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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Singularly Perturbed Control Systems Using Non-Commutative Computer Algebra, J. W. Helton, F. Dell Kronewitter, W. M. Mceneaney, Mark Stankus
Singularly Perturbed Control Systems Using Non-Commutative Computer Algebra, J. W. Helton, F. Dell Kronewitter, W. M. Mceneaney, Mark Stankus
Mathematics
Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly non-commutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. Here we investigate the usefulness of non-commutative computer algebra in a particular area of control theory − singularly perturbed dynamic systems − where working with the non-commutative polynomials involved is especially tedious. Our conclusion is that they have considerable potential for helping practitioners with such computations. Commutative Gröbner basis algorithms are powerful and make up the engines in symbolic algebra packages' …
Modelling The Dynamics Of Abyssal Equator-Crossing Currents, P. F. Choboter, G. E. Swaters
Modelling The Dynamics Of Abyssal Equator-Crossing Currents, P. F. Choboter, G. E. Swaters
Mathematics
No abstract provided.
Restricted Words By Adjacencies, Don Rawlings
Restricted Words By Adjacencies, Don Rawlings
Mathematics
A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to refinements (with up to two additional parameters) of known results on compositions, polyominoes, and permutations. Among the examples considered are (1) the introduction of the ascent variation on compositions, (2) the enumeration of directed vertically convex polyominoes by upper descents, area, perimeter, relative height, and column number, (3) a tri-variate extension of MacMahon's determinant formula for permutations with prescribed descent set, and (4) a combinatorial setting for an entire sequence of bibasic Bessel functions.
The Poisson Variation Of Montmort's Matching Problem, Don Rawlings
The Poisson Variation Of Montmort's Matching Problem, Don Rawlings
Mathematics
No abstract provided.
On The Baroclinic Instability Of Axisymmetric Rotating Gravity Currents With Bottom Slope, Paul F. Choboter, Gordone E. Swaters
On The Baroclinic Instability Of Axisymmetric Rotating Gravity Currents With Bottom Slope, Paul F. Choboter, Gordone E. Swaters
Mathematics
The baroclinic stability characteristics of axisymmetric gravity currents in a rotating system with a sloping bottom are determined. Laboratory studies have shown that a relatively dense fluid released under an ambient fluid in a rotating system will quickly respond to Coriolis effects and settle to a state of geostrophic balance. Here we employ a subinertial two-layer model derived from the shallow-water equations to study the stability characteristics of such a current after the stage at which geostrophy is attained. In the model, the dynamics of the lower layer are geostrophic to leading order, but not quasi-geostrophic, since the height deflections …
Nonstandard Analysis In Topology: Nonstandard And Standard Compactifications, S. Salbany, Todor D. Todorov
Nonstandard Analysis In Topology: Nonstandard And Standard Compactifications, S. Salbany, Todor D. Todorov
Mathematics
Let (X, T) be a topological space, and ∗X a non–standard extension of X. There is a natural “standard” topology ST on ∗X generated by ∗G,where G ∈ T . The topological space (∗X,ST) will be used to study, in a systematic way, compactifications of (X, T).
Alternative Empirical Distributions Based On Weigted Linear Combinations Of Order Statistics, Theodore P. Hill, James Mann
Alternative Empirical Distributions Based On Weigted Linear Combinations Of Order Statistics, Theodore P. Hill, James Mann
Research Scholars in Residence
A class of empirical distributions is introduced which are based on various weighted linear combinations of order statistics, and which have convergence properties the classical empirical distribution does not, or which stochastically or convexly dominate the classical empirical distribution