The Space Dilation: Analyzing Progressive Speed Reduction and Its Relativistic Parallels

This paper presents a conceptual exploration that draws an intriguing parallelbetween a hypothetical travel scenario and the principles of special relativity. The scenario involves a traveler who reduces their speed by an amount proportional to the distance traveled. Despite initially traveling at a high speed towards a given destination, the continual reduction in speed results in an asymptotic approach to the goal, analogous to the unattainable speed of light in relativity. Mathematically, the scenario is expressed through the Harmonic Series, demonstrating that the total travel time increases without bound, making the destination theoretically unreachable within a finite timeframe. This exploration mirrors the relativistic velocity addition and time dilation effects, providing a compelling analogy for understanding asymptotic limits. By highlighting the profound implications of diminishing returns and unattainable goals, this paper aims to stimulate further discussion and exploration of these fascinating parallels.

ALMOST EVERYWHERE CONVERGENCE AND APPROXIMATION OF SPHERICAL HARMONIC EXPANSIONS

This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.

A novel control scheme for simultaneous elimination of imbalance, disturbance and voltage harmonic in power systems

In recent years, the increasing application of nonlinear and unbalanced electronic equipment and large single phase loads have made voltage imbalance a serious problem in power distribution systems. A novel approach has been proposed to eliminate voltage imbalance and disturbances. The main strategy of this scheme is based on series active filter. By improving control circuit toward existing schemes and proposing a new strategy to control the voltage amplitude, simultaneous elimination of voltage imbalance, faults, voltage harmonics and also compensation of voltage drop in transmission lines become possible. Eventually, the voltage on the load side is a perfectly balanced three phase voltage with specific proper amplitude. The proposed scheme has been simulated in a test network and the results show high capability of this scheme for the complete elimination of imbalance without phase shift.

Spherical harmonic series solution of fields excited by vertical electric dipole in earth-ionosphere cavity

The spherical harmonic series expression of electromagnetic fields excited by ELF/SLF vertical electric dipole in the spherical earth-ionosphere cavity is derived when the earth and ionosphere are regarded as non-ideal conductors.A method of speeding numerical convergence has been presented.The electromagnetic fields in the cavity are calculated by this algorithm,and the results show that the electromagnetic fields between the earth and the ionosphere are the sum of two traveling waves in the SLF band.Moreover,the results are in complete agreement with that of the well-known spherical second-order approximation in the SLF band.The electromagnetic fields in the cavity are a type of standing wave in the ELF band and the variation of the amplitude versus frequency coincides with Schumann’s resonance.

Convergence of Spherical Harmonic Series Expansion of the Earth＇s Gravitational Potential

Given a continuous boundary value on the boundary of a ＂simply closed surface＂ as that encloses the whole Earth, a regular harmonic fictitious field V＊（P） in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V＊（P） coincides with the Earth＇s real field V（P） in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V＊（P） could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth＇s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.