Explicit Pieri Inclusions

By the Pieri rule, the tensor product of an exterior power and a finite-dimensional irreducible representation of a general linear group has a multiplicity-free decomposition. The embeddings of the constituents are called Pieri inclusions and were first studied by Weyman in his thesis and described explicitly by Olver. More recently, these maps have appeared in the work of Eisenbud, Fløystad, and Weyman and of Sam and Weyman to compute pure free resolutions for classical groups. In this paper, we give a new closed form, non-recursive description of Pieri inclusions. For partitions with a bounded number of distinct parts, the resulting algorithm has polynomial time complexity whereas the previously known algorithm has exponential time complexity.

Some properties of various graphs associated with finite groups

In this paper we investigate some properties of the power graph and commuting graph associated with a finite group, using their tree-numbers. Among other things, it is shown that the simple group L2(7) can be characterized through the tree-number of its power graph. Moreover, the classification of groups with power-free decomposition is presented. Finally, we obtain an explicit formula concerning the tree-number of commuting graphs associated with the Suzuki simple groups.

Cyclopropanation Reactions of Semi-stabilized and Non-stabilized Diazo Compounds

The cyclopropane ring is present in a large number of bio­active molecules as its incorporation often greatly alters their physiochemical properties. The synthesis of such motif is therefore of interest. Diazo compounds are versatile and powerful reagents that can be used in a broad range of reactions, including cyclopropanation processes. However, in case of unstable diazo reagents such as the donor-substituted­ variants, their inherent toxicity and instability have hampered their effective synthesis and utilization. Herein, we report the recent­ advances devoted to the safe and facile production of these potentially hazardous species and their subsequent application in cyclopropanation reactions, allowing the synthesis of more complex cyclopropylated motifs.1 Introduction2 Halomethylmetal-Mediated Cyclopropanations3 Cyclopropanations through Metallic- or Free Carbenes3.1 Transition-Metal-Catalyzed Decomposition of Diazo Compounds3.2 Metal-Free Decomposition of Diazo Compounds4 Michael Induced Ring Closure (MIRC) Reactions4.1 Sulfur Ylides4.2 1,3-Dipolar Cycloadditions5 Conclusion

Model-free decomposition of transient absorption spectra into components with time-dependent shape

Disentangling overlapping spectral signatures with time-dependent shape is performed using additional information contained in ultrafast transient absorption data, without applying any assumption on the underlying kinetics.