This paper focuses on the engineering trade-offs in designing capacitor voltage balancing schemes for modular multilevel converters (MMC) HVDC: regulation performance and switching loss. MMC is driven by the on/off switch operation of numerous submodules and the key design concern is balancing submodule capacitor voltages minimizing switching transition among submodules because it represents th...

Problem 1.(The Mapping Cone is a Homotopy Limit and a Homotopy Colimit) Let A be an Abelian category. Let A● and B● be objects in Ch●(A). Let f ● ∶ A● → B● be a morphism in Ch●(A). For every object T ● of Ch●(A), a left homotopy annihilator to T ● is a pair (Q●, σ●) of a morphism Q● ∶ B● → T ● in Ch●(A) and a nullhomotopy (σn ∶ An → T n−1)n∈Z of Q● ○ f ●, i.e., for every n ∈ Z, Q ○ f = dn−1 T ○...

LFSR-based stream ciphers with nonlinear filters or combiners are susceptible to algebraic attacks using linearization methods to solve an overdefined system of nonlinear equations. And this process is greatly enhanced if the filtering or combining function has a low degree annihilator. To prevent such an attack, one would choose the parameters of that function so that the degree of its annihil...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

Let R be a commutative ring with unity. And let E unitary R-module. This paper introduces the notion of 2-prime submodules as generalized concept ideal, where proper submodule H module F over is said to if , for r and x implies that or . we prove many properties this kind submodules, then only [N ] E, R. Also, non-zero multiplication module, [K: F] [H: every k such K. Furthermore, will study ba...