Related papers: Effective infinitesimals in R
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…
While there is a rich literature on robust methodologies for contamination in continuously distributed data, contamination in categorical data is largely overlooked. This is regrettable because many datasets are categorical and oftentimes…
A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar…
Furstenberg and Glasner proved that for an arbitrary k in N, any piecewise syndetic set contains k term arithmetic progressions and such collection is also piecewise syndetic in Z: They used algebraic structure of beta N. The above result…
We generalize the stochastic revealed preference methodology of McFadden and Richter (1990) for finite choice sets to settings with limited consideration. Our approach is nonparametric and requires partial choice set variation. We impose a…
We investigate exponential sums over those numbers $\leq x$ all of whose prime factors are $\leq y$. We prove fairly good minor arc estimates, valid whenever $\log^{3}x \leq y \leq x^{1/3}$. Then we prove sharp upper bounds for the $p$-th…
We develop a weakest-precondition-style calculus \`a la Dijkstra for reasoning about amortized expected runtimes of randomized algorithms with access to dynamic memory - the $\textsf{aert}$ calculus. Our calculus is truly quantitative, i.e.…
The theory of finitely supported algebraic structures is related to Pitts theory of nominal sets (by equipping finitely supported sets with finitely supported internal algebraic laws). It represents a reformulation of Zermelo Fraenkel set…
This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…
In the article the formulas for the modeling of conservative fields in piecewise infinite plate with a thin inclusion found. The accuracy of the found formulas is of order equal to the thickness of the outer layer. The problem for higher…
Integrity constraints (ICs) provide a valuable tool for expressing and enforcing application semantics. However, formulating constraints manually requires domain expertise, is prone to human errors, and may be excessively time consuming,…
It is well-known that within Zermelo-Fraenkel set theory (ZF), the Axiom of Choice (AC) implies the Maximal Ideal Theorem (MIT), namely that every nontrivial commutative ring has a maximal ideal. The converse implication MIT $\Rightarrow$…
It is well-known that a finite axiomatization of Zermelo-Fraenkel set theory (ZF) is not possible in the same first-order language. In this note we show that a finite axiomatization is possible if we extent the language of ZF with the new…
This paper investigates the behavior of sets and functions at infinity by introducing new concepts, namely directional normal cones at infinity for unbounded sets, along with limiting and singular subdifferentials at infinity in the…
In this note we present new examples of determinantal point processes with infinitely many particles. The particles live on the half-lattice {1,2,...} or on the open half-line (0,+\infty). The main result is the computation of the…
We give effective bounds for the set quasi-integral points in orbits of non-isotrivial rational maps over function fields under some conditions, generalizing previous work of Hsia and Silverman (2011) for orbits over function fields of…
Sofic entropy is an invariant for probability-preserving actions of sofic groups. It was introduced a few years ago by Lewis Bowen, and shown to extend the classical Kolmogorov-Sinai entropy from the setting of amenable groups. Some parts…
By combining several interesting applications of random sampling in geometric algorithms like point location, linear programming, segment intersections, binary space partitioning, Clarkson and Shor \cite{CS89} developed a general framework…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…