In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry and physics. Recently Connes, Kreimer and Kontsevich have introduced LSAs in mathematical physics (QFT and renormalization theory), where the name pre-Lie algebras is used quite often. Already Cayley wrote about such algebras more than hundred years ago. Indeed, LSAs aris...

We prove that RS-BL-algebras are MV-algebras.

We show that the celebrated operad of pre-Lie algebras is very rigid: it has no non-obvious degrees freedom from either three points view: deformations maps to and graces theory, homotopy automorphisms, operadic twisting.

Methods A retrospective review was undertaken of all patients presenting to Great Ormond Street Hospital NHS Foundation Trust between 2005-2013 with active JIA of the knee resulting in FFD and loss of knee extension range of movement (ROM) greater than -15 degrees extension and underwent a stretch and cast procedure alongside IAI for treatment of their disease. ROM was assessed pre and post pro...

This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles) ...

Central to the spirit of reflective teaching is the ability to focus critically on one’s own beliefs, cognitions, and concerns. Numerous proposals have been developed for implementing reflective practices in pre-service teacher education contexts with the aim of producing highly competent reflective teachers. However, it is imperative to identify the candidates’ beliefs and knowledge base befor...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

The cytomatrix at the active zone (CAZ) has been implicated in defining the site of Ca2+-dependent exocytosis of neurotransmitter. We have identified here a novel CAZ protein of approximately 120 kD from rat brain and named it CAST (CAZ-associated structural protein). CAST had no transmembrane segment, but had four coiled-coil domains and a putative COOH-terminal consensus motif for binding to ...

ing the data and the properties of our motivating example, we now define prefactorization algebras and strict factorization algebras. In the example above, we associate to each open subset U a vector space. This is the main example we are interested in, but more generally, we will define (pre) factorization algebras with values in a monoidal category (C,⊗). Definition 4.18. Let M be a topologic...