As a framework for
the effort to develop perspectives for work and promote autonomous career
development among young people, schools at all levels—from elementary schools
to universities—are introducing and conducting career education. One result of
these efforts has been that career education, which is supposed to be conducted
systematically while maintaining a certain level of quality, is currently not
functioning well. More specifically, the wide range of career education
curricula and the fact that the method of execution is completely up to each
teacher has led to inconsistent quality and a range of risks. To help address
this, and given that career education itself constitutes a project towards
achieving the education goals, this paper argues that using a project manager
in career education—a role that has been entirely left up to each teacher to
fill or provide—is effective in managing the risks involved in career education
projects and proactively providing countermeasures to offset these risks.

Abstract:
The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward B？cklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward B？cklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution. 1. Introduction The theory of surfaces is connected with the theory of solitons through a compatibility condition of the Gauss-Weingarten equations. Bobenko [1] gave an outline of eight classes of surfaces in the three-dimensional Euclidean space in the formulation of the theory of solitons. They are minimal surfaces, surfaces of constant mean curvature, surfaces of constant positive Gaussian curvature, surfaces of constant negative Gaussian curvature, Bonnet surfaces, harmonic inverse mean curvature surfaces, Bianchi surfaces, and Bianchi surfaces of positive curvature. For the investigation of these surfaces, a matrices representation of quaternions is used to write their moving frames. Their moving frames are integrated by Sym's formula [2]. Quaternionic analysis by Pedit and Pinkall [3] is a technology to investigate surfaces in the Euclidean three- or four-space which are related to the soliton theory. In this theory, the Euclidean four-space is modeled on the set of all quaternions . A quaternionic line trivial bundle with a complex structure over a Riemann surface is associated with a conformal map from the Riemann surface to . We can assume that a quaternionic line trivial bundle associated with a constrained Willmore surface in equips a harmonic complex structure [4]. If a constrained Willmore surface is neither minimal nor superconformal, then this complex structure defines a smooth family of flat connections on the line bundle. Then a holonomy spectral curve of a constrained Willmore torus is defined by a smooth family of holonomies of . The relation between a constrained Willmore torus and its holonomy spectral curve is discussed in detail in [4]. If a conformal map from a torus to is not a constrained Willmore torus, then the quaternionic line trivial bundle associated with the conformal map is accompanied with a nonharmonic complex structure. For a conformal map, its Darboux transform is

Abstract:
Basic properties of von Neumann entropy such as the triangle inequality and what we call MONO-SSA are studied for CAR systems. We show that both inequalities hold for any even state. We construct a certain class of noneven states giving counter examples of those inequalities. It is not always possible to extend a set of prepared states on disjoint regions to some joint state on the whole region for CAR systems. However, for every even state, we have its `symmetric purification' by which the validity of those inequalities is shown. Some (realized) noneven states have peculiar state correlations among subsystems and induce the failure of those inequalities.

Abstract:
We study characterization of separable (classically correlated) states for composite systems of distinguishable fermions that are represented as CAR algebras.

Abstract:
We provide a mathematically rigorous framework for supersymmetric fermion lattice systems. We construct supersymmetric C*-dynamics in terms of a nilpotent superderivation and a one-parameter group of automorphisms on the CAR-algebra. (We do not make use of Grassmann numbers.) We establish several basic properties of superderivations on the fermion lattice system. Among others, we obtain a criterion of superderivations to yield supersymmetic dynamics.

Abstract:
We summarize the present status of the theories of spin fluctuations in dealing with the anomalous or non-Fermi liquid behavior and unconventional superconductivity in strongly correlated electron systems around their magnetic instabilities or quantum critical points. Arguments are given to indicate that the spin fluctuation mechanisms is the common origin of superconductivity in heavy electron systems, 2-dimensional organic conductors and high-T_c cuprates.

Abstract:
The resolvent algebra is a new C*-algebra of the canonical commutation relations of a boson field given by Buchholz-Grundling. We study analytic properties of quasi-free dynamics on the resolvent algebra. Subsequently we consider a supersymmetric quasi-free dynamics on the graded C*-algebra made of a Clifford (fermion) algebra and a resolvent (boson) algebra. We establish an infinitesimal supersymmetry formula upon the GNS Hilbert space for any regular state satisfying some mild requirement which is standard in quantum field theory. We assert that the supersymmetric dynamics is given as a C*-dynamics.

Abstract:
We study quantum entanglement for CAR systems. Since the subsystems of disjoint regions are not independent for CAR systems, there are some distinct features of quantum entanglement which cannot be observed in tensor product systems. We show the failure of triangle inequality of von Neumann and the possible increase of entanglement degree under operations done in a local region for a bipartite CAR system.

Abstract:
It is easy to verify the equivalence of the quantum Markov property and the strong additivity of entropy for graded quantum systems as well. However, the structure of Markov states for graded systems is different from that for tensor product systems. For three-composed graded systems there are U(1)-gauge invariant Markov states whose restriction to the pair of marginal subsystems is non-separable.

Abstract:
The Clifford torus is a torus in a three-dimensional sphere. Homogeneous tori are simple generalization of the Clifford torus which still in a three-dimensional sphere. There is a way to construct tori in a three-dimensional sphere using the Hopf fibration. In this paper, all Hamiltonian stationary Lagrangian tori which is contained in a hypersphere in the complex Euclidean plane are constructed explicitly. Then it is shown that they are homogeneous tori. For the construction, flat quaternionic connections of Hamiltonian stationary Lagrangian tori are considered and a spectral curve of an associated family of them is used.