A new method for construction of bases for general distribution spaces is developed. This method allows the freedom to prescribe the nature and properties of the basis elements. The method is deployed to the construction of bases consisting of rational functions of uniformly bounded degrees for Besov and Triebel–Lizorkin spaces of holomorphic functions in the unit disc. In turn, this is utilize...

We calculate the two-loop β-functions for soft supersymmetry-breaking interactions in a general supersymmetric gauge theory, emphasising the role of the evanescent couplings and masses that are generic to a non-supersymmetric theory. We also show that a simple set of conditions sufficient for one-loop finiteness renders a theory two-loop finite, and we speculate on the possible significance of ...

In this paper we treat, under fairly general conditions, the question of whether asset prices admit a martingale measure when the markets are free of arbitrage opportunities. The arbitrage opportunities we consider are restricted to originate from simple trading strategies, which are most closely related to actual market portfolios. It is shown that if such simple arbitrage profits are excluded...

We propose a new bi-intuitionistic type theory called Dualized Type The-ory (DTT). It is a simple type theory with perfect intuitionistic duality, and correspondsto a single-sided polarized sequent calculus. We prove DTT strongly normalizing, andprove type preservation. DTT is based on a new propositional bi-intuitionistic logic calledDualized Intuitionistic Logic (DIL) that bui...

Nominal logic is an extension of first-order logic with features useful for reasoning about abstract syntax with bound names. For computational applications such as programming and formal reasoning, it is desirable to develop constructive type theories for nominal logic which extend standard type theories for propositional, firstor higher-order logic. This has proven difficult, largely because ...

in the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. in the second part we discuss some recent developments concurring the simplex algorithm. we describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.