Analytic derivation of the map of null rays passing near a naked singularity

Recently the energy emission from a naked singularity forming in spherical dust collapse has been investigated. This radiation is due to the particle creation in a curved spacetime. In this discussion, the central role is played by the mapping formula between the incoming and the outgoing null coordinates. For the self-similar model, this mapping formula has been derived analytically. But for the model with $C^{\infty}$ density profile, the mapping formula has been obtained only numerically. In the present paper, we argue that the singular nature of the mapping is determined by the local geometry around the point at which the singularity is first formed. If this is the case, it would be natural to expect that the mapping formula can be derived analytically. In the present paper, we analytically rederive the same mapping formula for the model with $C^{\infty}$ density profile that has been earlier derived using a numerical technique.Comment: 4 pages, submitted to Phys. Rev.

Can we see naked singularities?

We study singularities which can form in a spherically symmetric gravitational collapse of a general matter field obeying weak energy condition. We show that no energy can reach an outside observer from a null naked singularity. That means they will not be a serious threat to the Cosmic Censorship Conjecture (CCC). For the timelike naked singularities, where only the central shell gets singular, the redshift is always finite and they can in principle, carry energy to a faraway observer. Hence for proving or disproving CCC the study of timelike naked singularities will be more important. Our results are very general and are independent of initial data and the form of the matter.Comment: 10 page

Application or Tab Switching via Mouse Hover and Scroll

Many computer users use several applications simultaneously for various tasks. Switching between applications or browser tabs is cumbersome and requires the user to lift their fingers off the keyboard, move the cursor to the target application via a pointing device, and click the pointing device. This disclosure describes techniques that enable a user to rapidly switch between applications or browser tabs using the scroll of a mouse or a trackpad. The user can simply hover the mouse pointer over the system taskbar or browser tab-bar and scroll the mouse or trackpad to switch between apps or tabs

Updating the Taskbar with Contextual Actions Relevant to the Application in Focus

Users perform a variety of actions when interacting with a software application via various user interface (UI) controls provided by the application to perform operations corresponding to the actions. Differences in user interfaces across applications and the requirement to perform complex actions such as multi-click can be confusing and cumbersome. Users benefit from quick and easy access to high-priority contextual actions. This disclosure describes a dynamically updating taskbar provided by a device operating system. With user permission, the taskbar changes dynamically based on the currently active application as the user switches between applications. The taskbar provides quick access to the most important interactive elements within the application in focus (and optionally, the specific task being performed), such as specific buttons or controls. When the user switches to a different application, the interactive elements shown on the taskbar are updated with the appropriate interactive elements corresponding to the new application in focus

Quantum general relativity and Hawking radiation

In a previous paper we have set up the Wheeler-DeWitt equation which describes the quantum general relativistic collapse of a spherical dust cloud. In the present paper we specialize this equation to the case of matter perturbations around a black hole, and show that in the WKB approximation, the wave-functional describes an eternal black hole in equilibrium with a thermal bath at Hawking temperature.Comment: 13 pages, minor revisions in: (i) para 5 of Introduction, (ii) para following Eqn. (10). Revised version to appear in Phys. Rev.

HPTLC METHOD VALIDATION FOR DETECTION AND QUANTIFICATION OF BETULINIC ACID IN ANCISTROCLADUS HEYNEANUS WALL EX. J. GRAHAM

Objective: The present study aims at standardization of Thin Layer Chromatography (TLC) parameters and Validation of High Performance Thin Layer Chromatography (HPTLC) method for detection and quantification of Betulinic Acid (BA) in Ancistrocladus heyneanus Wall ex. J. Graham. Methods: HPTLC was performed on 20x10 cm HPTLC Plates coated with Silica gel 60 F254 using mobile phase Toluene: Ethyl Acetate: Methanol (16:2:2 v/v) and Anisaldehyde Sulphuric acid as derivatizing agent. The double developed plate was scanned at 540 nm for determination of Rf values and absorbance spectra corresponding to each band. The Method Validation was carried out according to ICH (International Conference on Harmonization) guidelines. The standard of Betulinic acid assayed along with sample for determination of concentration of Betulinic acid in stem extract. Results and Discussion: The TLC parameters were standardized and the Rf of BA was determined to be 0.67. The validation data was scrutinized. The values of Linearity (r2> 0.99), Method precision (% RSD=1.41), Intermediate precision (% RSD- 2.55-3.29), Accuracy (% recovery 93.6) were determined. The concentration of Betulinic Acid in the Stem extract of Ancistrocladus heyneanus was found to be 0.05 %. Conclusion: The results of Method Validation obtained found satisfactory and indicate the successful validation of HPTLC method for Quantitative determination of Betulinic Acid (BA) from stem extract of Ancistrocladus heyneanus Wall ex. J. Graham

Divergence of the Quantum Stress Tensor on the Cauchy Horizon in 2-d Dust Collapse

We prove that the quantum stress tensor for a massless scalar field in two dimensional non-selfsimilar Tolman Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular co-ordinates in the corresponding four dimensional spherical model.Comment: 16 pages, no figures, LaTeX fil

Preliminary in-vitro evaluation of marketed formulations for antacid activity

Background: Hydrochloric acid (pH 1.5-3.5) being the major component of gastric acid is produced by parietal cells of stomach. Its secretion is a complex and relatively energetically expensive process. The preservation of acidity of stomach is evidently important because of its implications in peptic and duodenal ulceration.Methods: In the present study, we attempted to compare the activity of 13 (F1-F13) antacid formulations (5-liquid, 4- quick releases and 4- tablets) by using acid-base neutralization studies. Preliminary antacid test (PAT) was performed to define whether the given formulation falls under the category of antacid wherein the pH of the antacid-acid (HCl) solution should be higher than pH of 3.5. The chosen antacids were further subjected to acid neutralizing capacity (ANC) (reaction between the sample of antacid and amount of acid neutralized by the formulation) and acid neutralizing potential (ANP) which explains the time duration during which a given sample of antacid can maintain pH above 3.5).Results: Out of the 13 samples tested, two formulations of pastels (F6, F12) were rejected as per the standard protocol of classifying formulations as antacids after screening for PAT. Sample F5 was found to have the highest ANC. F7 also showed highest ANC among the tablets tested. Also, F13 showed better ANC and ANP as in comparison to other quick releases.Conclusions: Digene products (F5, F7, and F13) showed better antacid properties. This data would provide insights into development of drug, comparison between antacids depending on their chemical formulation and determination of dosage to avoid plausible side effects

Gravitational Collapse, Black Holes and Naked Singularities

This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed.Comment: 17 pages, Latex File. Based on a talk given at the Discussion Workshop on Black Holes, Bangalore, 9-12 Dec. 1997, to appear in the Conference Proceeding