Thermodynamic Potential of Relativistic Electron Plasma

Within the real time formalism of quantum field theory at finite temperatures based on the closed-time-path Green's function approach, a closed analytical expression of the thermodynamic potential of a relativistic electron plasma is derived under the random phase approximation by summing up all ring diagrams. The result is natural extension to the relativistic case sf our previous formula derived in the case of a Coulomb gas.     

Dynamics of mode competition in the gyrotron backward-wave oscillator

The axial modes of the gyrotron backward-wave oscillator (gyro-BWO) each exhibit a distinctive asymmetry in axial field profile. As a result, and in sharp contrast to the behavior of the familiar resonator-based gyrotron oscillator, particle simulations of the gyro-BWO reveal a radically different pattern of mode competition in which a fast-growing and well-established mode is subsequently suppressed by a later-starting mode with a more favorable field profile. This is verified in a Ka-band experiment and the interaction dynamics are elucidated with a time-frequency analysis.     

An efficient algorithm for the complete set partitioning problem

The complete set partitioning problem is the well known set partitioning problem with all possible nonzero binary columns in the constraint matrix. A highly specialized enumerative algorithm, which never requires the explicit maintenance of the constraint matrix, is presented. Computational results, with data reflecting a particular corporate tax payment scenario that can be modelled as a complete set partitioning problem, is also given.     

Non-linear circle actions on the 4-sphere and twisting spun knots

CIRCLE actions on spheres form one of the most important problems in transformation groups. The aim of this paper is to study this problem in dimension 4. We answer a question of Montgomery and Yang[7], and show that there are infinitely many non-linear circle actions on S⁴. Moreover, if the 3-dimensional Poincaré conjecture is true, these actions plus the linear ones are the only possible circle actions on S⁴. The proof of this assertion involves identifying some homotopy 4-spheres. It is closely related to the work, twisting spun knots, of Zeeman[14]. We give a different treatment of this subject. This new setting yields new proofs and substantial strengthenings of some known results. In particular, we answer two questions of Zeeman[14, pp. 493–494, Questions 3 and 4].