A possible framework of the Lipkin model obeying the su(n)-algebra in arbitrary fermion number. I --- The su(2)-algebras extended from the conventional fermion-pair and determination of the minimum weight states ---

The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the su(n)-algebra are investigated systematically. The basic idea is to use the su(2)-algebra which is independent of the su(n)-algebra. This idea has been already presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the su(2)-algebra. If following this idea, the minimum weight states are determined for any fermion number occupying appropriately n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction. The cases n=2, 3, 4 and 5 are discussed in rather detail.Comment: 28 pages, 6 figur

A possible framework of the Lipkin model obeying the su(n)-algebra in arbitrary fermion number. II --- Two subalgebras in the su(n)-Lipkin model and an approach to the construction of linearly independent basis ---

Standing on the results for the minimum weight states obtained in the previous paper (I), an idea how to construct the linearly independent basis is proposed for the su(n)-Lipkin model. This idea starts in setting up m independent su(2)-subalgebras in the cases with n=2m and n=2m+1 (m=2,3,4,...). The original representation is re-formed in terms of the spherical tensors for the su(n)-generators built under the su(2)-subalgebras. Through this re-formation, the su(m)-subalgebra can be found. For constructing the linearly independent basis, not only the su(2)-algebras but also the su(m)-subalgebra play a central role. Some concrete results in the cases with n=2, 3, 4 and 5 are presented.Comment: 25 pages, 1 figur

Beyond the Schwinger boson representation of the su(2)-algebra. I -- New boson representation based on the su(1,1)-algebra and its related problems with application

With the use of two kinds of boson operators, a new boson representation of the su(2)-algebra is proposed. The basic idea comes from the pseudo su(1,1)-algebra recently given by the present authors. It forms a striking contrast to the Schwinger boson representation of the su(2)-algebra which is also based on two kinds of bosons. This representation may be suitable for describing time-dependence of the system interacting with the external environment in the framework of the thermo field dynamics formalism, i.e., the phase space doubling. Further, several deformations related to the su(2)-algebra in this boson representation are discussed. On the basis of these deformed algebra, various types of time-evolution of a simple boson system are investigated.Comment: 31 pages, 6 figure

Spin polarization in high density quark matter under a strong external magnetic field

In high density quark matter under a strong external magnetic field, possible phases are investigated by using the two-flavor Nambu-Jona-Lasinio model with tensor-type four-point interaction between quarks, as well as the axial-vector-type four-point interaction. In the tensor-type interaction under the strong external magnetic field, it is shown that a quark spin polarized phase is realized in all regions of the quark chemical potential under consideration within the lowest Landau level approximation. In the axial-vector-type interaction, it is also shown that the quark spin polarized phase appears in the wide range of the quark chemical potential. In both the interactions, the quark mass in zero and small chemical potential regions increases which indicates that the chiral symmetry breaking is enhanced, namely the magnetic catalysis occurs.Comment: 17 pages, 5 figure

Detection of miRNA in Cell Cultures by Using Microchip Electrophoresis with a Fluorescence-Labeled Riboprobe

The analysis of a microRNA (miRNA), miR-222 isolated from the PC12 cell line, was performed by use of the ribonuclease (RNase) protection assay, cyanine 5 (Cy5)-labeled miR-222 riboprobe, and a Hitachi SV1210 microchip electrophoresis system, which can be used to evaluate the integrity of total RNA. The fluorescence intensity corresponding to the protected RNA fragment increased in a dose-dependent manner with respect to the complementary-strand RNA. More highly sensitive detection of miRNA by microchip electrophoresis than by conventional method using fluorescence-labeled riboprobe could be obtained in 180 s. An obvious increase in miR-222 expression induced by nerve growth factor in PC12 cells could be observed. These results clearly indicate the potential of microchip electrophoresis for the analysis of miRNA using RNase protection assay with a fluorescence-labeled riboprobe

