Search results for "NOE"

ChemInform Abstract: Cycloaddition Reactions of 1-tert.-Butyl-4-vinylpyrazole.

1990

1-tert-Butyl-4-vinylpyrazole1 a reacts with dimethyl acetylenedicarboxylate (DMAD), methyl propiolate (MP) and N-phenylmaleimide (NPMI) affording the indazole derivatives2,3, and5 as a result of a Diels-Alder ([4 + 2]) cycloaddition. With diethylazodicarboxylate (DEAZD), tetracyanoethylene (TCNE) and 4-phenyl-1,2,4-triazole-3,5-dione (PTAD) the reaction takes place exclusively through the olefinic substituent and the adducts6,7, and9 were isolated. The alkenylpyrazoles1 b–d reacted withDMAD and N-phenylmaleimide to give polymers.

ChemInform Abstract: Diels-Alder Reactions of Methyl- and π-Acceptor-Substituted 2- Vinylindoles with Dimethyl Acetylenedicarboxylate and Tetracyanoe…

2010

The Diels-Alder reactions of the 2-vinylindoles 1a-1d, which are now readily accessible, with dimethyl acetylenedicarboxylate and tetracyanoethylene give rise to the novel 1,2-dihydro- and 1,2,3,4-tetrahydrocarbazoles 2, 4, and 5 as well as the fully aromatized carbazoles 3. With regard to the product spectrum, the mechanistic rationale comprises a Diels-Alder step, formal 1,3-hydrogen shift, ene reaction, and dehydrogenation. Conformational aspects of the 1,2-dihydrocarbazoles 2b and 2c are also discussed.

Diels-alder reactions of methyl- and π-acceptor-substituted 2-vinylindoles with dimethyl acetylenedicarboxylate and tetracyanoethylene: Novel functio…

1991

The Diels-Alder reactions of the 2-vinylindoles 1a-1d, which are now readily accessible, with dimethyl acetylenedicarboxylate and tetracyanoethylene give rise to the novel 1,2-dihydro- and 1,2,3,4-tetrahydrocarbazoles 2, 4, and 5 as well as the fully aromatized carbazoles 3. With regard to the product spectrum, the mechanistic rationale comprises a Diels-Alder step, formal 1,3-hydrogen shift, ene reaction, and dehydrogenation. Conformational aspects of the 1,2-dihydrocarbazoles 2b and 2c are also discussed.

Tomographical aspects of L-convex polyominoes

2007

An Efficient Algorithm for the Generation of Z-Convex Polyominoes

2014

We present a characterization of Z-convex polyominoes in terms of pairs of suitable integer vectors. This lets us design an algorithm which generates all Z-convex polyominoes of size n in constant amortized time.

Combinatorial aspects of L-convex polyominoes

2007

We consider the class of L-convex polyominoes, i.e. those polyominoes in which any two cells can be connected with an ''L'' shaped path in one of its four cyclic orientations. The paper proves bijectively that the number f"n of L-convex polyominoes with perimeter 2(n+2) satisfies the linear recurrence relation f"n"+"2=4f"n"+"1-2f"n, by first establishing a recurrence of the same form for the cardinality of the ''2-compositions'' of a natural number n, a simple generalization of the ordinary compositions of n. Then, such 2-compositions are studied and bijectively related to certain words of a regular language over four letters which is in turn bijectively related to L-convex polyominoes. In …

Recognizable picture languages and polyominoes

2007

We consider the problem of recognizability of some classes of polyominoes in the theory of picture languages. In particular we focus our attention oil the problem posed by Matz of finding a non-recognizable picture language for which his technique for proving the non-recognizability of picture languages fails. We face the problem by studying the family of L-convex polyominoes and some closed families that are similar to the recognizable family of all polyominoes but result to be non-recognizable. Furthermore we prove that the family of L-convex polyominoes satisfies the necessary condition given by Matz for the recognizability and we conjecture that the family of L-convex polyominoes is non…

Lagrangians, Hamiltonians and Noether’s Theorem

2015

This chapter is intended to remind the basic notions of the Lagrangian and Hamiltonian formalisms as well as Noether’s theorem. We shall first start with a discrete system with N degrees of freedom, state and prove Noether’s theorem. Afterwards we shall generalize all the previously introduced notions to continuous systems and prove the generic formulation of Noether’s Theorem. Finally we will reproduce a few well known results in Quantum Field Theory.

Reconstruction of L-convex Polyominoes.

2003

Abstract We introduce the family of L-convex polyominoes, a subset of convex polyominoes whose elements satisfy a special convexity property. We develop an algorithm that reconstructs an L-convex polyomino from the set of its maximal L-polyominoes.

Enumeration of L-convex polyominoes by rows and columns

2005

In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.