Determination of stochastic vs. deterministic trend in quarterly GDP of Pakistan

Many economic and financial time series show evidence of trending behavior or non stationarity in the mean. An important econometric goal is determining the most proper form of the trend in the data. The transformations of series depend on whether the series is trend stationary or difference stationary. In this paper, study is conducted to declare the nature of trend component in quarterly GDP of Pakistan whether it is trend stationary or difference stationary. It is necessary to know, because trend stationary and difference stationary models imply very different short run and long run dynamics. We have explored the type of trend in GDP series by ADF unit root test and also support our arguments by empirical distribution instead of asymptotical ones i.e., bootstrapping test. The purpose of the paper is not only to investigate the type of trend in the series by conventional methods but also to motivate small distribution theory like bootstrapping techniques that can helps ones in selection of advocate model for observed series.Bootstrapping, Stationarity, Pivotal statistic, Unit root

General Relativity Constraints the Proper Times and Predicts the Frozen Stars Instead of the Black Holes

In a static gravitational field an intersection of a worldline by a global hypersurface of simultaneity t=const gives an invariant constraint relating the proper time of this event by t. Since at any finite t the such constrained proper time intervals are less than reqiured for crossing a horizon, general relativity predicts the gravitational freezing of proper times in stars with time-like or null geodesics everywhere. The time dilation stabilizes contracting massive stars by freezing, which is maximal but finite at the centre, and the surface is frozen near the gravitational radius. The frozen stars (frozars) slowly defrost due to emissions and external interactions, the internal phase transitions can initiate refreezing with bursts and explosions.Comment: 10 pages. Submitted to Phys. Lett. B. Reviesed versio

Didacticism and the Male Reader in Samuel Richardson\u27s Pamela

In lieu of an abstract, below is the first paragraph of the paper. One might say that Samuel Richardson\u27s 18th century novel Pamela is essentially a love story that, like the chick lit of today, appeals mostly to a female audience. Contrary to the stereotype that women were the only ones who liked reading such works is the fact that males were also avid novelreaders. Admittedly, male readership is often a barely-trodden segment in the pathway of the study of novels - particularly novels such as Pamela, Frances Burney\u27s Evelina, and Thomas Hardy\u27s Tess of the D\u27Urbervilles. Considering Richardson\u27s emphasis on virtue, submissiveness, and obedience, it\u27s fairly straightforward to determine the messages that female readers are supposed to get from reading Pamela. The message intended for male readers, however, may be a bit more complicated. Young women know what they\u27re supposed to get from Richardson\u27s text, but male readers don\u27t, which means that multiple messages can be acquired from reading Pamela from a male perspectiv

Gravitation as a Quantum Diffusion

Inhomogeneous Nelson's diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold with this tensor of diffusion as a metric tensor. The influence of matter to the energy density of the stochastic background (vacuum) is considered. It is shown that gravitation can be represented as inhomogeneity of the quantum diffusion, the Einstein equations for the metrics can be derived as the equations for the corresponding tensor of diffusion.Comment: Published in: "Z.Zakir (2003) Structure of Space-Time and Matter, CTPA, Tashkent.

Simultaneous zeros of a Cubic and Quadratic form

We verify a conjecture of Emil Artin, for the case of a Cubic and Quadratic form over any $p$-adic field, provided the cardinality of the residue class field exceeds 293. That is any Cubic and Quadratic form with at least 14 variables has a non-trivial $p$-adic zero, with the aforementioned condition on the residue class field. A crucial step in the proof, involves generalizing a $p$-adic minimization procedure due to W. M. Schmidt to hold for systems of forms of arbitrary degrees.Comment: 19 page