NLS Bifurcations on the bowtie combinatorial graph and the dumbbell metric graph

We consider the bifurcations of standing wave solutions to the nonlinear Schr\"odinger equation (NLS) posed on a quantum graph consisting of two loops connected by a single edge, the so-called dumbbell, recently studied by Marzuola and Pelinovsky. The authors of that study found the ground state undergoes two bifurcations, first a symmetry-breaking, and the second which they call a symmetry-preserving bifurcation. We clarify the type of the symmetry-preserving bifurcation, showing it to be transcritical. We then reduce the question, and show that the phenomena described in that paper can be reproduced in a simple discrete self-trapping equation on a combinatorial graph of bowtie shape. This allows for complete analysis both by geometric methods and by parameterizing the full solution space. We then expand the question, and describe the bifurcations of all the standing waves of this system, which can be classified into three families, and of which there exists a countably infinite set

Observational asteroseismology of hot subdwarf stars

Hot subdwarf stars are particularly challenging for asteroseismology due to their rapid pulsation periods, intrinsic faintness and relative rarity both in the field and in clusters. These features have ensured that the preferred method of observation up to now has been white-light photometry, and all asteroseismological solutions to date have been made by model fitting of the frequency spectrum. Several attempts have been made to perform asteroseismology using time-resolved spectroscopy on the brightest of these stars, but with modest results. A few attempts at simultaneous multi-color photometry have also been made to identify modes with the amplitude ratio method. We will review the most recent observational results and progress in improving the observational methods for ground-based asteroseismology of these compact pulsators.Comment: 8 pages, to appear in Astronomische Nachrichten, Vol. 331, 102

Gluon Fragmentation to Gluonium

The fragmentation of gluons to gluonium states is analyzed qualitatively in the non-perturbative region. The convolution of this mechanism with perturbative gluon radiation leaves us with a hard component in the fragmentation of gluon to gluonium.Comment: 6 pages with 2 figures, LaTe

Price flexibility and full employment: a common misconception

This paper highlights and builds upon Michio Morishima’s sadly neglected thesis that multi-market economies should be envisaged, and modelled, as over-determined systems, in that the number of conditions to be satisfied for equilibrium exceeds the number of unknowns (equilibrium prices and quantities) to be discovered. This understanding undermines the comfortable supposition (underpinning both New Keynesian and New Classical theoretical approaches) that, even when the economy is not in a position of full employment, a potential equilibrium solution does exist which - if not instantly, at least eventually – will be achieved by market forces. In other words, contrary to the conventional view, observed price and wage stickiness should be considered as contributing to macroeconomic stability rather than inhibiting adjustment to full employment equilibrium. A further casualty of the Morishima perspective is the common textbook rationalisation that the Keynes theory applies only in the short run (with sticky prices) while the classical analysis comes into its own (with flexible prices) in the longer term.Price flexibility; General equilibrium (macro) models; Walras' Law and Say's Law; Over-determined systems

Forecasts 1985

An abstract for this article is not availableForecasting

How useful are consumer surveys as macroeconomic indicators?

Most economic indicators attempt to summarize what happened at a particular time in the past. Consumer surveys, however, examine attitudes and are thus fundamentally different from other widely reported indicators. Some surveys, such as those that measure inflation expectations, have proven to be useful to economists and policymakers, while the evidence is more mixed for others, such as forecasts of consumer spending.Business cycles ; Economic conditions

The national income and product accounts

Macroeconomics

Personal saving behavior and real economic activity

Consumers ; Saving and investment