Concept Of Boundedness Research Articles

Extension of local positive definite [formula omitted]-superfunctions

By defining a concept of boundedness for Z2n-superfunction, we show that each local positive definite Z2n-superfunctions, which is bounded in some sense, on a Z2n-Lie supergroup has a positive definite extension to all of the Z2n-Lie supergroup.

Preliminary evidence that applied cognitive linguistics is effective for novice learners regardless of their individual differences

Given the immense potential of cognitive linguistics for second language teaching and the need to produce more robust empirical evidence of its effectiveness for a range of learners in real classrooms, the current study set out to investigate the effectiveness of a novel cognitive linguistics-inspired approach for teaching Spanish prepositions and aspect to novice learners ( n = 30). Animated videos, which were created collaboratively with students to ensure their comprehensibility, presented Principled Polysemy Networks for the prepositions por and para and the concept of boundedness for aspect (preterite and imperfect). After presentation, practice, and feedback cycles, learners made significant gains on controlled production tasks and performed as well as more advanced learners recruited in prior studies, suggesting that the cognitive linguistics approach was effective for these novices. The study found no statistically significant correlations between learning outcomes and individual difference measures of executive function, working memory, motivation, or learning style, which was cautiously interpreted as suggesting that the applied cognitive linguistics approach benefited all learners, not just a subset with particular abilities.

ON BOUNDEDNESS WITH SPEED λ IN ULTRAMETRIC FIELDS

In the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K. Following Kangro [2, 3, 4], we introduce the concept of boundedness with speed λ or λ-boundedness. We then obtain a characterization of the matrix class (mλ , mµ ), where mλ denotes the set of all λ-bounded sequences in K. We conclude the paper with a remark about the matrix class (c λ , mµ ), where c λ denotes the set of all λ-convergent sequences in K.

Boundedness of the L-index in a direction of the sum and product of slice holomorphic functions in the unit ball

Let $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice $\{z^0+t\mathbf{b}: t\in\mathbb{C}\}$ with the unit ball $\mathbb{B}^n=\{z\in\mathbb{C}^{n}: \ |z|:=\sqrt{|z|_1^2+\ldots+|z_n|^2}<1\}$ for any $z^0\in\mathbb{B}^n$. For this class of functions there is considered the concept of boundedness of $L$-index in the direction $\mathbf{b},$ where ${L}: \mathbb{B}^n\to\mathbb{R}_+$ is a positive continuous function such that $L(z)>\frac{\beta|\mathbf{b}|}{1-|z|}$ and $\beta>1$ is some constant.There are presented sufficient conditions that the sum of slice holomorphic functions of bounded $L$-index in direction belong this class. This class of slice holomorphic functions is closed under the operation of multiplication.

Exploring Boundedness for Concept‐Based Instruction of Aspect: Evidence From Learning the Spanish Preterite and Imperfect

AbstractThis study investigated to what extent and how novice second‐language (L2) Spanish learners use the cognitive linguistics‐informed concept of boundedness to support their development of aspect—namely, the Spanish preterite and imperfect. The concept was presented within the framework of concept‐based instruction (CBI) as part of a regular, semester‐long U.S. college Spanish course for true beginners (N = 16). The sociocultural approach of CBI has been found to be effective for other complex L2 phenomena with more advanced learners, but the usefulness of the concept of boundedness for novice learners was untested. Definition, comprehension, verbalization, and performance data were triangulated to measure instructional effectiveness. Results suggest that the concept‐based instructional approach using the concept of boundedness supported students’ understanding of aspect, evidenced by multiple measures of conceptual development, as well as their accuracy in using aspect to create personal narratives.

Slice holomorphic functions in the unit ball: boundedness of $L$-index in a direction and related properties

