A skew brane is a codimension 2 submanifold in affine space such that the tangent spaces at any two distinct points are not parallel. We show that if an oriented closed manifold has a non-zero Euler characteristic χ then it is not a skew brane; generically, the number of oppositely oriented pairs of parallel tangent spaces is not less than χ/4. We give a version of this result for immersed surf...

In this work, we study a class of nonlinear eigenvalue problems related to fully discontinuous operators. In particular, we prove the existence of a critical point for two distinct problems. Connected with this problem, we also study a minimization problem with constraint and we investigate the existence of solutions for a resonant case near zero. Moreover, we give some estimates and qualitativ...

Let R be a unital ring with an involution. Necessary and sufficient conditions for the existence of the Bott-Duffin inverse of a ∈ R relative to a pair of self-adjoint idempotents (e, f) are derived. The existence of a {1, 3}-inverse, {1, 4}-inverse, and the Moore-Penrose inverse of a matrix product is characterized, and explicit formulas for their computations are obtained. Some applications t...

These Lecture Notes are devoted to some aspects of the theory of the Navier-Stokes-Fourier system. We shall discuss 1) existence of weak solutions, 2) existence of suitable weak solutions and relative entropies, 3) weak strong uniqueness property in the class of weak solutions. For physical reasons, we shall limit ourselves to the three dimensional physical space, and for the sake of simplicity...

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

The main theme of this paper is a relative version of the almost existence theorem for periodic orbits of autonomous Hamiltonian systems. We show that almost all low levels of a function on a geometrically bounded symplectically aspherical manifold carry contractible periodic orbits of the Hamiltonian flow, provided that the function attains its minimum along a closed symplectic submanifold. As...

In [Sh, chapter XI], Shelah shows that certain revised countable support (RCS) iterations do not add reals. His motivation is to establish the independence (relative to large cardinals) of Avraham’s problem on the existence

This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.

We give an affirmative answer to a question of Gorelic [5], by showing it is consistent, relative to the existence of large cardinals, that there is a proper class of cardinals α with cf(α) = ω1 and αω > α.

Results of targeted molecular dynamics simulations confirm the existence of a higher energy barrier for creation of the pocket where non-nucleoside reverse transcriptase inhibitors bind in the K103N mutant enzyme relative to wild-type.