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Second Order Balanced Truncation.
No full textWe consider second-order linear time-invariant systems. The objective of this paper is
to present a new method for constructing a reduced system by preserving the second-order
structure of the original system. This new model reduction method uses a variant of the wellknown
balanced truncation technique applied to second-order gramians. We also compare it
with another existing technique
Mutual information and capacity of a linear digital channel
No full textIn this paper we analyse a simple model of a digital communications channel. This model proves to be closely related to an iterated function system (IFS) related to the well-known Bernoulli convolution. We derive it from a randomly forced first-order ordinary differential equation. This allows the parameter of the Bernoulli convolution—the contraction rate, λ—to be related to the rate at which symbols are input to the channel. It is shown that for a channel with equiprobable binary inputs the mutual information between input and output distributions is the stationary measure of the complement of the overlap region of the IFS. We show that the mutual information is Hölder continuous with respect to λ and decreases hyper-exponentially as λ → 1. We also study the case of non-equiprobable binary inputs and show that the maximum of the mutual information—the channel capacity—does not always correspond to equiprobable inputs
Some model theory of sheaves of modules
Get PDFWe explore some topics in the model theory of sheaves of modules. First we describe the formal language that we use. Then we present some examples of sheaves obtained from quivers. These, and other examples, will serve as illustrations and as counterexamples. Then we investigate the notion of strong minimality from model theory to see what it means in this context. We also look briefly at the relation between global, local and pointwise versions of properties related to acyclicity
One-sided indecomposable pure-injective modules over string algebras
Get PDFWe classify one-sided indecomposable pure injective modules over (finite dimensional) string algebras
Computations of Eigenvalue Avoidance in Planar Domains
Get PDFThe phenomenon of eigenvalue avoidance is of growing interest in applications ranging from quantum mechanics to the theory of the Riemann zeta function. Until now the computation of eigenvalues of the Laplace operator in planar domains has been a difficult problem, making it hard to compute eigenvalue avoidance. Based on a new method this paper presents the computation of eigenvalue avoidance for such problems to almost machine precision
A 11,707,448,673,375 vertex graph related to the baby monster I
No full textThe structure of the point-line collinearity graph of the characteristic 2 minimal parabolic geometry for the Baby Monster simple group is studied
Envelope-Constrained Neutralization-Sensitive HIV-1 After Heterosexual Transmission
No full textHeterosexual transmission accounts for the majority of human immunodeficiency virus–1 (HIV-1) infections worldwide, yet the viral properties that determine transmission fitness or outgrowth have not been elucidated. Here we show, for eight heterosexual transmission pairs, that recipient viruses were monophyletic, encoding compact, glycan-restricted envelope glycoproteins. These viruses were also uniquely sensitive to neutralization by antibody from the transmitting partner. Thus, the exposure of neutralizing epitopes, which are lost in chronic infection because of immune escape, appears to be favored in the newly infected host. This reveals characteristics of the envelope glycoprotein that influence HIV-1 transmission and may have implications for vaccine design
G-reflectors: Analogues of householder transformations in scalar product spaces
No full textWe characterize the analogues of Householder transformations in matrix groups associated with scalar products, and precisely delimit their mapping capabilities: given a matrix group Image and vectors x, y, necessary and sufficient conditions are derived for the existence of a Householder-like analogue Image such that Gx=y. When G exists, we show how it can be constructed from x and y. Examples of matrix groups to which these results apply include the symplectic and pseudo-unitary groups
Instabilities in supersonic compression ramp flow
Get PDFSeparation of a supersonic boundary layer near a compression ramp is considered in the limit of large Reynolds numbers and for Mach numbers . When the ramp angle is small, the motion may be described by the well-known triple-deck theory describing viscous–inviscid interactions. For small values of the scaled ramp angle, steady stable solutions can be obtained. However, it is shown that when a recirculation zone is present and the ramp angle is sufficiently large, the flow in the recirculation zone is susceptible to convective instabilities when perturbations are introduced there. At still larger values of the scaled ramp angle, an absolute instability is shown to occur that leads to a violent local breakdown of the boundary layer. The calculated results are shown to be consistent with a theoretical criterion that is the necessary and sufficient condition for the onset of instability
Semidensities on odd symplectic supermanifolds
No full textWe consider semidensities on a supermanifold E with an odd symplectic structure. We define a new Δ-operator action on semidensities as the proper framework for the Batalin-Vilkovisky (BV) formalism. We establish relations between semidensities on E and differential forms on Lagrangian surfaces. We apply these results to Batalin-Vilkovisky geometry. Another application is to (1.1)-codimensional surfaces in E. We construct a kind of ``pull-back'' of semidensities to such surfaces. This operation and the Δ-operator are used for obtaining integral invariants for (1.1)-codimensional surfaces