Rough Convergence Research Articles

On Triple Sequence Spaces of Bernstein Operator of χ3 of Rough λ-Statistical Convergence in Probability of Random Variables Defined by Musielak-Orlicz Function

On Triple Sequence Spaces of Bernstein Operator of χ3 of Rough λ-Statistical Convergence in Probability of Random Variables Defined by Musielak-Orlicz Function

On Rough Convergence of Fuzzy Numbers based on α-level sets

In this paper we have established some basic properties of rough convergence for fuzzy number sequences. Also introduce the set of rough limit points of a sequence of fuzzy number using α-level set and prove some results associated with this set.

Generalised triple difference of rough intuitionistic statistical convergence in probability of fractional order defined by Musielak-Orlicz function

We generalised the concepts in probability of rough intuitionistic convergence and rough intuitionistic statistically convergence by introducing the generalised difference operator Δαγ of fractional order, where α is a proper fraction and γ = (γmnk) is any fixed sequence of non-zero real or complex numbers. We study some properties of this operator and investigate the topological structures of related of triple difference sequence spaces of ξ 3f (Δαγ xmnk). The main focus of the present paper is to generalised rough intuitionistic convergence and rough intuitionistic statistical difference of triple difference sequence spaces of χ3 and investigate their topological structures as well as some interesting results concerning the operator Δαγ.

On rough statistical convergence of double sequences in normed linear spaces

The idea of rough statistical convergence for single sequences was introduced by Salih Aytar as a generalization of rough convergence. In this paper we define and study rough statistical convergence of double sequences, the set of rough statistical limits of a double sequence. We also study the relation between the set of statistical cluster points and the set of rough limit points of a double sequence.

Rough I-Convergence

Abstract In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequence

Rough Convergence and Chebyshev Centers in Banach Spaces

By means of rough convergence, we introduce two new geometric properties in Banach spaces and relate them to Chebyshev centers and some well-known classical properties, such as Kalton's M property or Garkavi's uniform rotundity in every direction.

Rough convergence of double sequences

In this paper, we introduce the notion of rough convergence and the set of rough limit points of a double sequence and obtained two rough convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of cluster points and the set of rough limit points of a double sequence.

A Characterization of Uniform Rotundity in Every Direction in Terms of Rough Convergence

We characterize uniform rotundity in every direction by means of rough convergence. This characterization still holds if we shift to rough statistical convergence. We also study the latter convergence in normed spaces.

The morgana model for the rise of galaxies and active nuclei

We present the Model for the Rise of Galaxies and Active Nuclei (MORGANA), a new code for the formation and evolution of galaxies and active galactic nuclei (AGNs). Starting from the merger trees of dark matter (DM) haloes and a model for the evolution of substructure within the haloes, the complex physics of baryons is modelled with a set of state-of-the-art models that describe the mass, metal and energy flows between the various components (baryonic halo, bulge, disc) and phases (cold and hot gas, stars) of a galaxy. These flows are then numerically integrated to produce predictions for the evolution of galaxies. The processes of shock-heating and cooling, star formation, feedback, galactic winds and superwinds, accretion on to black holes and AGN feedback are described by new models. In particular, the evolution of the halo gas explicitly follows the thermal and kinetic energies of the hot and cold phases, while star formation and feedback follow the results of the multiphase model recently proposed by Monaco. The increased level of sophistication of these models allows to move from a phenomenological description of gas physics, based on simple scalings with the depth of the DM halo potential, towards a fully physically motivated one. We deem that this is fully justified by the level of maturity and rough convergence reached by the latest versions of numerical and semi-analytic models of galaxy formation. The comparison of the predictions of MORGANA with a basic set of galactic data reveals from the one hand an overall rough agreement, and from the other hand highlights a number of well- or less-known problems: (i) producing the cut-off of the luminosity function requires to force the quenching of the late cooling flows by AGN feedback, (ii) the normalization of the Tully‐Fisher relation of local spirals cannot be recovered unless the DM haloes are assumed to have a very low concentration, (iii) the mass function of H I gas is not easily fitted at small masses, unless a similarly low concentration is assumed, (iv) there is an excess of small elliptical galaxies at z = 0. These discrepancies, more than the points of agreement with data, give important clues on the missing ingredients of galaxy formation.

Rough Convergence in Infinite Dimensional Normed Spaces

For given r, ρ ≥ 0, a sequence (xi ) in some normed linear space X is said to be r-convergent if the r-limit set defined by is nonempty, and it is called a ρ-Cauchy sequence if This article investigates different aspects of this rough convergence, especially in infinite dimensional spaces, such as analytical properties of r-limit set, relation to other convergence notions, and the dependence of the r-limit set on the roughness degree r. Moreover, by using the Jung constant we find the minimal value of r such that an arbitrary ρ-Cauchy sequence in X is certainly r-convergent.

The Impact of Vintage and Survival on Productivity: Evidence from Cohorts of U.S. Manufacturing Plants

This paper examines the evolution of productivity in U.S. manufacturing plants from 1963 to 1992. We define a vintage effect as the change in productivity of recent cohorts of new plants relative to earlier cohorts of new plants, and a survival effect as the change in productivity of a particular cohort of surviving plants as it ages. Both factors contribute to industry productivity growth, but play offsetting roles in determining a cohort's relative position in the productivity distribution. Recent cohorts enter with higher productivity than earlier entrants did, whereas surviving cohorts show productivity increases as they age. These two effects roughly offset each other, however, so there is a rough convergence in productivity across cohorts in 1992 and 1987.

ROUGH CONVERGENCE IN NORMED LINEAR SPACES

x * ∈ X is said to be an r-limit point of a sequence (xi ) in some normed linear space (X,∥ · ∥) if (r ≥ 0). The set of all r-limit points of (xi , denoted by LIM r x i , is bounded closed and convex. Further properties, in particular the relation between this rough convergence and other convergence notions, and the dependence of LIM r x i on the roughness degree r, are investigated. For instance, the set-valued mapping r ↦ LIM r x i is strictly increasing and continuous on (), where . For a so-called ρ-Cauchy sequence (xi ) satisfying it is shown in case X = R n that r = (n/(n + 1))ρ (or for Euclidean space) is the best convergence degree such that LIM r x i ≠ Ø.