Proof of universality of the Bessel kernel for chiral matrix models in the microscopic limit

We prove the universality of correlation functions of chiral complex matrix models in the microscopic limit (N->\infty, z->0, N z=fixed) which magnifies the crossover region around the origin of the eigenvalue distribution. The proof exploits the fact that the three-term difference equation for orthogonal polynomials reduces into a universal second-order differential (Bessel) equation in the microscopic limit.Comment: 8 pages, no figures, LaTeX + elsart.sty, elsart12.sty. A typo correcte

Renormalization group approach to multiple-arc random matrix models

We study critical and universal behaviors of unitary invariant non-gaussian random matrix ensembles within the framework of the large-N renormalization group. For a simple double-well model we find an unstable fixed point and a stable inverse-gaussian fixed point. The former is identified as the critical point of single/double-arc phase transition with a discontinuity of the third derivative of the free energy. The latter signifies a novel universality of large-N correlators other than the usual single arc type. This phase structure is consistent with the universality classification of two-level correlators for multiple-arc models by Ambjorn and Akemann. We also establish the stability of the gaussian fixed point in the multi-coupling model.Comment: 11 pages, 1 figure, LaTeX + a4.sty, epsf.st

Flettner-rotor-powered VTOL’s theoretical performances

The demand for VTOLs is growing rapidly. From inspection to logistics, thanks to the evolution of autonomous technology. However, most of the fields remain just possibilities rather than actual usage cases due to the limited flight range, wall interaction, noise and instability of the aircraft. Alleviating an instability is especially an important key to achieve a reliable aerial system. One reason of instability is due to the limited four degrees of freedom. (i.e. VTOLs have to tilt to move horizontally) In this paper, a Flettner-force-powered VTOL that has sixdegrees of freedom, called Horizonist, is proposed and the stability of Horizonist is discussed in comparison to the conventional. (Horizonist is filed as a patent in Japan (issued as JP6938005) and PCT) The performances are evaluated in terms of settling time and power consumption against various inputs and a wind

コウドウ ブンセキガク カラ ミタ TEACCH プログラム

Recently, in the area of special education, a great deal of attention has been attracted to TEACCH (Treatment and Education of Autistic and related Communication handicapped CHildren). TEACCH is a comprehensive, life-time support model for people with autism, that the State of North Carolina in the US has provided over 30 years. In this paper, I report my site visits to Saga University Attached School for Handicapped Children and two welfare-institutions in the same region, which have been active in introducing TEACCH programs. The purpose of this paper is to analyze several aspects of programs from a behavior analysis perspective, and provide some insights and ideas that might help improving the system.国立情報学研究所『研究紀要公開支援事業』により電子化

Higher genus correlators for the hermitian matrix model with multiple cuts

An iterative scheme is set up for solving the loop equation of the hermitian one-matrix model with a multi-cut structure. Explicit results are presented for genus one for an arbitrary but finite number of cuts. Due to the complicated form of the boundary conditions, the loop correlators now contain elliptic integrals. This demonstrates the existence of new universality classes for the hermitian matrix model. The two-cut solution is investigated in more detail, including the double-scaling limit. It is shown, that in special cases it differs from the known continuum solution with one cut

Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory

A hermitian one-matrix model with an even quartic potential exhibits a third-order phase transition when the cuts of the matrix model curve coalesce. We use the known solutions of this matrix model to compute effective superpotentials of an N=1, SU(N) supersymmetric Yang-Mills theory coupled to an adjoint superfield, following the techniques developed by Dijkgraaf and Vafa. These solutions automatically satisfy the quantum tracelessness condition and describe a breaking to SU(N/2) x SU(N/2) x U(1). We show that the value of the effective superpotential is smooth at the transition point, and that the two-cut (broken) phase is more favored than the one-cut (unbroken) phase below the critical scale. The U(1) coupling constant diverges due to the massless monopole, thereby demonstrating Ferrari's general formula. We also briefly discuss the implication of the Painleve II equation arising in the double scaling limit.Comment: 15 pages, 7 figure

Symmetry Breaking in the Double-Well Hermitian Matrix Models

We study symmetry breaking in $Z_2$ symmetric large $N$ matrix models. In the planar approximation for both the symmetric double-well $\phi^4$ model and the symmetric Penner model, we find there is an infinite family of broken symmetry solutions characterized by different sets of recursion coefficients $R_n$ and $S_n$ that all lead to identical free energies and eigenvalue densities. These solutions can be parameterized by an arbitrary angle $\theta(x)$, for each value of $x = n/N < 1$. In the double scaling limit, this class reduces to a smaller family of solutions with distinct free energies already at the torus level. For the double-well $\phi^4$ theory the double scaling string equations are parameterized by a conserved angular momentum parameter in the range $0 \le l < \infty$ and a single arbitrary $U(1)$ phase angle.Comment: 23 pages and 4 figures, Preprint No. CERN-TH.6611/92, Brown HET-863, HUTP -- 92/A035, LPTHE-Orsay: 92/2

ブンショウ リカイ ノ リロンテキナ コウドウ ブンセキ

We conducted theoretical analyses on reading comprehension from a behavior analytic point of view. First, reading comprehension is defined as behavioral changes that are caused by function-altering effects of reading text. Then, we inferred the conditions in which such function-altering effects might evolve. At minimum, textual, tact, and intraverbal responding are required, to the verbal stimulus in the text, ideally with equivalence relationships to what is described. Furthermore, autoclitic repertoires such as "A is B" and "if X then Y" seem to be critical for the text to have function-altering effects. Furthermore, for more comprehensive understanding, other supplemental verbal behavior, such as repetition, imagination, and looking up a dictionary seem to be effective problem-solving behavior, which could be explicitly taught. A gap between theoretical and empirical research is found in the investigation of the acquisition process of autoclitic frames, which thus calls for future research

Multicritical microscopic spectral correlators of hermitian and complex matrices

We find the microscopic spectral densities and the spectral correlators associated with multicritical behavior for both hermitian and complex matrix ensembles, and show their universality. We conjecture that microscopic spectral densities of Dirac operators in certain theories without spontaneous chiral symmetry breaking may belong to these new universality classes