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Browsing Scholarly Works, Department of Mathematics by Issue Date
Now showing items 2140 of 233

Viscosity and density stratification in vertical Poiseuille flow
(AIP Publishing, 198706)The linear stability of plane three_layer vertical Poiseuille flow is considered. The layers are composed of two immiscible fluids, one next to the walls and one centrally located. The fluids have different viscosities and ... 
The thinlayer effect and interfacial stability in a twolayer Couette flow with similar liquids
(AIP Publishing, 198706)The linear stability of Couette flow composed of two layers of immiscible fluids, one lying on top of the other, is considered for the special case when the two fluids have similar mechanical properties. The interfacial ... 
Exact behavior of Jost functions at low energy
(AIP Publishing, 198801)For Schrödinger operators with central potential q(r) and angular momentuml, the behavior of the Jost function F l (k) as k→0 is investigated. It is assumed that ∫∞ 0 d r (1+r)σ‖q(r)‖<∞, where σ≥1. Situations where q is ... 
The semiclassical limit of quantum dynamics. I. Time evolution
(AIP Publishing, 198802)The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) =−(ℏ^{2}/2m)Δ+V on L^{2}(R^{n}) is studied for a large class of potentials. By convolving with certain Gaussian states, ... 
Couette flow of a binary gas mixture
(AIP Publishing, 198803)The linearized binary model described by Hamel [Phys. Fluids 8, 418 (1964)] is used to obtain a set of kinetic equations and boundary conditions for the Couette flow problem. The derived set of two coupled integrodifferential ... 
Location of essential spectrum of intermediate Hamiltonians restricted to symmetry subspaces
(AIP Publishing, 198810)A theorem is presented on the location of the essential spectrum of certain intermediate Hamiltonians used to construct lower bounds to bound‐state energies of multiparticle atomic and molecular systems. This result is an ... 
The effect of nonzero viscosity ratio on the stability of fingers and bubbles in a HeleShaw cell
(AIP Publishing, 198811)The linear stability of a steadily moving bubble or a finger in a Hele–Shaw cell is considered in the case when gravity and the ratio between the viscosities of the less and more viscous fluids are nonzero. The effect of ... 
Spectral properties of the KronigPenney Hamiltonian with a localized impurity
(AIP Publishing, 198906)It is shown that there exist bound states of the operator H ±λ=−(d 2/d x 2) +∑ m∈Z δ(⋅−(2m+1)π)±λW, W being an L 1(−∞,+∞) non‐negative function, in every sufficiently far gap of the spectrum of H 0=−d 2/d x 2 +∑ m∈Z ... 
Analytic theory for the selection of a twodimensional needle crystal at arbitrary Péclet number
(American Physical Society, 198910)An accurate analytic theory is presented for the velocity selection of a twodimensional needle crystal for arbitrary Péclet number for small values of the surfacetension parameter. The velocity selection is caused by the ... 
On the Levinson theorem for Dirac operators
(AIP Publishing, 199001)For the Dirac equation with potential V(r) obeying ∫∞ 0(1+r)‖V(r)‖d r<∞ we prove a relativistic version of Levinson’s theorem that relates the number of bound states in the spectral gap [−m,m] to the variation of an ... 
Asymptoticbehavior of Jost functions near resonance points for WignerVonneumann type potentials
(AIP Publishing, 199101)In this work are considered radial Schrodinger operators  psi" + V(r)psi = Epsi, where V(r) = a sin br/r + W(r) with W(r) bounded, W(r) = O(r2) at infinity (a,b real). The asymptotic behavior of the Jost function and ... 
A note on best approximation and invertibility of operators on uniformly convex Banach spaces
(Hindawi Publishing Corp, 19910101)It is shown that if X is a uniformly convex Banach space and S a bounded linear operator onX for which ?IS?=1, then S is invertible if and only if ?I12S? <1. From this it follows thatif S is invertible on X then either ... 
Anomaly meltdown
(AIP Publishing, 199108)It is shown that at nonzero temperature it is possible that anomalies in representations of symmetry groups and gauge groups, present at zero temperature, disappear. Several examples are given. Thus the idea that anomalies ... 
Inverse scattering on the line for a Dirac system
(AIP Publishing, 199111)The wholeline version of the GelfandLevitanMarchenko (GLM) equation for a Dirac system is studied. A new derivation of the GLM equation is given, under weaker hypotheses than Frolov's earlier treatment [Sov. Math. Dok1. ... 
The RiemannHilbert problem for nonsymmetric systems
(AIP Publishing, 199112)A comparison of the RiemannHilbert problem and the WienerHopf factorization problem arising in the solution of halfspace singular integral equations is presented. Emphasis is on the factorization of functions lacking ... 
Cohomology of Finite Groups
(University of Essen, 1992)This is a short lecture course on the cohomology of finite groups. Topics include Künneth formula, cup products and cohomology ring, differential graded algebras, Evens norm map and the Steenrod operations. 
Commutative rings with homomorphic power functions
(Hindawi, 19920101)A (commutative) ring R (with identity) is called mlinear (for an integer m≥2) if (a+b)m=am+bm for all a and b in R. The mlinear reduced rings are characterized, with special attention to the finite case. A structure ... 
Inverse scattering in 1D nonhomogeneous media and recovery of the wave speed
(AIP Publishing, 199204)The inverse scattering problem for the 1D Schrodinger equation d2psi/dx2 + k2psi = k2P(x)psi + Q(x)psi is studied. This equation is equivalent to the 1D wave equation with speed 1/ squareroot 1  P(x) in a nonhomogeneous ... 
Scattering and inverse scattering in onedimensional nonhomogeneous media
(AIP Publishing, 199205)The wave propagation in a onedimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrodinger equation d2psi/dx2 ... 
Cauchyproblem for the linearized version of the Generalized Polynomial KdV equation
(AIP Publishing, 199206)In the present paper results about the "Generalized Polynomial Kortewegde Vries equation" (GPKdV) are obtained, extending the ones by Sachs [SIAM J. Math. Anal. 14, 674 (1983)] for the Kortewegde Vries (KdV) equation. ...