It is indeed a pleasure and a privilege to be asked to give this lecture in memory of a fine medical scientist, whose career was cut so sadly short by violence. In looking at the program today I cannot help but think of another scientist, to whom this field owes so much, whose life was also cut short unexpectedly. Alick Isaacs, the discoverer of interferon, was a brilliant medical scientist and...

The organizers chose it. I’m not sure what ‘formal theory’ is supposed to cover, but they made the useful suggestion that my job is to summarize the parallel talks. There were 21 talks, covering a good range of interesting topics. With just a little squeezing the talks fall into four broad categories: perturbative methods in gauge theory and gravity, applications of AdS/CFT duality, vacuum ener...

For $$p \in (1,N)$$ and $$\Omega \subseteq {\mathbb {R}}^N$$ open, the Beppo-Levi space $${\mathcal {D}}^{1,p}_0(\Omega )$$ is completion of $$C_c^{\infty }(\Omega with respect to norm $$\left[ \int _{\Omega }|\nabla u|^p dx \right] ^ \frac{1}{p}.$$ Using p-capacity, we define a then identify Banach function {H}}(\Omega set all g in $$L^1_{loc}(\Omega that admits following Hardy–Sobolev ty...

 According to a class of constrained‎ ‎minimization problems‎, ‎the Schwartz symmetrization process and the‎ ‎compactness lemma of Strauss‎, ‎we prove that there is a‎ ‎nontrivial ground state solution for a class of $p$-Laplace‎ ‎equations without the Ambrosetti-Rabinowitz condition‎.

Despite the explicit and detailed reports of extensive financial ties between physicians and researchers on the one hand and device and drug companies on the other hand and notwithstanding a proliferation of conflict of interest policies by academic medical centers (AMCs) and professional medical societies, some recipients of industry largess continue to deny that these relationships are in any...

Combinatorial problems like TSP optimize a linear function over some polytope P. If we can obtain P as a projection from a larger-dimensional polytope with a small number of facets, then we get a small linear program for the optimization problem; if we obtain P as a projection from a small spectrahedron, then we get a small semidefinite program. The area of extension complexity studies the mini...

Over the past few months, NASA has been in the news numerous times both for the exciting discoveries of the pair of Mars Rovers as well as the country’s “Vision for Space Exploration.” This vision focuses on the joint human and robotic exploration of the solar system starting with a return to the moon and then the human exploration of Mars. In addition, the vision includes a continued array of ...

The concept of compactness is a necessary condition of any system that is going to call itself a finitary method of proof. However, it can also apply to predicates of sets of formulas in general and in that manner it can be used in relation to level functions, a flavor of measure functions. In what follows we will tie these concepts of measure and compactness together and expand some concepts w...

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...