• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.127-133
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• 2012

We establish the polynomial convergence of a new class of path-following methods for SDLCP whose search directions belong to the class of directions introduced by Monteiro [3]. We show that the polynomial iteration-complexity bounds of the well known algorithms for linear programming, namely the short-step path-following algorithm of Kojima et al. and Monteiro and Alder, carry over to the context of SDLCP.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.609-619
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• 2014

Nonsmooth equations with finitely many maximum functions is often used in the study of complementarity problems, variational inequalities and many problems in engineering and mechanics. In this paper, we consider the global convergence methods for nonsmooth equations with finitely many maximum functions. The steepest decent method and the smoothing gradient method are used to solve the nonsmooth equations with finitely many maximum functions. In addition, the convergence analysis and the applications are also given. The numerical results for the smoothing gradient method indicate that the method works quite well in practice.

• East Asian mathematical journal
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• 제26권1호
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• pp.9-23
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• 2010

In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(\kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(\sqrt[]{n}(\log\;n)^2\;\log\;\frac{n{\mu}o}{\epsilon})$ to $O\sqrt[]{n}(\log\;n)\log(\log\;n)\log\;\frac{m{\mu}o}{\epsilon}$.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제7권2호
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• Journal of Microbiology
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• 제39권1호
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• pp.49-55
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• 2001

We have developed four chicken hybridomas secreting monoclonal antibodies to induce a protective immune response against the chicken disease avian coccidiosis, caused by the intestinal parasite Eimeria acervulina. Huwever, since the amount of antibodies secreted from these hybridomas is too low or sometimes they lost their ability to produce antibodies, the hybridoma method is not satisfactory in the production of large amounts of chicken monoclonal antibodies. To bypass these problems, we applied the antibody engineering technology using polymerase chain reaction. We cloned and determined the sequences of variable domains of the four chicken monoclonal antibodies, namely, 2-1, 5D11, 13C8 and 8C3. The sequences comparison to germline sequences skewed that the gene con version mechanism might contribute to developing diversification of heavy and λ-light chains in chicken antibodies. Several pseudogene families regarded as donors in gene conversion were identified at each framework region and the complementarily determining region of λ-light chains. In addition, as expected, numerous changes of nucleotide sequences such as nucleotide substitution, insertion and deletion were found predominantly in complementarity determining regions, which are likely to be somatic hypermutations as a result of affinity maturation in antibody-producing cells.

• 무역상무연구
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• 제12권
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• pp.587-613
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• 1999

Environmental problems such as global climate change, depletion, ocean and air pollution, and resource degradation-compounded by an expanding world population-respect no border and threaten the health, prosperity and jobs of all mankind. Our efforts to promote democracy, free trade, and stability in the world will fall short unless people have a livable environment. We have an enormous stake in the management of the world's resources. By increasing demand for timber, natural gas, coal and consumer's goods have destroyed the grounds for living. Greenhouse gas emissions anywhere in the world have threatened coastal communities, and then changed the Earth's climate system. The burning of coal, oil, and other fossil fuels is increasing substantially the concentration of heat-trapping gasses such as carbon dioxide, methane, and nitrous oxide in our air. The earth's temperature and sea levels are rising as a result. Since 1972 there has been a marked growth in the number and scope of environmental treaties. In particular, after the 1992 Rio Conference, international legal instruments became more concentrated on addressing environment within the context of sustainable development and incorporated a number of new concepts and innovative approaches. A preliminary analysis of recent conventions and in particular those associated with the Rio Conference indicates various ideas, concepts and principles which have come to the fore including sustainable development, equity, common concern of humankind, common but differentiated responsibilities and global partnership. However, international trade also has an environmental impact which must be minimized or countered. Positive measures are to be preferred to achieve environmental goals, but where trade provisions are necessary, they should be appropriately used within environmental conventions to facilitate the reduction and limitation of the negative impacts of trade and to enhance the complementarity of the multilateral trade regime with the imperatives of environmental protection, in the interests of environmental protection and sustainable development generally. The international community has to recognize and endorse this need to achieve complementarity between trade and environment issues.

• East Asian mathematical journal
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• 제24권2호
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• pp.191-199
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• 2008

In this paper, we introduce and studied a system of nonlinear projection equations with perturbation in Hilbert spaces. By using the fixed point theorem, we prove an existence of solution for this system of nonlinear projection equations. We construct an algorithm for approximating the solution of the system of nonlinear projection equations with perturbation and show that the iterative sequence generated by the algorithm converges to the solution of the system of nonlinear projection equations with perturbation under some suitable conditions.

• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.133-150
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• 2007

In a development of efficient primal-dual interior-points algorithms for self-scaled convex programming problems, one of the important properties of such cones is the existence and uniqueness of "scaling points". In this paper through the identification of scaling points with the notion of "(metric) geometric means" on symmetric cones, we extend several well-known matrix inequalities (the classical L$\ddot{o}$wner-Heinz inequality, Ando inequality, Jensen inequality, Furuta inequality) to symmetric cones. We also develop a theory of spectral geometric means on symmetric cones which has recently appeared in matrix theory and in the linear monotone complementarity problem for domains associated to symmetric cones. We derive Nesterov-Todd inequality using the spectral property of spectral geometric means on symmetric cones.

• 한국수학사학회지
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• 제28권5호
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• pp.263-278
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• 2015

As intuition is more unreliable than logic or reason, its studies in mathematics and mathematics education have not been done that much. But it has played an important role in the invention and development of mathematics with logic. So, it is necessary to recognize and explore the value of intuition in mathematics education. In this paper, I investigate the function and role of intuition in terms of mathematical learning and problem solving. Especially, I discuss the positive and negative aspects of intuition with its characters. The intuitive acceptance is decided by self-evidence and confidence. In relation to the intuitive acceptance, it is discussed about the pedagogical problems and the role of intuitive thinking in terms of creative problem solving perspectives. Intuition is recognized as an innate ability that all people have. So, we have to concentrate on the mathematics education via intuition and the complementary between intuition and logic. For further research, I suggest the studies for the mathematics education via intuition for students' mathematical development.