Conservation laws of third order quasi-linear scalar evolution equations are studied via exterior differential system and characteristic cohomology. We find a subspace of 2-forms in the infinite prolongation space in which every conservation law has a unique representative. Analysis of the structure of this subspace based upon the symbol of the differential equation leads to a universal integra...

The natural relations for sets are those deenable in terms of the emptiness of the subsets corresponding to Boolean combinations of the sets. For pairs of sets, there are just ve natural relations of interest, namely, strict inclusion in each direction, disjointness, intersection with the universe being covered, or not. Let N denote f1; 2; : : :; ng and ? N 2 denote f(i; j) j i; j 2 N and i < j...

Industrialization has agreat impact on our lives. Philosophers have been warning us about the danger of industrialization .We realize the price paid for progress only when a nightmarish incident like Bhopal Gas Tragedy involving loss of numerous lives and many after effects occurs .In the present paper we will discuss the incident ,its impact on the health of the victims even today when two and...

Full-field transmission X-ray microscopy is a unique non-destructive technique for three-dimensional imaging of specimens at the nanometer scale. Here, the use of zone-doubled Fresnel zone plates to achieve a spatial resolution better than 20 nm in the hard X-ray regime (8-10 keV) is reported. By obtaining a tomographic reconstruction of a Ni/YSZ solid-oxide fuel cell, the feasibility of perfor...

ion example 3-state traffic light reduced to 2 states R G @ @ @ @I V Lr(R) = stop Lr(G) = stop Lr(V ) = go ⇒ relabeling stop stop @ @ @ @I go ⇒ collapsing stop 6 go

The Laws of Space and Observation unify the concepts of time, distance, matter, energy, gravity, and Space. The previously overlooked yet unifying factor is the concept that "Space" really exists as an entity unto itself. The Relative Space Density and Relative Space Warp equations as herein presented allows us to mathematically calculate an object’s gravity, mass, size, Space density, and more...

Light field microscopy methods together with three-dimensional (3D) deconvolution can be used to obtain single-shot 3D images of atomic clouds. We demonstrate the method using a test setup that extracts 3D images from a fluorescent Rb87 atomic vapor.