We introduce a Laplace-Beltrami type operator on the Fock space of symmetric functions and show that the Jack symmetric functions are the only family of eigenvectors of the differential operator, thus giving a new characterization of Jack polynomials. This was achieved by explicit computation of its action on generalized homogeneous symmetric functions. Using this new method we give a combinato...

We use the Jack symmetric functions as a basis of the Fock space, and study the action of the Virasoro generators Ln. We calculate explicitly the matrix elements of Ln with respect to the Jack-basis. A combinatorial procedure which produces these matrix elements is conjectured. As a limiting case of the formula, we obtain a Pieri-type formula which represents a product of a power sum and a Jack...

when a jack-up installed at a clay location and then leaves; it can create several meter deep footprints. in case of soft clay, the spudcan may have actually penetrated much deeper than the observed footprints. when the penetrated spudcan is pulled out, much of the soft remolded clay will flow around it and go back into the hole. this event, leaving a deep region of disturbed soil. the disturbe...

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [ x i ( xi ∂ ∂xi + (n− j)θ + u )]

The effect of four cooking methods was evaluated for proximate composition, fatty acid, calcium, iron, and zinc content in salmon and Chilean jack mackerel. The moisture content of steamed salmon decreased (64.94%) compared to the control (68.05%); a significant decrease was observed in Chilean jack mackerel in all the treatments when compared to the control (75.37%). Protein content in both sa...

We describe the main features of JACK (Java Applet Correctness Kit), a tool for the validation of Java applications, annotated with JML specifications. JACK has been especially designed to improve the quality of trusted personal device applications. JACK is fully integrated with the IDE Eclipse, and provides an easily accessible user interface. In particular, it allows to inspect the generated ...

We find a biorthogonal expansion of the Cayley transform of the non-symmetric Jack functions in terms of the non-symmetric Jack polynomials, the coefficients being Meixner–Pollaczek type polynomials. This is done by computing the Cherednik–Opdam transform of the non-symmetric Jack polynomials multiplied by the exponential function.