Related papers: A Generalized Theory of Power
It has been recently shown how the tensorial nature of real-time path integrals involving the Feynman-Vernon influence functional can be utilized using matrix product states, taking advantage of the finite length of the non-Markovian…
In this paper, a new mathematical method of electrical circuits calculus is proposed based on the theory of the complex linear operators in matrix form. The newly proposed method generalizes the theory of complex representation of…
During the normal operation of a power system all the voltages and currents are sinusoids with a frequency of 60 Hz in America and parts of Asia, or of 50Hz in the rest of the world. Forcing all the currents and voltages to be sinusoids…
We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of…
We consider power means of independent and identically distributed (i.i.d.) non-integrable random variables. The power mean is an example of a homogeneous quasi-arithmetic mean. Under certain conditions, several limit theorems hold for the…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
Turbulence is generally associated with universal power-law spectra in scale ranges without significant drive or damping. Although many examples of turbulent systems do not exhibit such an inertial range, power-law spectra may still be…
In this paper we propose and demonstrate the potential for unifying models and algorithms for the steady state and transient simulation of single-phase and three-phase power systems. At present, disparate algorithms and models are used for…
In this paper we consider symmetric powers representation and exterior powers representation of finite groups, which generated by the representation which has finite dimension over the complex field. We calculate the multiplicity of…
Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For…
Defining the generalized charge, potential, current and generalized fields as complex quantities where real and imaginary parts represent gravitation and electromagnetism respectively, corresponding field equation, equation of motion and…
The Cartesian material space approach to Maxwell's equations reveals the analytical solution of the continuous radial density for the extended elementary charge. Radial charges and their Coulomb fields carry equal passive and active…
A power structure over a ring is a method to give sense to expressions of the form $(1+a_1t+a_2t^2+\ldots)^m$, where $a_i$, $i=1, 2,\ldots$, and $m$ are elements of the ring. The (natural) power structure over the Grothendieck ring of…
We derive an expression for the mutual gravitational force and torque of two bodies having arbitrary shapes and mass distributions, as an expansion in power series of their products of inertia and of the relative coordinates of their…
When a non-hermitian hamiltonian has a certain symmetry, such as the PT pseudo-hermiticity, it is still possible that the hamiltonian has a real spectrum. In this note, by adding an imaginary potential proportional to ip_1p_2 to the…
It is demonstrated that the non-instantaneous response of the optically induced coherent polarization tremendously influences the real-space shift of electronic charges in semiconductors. The possibility to coherently control this…
Transient stability analysis (TSA) plays an important role in power system analysis to investigate the stability of power system. Traditionally, transient stability analysis methods have been developed using time domain simulation by means…
Robust simulation is essential for reliable operation and planning of transmission and distribution power grids. At present, disparate methods exist for steady-state analysis of the transmission (power flow) and distribution power grid…
We show that the compositions of positive integers may be interpreted in terms of powers of some power series, over arbitrary commutative ring. As consequences, several closed formulas for the compositions as well as for the generalized…
The concept of energy-dependent forces in quantum mechanics is re-analysed. We suggest a simplification of their study via the representation of each self-adjoint and energy-dependent Hamiltonian H=H(E) with real spectrum by an auxiliary…