This article is a further contribution to our research [1] into a class of infinite-dimensional Lie algebras L∞(N+, N−) generalizing the standardW∞ algebra, viewed as a tensor operator algebra of SU(1, 1) in a group-theoretic framework. Here we interpret L∞(N+, N−) either as infinite continuations of pseudo-unitary symmetries or as “higher-U(N+, N−)spin extensions” of the diffeomorphism algebra...

A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Itô algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular,...

This article is a further contribution to our research [1] into a class of infinite-dimensional Lie algebras L∞(N+, N−) generalizing the standard W∞ algebra, viewed as a tensor operator algebra of SU(1, 1) in a group-theoretic framework. Here we interpret L∞(N+, N−) either as a infinite continuation of pseudo-unitary symmetries U(N+, N−), or as a “higher-U(N+, N−)-spin extension” of the diffeom...

We survey a recent extension of the moving frames method for infinite-dimensional Lie pseudo-groups. Applications include a new, direct approach to the construction of Maurer–Cartan forms and their structure equations for pseudogroups, and new algorithms, based on constructive commutative algebra, for uncovering the structure of the algebra of differential invariants for pseudogroup actions.

Hollow nonwood baseball bats have performance advantages over wooden bats. The hollow barrel bats act as a spring or trampoline during the bat-ball collision. The trampoline effect can occur at different natural frequencies known as hoop modes. To examine the effect of the hoop mode on the bat-ball collision, modal analysis and performance measurements were performed on a sample of hollow nonwo...

In the paper [8], we introduced the notions of pseudo-hyperplane and pseudoembedding of a point-line geometry and proved that every generalized quadrangle of order (s, t), 2 ≤ s <∞, has faithful pseudo-embeddings. The present paper focuses on generalized quadrangles of order (3, t). Using the computer algebra system GAP [12] and invoking some theoretical relationships between pseudo-hyperplanes...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A “quantum” Godbillon-Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand-Fuchs 3-cocycle on periodic vector fields. We describe a nontrivial embed...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand Fuchs 3-cocycle on periodic vector fields. A nontrivial embedding of th...

Introduction During the summer and fall of 1997, the Hoop Research Complex was developed at the Iowa State University (ISU) Rhodes Research Farm for comparing hoop structures to confinement for swine finishing. The site consists of three hoop structures and one modular confinement building. The hoops, each 30 ft × 60 ft, are oriented north/south. The south end of each hoop has a concrete floor ...

Resonance Raman studies of visual pigment analogues regenerated with 10-D, 10,l 1-D2, 11-D, 1 1,12-D2, 12-D, 15-D, and 20,14-D4 isotopic derivatives of retinal have been used to assign the intense hydrogen outsf-plane (HOOP) vibrations in the spectra of rhodopsin, isorhodopsin, and bathorhodopsin. Low temperature 77 K photostationary steady-state experiments show that the unique 853-, 875-, and...