Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra

Copyright © 2002 IEEEThe influence of a point spectrum on large sample statistics of the autoregressive (AR) spectral estimator is addressed. In particular, the asymptotic distributions of the AR coefficients, the innovations variance, and the spectral density estimator of a finite-order AR(p) model to a mixed spectrum process are presented. Various asymptotic results regarding AR modeling of a regular process with a continuous spectrum are arrived at as special cases of the results for the mixed spectrum setting. Finally, numerical simulations are performed to verify the analytical resultsSoon-Sen Lau, P. J. Sherman and L. B. Whit

Hydrogen-Air-Steam Combustion Regimes In Large Volumes

Dangerous pressure waves can be generated by the combustion of H2-air-steam mixtures if ordinary deflagrations accelerate to high speed or undergo deflagration-to-detonation transition (DDT). The purpose of this paper is to estimate the potentially dangerous mixtures in large volumes. There is a limited experimental data base for flame acceleration and DDT of EL-airsteam mixtures in smaller geometries. There is concern about the possible explosive combustion in the Space Shuttle main engine exhaust duct at Vandenberg AFB. There are no relevant experimental data or valid theories at this large scale (duct width, W, ~ 10 m) to predict flame acceleration and DDT. We have estimated potentially dangerous mixtures by extrapolating correlations used at smaller scale based on the detonation cell width, X. In square ducts DDTs are possible if W/X \u3e 1. We delineate three combustion regions: nonflammable, weakly flammable, and strongly flammable and potentially detonable. The nonflammable region is the region outside the flammability limit where self-sustaining combustion cannot occur. Flammability limits are independent of scale in large volumes. The strongly flammable region, where dangerous flame acceleration or DDT is possible, is bounded by mixtures with X = 10 m. We estimate detonations are possible when there is less than 45% steam. The weakly flammable region, which lies between the other two, should support only slow combustion, where no significant pressure waves should be generated

Pupillometry, a bioengineering overview

The pupillary control system is examined using a microprocessor based integrative pupillometer. The real time software functions of the microprocessor include: data collection, stimulus generation and area to diameter conversion. Results of an analysis of linear and nonlinear phenomena are presented

One-loop approximation for the Heisenberg antiferromagnet

We use the diagram technique for spin operators to calculate Green's functions and observables of the spin-1/2 quantum Heisenberg antiferromagnet on a square lattice. The first corrections to the self-energy and interaction are taken into account in the chain diagrams. The approximation reproduces main results of Takahashi's modified spin-wave theory [Phys. Rev. B 40, 2494 (1989)] and is applicable in a wider temperature range. The energy per spin calculated in this approximation is in good agreement with the Monte Carlo and small-cluster exact-diagonalization calculations in the range 0 <= T < 1.2J where J is the exchange constant. For the static uniform susceptibility the agreement is good for T < 0.6J and becomes somewhat worse for higher temperatures. Nevertheless the approximation is able to reproduce the maximum in the temperature dependence of the susceptibility near T = 0.9J.Comment: 15 pages, 6 ps figure

Applications of BGP-reflection functors: isomorphisms of cluster algebras

Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism between two cluster algebras associated to the matrix $A$ (see section 4 for precise meaning). When $A$ is of finite type, these isomorphisms behave nicely, they are compatible with the BGP-reflection functors of cluster categories defined in [Z1, Z2] if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras, and they are also compatible with the "truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of preprojective or preinjective modules of hereditary algebras by Dlab-Ringel [DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types.Comment: revised versio

Pitot pressure in hypersonic flow with condensation.

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76722/1/AIAA-6518-763.pd

A homological interpretation of the transverse quiver Grassmannians

In recent articles, the investigation of atomic bases in cluster algebras associated to affine quivers led the second-named author to introduce a variety called transverse quiver Grassmannian and the first-named and third-named authors to consider the smooth loci of quiver Grassmannians. In this paper, we prove that, for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable representation M is the set of points N in the quiver Grassmannian of M such that Ext^1(N,M/N)=0. As a corollary we prove that the transverse quiver Grassmannian coincides with the smooth locus of the irreducible components of minimal dimension in the quiver Grassmannian.Comment: final version, 7 pages, corollary 1.2 has been modifie