let $g$ be an infinite group and $nin {3‎, ‎6}cup{2^k| kin mathbb{n}}$‎. ‎in this paper‎, ‎we prove that $g$ is an $n$-kappe group if and only if for any two infinite subsets $x$ and $y$ of $g$‎, ‎there exist $xin x$ and $yin y$ such that $[x^n‎, ‎y‎, ‎y]=1$‎.

Perception of olfactory stimuli is mediated by distinct populations of olfactory sensory neurons, each with a characteristic set of morphological as well as functional parameters. Beyond two large populations of ciliated and microvillous neurons, a third population, crypt neurons, has been identified in teleost and cartilaginous fishes. We report here a novel, fourth olfactory sensory neuron po...

The fields of combinatorial and automated medicinal chemistry have emerged to meet the increasing requirement of new compounds for drug discovery, where speed is of the essence (Loupy, 2002). In this regard, domino (or tandem, or cascade) reactions where “two or more bond-forming transformations take place under the same reaction conditions without adding additional reagents and catalysts, and ...

Microwave dielectric heating was firstly reported on the use in organic chemistry by Gedye (Gedye, R. et al., 1986) and Giguere/Majetich (Giguere, R. J. et al., 1986) in the mid-1980s. However, it takes a long time before the wide application of this technology in the late 1980s and early 1990s. This has been principally attributed to the lack of controllability and reproducibility of the initi...

Languages differ in how they categorize spatial relations: While German differentiates between containment (in) and support (auf) with distinct spatial words-(a) den Kuli IN die Kappe stecken ("put pen in cap"); (b) die Kappe AUF den Kuli stecken ("put cap on pen")-Korean uses a single spatial word (kkita) collapsing (a) and (b) into one semantic category, particularly when the spatial enclosur...

Levi-properties were first introduced by L. C. Kappe and are modeled after groups investigated by F. W. Levi where conjugates commute. Let X be a group theoretic class. A group is in the derived class L(X) if the normal closure of each element in the group is an X -group. The property of being in the class L (X) is called the Levi-property generated by X . In the case where X is a variety, we s...

Advanced process analytics are becoming an increasingly important part of continuous flow chemistry. In their Research Article on page 8139, Jason D. Williams, C. Oliver Kappe and co-workers describe the use four different analytical technologies, controlled by one central system, in a multistep process. data processing methods, including artificial intelligence, used to accurately quantify up ...