local time

It is elucidated, herein, that the cosmos is, in essence, a gigantic computer with time as the central agent that spearheads the execution of its operating software. It is composed of a core that represents an omnipotent conscious energetic reactor that supports and keeps everything at bay by imposing the constraint that everything must inevitably gravitate towards it. And, it is this very mandate of gravitation to the central SOURCE that epitomizes the phenomenon of time. Time may be depicted as a tensorial quantity, a rotating vector that can stretch while freely flowing spinning about the central SOURCE, giving rise to a continuum that reflects the body of such a Prime Creator that may be referred to as the 'cosmos.' And, as the vector of time stretches within the cosmos while freely subtending revolution about the SOURCE, it progressively congeals to create the said space continuum. It may be regarded that the process of congealment as to create space completes when the vector of time subtends a full revolution about the SOURCE. This gives rise to a curvilinear (spheroidal) surface to depict the space and the radius of its curvature to epitomize the time aspect of creation. Such a continuum of time and space is referred to as a 'dimension.' And, this process of creation of dimensions continues until a nested edifice of spheroidal surfaces is created. It is clear that the process of creation of dimensional space-time occurs in a discrete manner involving the constraint or the requisite of completion

This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal comparison method, Rice method, Stein-Chen method, a general m-dependent method] used to obtain them; these methods are also very useful in the general context of Gaussian fields. Finally some extensions [time occupation functionals, number of maxima in an interval, process indexed by a bidimensional set] are proposed, illustrating the generality of the methods. A large inventory of papers and books on the subject ends the survey.

We consider a filtering problem when the state process is a reflected Brownian motion Xt and the observation process is its local time Λs, for s ≤ t. For this model we derive an approximation scheme based on a suitable interpolation of the observation process Λt. The convergence of the approximating filter to the original one combined with an explicit con-struction of the approximating filter allows us to derive the explicit form of the original filter. The last result can be obtained also by means of the Azéma martingale.

The myopic (or `true') self-avoiding walk model (MSAW) was introduced in the physics literature by Amit, Parisi and Peliti (1983). It is a random motion in Z^d pushed towards domains less visited in the past by a kind of negative gradient of the occupation time measure. We investigate the asymptotic behaviour of MSAW in the non-recurrent dimensions. For a wide class of self-interaction functions, we identify a natural stationary (in time) and ergodic distribution of the environment (the local time profile) as seen from the moving particle and we establish diffusive lower and upper bounds for the displacement of the random walk. For a particular, more restricted class of interactions, we prove full CLT for the finite dimensional distributions of the displacement. This result settles part of the conjectures (based on non-rigorous renormalization group arguments) in Amit, Parisi and Peliti (1983). The proof of the CLT follows the non-reversible version of Kipnis-Varadhan-theory. On...

A moment magnitude (Mw) 6.2 earthquake struck beneath the outer suburbs of Christchurch, New Zealand's second largest city, on 22 February 2011 local time. The Christchurch earthquake was the deadliest in New Zealand since the 1931 Mw 7.8 Hawkes Bay earthquake and the most expensive in New Zealand's recorded history. The effects of the earthquake on the region's population and

A financial market is called “diverse ” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itô-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of “weak diversity ” and “asymptotic weak diversity”) in precise terms. We show that diversity is possible to achieve, but delicate. Several illustrative examples are provided, which demonstrate that weakly-diverse financial markets contain relative arbitrage opportunities: it is possible to outperform (or underperform) such markets over arbitrary time-horizons. The existence of such relative arbitrage does not interfere with the development of option pricing, and has interesting consequences for the pricing of long-term warrants and for put-call parity. Several open questions are suggested for further study.

The classic paper of Clauser et al proved that Bell's Theorem experiments rule out all theories of physics which assume locality, time-forwards causality and the existence of an objective real world. The Backwards-Time Interpretation (BTI) tries to recover realism and locality by permitting backwards time causality. BTI should permit dramatic simplification of the assumptions or axioms of physics, but requires new work in fundamental mathematics, such as new tools for the "closure of turbulence," the derivation of statistics generated by ODE or PDE. Recent events like the Delayed Choice Quantum Eraser experiment of Kim, Shih et al have increased mainstream interest in the possibility of backwards causality. The Backwards Time Quantum Teleportation (BTQT) experiment will take this further. True backwards time communication channels (BTCC) are absolutely impossible in most formulations of quantum theory but only almost impossible in the BTI formulation. This paper discus...

Microwave brightness temperatures are obtained from the SeaWinds scatterometer on the QuikSCAT satellite. These QuikSCAT Radiometer (QRad) measurements are used to infer instantaneous oceanic rain rates using a statistical retrieval algorithm that is based upon collocated TMI measurements. QRad instantaneous rain rate measurements have been binned in 0.5 hour local time windows onto a 0.5°×0.5° ocean grid. Also, an average rain rate product is produced, where QRad instantaneous rain rates have been averaged for five-day intervals (pentads) in the 0.5 hour local time windows. The scientific utility of QRad rain measurements is that they provide increased temporal and spatial sampling, which complements that provided by the TRMM Microwave Imager (TMI) and the Special Sensor Microwave Imagers (SSMIs) on the three DMSP satellites. Examples for the year 2000 are presented with corresponding rain rate measurements derived from TMI and SSMI. The results demonstrate that QRad rain measureme...