Polycondensed Heterocycles.VI. A new efficient synthesis of 4H-pyrrolo [2,1-c][1, 4] Benzothiazines

A novel and efficient method to obtain 4H-pyrrolo [2,1-c][1,4] benzothiazine and its 4-alkyl and 4-aryl derivatives via an intramolecular nucleophilic aromatic fluoride displacement has been developed.     

Active manganese dioxide promoted cyclization of ortho-(1H-pyrrol-1-yl)aryl and heteroaryl carboxylic acids to 5H-pyrrolo[1,2-a][3,1]benzoxazin-5-one derivatives

The hitherto unknown lactone 5H-pyrrolo[1,2-a][3,1]benzoxazin-5-one and six of its substituted derivatives have been prepared by active manganese dioxide promoted oxidative cyclization of the corresponding 2-(1H-pyrrol-1-yl)benzoic acids, under mild conditions, in moderate yields. The method was successfully extended to the cyclization of some ortho-(1H-pyrrol-1-yl)heteroaryl carboxylic acids and 2-(1H-indol-1-yl)benzoic acids.     

Accidental politicians: How randomly selected legislators can improve parliament efficiency

We study a prototypical model of a Parliament with two Parties or two Political Coalitions and we show how the introduction of a variable percentage of randomly selected independent legislators can increase the global efficiency of a Legislature, in terms of both the number of laws passed and the average social welfare obtained. We also analytically find an “efficiency golden rule” which allows to fix the optimal number of legislators to be selected at random after that regular elections have established the relative proportion of the two Parties or Coalitions. These results are in line with both the ancient Greek democratic system and the recent discovery that the adoption of random strategies can improve the efficiency of hierarchical organizations.     

A constant-stress,vacuum creep-testing apparatus

A mathematical analysis is presented for a direct-linkage tensile and compression creep-testing mechanism. A particular design, employing a dead weight, a cam and a linkage system, achieves constant stress in a tensile specimen during uniform creep deformation. Superiority has been achieved over previous designs in: (1) compactness with mechanical advantages up to 10:1, (2) higher structural rigidity and (3) higher sensitivity in the region of small displacements. The advantage of compactness has now made possible the successful design of a vacuum system for high-temperature creep testing at constant stress. Typical creep curves on iron specimens are induced.     

Herding as a consensus problem

In this paper, we show that herding phenomena in financial markets can be interpreted using the theoretical tools of pinning control. This is accomplished by viewing herding as a diffusion of a certain opinion in a network of financial agents, whose trading strategies dynamically depend on that of their neighbors according to a nonlinear state-dependent law. The interaction among the agents is modeled through a directed weighted graph, and following the logic of pinning control, we model the generic exogenous information triggering herding behavior as a control signal fed by an external entity to a subset of agents that, by virtue of the received information, can play the correct trading action. The topological conditions of partial pinning control theory enable us to predict the number of agents reaching consensus, i.e., the diffusion of information through the network, and thus the magnitude of the herding phenomenon triggered by the informed/pinned nodes. By testing our model of opinion dynamics in an artificial agent-based financial market, we prove that it is capable of replicating herding phenomena of different and predictable intensities.     

On the best possible character of the norm in some a priori estimates for non-divergence form equations in Carnot groups

Let be a group of Heisenberg type with homogeneous dimension . For every we construct a non-divergence form operator and a non-trivial solution to the Dirichlet problem: in , on . This non-uniqueness result shows the impossibility of controlling the maximum of with an norm of when . Another consequence is the impossiblity of an Alexandrov-Bakelman type estimate such as

where is the dimension of the horizontal layer of the Lie algebra and is the symmetrized horizontal Hessian of .