Completeness Properties of Perturbed Sequences
نویسنده
چکیده
If S is an arbitrary sequence of positive integers, let P(S) be the set of all integers which are representable as a sum of distinct terms of S . Call S complete if P(S) contains all large integers, and subcomplete if P(S) contains an infinite arithmetic progression . It is shown that any sequence can be perturbed in a rather moderate way into a sequence which is not subcomplete . On the other hand, it is shown that if S is any sequence satisfying a mild growth condition, then a surprisingly gentle perturbation suffices to make S complete in a strong sense . Various related questions are also considered .
منابع مشابه
A Perturbed Half-normal Distribution and Its Applications
In this paper, a new generalization of the half-normal distribution which is called the perturbed half-normal distribution is introduced. The new distribution belongs to a family of distributions which includes the half-normal distribution along with an extra parameter to regulate skewness. The probability density function (pdf) is derived and some various properties of the new distribution are...
متن کاملEquality propositional logic and its extensions
We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...
متن کاملBasicity of System of Exponents with Complex Coefficients in Generalized Lebesgue Spaces
We consider a perturbed system of exponents { en } n∈Z, when the sequence {λn }n∈Z has a definite asymptotics. We study basis properties (completeness, minimality, basicity) of this system in Lebesgue space of functions Lp(·) (−π, π) with variable summability exponent p(·), subject to parameters contained in the asymptotics {λn}n∈Z.
متن کاملGeneralized concept of $J$-basis
A generalization of Schauder basis associated with the concept of generalized analytic functions is introduced. Corresponding concepts of density, completeness, biorthogonality and basicity are defined. Also, corresponding concept of the space of coefficients is introduced. Under certain conditions for the corresponding operators, some properties of the space of coefficients and basicity crite...
متن کاملCharacterization of fuzzy complete normed space and fuzzy b-complete set
The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.
متن کامل