Journal of the Chungcheong Mathematical Society

GENERATION OF RAY CLASS FIELDS OF IMAGINARY QUADRATIC FIELDS

Ho Yun Jung — 2021-11-15

Let K be an imaginary quadratic field other than Q( and Q( −3), and let OK be its ring of integers. Let N be a positive integer such that N = 5 or N ≥ 7. In this paper, we generate the ray class field modulo N OK over K by using a single x-coordinate of an elliptic curve with complex multiplication by OK .

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FIBONACCI SEQUENCES IN kTH POWER RESIDUES

Youchan Chung — 2021-11-15

In this paper, we find all the prime numbers p that satisfy the following statement. If a positive integer k is a divisor of p − 1, then there is a sequence consisting of all k-th power residues modulo p, satisfying the recurrence equation of the Fibonacci sequence modulo p.

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VARIOUS REMARKS ON HOMOLOGICAL INVARIANTS OF LOCAL RINGS

Kisuk Lee — 2021-11-15

In this article, we investigate the finiteness of Auslander Index when a ring A has not necessarily a canonical module, or a Gorenstein module. We also study the relations between column invariants and row invariants.

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FIXED POINT THEOREMS FOR M ¨ONCH TYPE MAPS IN ABSTRACT CONVEX UNIFORM SPACES

Hoonjoo Kim — 2021-11-15

In this paper, first, we present new fixed point theorems for M¨onch type multimaps on abstract convex uniform spaces and, also, a fixed point theorem for M¨onch type multimaps in Hausdorff KKM LΓ-spaces. Second, we show that M¨onch type multimaps in the better admissible class defined on an LΓ-space have fixed point properties whenever their ranges are Klee approximable. Finally, we obtain fixed point theorems on KC-maps whose ranges are Φ-sets.

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CONTROLLABILITY FOR SEMILINEAR STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DELAYS IN HILBERT SPACES

Daewook Kim — 2021-11-15

In this paper, we investigate necessary and suﬃcient conditions for the approximate controllability for semilinear stochastic functional differential equations with delays in Hilbert spaces without the strict range condition on the controller even though the equations contain unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term.

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FUNDAMENTAL TONE OF COMPLETE WEAKLY STABLE CONSTANT MEAN CURVATURE HYPERSURFACES IN HYPERBOLIC SPACE

Sung-Hong Min — 2021-11-15

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L2-norm of the If M is weakly stable, then traceless second fundamental form. λ1(M ) is bounded above by n2 + O(n2+s) for arbitrary s > 0.

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ON MINIMAL SURFACES WITH GAUSSIAN CURVATURE OF BIANCHI SURFACE TYPE

Sung-Hong Min — 2021-11-15

We consider the local uniqueness of a catenoid under the condition for the Gaussian curvature analogous to Bianchi surfaces. More precisely, if a nonplanar minimal surface in R3 has the 1 Gaussian curvature K = − (U (u)+V (v))2 for any functions U (u) and V (v) with respect to a line of curvature coordinate system (u, v), then it is part of a catenoid. To do this, we use the relation between a conformal line of curvature coordinate system and a Chebyshev coordinate system.

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CMC SURFACES WITH CONSTANT CONTACT ANGLE ALONG A CIRCLE

Sung-Hong Min — 2021-11-15

In this paper, we give a characterization of a Delaunay surface in R3. Let Σ be a CMC-H surface in R3 with H (cid:54)= 0. If Σ meets a plane with constant contact angle along a circle, then it is rotationally symmetric, i.e., Σ is part of a Delaunay surface.

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RIEMANNIAN AND LORENTZIAN VOLUME COMPARISONS WITH THE BAKRY-EMERY RICCI TENSOR

Jong Ryul Kim — 2021-11-15

The Bishop and Bishop-Gromov volume comparisons with the Bakry-Emery Ricci tensor in a metric measure space are studied by the comparisons of the Jacobi differential equations in a Riemannian and Lorentzian manifold.

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