Tatsuhiro Honda

Questions and Answers Database Construction for Adaptive Online IRT Testing Systems: Analysis Course and Linear Algebra Course

To take care of students who were taught insufficiently in high schools and junior high schools, we have recently established the follow-up program aimed at helping students who need basic learning and aimed at assisting teachers who have to engage in teaching a variety of educational students. The follow-up systems are recognized as a part of the follow-up program, and consist of the learning check testing, follow-up program testing, and collaborative work testing. These testing systems use a large number of structured problem items installed in the database (i.e., item bank). In this paper, we introduce the database system configuration and show how we have constructed the database. The novel aspect is the item registration scheme. The databases were constructed by expertise such as mathematics professors in a way of collaborative work. For one subject teaching in one semester, such as Analysis or Linear Algebra, more than 20 sections are covered, and more than 50 problem items to each section are collected from the contributors.

QUASICONFORMAL EXTENSIONS OF STARLIKE HARMONIC MAPPINGS IN THE UNIT DISC

Abstract. Let f be a harmonic mapping on the unit disc ∆ in C. Wegive some condition for f to be a quasiconformal homeomorphism on ∆and to have a quasiconformal extension to the whole plane C. We alsoobtain quasiconformal extension results for starlike harmonic mappingsof order α ∈(0,1). 1. IntroductionLet f be a complex-valued function of class C 1 on ∆ = {z∈ C;|z| 0 in ∆) or sense-reversing (if J f (z) <0 in ∆). A harmonic mappingof ∆ has the unique representation f= h+g, where hand gare analytic in ∆and g(0) = 0. Note that fis sense-preserving if and only if |g ′ (z)| <|h ′ (z)| forall z∈ ∆ (For univalent harmonic mappings, see [5]).Let f= h+ gbe a harmonic mapping of the form(1.1) h(z) = z+X ∞n=2 a n z n , g(z) =X

Linear lsometries on hilbert spaces

Let B be the open unit ball of a complex Hilbert space E; and let f : B → B be a holomorphic map with f (0) = 0. In this paper, we consider a condition so that f is a linear isometry on E.

Bloch Mappings on Bounded Symmetric Domains

We introduce Bloch mappings on bounded symmetric domains which can be infinite dimensional and generalize Bonk’s distortion theorem on \(\mathbb {C}\) to locally biholomorphic Bloch mappings on finite dimensional bounded symmetric domains. As an application, we give a lower bound of the Bloch constant for these locally biholomorphic Bloch mappings. Finally, we show that there exist no isometric composition operators from the space \(H^{\infty }(\mathbb {B}_X)\) of bounded and holomorphic functions on \(\mathbb {B}_X\) into the \(\alpha \)-Bloch space \(\mathcal {B}^\alpha (\mathbb {B}_X)\) on \(\mathbb {B}_X\).

A Note on Strongly Starlike Mappings in Several Complex Variables

Let be a normalized biholomorphic mapping on the Euclidean unit ball in and let . In this paper, we will show that if is strongly starlike of order in the sense of Liczberski and Starkov, then it is also strongly starlike of order in the sense of Kohr and Liczberski. We also give an example which shows that the converse of the above result does not hold in dimension .

Hyperholomorphic Function Theory and Clifford Analyticity

As a special issue of this highly esteemed journal, we were pleased to invite the interested authors to contribute their original research papers as well as good expository papers to this special issue that will make better improvement on the theory of Clifford analysis and its application tomathematical physics, providing new approaches to differential geometry using Clifford’s geometric analysis. We suggested the following topics: theory of hyperholomorphic functions, regular functions,monogenic functions, hypercomplex number, dual number systems, spilt number systems, bicomplex numbers, and split biquaternions and pseudoquaternions; analytic extensions and applications; general theory of complex analytic spaces; complex partial differential operators, quaternion matrix equations, and generalized Cauchy-Riemann systems; domains of hyperholomorphy; and complex function spaces and hyperconjugate harmonic function. Certain papers that have significant results on complex analysis in the widest sense were intended to be welcome. Besides some papers belonging to the above-intended topics, we are also happy to publish, in this special issue, several other papers regarding analytic number theory, qseries and combinatorics, and special functions and the theory of group representations.

The Growth Theorem and Schwarz Lemma on Infinite Dimensional Domains

Let D be a balanced convex domain in a sequentially complete locally convex space E. If f : D E is a convex biholomorphic mapping with f(0) = 0 and df(0) = id, we have an upper bound of the growth of f. Also let D1, D2 be bounded balanced pseudoconvex domains in complex normed spaces E1, E2 respectively. When f : D1 D2 is a holomorphic mapping, we discuss a condition whereby f is linear or injective.

Holomorphic maps into complex ellipsoids which are kobayashi isometries at one point

Let M be a connected taut complex manifold of dimension n and let D be a bounded balanced pseudoconvex domain in with continuous Minkowski function. Assume that there exist a finite number of complex hyperplanes H j through the origin such that every point of is an extreme point for . Let f:→D be a holomorphic map. Let p be a point of M. Assume that f(p) = 0 and that df p is an isometry for the infinitesimal Kobayashi metric. In this case, we will show that f is a biholomorphic map.