Some identities on derangement and degenerate derangement polynomials

In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate versions of the companions we introduce derangement polynomials and degenerate derangement polynomials. We give some of their properties, recurrence relations and identities for those polynomials which are related to some special numbers and polynomials.Comment: 12 page

Social Context Modulates Tolerance For Pragmatic Violations In Binary But Not Graded Judgments

A common method for investigating pragmatic processing and its development in children is to have participants make binary judgments of underinformative (UI) statements such as Some elephants are mammals. Rejection of such statements indicates that a (not-all) scalar implicature has been computed. Acceptance of UI statements is typically taken as evidence that the perceiver has not computed an implicature. Under this assumption, the results of binary judgment studies in children and adults suggest that computing an implicature may be cognitively costly. For instance, children under 7 years of age are systematically more likely to accept UI statements compared to adults. This makes sense if children have fewer processing resources than adults. However, Katsos and Bishop (2011) found that young children are able to detect violations of informativeness when given graded rather than binary response options. They propose that children simply have a greater tolerance for pragmatic violations than do adults. The present work examines whether this pragmatic tolerance plays a role in adult binary judgment tasks. We manipulated social attributes of a speaker in an attempt to influence how accepting a perceiver might be of the speaker’s utterances. This manipulation affected acceptability rates for binary judgments (Experiment 1) but not for graded judgments (Experiment 2). These results raise concerns about the widespread use of binary choice tasks for investigating pragmatic processing and undermine the existing evidence suggesting that computing scalar implicatures is costly

The employment effect in retail trade of California's 1988 minimum wage increase

In this paper, the authors study the outcome of an unusually clean natural experiment--California's large minimum wage increase of 1988. Two different approaches to evaluating the experiment result in the same conclusion: the textbook analysis of minimum wages holds true. In particular, the authors find that employment growth in California's low-wage retail trade industry was slowed by the minimum wage increase.

A criterion for the nature of the superconducting transition in strongly interacting field theories : Holographic approach

It is beyond the present techniques based on perturbation theory to reveal the nature of phase transitions in strongly interacting field theories. Recently, the holographic approach has provided us with an effective dual description, mapping strongly coupled conformal field theories to classical gravity theories. Resorting to the holographic superconductor model, we propose a general criterion for the nature of the superconducting phase transition based on effective interactions between vortices. We find "tricritical" points in terms of the chemical potential for U(1) charges and an effective Ginzburg-Landau parameter, where vortices do not interact to separate the second order (repulsive) from the first order (attractive) transitions. We interpret the first order transition as the Coleman-Weinberg mechanism, arguing that it is relevant to superconducting instabilities around quantum criticality.Comment: 7 pages, 7 figure

Thermal stability of metastable magnetic skyrmions: Entropic narrowing and significance of internal eigenmodes

We compute annihilation rates of metastable magnetic skyrmions using a form of Langer's theory in the intermediate-to-high damping (IHD) regime. For a N\'eel skyrmion, a Bloch skyrmion, and an antiskyrmion, we look at two possible paths to annihilation: collapse and escape through a boundary. We also study the effects of a curved vs. a flat boundary, a second skyrmion and a non-magnetic defect. We find that the skyrmion's internal modes play a dominant role in the thermally activated transitions compared to the spin-wave excitations and that the relative contribution of internal modes depends on the nature of the transition process. Our calculations for a small skyrmion stabilized at zero-field show that collapse on a defect is the most probable path. In the absence of a defect, the annihilation is largely dominated by escape mechanisms, even though in this case the activation energy is higher than that of collapse processes. Escape through a flat boundary is found more probable than through a curved boundary. The potential source of stability of metastable skyrmions is therefore found not to lie in high activation energies, nor in the dynamics at the transition state, but comes from entropic narrowing in the saddle point region which leads to lowered attempt frequencies. This narrowing effect is found to be primarily associated with the skyrmion's internal modes.Comment: 14 pages, 9 figure

Resonance enhanced turbulent transport

The effect of oscillatory shear flows on turbulent transport of passive scalar fields is studied by numerical computations based on the results provided by E. Kim [Physics of Plasmas 13, 022308 (2006)] . Turbulent diffusion is found to depend crucially on the competition between suppression due to shearing and enhancement due to resonances, depending on the characteristic time and length scales of shear flow and turbulence. Enhancements in transport occur for turbulence with finite memory time either due to Doppler or parametric resonances. Scalings of turbulence amplitude and transport are provided in different parameter spaces. The results suggest that oscillatory shear flows are not only less efficient in regulating turbulence, but also can enhance the value of turbulent diffusion, accelerating turbulent transport

Thermodynamics and kinetics of the undercooled liquid and the glass transition of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy

Differential scanning calorimetry (DSC) was used to determine the thermodynamic functions of the undercooled liquid and the amorphous phase with respect to the crystalline state of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5bulk metallic glass forming alloy. The specific heat capacities of this alloy in the undercooled liquid, the amorphous state and the crystal were determined. The differences in enthalpy, ∆H, entropy, ∆S, and Gibbs free energy, ∆G, between crystal and the undercooled liquid were calculated using the measured specific heat capacity data as well as the heat of fusion. The results indicate that the Gibbs free energy difference between metastable undercooled liquid and crystalline solid, ∆G, stays small compared to conventional metallic glass forming alloys even for large undercoolings. Furthermore, the Kauzmann temperature, TK, where the entropy of the undercooled liquid equals to that of the crystal, was determined to be 560 K. The Kauzmann temperature is compared with the experimentally observed rate-dependent glass transition temperature, Tg. Both onset and end temperatures of the glass transition depend linearly on the logarithm of the heating rate based on the DSC experiments. Those characteristic temperatures for the kinetically observed glass transition become equal close to the Kauzmann temperature in this alloy, which suggests an underlying thermodynamic glass transition as a lower bound for the kinetically observed freezing process