Suppose that (A0, A1) and (B0, B1) are Banach couples, and that T is a linear operator which maps A0 compactly into B0 and A1 boundedly (or even compactly) into B1. Does this imply that T : [A0, A1]θ → [B0, B1]θ compactly? (Here, as usual, [A0, A1]θ denotes the complex interpolation space of Alberto Calderón.) This question has been open for 44 years. Affirmative answers are known for it in man...

Let A be an arrangement of n pseudolines in the real projective plane and let p 3 (A) be the number of triangles of A. Grünbaum has proposed the following question. Are there infinitely many simple arrangements of straight lines with p 3 (A) = 1 3 n(n − 1)? In this paper we answer this question affirmatively.

We present here strong numerical and statistical evidence of the fact that the Smale’s 7th problem can be answered affirmatively. In particular, we show that a local minimum for the logarithmic potential energy in the 2-sphere satisfying the Smale’s conditions can be identified with a computational cost of approximately O(N10).

It has long been an open question whether the formula XCB = EpEEEpqErqr is, with the rules of substitution and detachment, a single axiom for the classical equivalential calculus. This paper answers that question affirmatively, thus completing a search for all such eleven-symbol single axioms that began seventy

Let X be a smooth closed oriented non-spin 4-manifold with even intersection form kE8⊕nH . In this article we show that we should have n ≥ |k| on X. Thus we confirm the 10 8 -conjecture affirmatively. As an application, we also give an estimate of intersection forms of spin coverings of non-spin 4-manifolds with even intersection forms.

We prove necessary and sufficient conditions for locally Lipschitz Löwner operators to be monotone, strictly monotone and strongly monotone. Utilizing our characterization of the strict monotonicity of Löwner operators, we generalize Mangasarian class of Nonlinear Complementarity Problem (NCP)-functions to the setting of symmetric cone complementarity problem. This affirmatively answers a quest...

Physicians do not measure biomarkers simply to predict risk. Rather, they do so to better target therapy and improve the lives of their patients. Thus, when considering the use of any biomarker for cardiovascular risk prediction in primary prevention, thoughtful clinicians, and those writing guidelines should insist that two fundamental questions be answered affirmatively. First, is there clear...

A rational map $\phi: \mathbb{P}_k^m \dashrightarrow \mathbb{P}_k^n$ is defined by homogeneous polynomials of a common degree $d$. We establish linear bound in terms $d$ for the number $(m-1)$-dimensional fibers $\phi$, using ideals minors Jacobian matrix. In particular, we answer affirmatively Question~11 arXiv:1511.02933v2.

Across the globe individuals and organizations are creating geographic data work products with little ability to efficiently or effectively make known and share those digital products with others. This article outlines a conceptual model and the accompanying research challenges for providing easy legal and technological mechanisms by which any creator might affirmatively and permanently mark an...

Irreversible k-conversion set is introduced in connection with the mathematical modeling of the spread of diseases or opinions. We show that the problem to find a minimum irreversible 2-conversion set can be solved in O(n2 log6 n) time for graphs with maximum degree at most 3 (subcubic graphs) by reducing it to the graphic matroid parity problem, where n is the number of vertices in a graph. Th...