the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d'subseteq m$ such that $n+d'$ is a strongly dense submodule of $m$...

An perfectly matched layers absorbing boundary condition (PML) with an unsplit field is derived for the acoustic wave equation by introducing the auxiliary variables and their associated partial differential equations. Unlike the conventional split-variable PML which is only weakly well-posed, the unsplit PML is proven to be strongly well-posed. Both the split-field PML (SPML) and the well-pose...

Using optical levitation of individual 3-10-/Lm droplets, we investigate the resonance structure of the light intensity scattered at an angle of approximately 900 by a dielectric droplet, a slightly absorbing droplet, and composite inhomogeneous droplets. We find in all the cases that the resonance structures of dielectric, weakly absorbing, and composite inhomogeneous spheres are almost identi...

In a finite-dimensional vector space, every subspace is finite-dimensional and the dimension of a subspace is at most the dimension of the whole space. Unfortunately, the naive analogue of this for modules and submodules is wrong: (1) A submodule of a finitely generated module need not be finitely generated. (2) Even if a submodule of a finitely generated module is finitely generated, the minim...

In this work, in terms of suitable superpositions of equal-frequency Bessel beams, we develop a theoretical method to obtain nondiffractive beams in (weakly conductive) absorbing media capable to resist the loss effects for long distances.

It is challenging to realize the complete broadband absorption of near-infrared in thin optical devices. In this paper, we studied high light two devices: a stack Au-pattern/insulator/Au-film and Au-pattern/weakly-absorbing-material/Au-film where Au-pattern was structured graded photonic super-crystal. We observed multiple-band absorption, including one near 1500 nm, Au-pattern/spacer/Au-film. ...

The full-bridge submodules (FB-SMs) in hybrid modular multilevel converters need to absorb the enormous energy stored dc side and arm inductors during fault blocking, which may lead severe overvoltage. An energy-absorbing branch (EAB) composed of metal oxide varistor (MOV) thyristors is proposed this letter. No extra power loss produced by EAB normal operation. can a part reduce absorbed FB-SMs...