We examine the phase structures of the supersymmetric O(N) sigma model in two and three dimensions by using the tadpole method. Using this simple method, the calculation is largely simplified and the characteristics of this theory become clear. We also examine the problem of the fictitious negative energy state.

The limit distribution of energy level spacing is studied for the system of two harmonic oscillators with generic ratio of frequencies. It is proved that for any fixed generic ratio e no limit distribution exists, but for random e with any absolutely continuous distribution p(e)de on [0, 1] a universal random limit distribution of the energy level spacing exists. Some properties of the random l...

This paper presents the results of a feasibility study of potential wind energy developments on the islands of New England. The study included the compilation of an inventory of New England coastal islands, a categorization of the islands according to energy related criteria, and an overview of the current energy supply situation on those islands where energy demanding activities take place. Th...

We discuss the basic difficulties in understanding the origin of the highest energy particles in the Universe the ultrahigh energy cosmic rays (UHECR). It is difficult to imagine the sources they are accelerated in. Because of the strong attenuation of UHECR on their propagation from the sources to us these sources should be at cosmologically short distance from us but are currently not identif...

Unfit drivers are the cause of tens of thousands of incidents on the roadswhich lead to injuries anddeaths. Therefore, it is very important to take preventive measures against such incidents. One of the unfit driving conditions is driving while being drowsy. Using image processing techniques, drowsiness of the driver could be detected and hence such incidents could be prevented. In this work, i...

The capture of a muon bound to an atomic nucleus is a singular phenomenon because it involves three forces: an electromagnetic force binds the muon to the nucleus and produces the muon’s energy levels, including the hyperfine structure; the nuclear force produces the structure of the nucleus; and finally, the weak force is responsible for the capture. In this note, I describe the rather bizarre...

State = R≥0 ×R≥0 For an abstract state (d, a), we call dist(d, a) = d+ a the energy-adjusted distance. The computational state comprises: • A simple distance d ∈ R≥0 to the base station, like the simple distance of an abstract state. • An energy level e ∈ Energy. • An energy-faithful adjustment f ∈ R≥0 capturing energy deficiencies along the route to the base station. • A table nt containing en...

The internuclear potential V(r) of a diatomic molecule is spherically symmetric. It depends only on r, the internuclear separation. The internuclear potential v(r) can be determined using the Born-Oppenheimer approximation, where we assume that the motion of the nuclei is very slow compared to that of the electrons. We solve for the energy of ground electronic state as a function of the internu...

We begin with a prior observation by one of us that Thomas precession in the nonrelativistic limit of the Dirac equation may be attributed to a nonabelian Berry vector potential. We ask what object produces the nonabelian potential in parameter space, in the same sense that the abelian vector potential arising in the adiabatic transport of a nondegenerate level is produced by a monopole, (cente...