Elsevier BVActa Medica Okayama0022-03964292025Polyhedral entire solutions in reaction-diffusion equations529565ENMasaharuTaniguchiResearch Institute for Interdisciplinary Science, Okayama UniversityThis paper studies polyhedral entire solutions to a bistable reaction-diffusion equation in Rn. We consider a pyramidal traveling front solution to the same equation in Rn+1. As the speed goes to infinity, its projection converges to an n-dimensional polyhedral entire solution. Conversely, as the time goes to -infinity, an n-dimensional polyhedral entire solution gives n-dimensional pyramidal traveling front solutions. The result in this paper suggests a correlation between traveling front solutions and entire solutions in general reaction-diffusion equations or systems.No potential conflict of interest relevant to this article was reported.Springer Science and Business Media LLCActa Medica Okayama0003-952724912025Traveling Front Solutions of Dimension n Generate Entire Solutions of Dimension (n-1) in Reaction-Diffusion Equations as the Speeds Go to Infinity13ENHirokazuNinomiyaSchool of Interdisciplinary Mathematical Sciences, Meiji UniversityMasaharuTaniguchiResearch Institute for Interdisciplinary Science, Okayama UniversityMultidimensional traveling front solutions and entire solutions of reaction-diffusion equations have been studied intensively. To study the relationship between multidimensional traveling front solutions and entire solutions, we study the reaction-diffusion equation with a bistable nonlinear term. It is well known that there exist multidimensional traveling front solutions with every speed that is greater than the speed of a one-dimensional traveling front solution connecting two stable equilibria. In this paper, we show that the limit of the n-dimensional multidimensional traveling front solutions as the speeds go to infinity generates an entire solution of the same reaction-diffusion equation in the (n-1)-dimensional space.No potential conflict of interest relevant to this article was reported.Springer Science and Business Media LLCActa Medica Okayama0025-583139032024Entire solutions with and without radial symmetry in balanced bistable reaction–diffusion equations39313967ENMasaharuTaniguchiResearch Institute for Interdisciplinary Science, Okayama UniversityLet n ≥ 2 be a given integer. In this paper, we assert that an n-dimensional traveling front converges to an (n|1)-dimensional entire solution as the speed goes to infinity in a balanced bistable reaction–diffusion equation. As the speed of an n-dimensional axially symmetric or asymmetric traveling front goes to infinity, it converges to an (n|1)-dimensional radially symmetric or asymmetric entire solution in a balanced bistable reaction–diffusion equation, respectively. We conjecture that the radially asymmetric entire solutions obtained in this paper are associated with the ancient solutions called the Angenent ovals in the mean curvature flows.No potential conflict of interest relevant to this article was reported.American Institute of Mathematical SciencesActa Medica Okayama1078-09474062020Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations39813995ENMasaharuTaniguchi Research Institute for Interdisciplinary Science, Okayama UniversityFor a balanced bistable reaction-diffusion equation, the existence of axisymmetric traveling fronts has been studied by Chen, Guo, Ninomiya, Hamel and Roquejoffre [4]. This paper gives another proof of the existence of axisymmetric traveling fronts. Our method is as follows. We use pyramidal traveling fronts for unbalanced reaction-diffusion equations, and take the balanced limit. Then we obtain axisymmetric traveling fronts in a balanced bistable reaction-diffusion equation. Since pyramidal traveling fronts have been studied in many equations or systems, our method might be applicable to study axisymmetric traveling fronts in these equations or systems.No potential conflict of interest relevant to this article was reported.Department of Mathematics, Faculty of Science, Okayama UniversityActa Medica Okayama0030-15666212020Existence and stability of stationary solutions to the Allen-Cahn equation discretized in space and time197210ENAmy Poh Ai LingDivision of Mathematics and Physics, Graduate School of Natural Science and Technology, Okayama UniversityMasaharuTaniguchiResearch Institute for Interdisciplinary Science, Okayama University The existence and stability of the Allen–Cahn equation discretized in space and time are studied in a finite spatial interval. If a parameter is less than or equals to a critical value, the zero