow properties, such as the pressure drop, were investigated. Velocity measurements were also attempted with an LDV on plastic pellets, with effective diameters of 2 to 3 mm and varying degrees of success were achieved. The optical properties of the particles appears to be important when applying the laser-Doppler particle measuring technique to flows conveying particles of this size

The comprehensive school: its theory and history

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The conditional process model of mindfulness and emotion regulation: An empirical test

BACKGROUND: The conditional process model (CPM) of mindfulness and emotion regulation posits that specific mediators and moderators link these constructs to mental health outcomes. The current study empirically examined the central tenets of the CPM, which posit that nonreactivity moderates the indirect effect of observation on symptoms of emotional disorders through cognitive emotion regulation strategies. METHODS: A clinical sample (n=1667) of individuals from Japan completed a battery of self-report instruments. Several path analyses were conducted to determine whether cognitive emotion regulation strategies mediate the relationship between observation and symptoms of individual emotional disorders, and to determine whether nonreactivity moderated these indirect effects. RESULTS: Results provided support the CPM. Specifically, nonreactivity moderated the indirect effect of observation on symptoms through reappraisal, but it did not moderate the indirect effect of observation on symptoms through suppression. LIMITATIONS: Causal interpretations are limited, and cultural considerations must be acknowledged given the Japanese sample CONCLUSIONS: These results underscore the potential importance of nonreactivity and emotion regulation as targets for interventions.R01 AT007257 - NCCIH NIH HHS; R34 MH099311 - NIMH NIH HH

A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation