Related papers: A more intuitive definition of limit
The notion of topological entropy can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution $\varepsilon$ within $T$ time units. It can then be formally defined as a limit of a limit…
Statistical limits are defined relaxing conditions on conventional convergence. The main idea of the statistical convergence of a sequence l is that the majority of elements from l converge and we do not care what is going on with other…
Fatou's lemma states under appropriate conditions that the integral of the lower limit of a sequence of functions is not greater than the lower limit of the integrals. This note describes similar inequalities when, instead of a single…
We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are essentially the same program. The set of…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
In this paper we give a definition of "algorithm," "finite algorithm," "equivalent algorithms," and what it means for a single algorithm to dominate a set of algorithms. We define a derived algorithm which may have a smaller mean execution…
These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…
Axiom pinpointing refers to the task of finding the specific axioms in an ontology which are responsible for a consequence to follow. This task has been studied, under different names, in many research areas, leading to a reformulation and…
The kernel of analysis, to me anyway, is the following idea: A point is arbitrarily close to a set if every neighborhood of the point intersects the set. Defining ``arbitrarily close'' in this way provides a foundation for classical results…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
We develop a unified approach to defining a point at infinity for an arbitrary space and formalizing convergence to this point. Central to our work is a method to quantify and classify the rates at which functions approach their limits at…
The formal definition of limit is one mathematical idea that gives difficulties to most students. Therefore, it is necessary to provide engaging activity in order to construct the students' understanding about the definition. This study…
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.
Based on a new analytical approach to the definition of additive free convolution on probability measures on the real line we prove free analogs of limit theorems for sums for non-identically distributed random variables in classical…
We define the notion of 2-filtered 2-category and give an explicit construction of the bicolimit of a category valued 2-functor. A category considered as a trivial 2-category is 2-filtered if and only if it is a filtered category, and our…
We introduce a new natural notion of convergence for permutations at any specified scale, in terms of the density of patterns of restricted width. In this setting we prove that limits may be chosen independently at a countably infinite…
Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…
We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of…
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…