Theoretical analyses of the stability of symmetric and asymmetric vortex pairs over slender conical wing-body combinations consisting of a slender circular or elliptic cone and a flat-plate delta wing under small perturbations in an inviscid incompressible steady flow at high angles of attack with or without sideslip are presented. The three-dimensional flow problem is reduced to a problem in t...

we consider the semilinear elliptic boundary value problem  = ∈∂ω− δ = ∈ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, ω is a bounded region in rn with a smooth boundary, and f is asmooth function. we prove, under some additional conditions, the existence of a positive solution for λlarge. we prove that our solution u for λ large is such that = →∞∈ω|| u ||: sup| u(x) |xas λ ...

We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space R. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone Γ ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This a...

Let Ω ⊂ R be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu = λa (x, t) u − b (x, t) u in Ω × R, where 0 < p, q < 1 and λ > 0. In some cases we also show the...

The azimuthal elliptic asymmetry v2 observed in heavy ion collisions, is usually associated with properties of the medium created in the final state. We compute the azimuthal asymmetry which is due to multiple interactions of partons at the initial stage of nuclear collisions, and which is also present in pA collisions. In our approach the main source of azimuthal asymmetry is the combination o...

In this note we will present an extension of the Krein-Rutman theorem for an abstract non-linear, compact, positively 1-homogeneous operators on a Banach space having the properties of being increasing with respect to a convex cone K and such that there is a non-zero u ∈ K for which M Tu < u for some positive constant M . This will provide a uniform framework for recovering the Krein-Rutman-lik...

We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space R. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone Γ ⊂ Rp, we construct a unique “symbol valued trace”, which extends the L2–trace on operators of small order. This c...

For fully nonlinear $k$-Hessian operators on bounded strictly $(k-1)$-convex domains $\Omega$ of $\mathbb{R}^N$, a characterization the principal eigenvalue associated to $k$-convex and negative eigenfunction will be given as supremum over values spectral parameter for which admissible viscosity supersolutions obey minimum principle. The admissibility condition is phrased in terms natura...

In this paper we explore the Isotropic Subspace Theorems of Catanese and Bauer, establishing relations between isotropic subspaces in the 1cohomology of a quasi-projective variety M and certain irrational pencils f : M → C, from the point of view of the Tangent Cone Theorem due to Papadima, Suciu and the author. In the proper case the picture is completely clear, and is described in section 3. ...