• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.513-519
• /
• 1997

We show that each orthomodular lattice containing only atomic nonpath-connected blocks is a full subalgebra of an irreducible path-connected orthomodular lattice and there is a path-connected orthomodualr lattice L containing a weakly path-connected full subalgebra C(x) for some element x in L.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.845-856
• /
• 2009

A block of an orthomodular lattice L is a maximal Boolean subalgebra of L. A site is a subalgebra of an orthomodular lattice L of the form S = A $\cap$ B, where A and B are distinct blocks of L. An orthomodular lattice L is called with finite sites if |A $\cap$ B| < $\infty$ for all distinct blocks A, B of L. We prove that there exists a weakly path-connected orthomodular lattice with finite sites which is not path-connected and if L is an orthomodular lattice such that the height of the join-semilattice [ComL]$\vee$ generated by the commutators of L is finite, then L is pathconnected.

• Journal of Electrical Engineering and Technology
• /
• v.13 no.2
• /
• pp.608-619
• /
• 2018

As distributed generation (DG) is connected to grid, there is new node-type occurring in distribution network. An efficient algorithm is proposed in this paper to calculate power flow for weakly meshed distribution network with DGs in different load models. The algorithm respectively establishes mathematical models focusing on the wind power, photovoltaic cell, fuel cell, and gas turbine, wherein the different DGs are respectively equivalent to PQ, PI, PQ (V) and PV node-type. When dealing with PV node, the algorithm adopts reactive power compensation device to correct power, and the reactive power allocation principle is proposed to determine reactive power initial value to improve convergence of the algorithm. In addition, when dealing with the weakly meshed network, the proposed algorithm, which builds path matrix based on loop-analysis and establishes incident matrix of node voltage and injection current, possesses good convergence and strong ability to process the loops. The simulation results in IEEE33 and PG&G69 node distribution networks show that with increase of the number of loops, the algorithm's iteration times will decrease, and its convergence performance is stronger. Clearly, it can be effectively used to solve the problem of power flow calculation for weakly meshed distribution network containing different DGs.