In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Among the various faults of power transformers, winding are particularly common. It is known that short-circuit parameters can reflect condition, so on-line identification great significance for monitoring transformer health. An instantaneous phasor extraction method based on Second-Order Generalised Integrator Frequency-Locked Loop introduced, and then an algorithm proposed. In this algorithm,...

We experimentally demonstrate, for the first time to our knowledge, an ultrafast photonic high-order (second-order) complex-field temporal integrator. The demonstrated device uses a single apodized uniform-period fiber Bragg grating (FBG), and it is based on a general FBG design approach for implementing optimized arbitrary-order photonic passive temporal integrators. Using this same design app...

We present a systematic method for deriving reversible measure-preserving integrators for non-Hamiltonian systems such as the Nosé-Hoover thermostat and generalized Gaussian moment thermostat (GGMT). Our approach exploits the (non-Poisson) bracket structure underlying the thermostat equations of motion. Numerical implementation for the GGMT system shows that our algorithm accurately conserves t...

In this paper the current harmonic can be compensated by using the Shunt Active Power Filter, Passive Power Filter and the combination of both. The system has the function of voltage stability, and harmonic suppression. The reference current can be calculated by dq transformation. An improved generalized integrator control was proposed to improve the performance of APF. The simulation results o...

Modelling neutral beam injection (NBI) in fusion reactors requires computing the trajectories of large ensembles particles. Slowing down times up to one second combined with nanosecond time steps make these simulations computationally very costly. This paper explores performance BGSDC, a new numerical stepping method, for tracking ions generated by NBI DIII-D and JET reactors. BGSDC is high-ord...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

This paper considers transfer functions in consensus systems where agents have identical SISO dynamics of arbitrary order. The interconnecting structure is a directed graph. The transfer functions for various inputs and outputs are presented in simple product forms with a similar structure of the numerator and the denominator. This structure combines the network properties and the agent model i...

We studied a method of using symplectic integrator to simulate incoherent synchrotron radiation in an electron storage ring. The simulation includes both classical radiation and its quantum uctuations. We found that the emission process of photon using a compound Poisson process cannot be applied to the fourth-order integrator because it has negative path length which implies a negative n umber...

In this work, we present a new proposal for the second-order Adaptive Sigma Delta Modulation (ASDM). The new proposed Adaptation scheme is based on using Operational Transconductance Amplifier (OTAs) as an Integrator and as an Amplifier to adapt the quantizer stepsize to control the voltage gain by feedback the quantizer output through adaptation scheme. The stepsize is changing up or down by t...