In this paper, we introduce and study a strict generalization of symmetric rings. We call ring $R$ \textit{`$P$-symmetric' } if for any $a,\, b,\, c\in R,\, abc=0$ implies $bac\in P(R)$, where $P(R)$ is the prime radical $R$. It shown that class $P$-symmetric rings lies between central generalized weakly Relations are provided some other known classes From an arbitrary ring, produce many families

This is a study of weakly integral braided fusion categories with elementary rules to determine which possess nondegenerately extensions theoretically minimal dimension, or equivalently in this case, satisfy the modular extension conjecture. We classify near-group satisfying conjecture; remaining Tambara-Yamagami provide arbitrarily large families identical violating These examples generalize r...

experimental determination of solubility and ternary phase diagram of chiral compound are of tedious and time consuming tasks, and in many cases, there is not enough experimental data for different enantiomeric compositions to access the experimental ternary phase diagram. using thermodynamic models with predictive capability, having less dependency on experimental data, affords a great advanta...

A concept of ideal extensions in ternary semigroups is introduced and throughly investigated. The connection between an ideal extensions and semilattice congruences in ternary semigroups is considered.

A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say b2, each having repeated elements. We prove some necessary conditions on b2 and show the existence of some particular BPTDs. We also give constructions of infinite families of BPTDs with b1 = 0, including families of ternary t-designs with t ≥ 3.

We investigated the impact of contextual constraint on the integration of novel word meanings into semantic memory. Adults read strongly or weakly constraining sentences ending in known or unknown (novel) words as scalp-recorded electrical brain activity was recorded. Word knowledge was assessed via a lexical decision task in which recently seen known and unknown word sentence endings served as...

We show that every simple, (weakly) connected, possibly directed and infinite, hypergraph has a unique prime factor decomposition with respect to the (weak) Cartesian product, even if it has infinitely many factors. This generalizes previous results for graphs and undirected hypergraphs to directed and infinite hypergraphs. The proof adopts the strategy outlined by Imrich and Žerovnik for the c...

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ, or are weakly rigid. As a consequence we obtain that ...

We introduce the notion of L2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that L2-rigidity passes to normalizers and is satisfied by nonamenable II1 factors which are non-prime, have property Γ , or are weakly rigid. As a consequence we obtain tha...