The Lipkin Model in Many-Fermion System as an Example of the su(1,1) times su(1,1)-Algebraic Model

Following the idea, recently, proposed by the present authors for the two-level pairing model, the Lipkin model is reexamined. It is a natural generalization of the method already developed by the present authors with Kuriyama. This model is a schematic model for many-fermion system and obeys the su(2)-algebra. It is shown that the use of the Schwinger boson representation, the model is expressed in terms of the su(1,1) times su(1,1)-algebra and with the aid of the MYT mapping method, it is disguised from the orginal form in terms of the Holstein-Primakoff representation. Further, under various coherent states, the classical counterparts are derived. It is concluded that the Lipkin model can be treated in the common ring as that of the two-level pairing model.Comment: 22 pages, no figure, using PTPTeX.cl

c-Abl Inhibition Exerts Antiparkinsonian Effects

Parkinson’s disease (PD) is caused by a progressive degeneration of nigral dopaminergic cells leading to striatal dopamine deficiency. From the perspective of antiparkinsonian drug mechanisms, pharmacologic treatment of PD can be divided into symptomatic and disease-modifying (neuroprotective) therapies. An increase in the level and activity of the Abelson non-receptor tyrosine kinase (c-Abl) has been identified in both human and mouse brains under PD conditions. In the last decade, it has been observed that the inhibition of c-Abl activity holds promise for protection against the degeneration of nigral dopaminergic cells in PD and thereby exerts antiparkinsonian effects. Accordingly, c-Abl inhibitors have been applied clinically as a disease-modifying therapeutic strategy for PD treatment. Moreover, in a series of studies, including that presented here, experimental evidence suggests that in a mouse model of parkinsonism induced by N-methyl-4-phenyl-1,2,3,6-tetrahydropyridine, c-Abl inhibition exerts an immediate effect improving motor impairments by normalizing altered activity in striatal postsynaptic signaling pathways mediated by Cdk5 (cyclin-dependent kinase 5) and DARPP-32 (dopamine- and cyclic AMP-regulated phosphoprotein 32 kDa). Based on this, we suggest that c-Abl inhibitors represent an ideal antiparkinsonian agent that has both disease-modifying and symptomatic effects. Future research is required to carefully evaluate the therapeutic efficacy and clinical challenges associated with applying c-Abl inhibitors to the treatment of PD

c-Abl Inhibition Exerts Symptomatic Antiparkinsonian Effects Through a Striatal Postsynaptic Mechanism

Parkinson’s disease (PD) is caused by a progressive degeneration of nigral dopaminergic cells leading to striatal dopamine deficiency. From the perspective of antiparkinsonian drug mechanisms, pharmacologic treatment of PD can be divided into symptomatic and disease-modifying (neuroprotective) therapies. An increase in the level and activity of the Abelson non-receptor tyrosine kinase (c-Abl) has been identified in both human and mouse brains under PD conditions. In the last decade, it has been observed that the inhibition of c-Abl activity holds promise for protection against the degeneration of nigral dopaminergic cells in PD and thereby exerts antiparkinsonian effects. Accordingly, c-Abl inhibitors have been applied clinically as a disease-modifying therapeutic strategy for PD treatment. Moreover, in a series of studies, including that presented here, experimental evidence suggests that in a mouse model of parkinsonism induced by N-methyl-4-phenyl-1,2,3,6-tetrahydropyridine, c-Abl inhibition exerts an immediate effect improving motor impairments by normalizing altered activity in striatal postsynaptic signaling pathways mediated by Cdk5 (cyclin-dependent kinase 5) and DARPP-32 (dopamine- and cyclic AMP-regulated phosphoprotein 32 kDa). Based on this, we suggest that c-Abl inhibitors represent an ideal antiparkinsonian agent that has both disease-modifying and symptomatic effects. Future research is required to carefully evaluate the therapeutic efficacy and clinical challenges associated with applying c-Abl inhibitors to the treatment of PD