Whitehead test modules

A (right -) module is said to be a Whitehead test module for projectivity (shortly: a p-test module) provided for each module , implies is projective. Dually, i-test modules are defined. For example, is a p-test abelian group iff each Whitehead group is free. Our first main result says that if is a right hereditary non-right perfect ring, then the existence of p-test modules is independent of ZFC + GCH. On the other hand, for any ring , there is a proper class of i-test modules. Dually, there is a proper class of p-test modules over any right perfect ring.

A non-semisimple ring is said to be fully saturated (-saturated) provided that all non-projective (-generated non-projective) modules are i-test. We show that classification of saturated rings can be reduced to the indecomposable ones. Indecomposable 1-saturated rings fall into two classes: type I, where all simple modules are isomorphic, and type II, the others. Our second main result gives a complete characterization of rings of type II as certain generalized upper triangular matrix rings, . The four parameters involved here are skew-fields and , and natural numbers . For rings of type I, we have several partial results: e.g. using a generalization of Bongartz Lemma, we show that it is consistent that each fully saturated ring of type I is a full matrix ring over a local quasi-Frobenius ring. In several recent papers, our results have been applied to Tilting Theory and to the Theory of -modules.

     

Vortex rings interacting with a wall

Accurate numerical simulations of vortex rings impinging on flat boundaries have revealed the same features observed in the experiment of Walkeret al. (1987). They observed atRe _v >1250 the formation of azimuthal instabilities in the secondary ring during its compression within the primary ring. In the present numerical simulation the number of waves agrees very well with those observed in the experiment. The distributions of the vorticities together with the distribution of each term in the vorticity equations give insights on the formation of azimuthal instabilities.     

Synthesis of novel fused isoxazoles and isoxazolines by sequential Ugi/INOC reactions

We report the synthesis of novel fused isoxazoles and isoxazolines by employing an unprecedented Ugi/INOC synthetic sequence. The coupling of the Ugi multicomponent reaction with the intramolecular N-oxide cyclization provides access to unique heterocyclic ring systems in two steps from easily available starting materials in moderate to good overall yields.     

关于Liesegang环形成机理的研究

本文研究了Ｌｉｅｓｅｇａｎｇ环的形成，受到两扩散电解质溶液的浓度比、离子浓度积及光照等条件影响。侧重对成环的微观汇聚过程进行了探讨。     

The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

Smiles rearrangement for the synthesis of 5-amino-substituted [1]benzothieno[2,3-b]pyridine

The Smiles rearrangement was successfully applied to 4-hydroxybenzo[b]thiophene furnishing a facile entry to the 4-amino derivative. The rearrangement was extended to 5-methoxy-4-methoxycarbonyl[1]benzothieno[2,3-b]pyridine obtained via aza-Wittig/electrocyclization reaction of novel N-(4-methoxybenzothiophen-2-yl)iminomethyldiphenylphosphorane with methyl trans-4-oxo-2-pentenoate. The preparation of a novel 5-amino-4-methoxycarbonyl[1]benzothieno[2,3-b]pyridine, which is of interest as a potential secondary peptide structure mimic, was successfully achieved.     

Azides in the Synthesis of Various Heterocycles

In this review, we focus on some interesting and recent examples of various applications of organic azides such as their intermolecular or intramolecular, under thermal, catalyzed, or noncatalyzed reaction conditions. The aforementioned reactions in the aim to prepare basic five-, six-, organometallic heterocyclic-membered systems and/or their fused analogs. This review article also provides a report on the developed methods describing the synthesis of various heterocycles from organic azides, especially those reported in recent papers (till 2020). At the outset, this review groups the synthetic methods of organic azides into different categories. Secondly, the review deals with the functionality of the azido group in chemical reactions. This is followed by a major section on the following: (1) the synthetic tools of various heterocycles from the corresponding organic azides by one-pot domino reaction; (2) the utility of the chosen catalysts in the chemoselectivity favoring C−H and C-N bonds; (3) one-pot procedures (i.e., Ugi four-component reaction); (4) nucleophilic addition, such as Aza-Michael addition; (5) cycloaddition reactions, such as [3+2] cycloaddition; (6) mixed addition/cyclization/oxygen; and (7) insertion reaction of C-H amination. The review also includes the synthetic procedures of fused heterocycles, such as quinazoline derivatives and organometal heterocycles (i.e., phosphorus-, boron- and aluminum-containing heterocycles). Due to many references that have dealt with the reactions of azides in heterocyclic synthesis (currently more than 32,000), we selected according to generality and timeliness. This is considered a recent review that focuses on selected interesting examples of various heterocycles from the mechanistic aspects of organic azides.     

Ni‐Catalyzed [4+3+2] Cycloaddition of Ethyl Cyclopropylideneacetate and Dienynes: Scope and Mechanistic Insights

A detailed study of the Ni‐catalyzed [4+3+2] cycloaddition reaction between ethyl cyclopropylideneacetate and dienynes has been conducted, resulting in the development of a new method for the synthesis of compounds containing nine‐membered rings. We studied the reactivity of various dienynes, together with their substituent and conformational effects. The mechanism of the reaction was probed by examining the stoichiometric reactions of the Ni complexes and dienynes.