• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1573-1594
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• 2017

This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.291-298
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• 2001

When the compression members have the variable cross sections along their member axes, the determination of the elastic critical loads by classical methods becomes impossible and if possible involves complicated calculation only to obtain the approximate values of critical load. In this paper the elastic critical load coefficients of the tapered members with simply supported ends were determined by finite element method. And then the results were represented by simple algebraic equations of two parameters, a( =taper parameter) and m ( = sectional property parameter). One the basis of algebraic equations, the equivalent moment of inertia concept originally proposed by Bleich for a spesific case, are extended to the general cases.

• East Asian mathematical journal
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• v.37 no.4
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1311-1325
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• 2021

One says that a ring homomorphism R → S is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element f ∈ S, there is a unique smallest ideal of R whose extension to S contains f, called the content of f. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically 'yes' in dimension one, but 'no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.499-507
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• 2010

In this note, we study the local spectral properties of semi-shifts. If $T\;{\in}\;L(X)$ is a semi-shift on a complex Banach space X, then T is admissible. We also prove that if $T\;{\in}\;L(X)$ is subadmissible, then $X_T(F)\;=\;E_T(F)$ for all closed $F\;{\subseteq}\;\mathbb{C}$. In particular, every subscalar operator on a Banach space is admissible.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.143-159
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• 2017

In this paper, we show that algebraic properties of Toeplitz operators on both Bergman spaces and Hardy spaces on the unit disc essentially generalizes on arbitrary bounded domains in the plane. In particular, we obtain results for the uniqueness property and commuting problems of the Toeplitz operators on the Hardy and the Bergman spaces associated to bounded domains.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.169-171
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• 1988

This paper deals with the robustness property of Kalman filters for linear systems with delay in output. The operator-type Riccati equation is transformed to algebraic equations, and the circle condition is derived. Based on the circle condition, it is shown that the same nondivergence margin, (1/2, .inf.) gain margin and +-60.deg. phase margin, is guaranteed as for ordinary systems.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1841-1851
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• 2017

Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin's conjecture in the setting of $hyperk{\ddot{a}}hler$ varieties, and we prove this reformulated conjecture for one family of $hyperk{\ddot{a}}hler$ fourfolds.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.13-23
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• 2023

In this paper, we show that for an isometry on a Banach space the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a bounded linear operator with property (δ) on a Banach space X. And let S be an isometry on a Banach space Y . Then every generalized intertwining linear operator θ : X → Y for (S, T) is continuous if and only if the pair (S, T) has no critical eigenvalue.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.495-504
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• 2023

This article deals with non-degenerate linear transformations on Euclidean Jordan algebras. First, we study non-degenerate for cone invariant, copositive, Lyapunov-like, and relaxation transformations. Further, we study that the non-degenerate is invariant under principal pivotal transformations and algebraic automorphisms.