We consider real valued functions $f$ defined on a subinterval $I$ of the positive real axis and prove that if all of $f$’s quantum differences are nonnegative then $f$ has a power series representation on $I$. Further, if the quantum differences have fixed sign on $I$ then $f$ is analytic on $I$.
We define Bernstein-type operators on the half line $\mathopen [0,+\infty \mathclose [$ by means of two sequences of strictly positive real numbers. After studying their approximation properties, we also establish a Voronovskaja-type result with respect to a suitable weighted norm.
Beta-integers were defined as a generalization of integers by Alfréd Rényi in 1957 in the course of his study of expansions of real numbers in non-integer bases. Together with mathematicians, crystallographers are also interested in this unusual structure. They have found out that beta-lattices are in particular convenience for the description of quasicrystals and their diffraction images., Ľubomíra Balková., and Obsahuje bibliografii
The subject of this paper is the notion of similarity between the actual and impossible worlds. Many believe that this notion is governed by two rules. According to the first rule, every non-trivial world is more similar to the actual world than the trivial world is. The second rule states that every possible world is more similar to the actual world than any impossible world is. The aim of this paper is to challenge both of these rules. We argue that acceptance of the first rule leads to the claim that the rule ex contradictione sequitur quodlibet is invalid in classical logic. The second rule does not recognize the fact that objects might be similar to one another due to various features., Předmětem této práce je pojem podobnosti mezi skutečnými a nemožnými světy. Mnozí se domnívají, že tento pojem se řídí dvěma pravidly. Podle prvního pravidla je každý netriviální svět více podobný skutečnému světu, než je triviální svět. Druhé pravidlo uvádí, že každý možný svět je více podobný skutečnému světu, než jakýkoli nemožný svět. Cílem tohoto článku je zpochybnit obě tato pravidla. Tvrdíme, že přijetí prvního pravidla vede k tvrzení, že pravidlo ex contradictione sequitur quodlibet je v klasické logice neplatné. Druhé pravidlo neuznává skutečnost, že by objekty mohly být podobné vzhledem k různým vlastnostem., and Maciej Sendlak