Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,bin R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpotent elements‎, ‎introducing‎ the concept of commutativity of nilpotent elements at zero (simply‎, ‎a CNZ ring)‎. ‎In this paper‎, ‎we extend the CNZ pr...

this paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical galois theory and involves generalized central extensions, commutators, and internal groupoids in barr exact mal’tsev and more general categories. galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...

A recent framework for generalizing the Erdős-KoRado Theorem, due to Holroyd, Spencer, and Talbot, defines the Erdős-Ko-Rado property for a graph in terms of the graph’s independent sets. Since the family of all independent sets of a graph forms a simplicial complex, it is natural to further generalize the Erdős-Ko-Rado property to an arbitrary simplicial complex. An advantage of working in sim...

We study the nonlinearity (NL) in the conversion from charge to voltage in infrared detectors (HXRG) for use in precision astronomy. We present laboratory measurements of the NL function of a H2RG detector and discuss the accuracy to which it would need to be calibrated in future spacemissions to perform cosmologicalmeasurements through theweak gravitational lensing technique. In addition, we p...

Phase-shifting digital holography is a digital measurement technology of a complex optical field profile that uses focal plane array detectors without the loss of bandwidth. It has been known that the accuracy of phase-shifting digital holography is limited mainly by the phase tolerance of reference. In this Letter, it is revealed that the uncertainty in an expected signal is highly dependent o...

Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting and random scaling of insurance risks focusing in particular on credibility models, dependence structure of claim sizes in collective risk models, and extre...

Two related trends characterize the recent past: value propositions are migrating from the physical to the informational, and value creation is shifting from firms to consumers. These two trends meet in the phenomenon of “consumer-generated intellectual property” (CGIP). This article addresses the question: “How should firms manage the intellectual property that their customers create?” It expl...

Proof of Proposition 1.1. The first two properties can be directly verified from the definition. The third property which will turn out to be crucial follows since applying Zf n times cycles the vector back to its original form but with all entries scaled by f . The fourth property follows becauses Zf−1 cancels the downward shift-and-scale action of Zf . The fifth property can be verified by ob...