Class Problem!: Why the Inconsistent Application of Rule 23\u27s Class Certification Requirements During Overbreadth Analysis is a Threat to Litigant Certainty

Rule 23 of the Federal Rules of Civil Procedure is home to the class action device. It is well-documented that this rule significantly impacts our legal system. As a result, the need for its effective utilization has been apparent since its introduction. Despite this, federal courts have inconsistently applied the rule during their analyses of overbroad class definitions at the class certification stage. Consequently, parties involved in such litigation have been exposed to unnecessary costs and the potential for forum shopping. Nonetheless, this judicial inconsistency has gone largely unrecognized because it does not implicate the results of class certification. Hence, courts here must first recognize the general need for uniformity before a precise standard for overbreadth analysis may be chosen. Only then, this Note argues, may the aforementioned detrimental consequences be avoided

Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions

We consider the reduction of the duality invariant approach to M-theory by a U-duality group valued Scherk-Schwarz twist. The result is to produce potentials for gauged supergravities that are normally associated with non-geometric compactifications. The local symmetry reduces to gauge transformations with the gaugings exactly matching those of the embedding tensor approach to gauged supergravity. Importantly, this approach now includes a nontrivial dependence of the fields on the extra coordinates of the extended space.Comment: 22 pages Latex; v2: typos corrected and references adde

6'-Methoxy Raloxifene-analog enhances mouse bone properties with reduced estrogen receptor binding

Raloxifene (RAL) is an FDA-approved drug used to treat osteoporosis in postmenopausal women. RAL suppresses bone loss primarily through its role as a selective estrogen receptor modulator (SERM). This hormonal estrogen therapy promotes unintended side effects, such as hot flashes and increased thrombosis risk, and prevents the drug from being used in some patient populations at-risk for fracture, including children with bone disorders. It has recently been demonstrated that RAL can have significant positive effects on overall bone mechanical properties by binding to collagen and increasing bone tissue hydration in a cell-independent manner. A Raloxifene-Analog (RAL-A) was synthesized by replacing the 6-hydroxyl substituent with 6-methoxy in effort to reduce the compound's binding affinity for estrogen receptors (ER) while maintaining its collagen-binding ability. It was hypothesized that RAL-A would improve the mechanical integrity of bone in a manner similar to RAL, but with reduced estrogen receptor binding. Molecular assessment showed that while RAL-A did reduce ER binding, downstream ER signaling was not completely abolished. In-vitro, RAL-A performed similarly to RAL and had an identical concentration threshold on osteocyte cell proliferation, differentiation, and function. To assess treatment effect in-vivo, wildtype (WT) and heterozygous (OIM+/-) female mice from the Osteogenesis Imperfecta (OI) murine model were treated with either RAL or RAL-A from 8 weeks to 16 weeks of age. There was an untreated control group for each genotype as well. Bone microarchitecture was assessed using microCT, and mechanical behavior was assessed using 3-point bending. Results indicate that both compounds produced analogous gains in tibial trabecular and cortical microarchitecture. While WT mechanical properties were not drastically altered with either treatment, OIM+/- mechanical properties were significantly enhanced, most notably, in post-yield properties including bone toughness. This proof-of-concept study shows promising results and warrants the exploration of additional analog iterations to further reduce ER binding and improve fracture resistance

The local symmetries of M-theory and their formulation in generalised geometry

In the doubled field theory approach to string theory, the T-duality group is promoted to a manifest symmetry at the expense of replacing ordinary Riemannian geometry with generalised geometry on a doubled space. The local symmetries are then given by a generalised Lie derivative and its associated algebra. This paper constructs an analogous structure for M-theory. A crucial by-product of this is the derivation of the physical section condition for M-theory formulated in an extended space.Comment: 20 pages, v2: Author Name corrected, v3: typos correcte

Strings and branes are waves

We examine the equations of motion of double field theory and the duality manifest form of M-theory. We show the solutions of the equations of motion corresponding to null pp-waves correspond to strings or membranes from the usual spacetime perspective. A Goldstone mode analysis of the null wave solution in double field theory produces the equations of motion of the duality manifest string.Comment: 31 pages, LaTex, v2 some typos corrected and refs adde

