Related papers: Summability
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
We establish a necessary and sufficient condition for a normal subgroup of a finite group to be a subgroup perfect code.
We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.
We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.
In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
We give simple necessary and sufficient conditions for the inclusion-exclusion identity to hold for an infinite countable number of sets. In terms of a random variable, whose range are nonnegative integers, this condition is equivalent to…
We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard…
In this paper, we propose various sufficient conditions to determine if a given real number is an irrational number or a transcendental number and also apply these conditions to some interesting examples, particularly,one of them comes from…
We prove that an equivalent condition for a uniform space to be coverable is that the images of the natural projections in the fundamental inverse system are uniformly open in a certain sense. As corollaries we (1) obtain a concrete way to…
We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…
This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several…
Necessary and sufficient condition is given for a set $A\subset R^1$ to be a subset of the critical values set for a $C^k$ function $f:R^m \to R^1$.
In this paper, we give some generalizations the concept of element order and we study some of the properties of these generalized order. In particular, with using this generalization we derive two solvability criteria.
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
In this note, we propose simple summations for primes, which involve two finite nested sums and Bernoulli numbers. The summations can also be expressed in terms of Bernoulli polynomials.
For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system's semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the…
We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given…