19,887 research outputs found
On vanishing sums of th roots of unity in finite fields
In an earlier work, the authors have determined all possible weights for
which there exists a vanishing sum of th roots
of unity in characteristic 0. In this paper, the same problem is
studied in finite fields of characteristic . For given and , results
are obtained on integers such that all integers are in the
``weight set'' . The main result in this paper guarantees,
under suitable conditions, the existence of solutions of
with all coordinates not equal to zero over a finite field
Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices
We give elementary proofs of two theorems concerning bounds on the maximum
argument of the eigenvalues of a product of two unitary matrices --- one by
Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one
by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary
and sufficient conditions for equalities are apparent and that they can be
readily generalized to the case of infinite-dimensional unitary operators.Comment: 8 pages in Revtex 4.1 preprint format, to appear in Journal of
Inequalities and Application
Orientation of particle attachment and local isotropy in diffusion limited aggregation (DLA)
We simulate 50 off-lattice DLA clusters, one million particles each. The
probability distribution of the angle of attachment of arriving particles with
respect to the local radial direction is obtained numerically. For increasing
cluster size, , the distribution crosses over extremely accurately to a
cosine, whose amplitude decreases towards zero as a power-law in . From this
viewpoint, asymptotically large DLA clusters are locally . This
contradicts previous conclusions drawn from density-density correlation
measurements [P. Meakin, and T. Viscek, Phys. Rev. A {\bf 32}, 685 (1985)]. We
present an intuitive phenomenological model random process for our numerical
findings.Comment: 10 pages, RevTex 3.0, 11-9
Schubert Polynomials for the affine Grassmannian of the symplectic group
We study the Schubert calculus of the affine Grassmannian Gr of the
symplectic group. The integral homology and cohomology rings of Gr are
identified with dual Hopf algebras of symmetric functions, defined in terms of
Schur's P and Q-functions. An explicit combinatorial description is obtained
for the Schubert basis of the cohomology of Gr, and this is extended to a
definition of the affine type C Stanley symmetric functions. A homology Pieri
rule is also given for the product of a special Schubert class with an
arbitrary one.Comment: 45 page
Analysis and control of bifurcation and chaos in averaged queue length in TCP/RED model
This paper studies the bifurcation and chaos phenomena in averaged queue length in a
developed Transmission Control Protocol (TCP) model with Random Early Detection
(RED) mechanism. Bifurcation and chaos phenomena are nonlinear behaviour in network
systems that lead to degradation of the network performance. The TCP/RED model used
is a model validated previously. In our study, only the average queue size k q
−
is
considered, and the results are based on analytical model rather than actual measurements.
The instabilities in the model are studied numerically using the conventional nonlinear
bifurcation analysis. Extending from this bifurcation analysis, a modified RED algorithm
is derived to prevent the observed bifurcation and chaos regardless of the selected
parameters. Our modification is for the simple scenario of a single RED router carrying
only TCP traffic. The algorithm neither compromises the throughput nor the average
queuing delay of the system
A new model for time-delay systems with application to network based control
This paper proposes a new model for time-delay systems, which contains multiple successive delay components in the state and has important applications in remote control and network based control. New results on stability and H∞ performance are obtained for systems with two successive delay components. The second part of this paper applies the proposed new model to network based control, which has emerged as a topic of significant interest in the control community. A sampled-data networked control system with simultaneous consideration of network induced delays, data packet dropouts and measurement quantization is modelled as a time-delay system with two successive delay components in the state and, the problem of network based H∞ control is solved accordinglypublished_or_final_versio
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