Wigner Function Description of the A.C.-Transport Through a Two-Dimensional Quantum Point Contact

We have calculated the admittance of a two-dimensional quantum point contact (QPC) using a novel variant of the Wigner distribution function (WDF) formalism. In the semiclassical approximation, a Boltzman-like equation is derived for the partial WDF describing both propagating and nonpropagating electron modes in an effective potential generated by the adiabatic QPC. We show that this quantum kinetic approach leads to the well-known stepwise behavior of the real part of the admittance (the conductance), and of the imaginary part of the admittance (the emittance), in agreement with the latest results, which is determined by the number of propagating electron modes. It is shown, that the emittance is sensitive to the geometry of the QPC, and can be controlled by the gate voltage. We established that the emittance has contributions corresponding to both quantum inductance and quantum capacitance. Stepwise oscillations in the quantum inductance are determined by the harmonic mean of the velocities for the propagating modes, whereas the quantum capacitance is a significant mesoscopic manifestation of the non-propagating (reflecting) modes.Comment: 23 pages (latex), 3 figure

Single-Electron Spectroscopy

Contains an introduction, reports on four research projects and a list of publications,Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Young Investigator AwardU.S. Navy - Office of Naval Research Grant N00014-93-1-063

Unravelling the atomic and electronic structure of nanocrystals on superconducting Nb(110): Impact of the oxygen monolayer

The Niobium surface is almost always covered by a native oxide layer which greatly influences the performance of superconducting devices. Here we investigate the highly stable Niobium oxide overlayer of Nb(110), which is characterised by its distinctive nanocrystal structure as observed by scanning tunnelling microscopy (STM). Our ab-initio density functional theory (DFT) calculations show that a subtle reconstruction in the surface Niobium atoms gives rise to rows of 4-fold coordinated oxygen separated by regions of 3-fold coordinated oxygen. The 4-fold oxygen rows are determined to be the source of the nanocrystal pattern observed in STM, and the two chemical states of oxygen observed in core-level X-ray photoelectron spectroscopy (XPS) are ascribed to the 3-fold and 4-fold oxygens. Furthermore, we find excellent agreement between the DFT calculated electronic structure with scanning tunnelling spectroscopy and valence XPS measurements.Comment: 8 pages, 4 figures, plus 3 pages of Supporting Informatio

Duality Invariant Actions and Generalised Geometry

We construct the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation at lowest order and appropriate to spacetime dimensions four to seven. This leads to a non-linear realisation of the duality groups and introduces fields that depend on a generalised space which possess a generalised vielbein. We focus on the part of the generalised space on which the duality groups alone act and construct an invariant action.Comment: 59 pages (typos fixed and added comments

Superfluidity of "dirty" indirect excitons and magnetoexcitons in two-dimensional trap

The superfluid phase transition of bosons in a two-dimensional (2D) system with disorder and an external parabolic potential is studied. The theory is applied to experiments on indirect excitons in coupled quantum wells. The random field is allowed to be large compared to the dipole-dipole repulsion between excitons. The slope of the external parabolic trap is assumed to change slowly enough to apply the local density approximation (LDA) for the superfluid density, which allows us to calculate the Kosterlitz-Thouless temperature $T_{c}(n(r))$ at each local point $r$ of the trap. The superfluid phase occurs around the center of the trap ($\mathbf{r}=0$) with the normal phase outside this area. As temperature increases, the superfluid area shrinks and disappears at temperature $T_{c}(n(r=0))$. Disorder acts to deplete the condensate; the minimal total number of excitons for which superfluidity exists increases with disorder at fixed temperature. If the disorder is large enough, it can destroy the superfluid entirely. The effect of magnetic field is also calculated for the case of indirect excitons. In a strong magnetic field $H$, the superfluid component decreases, primarily due to the change of the exciton effective mass.Comment: 13 pages, 3 figure