The generalized multiplier space and its Köthe-Toeplitz and null duals

The purpose of the present study is to generalize the multiplier space for introducing the concepts of (alphaB-), (betaB-), (gamaB-duals) and NB-duals, where (B = (b_{n,k})) is an infinite matrix with real entries. Moreover, these duals are computed for the sequence spaces X and (X(delta)), where (Xin{l_p; c; c_0}) and (1< p<infty )

The generalized multiplier space and its Köthe-Toeplitz and null duals

The purpose of the present study is to generalize the multiplier space for introducing the concepts of (alphaB-), (betaB-), (gamaB-duals) and NB-duals, where (B = (b_{n,k})) is an infinite matrix with real entries. Moreover, these duals are computed for the sequence spaces X and (X(delta)), where (Xin{l_p; c; c_0}) and (1< p<infty )

AI Thinking for Cloud Education Platform with Personalized Learning

Artificial Intelligence (AI) thinking is a framework beyond procedural thinking and based on cognitive and adaptation to automatically learn deep and wide rules and semantics from experiments. This paper presents Cloud-eLab, an open and interactive cloud-based learning platform for AI Thinking, aiming to inspire i) Deep and Wide learning, ii) Cognitive and Adaptation learning concepts for education. It has been successfully used in various machine learning courses in practice, and has the expandability to support more AI modules. In this paper, we describe the block diagram of the proposed AI Thinking education platform, and provide two education application scenarios for unfolding Deep and Wide learning as well as Cognitive and Adaptation learning concepts. Cloud-eLab education platform will deliver personalized content for each student with flexibility to repeat the experiments at their own pace which allow the learner to be in control of the whole learning process

Transformative Effects of IoT, Blockchain and Artificial Intelligence on Cloud Computing: Evolution, Vision, Trends and Open Challenges

Cloud computing plays a critical role in modern society and enables a range of applications from infrastructure to social media. Such system must cope with varying load and evolving usage reflecting societies’ interaction and dependency on automated computing systems whilst satisfying Quality of Service (QoS) guarantees. Enabling these systems are a cohort of conceptual technologies, synthesised to meet demand of evolving computing applications. In order to understand current and future challenges of such system, there is a need to identify key technologies enabling future applications. In this study, we aim to explore how three emerging paradigms (Blockchain, IoT and Artificial Intelligence) will influence future cloud computing systems. Further, we identify several technologies driving these paradigms and invite international experts to discuss the current status and future directions of cloud computing. Finally, we proposed a conceptual model for cloud futurology to explore the influence of emerging paradigms and technologies on evolution of cloud computing

Bounds of operators on the Hilbert sequence space

The author has computed the bounds of the Hilbert operator on some sequence spaces [18, 19]. Through this study the author has investigated the bounds of operators on the Hilbert sequence space and the present study is a complement of those previous research

Bounds for the norm of lower triangular matrices on the Cesàro weighted sequence space

Abstract This paper is concerned with the problem of finding bounds for the norm of lower triangular matrix operators from l p ( w ) $l_{p}(w)$ into c p ( w ) $c_{p} (w)$ , where c p ( w ) $c_{p}(w)$ is the Cesàro weighted sequence space and ( w n ) $(w_{n})$ is a non-negative sequence. Also this problem is considered for lower triangular matrix operators from c p ( w ) $c_{p}(w)$ into l p ( w ) $l_{p} (w)$ , and the norms of certain matrix operators such as Cesàro, Nörlund and weighted mean are computed

The norm of certain matrix operators on the new difference sequence spaces II

The purpose of the present study is to introduce the sequence space[{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},]where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. The topological properties and inclusion relations of this space are studied. Moreover, the problem of finding  the norm of certain matrix operators such as Copson and Hilbert from  $l_p$ into $l_p(E,Delta)$  is  investigated

Fractional Cesaro Matrix and its Associated Sequence Space

In this research, we introduce a new fractional Cesaro matrix and investigate the topological properties of the sequence space associated with this matrix. We also introduce a fractional Gamma matrix as well and obtain some factorizations for the Hilbert operator based on Cesaro and Gamma matrices. The results of these factorizations are two new inequalities one of which is a generalized version of the well-known Hilbert's inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.WOS:0006406030000012-s2.0-8510226707