Solutions of Conformal Turbulence on a Half Plane

Exact solutions of conformal turbulence restricted on a upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tunning of coefficients. The simplest solution in our case is given by the minimal model of $p=2, q=33$ and moreover we find a fixed point of solutions when $p,q$ become large.Comment: 10pages, KHTP-93-07, SNUCTP-93-3

A model comparison of resonance lifetime modifications, a soft equation of state and non-Gaussian effects on π−π\pi-\pi correlations at FAIR/AGS energies

HBT correlations of $\pi^--\pi^-$ pairs at FAIR/AGS energies are investigated by using the UrQMD transport model and the CRAB analyzing program. Three different possible sources (treatment of resonance lifetimes, a soft equation of state and non-Gaussian effects) to understand the HBT $R_O/R_S$ puzzle are investigated. Firstly, we find that different treatments of the resonance decay time can not resolve the HBT time-related puzzle, however it can modify the HBT radii at low transverse momenta to some extent to explain the data slightly. Secondly, with a soft equation of state with momentum dependence, the measured transverse momentum dependent HBT radii and $R_O/R_S$ ratio can be described fairly well. Thirdly, non-Gaussian effects are visible in the calculated correlation function. Using the Edgeworth expansion, one finds that the non-Gaussian effect is strongest in the longitudinal direction and weakest in the sideward direction.Comment: 18 pages, 6 figures. To be published in J.Phys.

Legal Bills That Make Sense: A Case of a Strategic Pricing DSS

The complexity and heterogeneity of today\u27s world have resulted in an increasingly litigious society which finds a growing need for more lawyers. In the midst of such growth, many law firms are challenged by their clients over their legal bills. Problematic billing practices are not a secret in the law practitioners\u27 circle [4][7][10][16]. The amount of legal fees paid to a lawyer is typically determined by such factors as the lawyer\u27s specialty, education, experience, title, and reputation. Although clients would hire a law firm that would charge less, the cost alone is not a deciding factor when selecting attorneys, which implies that a low price or a good pricing strategy may not be a core competence [11][12] for a law firm. Nevertheless, a good pricing strategy coupled with reliable analytical techniques remains an important business factor. Take legal fee disputes for instance. As the demographics of clients shift from individuals to corporations, more clients can afford the financial and human resources to fight their legal bills [1][2][5][7][10][22]. This trend calls for a serious reconsideration on how to structure and determine legal fees, not simply because of disputes and nuisance but because the billing process must be approached from a strategic point of view so that legal bills may make sense for both the law firms and the clients. In the law practitioner\u27s community, numerous forums are being reported surrounding the issue of how to structure legal fees [13][17][18][24]. This phenomenon clearly indicates two facts: (i) there is no consensus among law practitioners on how legal fees should be determined, and (ii) a \u27system\u27 or a rational model of fee determination is acutely in need. While various methods are currently employed by law practitioners for different types of services, they can be categorized into a few groups. The most popular billing method is called \u27hourly billing.\u27 Legal fees are calculated by multiplying a predetermined hourly rate by the number of hours the lawyer spends on the case. While law firms find it inadequate to set fees arbitrarily (which they do), surveys confirm that this billing method is predominant [8][24]. As this approach was found inappropriate in some special cases, several alternative billing methods were introduced. Such alternative methods are often referred to as \u27value billing.\u27 Three commonly used value billingapproaches are: fixed fees, unconventional time-based billing, and result-based billin

Pion-photon and photon-pion transition form factors in light-cone formalism

We derive the minimal Fock-state expansions of the pion and the photon wave functions in light-cone formalism, then we calculate the pion-photon and the photon-pion transition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma$ and $\gamma ^{\ast}\gamma \to \pi ^{0}$ processes by employing these quark-antiquark wave functions of the pion and the photon. We find that our calculation for the $\gamma ^{\ast}\gamma \to \pi ^{0}$ transition form factor agrees with the experimental data at low and moderately high energy scale. Moreover, the physical differences and inherent connections between the transition form factors of $\gamma ^{\ast}\pi ^{0}\to \gamma$ and $\gamma ^{\ast}\gamma \to \pi ^{0}$ have been illustrated, which indicate that these two physical processes are intrinsically related. In addition, we also discuss the $\pi ^{0}\to \gamma \gamma$ form factor and the decay width $\mathit{\Gamma}(\pi \to \gamma \gamma)$ at $Q^{2}=0$.Comment: 20 pages, 2 figure

A Model of Occupational Licensing and Statistical Discrimination

We develop a model of statistical discrimination in occupational licensing. In the model, there is endogenous occupation selection and wage determination that depends on how costly it is to obtain the license and the productivity of the human capital that is bundled with the license. Under these assumptions, we find a unique equilibrium with sharp comparative statics for the licensing premiums. The key theoretical result in this paper is that the licensing premium is higher for workers who are members of demographic groups that face a higher cost of licensing. The intuition for this result is that the higher cost of licensing makes the license a more informative labor market signal. (This is a similar insight to Spence 1973). The predictions of the model can explain, for example, the empirical finding in the literature that occupational licenses that preclude felons close the racial wage gap among men by conferring a higher premium to black men than to white men (Blair and Chung 2018). Moreover, we show that in general the optimal cost of licensing is nonzero: an infinitely costly licenses screens out all workers, while a costless license is no screen at all