Volt-ampere characteristics of cylindrical and spherical Langmuir probes for various potential models Scientific report

Volt-ampere characteristics of cylindrical and spherical Langmuir probes for various potential model

The Practical Approach: How the Roberts Court Has Enhanced Class Action Procedure by Strategically Carving at the Edges

This Article explores the practical impacts of the Court’s class-action jurisprudence from 30,000 feet, observing that, with some notable exceptions, the Court has nibbled away at the rough edges of class-action procedure while passing on chances to dictate more drastic reform. Part II is a chronological summary of notable Roberts Court cases that have come to define its approach toward class litigation. Perhaps surprisingly, the Court eased its way to this point, neglecting to grant certiorari in any significant class-action cases for the first four years after the swearing in of Chief Justice Roberts in 2005. That changed in 2009 when the Court began to grant certiorari over a group of cases that are widely perceived as changing the landscape of class litigation. In Part III, the Article examines the practical impacts of the Court’s class-action decisions and its certiorari denials, concluding that the Court seems to be focused on fine-tuning class-action procedure rather than ending it. The Court’s restrained attitude is reflected by a hesitancy to make broad pronouncements in the class action cases it decides and in its selectivity in choosing cases to begin with. Also in Part III, the Article explores how the Court’s reluctance to issue broad landscape-changing rulings has left breathing room for lower courts to fill in the doctrinal gaps. The Court has undeniably dictated a large amount of change in a few specific areas, especially in the arena of arbitration and class waivers. But the impact of change has been just as overstated regarding topics such as standard of review, federalism, merits consideration, employment, and overbroad classes—all areas that remain friendly enough to class actions that the procedure continues to thrive. Indeed, activity among the lower courts on class-action jurisprudence has often enabled the Court to approve of standards already in place, rather than write new class-action rules. In Part IV, the Article examines the areas of class-action opportunities that the Court either has not addressed yet or simply has overlooked. In some cases, the Court’s lack of action has enabled classaction practice to thrive, whereas in other areas, the Court’s guidance may be needed to provide clearer guidelines, much in the way the Court has done with respect to class waivers in arbitration agreements. The Article concludes by pointing out that this is not a Court that seems intent on ending class litigation or even significantly culling it. Instead, the Court appears quite comfortable pulling, tugging, and shaping the edges of class-action practice. Remarkably, though aggregate litigation looks different in many ways now than it did before the Roberts Court era, much of that change has come from the lower courts. The Supreme Court’s influence is reflected mainly in its endorsement of lower court

Factorized domain wall partition functions in trigonometric vertex models

We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: 1. The N-state Deguchi-Akutsu models, for N = {2, 3, 4} (and conjecture the result for all N >= 5), and 2. The sl(r+1|s+1) Perk-Schultz models, for {r, s = \N}, where (given the symmetries of these models) the result is independent of {r, s}.Comment: 12 page

Topologies generated by discrete subspaces

A topological space X is called discretely generated if for every subset A X we have A = {D : D A and D is a discrete subspace of X}. We say that X is weakly discretely generated if A X and A A implies D A for some discrete D A. It is established that sequential spaces, monotonically normal spaces and compact countably tight spaces are discretely generated. We also prove taht every compact space is weakly discretely generated and under the Continuum Hypothesis any dyadic discretely generated space is metrizable

Topologies generated by discrete subspaces

A topological space X is called discretely generated if for every subset A X we have A = {D : D A and D is a discrete subspace of X}. We say that X is weakly discretely generated if A X and A A implies D A for some discrete D A. It is established that sequential spaces, monotonically normal spaces and compact countably tight spaces are discretely generated. We also prove taht every compact space is weakly discretely generated and under the Continuum Hypothesis any dyadic discretely generated space is metrizable

On the domain wall partition functions of level-1 affine so(n) vertex models

We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.Comment: 14 pages, 13 figures included in latex fil

Theory of High-Tc Superconductivity: Accurate Predictions of Tc

The superconducting transition temperatures of high-Tc compounds based on copper, iron, ruthenium and certain organic molecules are discovered to be dependent on bond lengths, ionic valences, and Coulomb coupling between electronic bands in adjacent, spatially separated layers [1]. Optimal transition temperature, denoted as T_c0, is given by the universal expression $k_BT_c0 = e^2 \Lambda / \ell\zeta$; $\ell$ is the spacing between interacting charges within the layers, \zeta is the distance between interacting layers and \Lambda is a universal constant, equal to about twice the reduced electron Compton wavelength (suggesting that Compton scattering plays a role in pairing). Non-optimum compounds in which sample degradation is evident typically exhibit Tc < T_c0. For the 31+ optimum compounds tested, the theoretical and experimental T_c0 agree statistically to within +/- 1.4 K. The elemental high Tc building block comprises two adjacent and spatially separated charge layers; the factor e^2/\zeta arises from Coulomb forces between them. The theoretical charge structure representing a room-temperature superconductor is also presented.Comment: 7 pages 5 references, 6 figures 1 tabl

Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit

We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several novel routes to induce vortex lattice formation in a dipolar condensate.Comment: 12 pages with 6 figure