Let $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice $\{z^0+t\mathbf{b}: t\in\mathbb{C}\}$ with the unit ball $\mathbb{B}^n=\{z\in\mathbb{C}^: \ |z|:=\sqrt{|z|_1^2+\ldots+|z_n|^2}<1\}$ for any $z^0\in\mathbb{B}^n$. For this class of functions we consider the concept of boundedness of $L$-index in the direction $\mathbf{b},$ where $\mathbf{L}: \mathbb{B}^n\to\mathbb{R}_+$ is a positive continuous function such that $L(z)>\frac{\beta|\mathbf{b}|}{1-|z|}$ and $\beta>1$ is some constant.For functions from this class we deduce analog of Hayman's Theorem. It is criterion useful in applications todifferential equations. We introduce a concept of function having bounded value $L$-distribution in direction forthe slice holomorphic functions in the unit ball. It is proved that slice holomorphic function in the unit ball has bounded value $L$-distribution in a direction if and only if its directional derivative has bounded $L$-index in the same direction. Other propositions concern existence theorems. We show that for any slice holomorphic function $F$ with bounded multiplicities of zeros on any slice in the fixed direction there exists such a positive continuous function $L$that the function $F$ has bounded $L$-index in the direction.

Slice Holomorphic Functions in the Unit Ball Having a Bounded L-Index in Direction

Let b∈Cn\{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e., we study functions that are analytic in the intersection of every slice {z0+tb:t∈C} with the unit ball Bn={z∈C:|z|:=|z|12+…+|zn|2<1} for any z0∈Bn. For this class of functions, there is introduced a concept of boundedness of L-index in the direction b, where L:Bn→R+ is a positive continuous function such that L(z)>β|b|1−|z|, where β>1 is some constant. For functions from this class, we describe a local behavior of modulus of directional derivatives on every ’circle’ {z+tb:|t|=r/L(z)} with r∈(0;β],t∈C,z∈Cn. It is estimated by the value of the function at the center of the circle. Other propositions concern a connection between the boundedness of L-index in the direction b of the slice holomorphic function F and the boundedness of lz-index of the slice function gz(t)=F(z+tb) with lz(t)=L(z+tb). In addition, we show that every slice holomorphic and joint continuous function in the unit ball has a bounded L-index in direction in any domain compactly embedded in the unit ball and for any continuous function L:Bn→R+.

Characterization of statistical convergence of complex uncertain double sequence

The main aim of this paper is to introduce statistical convergence of a complex uncertain double sequence. Characterization of statistical convergence is given via uncertain measure, uncertain expected value operator, uncertain distribution function and also with respect to almost surely, uniformly almost surely. The concept of boundedness is introduced to establish some results. Finally, the notion of statistically complex uncertain double Cauchy sequence is proposed to obtain interrelationship with statistically convergent complex uncertain double sequence.

Analytic vector-functions in the unit ball having bounded $\mathbf{L}$-index in joint variables

In this paper, we consider a class of vector-functions, which are analytic in the unit ball. For this class of functions there is introduced a concept of boundedness of $\mathbf{L}$-index in joint variables, where $\mathbf{L}=(l_1,l_2): \mathbb{B}^2\to\mathbb{R}^2_+$ is a positive continuous vector-function, $\mathbb{B}^2=\{z\in\mathbb{C}^2: |z|=\sqrt{|z_1|^2+|z_2|^2}\le 1\}.$ We present necessary and sufficient conditions of boundedness of $\mathbf{L}$-index in joint variables. They describe the local behavior of the maximum modulus of every component of the vector-function or its partial derivatives.

Slice Holomorphic Functions in Several Variables with Bounded L-Index in Direction

In this paper, for a given direction b ∈ C n \ { 0 } we investigate slice entire functions of several complex variables, i.e., we consider functions which are entire on a complex line { z 0 + t b : t ∈ C } for any z 0 ∈ C n . Unlike to quaternionic analysis, we fix the direction b . The usage of the term slice entire function is wider than in quaternionic analysis. It does not imply joint holomorphy. For example, it allows consideration of functions which are holomorphic in variable z 1 and continuous in variable z 2 . For this class of functions there is introduced a concept of boundedness of L-index in the direction b where L : C n → R + is a positive continuous function. We present necessary and sufficient conditions of boundedness of L-index in the direction. In this paper, there are considered local behavior of directional derivatives and maximum modulus on a circle for functions from this class. Also, we show that every slice holomorphic and joint continuous function has bounded L-index in direction in any bounded domain and for any continuous function L : C n → R + .

Functions analytic in a unit ball of bounded L-index in joint variables

The concept of boundedness of the L-index in joint variables (see Mat. Stud., 45, 12–26 (2016), dx. doi.org/10.15330/ms.45.1.12-26 ) is generalized for a function analytic in a ball. The criteria of boundedness of the L-index in joint variables, which describe the local behavior of partial derivatives on the skeleton of a polydisc, are proved.

