ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES

In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion

Using a Grandfather Pendulum Clock to Measure the World’s Shortest Time Interval, the Planck Time (With Zero Knowledge of <i>G</i>)

Haug has recently introduced a new theory of unified quantum gravity coined “Collision Space-Time”. From this new and deeper understanding of mass, we can also understand how a grandfather pendulum clock can be used to measure the world’s shortest time interval, namely the Planck time, indirectly, without any knowledge of G. Therefore, such a clock can also be used to measure the diameter of an indivisible particle indirectly. Further, such a clock can easily measure the Schwarzschild radius of the gravity object and what we will call “Schwarzschild time”. These facts basically prove that the Newton gravitational constant is not needed to find the Planck length or the Planck time;it is also not needed to find the Schwarzschild radius. Unfortunately, there is significant inertia towards new ideas that could significantly alter our perspective on the fundamentals in the current physics establishment. However, this situation is not new in the history of science. Still, the idea that the Planck time can be measured totally independently of any knowledge of Newton’s gravitational constant could be very important for moving forward in physics. Interestingly, an old instrument that today is often thought of as primitive instrument can measure the world’s shortest possible time interval. No atomic clock or optical clock is even close to be able to do this.

The final collision of the CAOB:Constraint from the zircon U-Pb dating of the Linxi Formation,Inner Mongolia

The Linxi Formation occupies an extensive area in the eastern Inner Mongolia in the Central Asian Orogenic Belt （CAOB）. The Linxi Formation is composed of slate, siltstone, sandstone and plant, lamellibranch microfossils in the associated strata. Major and trace element data （including REE） for sandstones from the formation indicate that these rocks have a greywacke protolith and have been deposited during a strong tectonic activity. LA-ICPMS U-Pb dating of detrital zircons yield ages of 1801 to 238 Ma for four samples from the Linxi Formation. 425-585 Ma, together with the ~500 Ma age for the metamorphism event previously determined for Northeast China, indicates that their provenance is the metamorphic rocks of Pan-African age that have a tectonic affinity to NE China. A few older zircons with U-Pb ages at 1689-1801 Ma, 1307 1414 Ma, 593-978 Ma are also present, revealing the Neoproterozoic history of NE China. The youngest population shows a peak at ca. 252 Ma, suggesting that the main deposition of the Linxi Formation was at late Permain. Moreover, the ca. 250 Ma zircon grains of all four samples yield weighted mean ^206pb/^238U ages of 250 ± 3 Ma, 248 ± 3 Ma, 249 ± 3 Ma, and 250 ± 2 Ma, respectively. These ages, together with the youngest zircon age in the sample ZJB-28 （ca. 238 Ma）, suggest that the deposition of the Linxi Formation extended to the early Triassic. Combining with previous results, we suggest that the final collision of the Central Asian Orogenic Belt （CAOB） in the southern of Linxi Formation, which located in the Solonker-Xra Moron-Changchun suture, and the timing for final collision should be at early Triassic.

Using microscopic video data measures for driver behavior analysis during adverse winter weather:opportunities and challenges

This paper presents a driver behavior analysis using microscopic video data measures including vehicle speed, lane-changing ratio, and time to collision. An analytical framework was developed to evaluate the effect of adverse winter weather conditions on highway driving behavior based on automated （computer） and manual methods. The research was conducted through two case studies. The first case study was conducted to evaluate the feasibility of applying an au- tomated approach to extracting driver behavior data based on 15 video recordings obtained in the winter 2013 at three dif- ferent locations on the Don Valley Parkway in Toronto, Canada. A comparison was made between the automated approach and manual approach, and issues in collecting data using the automated approach under winter conditions were identified. The second case study was based on high quality data collected in the winter 2014, at a location on Highway 25 in Montreal, Canada. The results demonstrate the effectiveness of the automated analytical framework in analyzing driver behavior, as well as evaluating the impact of adverse winter weather conditions on driver behavior. This approach could be applied to evaluate winter maintenance strategies and crash risk on highways during adverse winter weather conditions.

Smoothness of local times and self-intersection local times of Gaussian random fields

This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.