We derive a new non-abelian Stokes theorem by rewriting the Wilson loop as a gauge-invariant area integral, at the price of integrating over an auxiliary field from the coset SU(N)/[(U(1)]N−1 space. We then introduce the relativistic quark-monopole interaction as a Wess–Zumino-type action, and extend it to the non-abelian case. We show that condensation of monopoles and confinement can be inves...

The electromagnetic field solution for a spherical invisibility cloak with an active device inside is established. Extraordinary electric and magnetic surface voltages are induced at the inner boundary of a spherical cloak, which prevent electromagnetic waves from going out. The phase and handness of polarized waves obliquely incident on such boundaries are kept in the reflected waves. The surf...

The advantages to the engineer of a radical change of approach to electromagnetism are outlined and discussed. Attention is directed away from the fields in empty spaces around the conductors to the source charges and currents inside them by redefining energy, momentum and power flow as properties of the charges. The potentials acquire a greater significance than the field vectors, giving a des...

The submodular flow problem is extended by considering a nonseparable cost function, which is assumed to enjoy a variant of the exchange property of the base polyhedron of a submodular system. Two optimality criteria are established, one in terms of potentials associated with vertices and the other in terms of negative cycles in an auxiliary graph. These are natural extensions of the well-known...

Effectively incorporating external advice is an important problem in reinforcement learning, especially as it moves into the real world. Potential-based reward shaping is a way to provide the agent with a specific form of additional reward, with the guarantee of policy invariance. In this work we give a novel way to incorporate an arbitrary reward function with the same guarantee, by implicitly...

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so-called "monodromy transform" approach and our new method for the solution of the l...

The results obtained in our previous paper are now extended to the case of stationary axially symmetric dyonic black boles within theory two electromagnetic potentials. We slightly enlarge classical Ernst formalism by introducing, with aid $t$ and $\ensuremath{\varphi}$ components dual potential ${B}_{\ensuremath{\mu}}$, magnetic ${\mathrm{\ensuremath{\Phi}}}_{m}$ which, similar known electric ...

performing fast and accurate methods for modeling the electrical machines has been the subject of several studies and many authors proposed different procedures to attain this aim. beside the accuracy, the speed of the method is of great concern. on the other hand, the capability of the method to be changed according to the need is another important issue. finite element method provides relativ...

The method of difference potentials was originally proposed by Ryaben’kii and can be interpreted as a generalized discrete version of the method of Calderon’s operators in the theory of partial differential equations. It has a number of important advantages; it easily handles curvilinear boundaries, variable coefficients, and non-standard boundary conditions while keeping the complexity at the ...

Based on a correlation analysis method, a subwaveform threshold retracker is developed and coded in FORTRAN for satellite altimetry to determine the leading edge and retracking gate, and to improve the precision of sea surface heights (SSHs) and gravity anomalies (GAs). Using ERS-1/ERM waveforms, the subwaveform threshold retracker outperforms full-waveform threshold retrackers at the tide gage...