Analytic in a polydisc functions of bounded $\mathbf{L}$-index in joint variables

A concept of boundedness of L-index in joint variables (see in Bordulyak M.T. The space of entire in $\mathbb{C}^n$ functions of bounded L-index, Mat. Stud., 4 (1995), 53--58. (in Ukrainian)) is generalised for analytic in a bidisc function. We proved criteria of boundedness of $\mathbf{L}$-index in joint variables which describe local behaviour of partial derivative and give an estimate of maximum modulus on a skeleton of polydisc. Some improvements of known sufficient conditions of boundednees of $\mathbf{L}$-index in joint variables are obtained.

Non-Recursive Relations Structure-Functionality

Non-recursive relations structure-functionality is an exclusive property of the recently introduced concept of boundedness. They provide a leading role of the hierarchy of the functional organization in the evolution of each and every complex system. The novel evolution strategy appears as a counterpart rather than as opponent to the survival of the fittest strategy because the survival of the fittest is more advantageous strategy in a slow varying environment while the novel strategy is more advantageous for a rapidly changing environment. Alongside, the non-recursive relations structure-functionality serves as grounds for coexistence of scaling dependent and scaling independent properties of complex systems.

Temperature and Concentration under Boundedness

In the present paper I have proved that in the setting of recently introduced concept of boundedness the intensive macroscopic variables such as temperature and concentration are well-defined even for structured objects and nano-objects. I have proved that the Poisson distribution is generic distribution for all fluctuations. An indispensable part of the proof is the existence of a general dynamical mechanism which provides damping out of the arbitrary accumulation of matter/ energy in every given location and in every moment.

Characterizations and properties of bounded $L$-fuzzy sets

In 1997, Fang proposed the concept of boundedness of $L$-fuzzy setsin $L$-topological vector spaces. Since then, this concept has beenwidely accepted and adopted in the literature. In this paper,several characterizations of bounded $L$-fuzzy sets in$L$-topological vector spaces are obtained and some properties ofbounded $L$-fuzzy sets are investigated.

Pointwise bornological spaces

With each metric space ( X , d ) we can associate a bornological space ( X , B d ) where B d is the set of all subsets of X with finite diameter. Equivalently, B d is the set of all subsets of X that are contained in a ball with finite radius. If the metric d can attain the value infinite, then the set of all subsets with finite diameter is no longer a bornology. Moreover, if d is no longer symmetric, then the set of subsets with finite diameter does not coincide with the set of subsets that are contained in a ball with finite radius. In this text we will introduce two structures that capture the concept of boundedness in both symmetric and non-symmetric extended metric spaces.

Criteria on boundedness in terms of two measures for discrete systems

A new concept of boundedness, which unifies various boundedness notions and leads to other notions connecting them, is defined in terms of two measures. An attempt for discrete systems tries to offer sufficient conditions for obtaining boundedness criteria for such concepts. The employing of vector Lyapunov functions and a new comparison principle covers several known results in usual boundedness theory and, therefore, the present framework provides an additional unification.

Boundedness, one-point extensions and B-extensions

Abstract The general concept of boundedness in a topological space generalizes both metric boundedness and relative compactness. A one-point extension o(ℱ X) of the space X is naturally associated to each boundedness ℱ X and every Hausdorff one-point extensions of a space X can be obtained in this way. Imitating this construction, it is possible to define a much more general class of Hausdorff extensions of a locally bounded space with respect to a given boundedness, the so-called B-extensions. In this paper we study separation properties and metrizability of this kind of extension.

Boundedness dan Polusi pada Situs Islam Cirebon Abad XVI—XVIII

Archaeological sites are the traces of people ‘s lives in the past. The remaining traces are texts, simply waiting to be read. This article tries to interpret the housing patterns in the sites of palaces in Cirebon using the concepts of boundedness, the sacred, the profane, and the pollution.

Newel-pseudotopologiese vektorruimtes

Pseudo-topological spaces (i.e. limit spaces) were defined by Fischer in 1959. In this paper the theory of fuzzy pseudo-topological spaces is applied to vector spaces. We introduce the concept of boundedness in fuzzy pseudo-topological vector spaces.