The distribution of nuclei in condia of cultures having different average numbers of nuclei

The distribution of nuclei in condia of cultures having different average numbers of nucle

Special growth tubes for the study of transport of growth factors and other phenomena

Special growth tubes for the study of transport of growth factors and other phenomen

Crossing techniques for large numbers of isolates

Crossing techniques for large numbers of isolate

Conidial plating techniques and the determination of nuclear ratios in heterokaryotic cultures

Conidial plating techniques and the determination of nuclear ratios in heterokaryotic culture

Cytochrome spectra of cytoplasmic mutants

Cytochrome spectra of cytoplasmic mutant

Determination of mitochondriol cytochromes

Determination of mitochondriol cytochrome

Observations of perpetual hyphal propagation in Neurospora crassa

Observations of perpetual hyphal propagation in Neurospora crass

Cytochrome spectra of cytoplasmic mutants

Cytochrome spectra of cytoplasmic mutant

Method of convex rigid frames and applications in studies of multipartite quNit pure-states

In this Letter we suggest a method of convex rigid frames in the studies of the multipartite quNit pure-states. We illustrate what are the convex rigid frames and what is the method of convex rigid frames. As the applications we use this method to solve some basic problems and give some new results (three theorems): The problem of the partial separability of the multipartite quNit pure-states and its geometric explanation; The problem of the classification of the multipartite quNit pure-states, and give a perfect explanation of the local unitary transformations; Thirdly, we discuss the invariants of classes and give a possible physical explanation.Comment: 6 pages, no figur

Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems

It is shown that for a given bipartite density matrix and by choosing a suitable separable set (instead of product set) on the separable-entangled boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via optimization for a generic entangled density matrix. Based on this, We obtain optimal L-S decomposition for some bipartite systems such as $2\otimes 2$ and $2\otimes 3$ Bell decomposable states, generic two qubit state in Wootters basis, iso-concurrence decomposable states, states obtained from BD states via one parameter and three parameters local operations and classical communications (LOCC), $d\otimes d$ Werner and isotropic states, and a one parameter $3\otimes 3$ state. We also obtain the optimal decomposition for multi partite isotropic state. It is shown that in all $2\otimes 2$ systems considered here the average concurrence of the decomposition is equal to the concurrence. We also show that for some $2\otimes 3$ Bell decomposable states the average concurrence of the decomposition is equal to the lower bound of the concurrence of state presented recently in [Buchleitner et al, quant-ph/0302144], so an exact expression for concurrence of these states is obtained. It is also shown that for $d\otimes d$ isotropic state where decomposition leads to a separable and an entangled pure state, the average I-concurrence of the decomposition is equal to the I-concurrence of the state. Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition, Concurrence, Bell decomposable states, LOCC} PACS Index: 03.65.UdComment: 31 pages, Late