Black hole polarization and new entropy bounds

Zaslavskii has suggested how to tighten Bekenstein's bound on entropy when the object is electrically charged. Recently Hod has provided a second tighter version of the bound applicable when the object is rotating. Here we derive Zaslavskii's optimized bound by considering the accretion of an ordinary charged object by a black hole. The force originating from the polarization of the black hole by a nearby charge is central to the derivation of the bound from the generalized second law. We also conjecture an entropy bound for charged rotating objects, a synthesis of Zaslavskii's and Hod's. On the basis of the no hair principle for black holes, we show that this last bound cannot be tightened further in a generic way by knowledge of ``global'' conserved charges, e.g., baryon number, which may be borne by the object.Comment: 21 pages, RevTex, Regularization of potential made clearer. Error in energy of the particle corrected with no consequence for final conclusions. New references adde

Vangl2-environment interaction causes severe neural tube defects, without abnormal neuroepithelial convergent extension

Planar cell polarity (PCP) signalling is vital for initiation of mouse neurulation, with diminished convergent extension (CE) cell movements leading to craniorachischisis, a severe neural tube defect (NTD). Some humans with NTDs also have PCP gene mutations but these are heterozygous, not homozygous as in mice. Other genetic or environmental factors may interact with partial loss of PCP function in human NTDs. We found that reduced sulfation of glycosaminoglycans interacts with heterozygosity for the Lp allele of Vangl2 (a core PCP gene), to cause craniorachischisis in cultured mouse embryos, with rescue by exogenous sulphate. We hypothesised this glycosaminoglycan-PCP interaction may regulate CE but, surprisingly, DiO labeling of the embryonic node demonstrates no abnormality of midline axial extension in sulfation-depleted Lp/+ embryos. Positive-control Lp/Lp embryos show severe CE defects. Abnormalities were detected in the size and shape of somites that flank the closing neural tube in sulfation-depleted Lp/+ embryos. We conclude that failure of closure initiation can arise by a mechanism other than faulty neuroepithelial CE, with possible involvement of matrix-mediated somite expansion, adjacent to the closing neural tube

Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes

We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-reversal of these in the case of stationary spacetimes is discussed. Further insight is gained in the case of static spacetime by considering the phenomena in a spacetime conformal to the original one. Gravi-electric and gravi-magnetic fields are studied and their relation to inertial forces is established.Comment: 21 pages, latex, no figures, http://202.41.67.76/~nayak/gpifass.te

Diagnosis and Management of Infantile Hemangioma

Infantile hemangiomas (IHs) are the most common tumors of childhood. Unlike other tumors, they have the unique ability to involute after proliferation, often leading primary care providers to assume they will resolve without intervention or consequence. Unfortunately, a subset of IHs rapidly develop complications, resulting in pain, functional impairment, or permanent disfigurement. As a result, the primary clinician has the task of determining which lesions require early consultation with a specialist. Although several recent reviews have been published, this clinical report is the first based on input from individuals representing the many specialties involved in the treatment of IH. Its purpose is to update the pediatric community regarding recent discoveries in IH pathogenesis, treatment, and clinical associations and to provide a basis for clinical decision-making in the management of IH

Charge and Spin Response of the Spin--Polarized Electron Gas

The charge and spin response of a spin--polarized electron gas is investigated including terms beyond the random phase approximation. We evaluate the charge response, the longitudinal and transverse spin response, and the mixed spin--charge response self--consistently in terms of the susceptibility functions of a non--interacting system. Exchange--correlation effects between electrons of spin $\sigma$ and $\sigma^{'}$ are included following Kukkonen and Overhauser, by using spin--polarization dependent generalized Hubbard local field factors ${G_\sigma}^{\pm}$ and ${G_{\bar\sigma}}^{\pm}$. The general condition for charge--density and spin--density--wave excitations of the system is discussed.Comment: 4 pages, latex, no figure

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Arene oxidation with malonoyl peroxides

Malonoyl peroxide 7, prepared in a single step from the commercially available diacid, is an effective reagent for the oxidation of aromatics. Reaction of an arene with peroxide 7 at room temperature leads to the corresponding protected phenol which can be unmasked by aminolysis. An ionic mechanism consistent with the experimental findings and supported by isotopic labeling, Hammett analysis, EPR investigations and reactivity profile studies is proposed

The postulates of gravitational thermodynamics

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.Comment: 28 pages, Revtex, no figures. An important sentence and several minor corrections included. To appear in Physical Review