Presenting Unemployment in Principles Classes: Micro and Macro Perspectives

The interpretation of unemployment can differ, depending on whether it is presented in a micro or macro context. Instead of glossing over these different perspectives, instructors can expound on them as a means to reinforce basic graphical analysis, to introduce or review the distinction between stocks and flows, and to discuss policy issues related to unemployment, the measurement of unemployment and the labor market.unemployment, labor market, minimum wage, stocks and flows

Dynamical zeta functions and Kummer congruences

We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to settle positively the question of the existence of a map T such that the number of fixed points of the n-th iterate of T is equal to the absolute value of the 2n-th Euler number. Also we solve a problem of Gabcke related to the coefficients of Riemann-Siegel formula.Comment: 12 pages, AMS-LaTe

Self-dual formulations of d=3 gravity theories in the path-integral framework

We study the connection, at the quantum level, between d=2+1 dimensional self-dual models with actions of growing (from first to fourth) order, governing the dynamics of helicity +2 (or -2) massive excitations. We obtain identities between generating functionals of the different models using the path-integral framework, this allowing to establish dual maps among relevant vacuum expectation values. We check consistency of these v.e.v.'s with the gauge invariance gained in each mapping.Comment: 26 pages. LaTeX. Minor changes. Published in Int. J Modern Phys. A; http://www.worldscinet.com/ijmp

Algorithms for determining integer complexity

We present three algorithms to compute the complexity $\Vert n\Vert$ of all natural numbers $n\le N$. The first of them is a brute force algorithm, computing all these complexities in time $O(N^2)$ and space $O(N\log^2 N)$. The main problem of this algorithm is the time needed for the computation. In 2008 there appeared three independent solutions to this problem: V. V. Srinivas and B. R. Shankar [11], M. N. Fuller [7], and J. Arias de Reyna and J. van de Lune [3]. All three are very similar. Only [11] gives an estimation of the performance of its algorithm, proving that the algorithm computes the complexities in time $O(N^{1+\beta})$, where $1+\beta =\log3/\log2\approx1.584963$. The other two algorithms, presented in [7] and [3], were very similar but both superior to the one in [11]. In Section 2 we present a version of these algorithms and in Section 4 it is shown that they run in time $O(N^\alpha)$ and space $O(N\log\log N)$. (Here $\alpha = 1.230175$). In Section 2 we present the algorithm of [7] and [3]. The main advantage of this algorithm with respect to that in [11] is the definition of kMax in Section 2.7. This explains the difference in performance from $O(N^{1+\beta})$ to $O(N^\alpha)$. In Section 3 we present a detailed description a space-improved algorithm of Fuller and in Section 5 we prove that it runs in time $O(N^\alpha)$ and space $O(N^{(1+\beta)/2}\log\log N)$, where $\alpha=1.230175$ and $(1+\beta)/2\approx0.792481$.Comment: 21 pages. v2: We improved the computations to get a better bound for $\alpha

Reactions induced by 9^9Be in a four-body continuum-discretized coupled-channels framework

We investigate the elastic scattering of $^9$Be on $^{208}$Pb at beam energies above (50 MeV) and below (40 MeV) the Coulomb barrier. The reaction is described within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The $^9$Be projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Our calculations confirm the importance of continuum effects at low energies.Comment: 2 pages, 1 figure. Proceedings of the International Scientific Meeting on Nuclear Physics, RABIDA15, La R\'abida (Spain), June 1-5, 201