scholarly journals Algebras of quotients with bounded evaluation of a normed semiprime algebra

2003 ◽  
Vol 154 (2) ◽  
pp. 113-135
Author(s):  
M. Cabrera ◽  
Amir A. Mohammed
Keyword(s):  
Semiprime Algebra ◽  
Bounded Evaluation

scholarly journals Bounded evaluation operators from Hpinto lq

2007 ◽  
Vol 179 (1) ◽  
pp. 1-6
Author(s):  
Martin Smith
Keyword(s):  
Bounded Evaluation

scholarly journals ACTIONS OF LIE SUPERALGEBRAS ON SEMIPRIME ALGEBRAS WITH CENTRAL INVARIANTS

2010 ◽  
Vol 52 (A) ◽  
pp. 93-102
Author(s):  
PIOTR GRZESZCZUK ◽  
MAŁGORZATA HRYNIEWICKA
Keyword(s):  
Polynomial Identity ◽  
Characteristic Zero ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Finite Dimensional ◽  
Semiprime Algebra ◽  
Algebra Over A Field

AbstractLet R be a semiprime algebra over a field of characteristic zero acted finitely on by a finite-dimensional Lie superalgebra L = L0 ⊕ L1. It is shown that if L is nilpotent, [L0, L1] = 0 and the subalgebra of invariants RL is central, then the action of L0 on R is trivial and R satisfies the standard polynomial identity of degree 2 ⋅ [$\sqrt{2^{\dim_{\mathbb{K}}L_1}}$]. Examples of actions of nilpotent Lie superalgebras, with central invariants and with [L0, L1] ≠ 0, are constructed.

scholarly journals Bounded Evaluation: Querying Big Data with Bounded Resources

2020 ◽  
Vol 17 (4) ◽  
pp. 502-526
Author(s):  
Yang Cao ◽  
Wen-Fei Fan ◽  
Teng-Fei Yuan
Keyword(s):  
Big Data ◽  
Bounded Evaluation

Bounded Graph Pattern Matching With View

2021 ◽  
Vol 2 (3) ◽  
pp. 368-387
Author(s):  
Xin Wang ◽  
Yang Wang ◽  
Ji Zhang ◽  
Yan Zhu
Keyword(s):  
Pattern Matching ◽  
Optimization Technique ◽  
Real Life ◽  
Synthetic Data ◽  
Optimization Strategy ◽  
Matching Algorithm ◽  
Graph Pattern Matching ◽  
Graph Pattern ◽  
Bounded Graph ◽  
Bounded Evaluation

Bounded evaluation using views is to compute the answers $Q({\cal D})$ to a query $Q$ in a dataset ${\cal D}$ by accessing only cached views and a small fraction $D_Q$ of ${\cal D}$ such that the size $|D_Q|$ of $D_Q$ and the time to identify $D_Q$ are independent of $|{\cal D}|$, no matter how big ${\cal D}$ is. Though proven effective for relational data, it has yet been investigated for graph data. In light of this, we study the problem of bounded pattern matching using views. We first introduce access schema ${\cal C}$ for graphs and propose a notion of joint containment to characterize bounded pattern matching using views. We show that a pattern query $\sq$ can be boundedly evaluated using views ${\cal V}(G)$ and a fraction $G_Q$ of $G$ if and only if the query $\sq$ is jointly contained by ${\cal V}$ and ${\cal C}$. Based on the characterization, we develop an efficient algorithm as well as an optimization strategy to compute matches by using ${\cal V}(G)$ and $G_Q$. Using real-life and synthetic data, we experimentally verify the performance of these algorithms, and show that (a) our algorithm for joint containment determination is not only effective but also efficient; and (b) our matching algorithm significantly outperforms its counterpart, and the optimization technique can further improve performance by eliminating unnecessary input.

π-Complementation in the Unitisation and Multiplication Algebras of a Semiprime Algebra

2012 ◽  
Vol 40 (9) ◽  
pp. 3507-3531 ◽  
Author(s):  
J. C. Cabello ◽  
M. Cabrera ◽  
R. Roura
Keyword(s):  
Semiprime Algebra

scholarly journals Making big data small

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190034 ◽  
Author(s):  
Wenfei Fan
Keyword(s):  
Big Data ◽  
Parallel Processing ◽  
Data Analytics ◽  
Big Data Analytics ◽  
Data Driven ◽  
Limited Resources ◽  
Small Companies ◽  
Small Set ◽  
Bounded Evaluation ◽  
Available Resources

Big data analytics is often prohibitively costly and is typically conducted by parallel processing with a cluster of machines. Is big data analytics beyond the reach of small companies that can only afford limited resources? This paper tackles this question by presenting Boundedly EvAlable SQL ( BEAS ), a system for querying big relations with constrained resources. The idea is to make big data small. To answer a query posed on a dataset, it often suffices to access a small fraction of the data no matter how big the dataset is. In the light of this, BEAS answers queries on big data by identifying and fetching a small set of the data needed. Under available resources, it computes exact answers whenever possible and otherwise approximate answers with accuracy guarantees. Underlying BEAS are principled approaches of bounded evaluation and data-driven approximation, the focus of this paper.

scholarly journals Identities related to generalized derivations and jordan (*,*)-derivations

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2349-2360
Author(s):  
Amin Hosseinia
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Additive Mapping ◽  
Jordan Derivation ◽  
Generalized Derivations ◽  
Free Ring ◽  
Functional Identities ◽  
Invertible Elements ◽  
Semiprime Algebra

The main purpose of this research is to characterize generalized (left) derivations and Jordan (*,*)-derivations on Banach algebras and rings using some functional identities. Let A be a unital semiprime Banach algebra and let F,G : A ? A be linear mappings satisfying F(x) =-x2G(x-1) for all x ? Inv(A), where Inv(A) denotes the set of all invertible elements of A. Then both F and G are generalized derivations on A. Another result in this regard is as follows. Let A be a unital semiprime algebra and let n > 1 be an integer. Let f,g : A ? A be linear mappings satisfying f (an) = nan-1g(a) = ng(a)an-1 for all a ? A. If g(e) ? Z(A), then f and g are generalized derivations associated with the same derivation on A. In particular, if A is a unital semisimple Banach algebra, then both f and 1 are continuous linear mappings. Moreover, we define a (*,*)-ring and a Jordan (*,*)-derivation. A characterization of Jordan (*,*)-derivations is presented as follows. Let R be an n!-torsion free (*,*)-ring, let n > 1 be an integer and let d : R ? R be an additive mapping satisfying d(an) = ?nj =1 a*n-jd(a)a* j-1 for all a ? R. Then d is a Jordan (*,*)-derivation on R. Some other functional identities are also investigated.

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