solution is the only stationary solution. If the parameter is larger than the critical value, one has a positive stationary solution and this positive stationary solution is asymptotically stable.No potential conflict of interest relevant to this article was reported.ElsevierActa Medica Okayama029414493672019Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations17911816ENMasaharuTaniguchiResearch Institute for Interdisciplinary Science, Okayama University For a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been well known. This paper proves that an axially asymmetric traveling front with any positive speed does exist in a balanced bistable reaction-diffusion equation. Our method is as follows. We use a pyramidal traveling front for an unbalanced reaction-diffusion equation whose cross section has a major axis and a minor axis. Preserving the ratio of the major axis and a minor axis to be a constant and taking the balanced limit, we obtain a traveling front in a balanced bistable reaction-diffusion equation. This traveling front is monotone decreasing with respect to the traveling axis, and its cross section is a compact set with a major axis and a minor axis when the constant ratio is not 1.No potential conflict of interest relevant to this article was reported.Academic PressActa Medica Okayama0022039626052016Convex compact sets in RN-1 give traveling fronts of cooperation-diffusion systems in R-N43014338ENMasaharuTaniguchiThis paper studies traveling fronts to cooperation diffusion systems in R-N for N >= 3. We consider (N - 2)-dimensional smooth surfaces as boundaries of strictly convex compact sets in RN-1, and define an equivalence relation between them. We prove that there exists a traveling front associated with a given surface and show its stability. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation. No potential conflict of interest relevant to this article was reported.PUBLIC LIBRARY SCIENCEActa Medica Okayama1932-6203832013Essential Role of the Zinc Transporter ZIP9/SLC39A9 in Regulating the Activations of Akt and Erk in B-Cell Receptor Signaling Pathway in DT40 Cellse58022ENMasanariTaniguchiAyakoFukunakaMitsueHagiharaKeikoWatanabeShinichiroKaminoTaihoKambeShuichiEnomotoMakotoHiromuraThe essential trace element zinc is important for all living organisms. Zinc functions not only as a nutritional factor, but also as a second messenger. However, the effects of intracellular zinc on the B cell-receptor (BCR) signaling pathway remain poorly understood. Here, we present data indicating that the increase in intracellular zinc level induced by ZIP9/SLC39A9 (a ZIP Zrt-/Irt-like protein) plays an important role in the activation of Akt and Erk in response to BCR activation. In DT40 cells, the enhancement of Akt and Erk phosphorylation following BCR activation requires intracellular zinc. To clarify this event, we used chicken ZnT5/6/7-gene-triple-knockout DT40 (TKO) cells and chicken Zip9-knockout DT40 (cZip9KO) cells. The levels of Akt and ERK phosphorylation significantly decreased in cZip9KO cells. In addition, the enzymatic activity of protein tyrosine phosphatase (PTPase) increased in cZip9KO cells. These biochemical events were restored by overexpressing the human Zip9 (hZip9) gene. Moreover, we found that the increase in intracellular zinc level depends on the expression of ZIP9. This observation is in agreement with the increased levels of Akt and Erk phosphorylation and the inhibition of total PTPase activity. We concluded that ZIP9 regulates cytosolic zinc level, resulting in the enhancement of Akt and Erk phosphorylation. Our observations provide new mechanistic insights into the BCR signaling pathway underlying the regulation of intracellular zinc level by ZIP9 in response to the BCR activation.No potential conflict of interest relevant to this article was reported.Society for Industrial and Applied MathematicsActa Medica Okayama0036-14104712015An (N-1)-dimensional convex compact set gives an N-dimensional traveling front in the Allen--Cahn equation455476ENMasaharuTaniguchiThis paper studies traveling fronts to the Allen–Cahn equation in RN for N ≥ 3. Let
(N |2)-dimensional smooth surfaces be the boundaries of compact sets in RN|1 and assume that all principal curvatures are positive everywhere. We define an equivalence relation between them and prove that there exists a traveling front associated with a given surface and that it is asymptotically stable for given initial perturbation. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.No potential conflict of interest relevant to this article was reported.