- 追加された行はこの色です。
- 削除された行はこの色です。
#norelated
// #ref(sky.jpg,nolink,left)
// #ref(binomial.png,nolink,center)
#br
* &size(30){kenichiro のホームページへようこそ}; [#b8a4f17c]
//#br
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//&size(35){&color(red){新年あけましておめでとうございます};};
//&br;
//&br;
//&size(30){&color(red){本年もよろしくお願い申し上げます};};
//&br;
//&br;
//&size(25){&color(red){令和2年元旦};};
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//#br
//* &color(red,yellow){7/6-13 は出張のため不在です}; [#z06dae5b]
//&color(文字色,背景色){インライン要素};
//&size(サイズ){インライン要素};
//RIGHT:&size(15){[[数学選修・数学教育専修学生用連絡ページへ:http://math.edu.ibaraki.ac.jp/index.php?id=9]] &br; [[（茨城大学教育学部数学教育教室）:http://math.edu.ibaraki.ac.jp/]]};
&size(15){梅津 健一郎（うめづ けんいちろう）}; &br;
[[茨城大学教育学部数学教育教室:http://math.edu.ibaraki.ac.jp/]]・教授 &br;
''住所：'' 〒310-8512 茨城県水戸市文京2-1-1 茨城大学教育学部 &br;
[[茨城大学水戸キャンパスマップ:http://www.ibaraki.ac.jp/generalinfo/campus/mito/index.html]]
''Email:'' &ref(emailaddr.png,nolink,95%); &br;
//E-mail: &ref(150s_email.jpg);
''研究室：'' 教育学部 D 棟 D307 &br;
//[[茨城大学水戸キャンパスへのアクセス:https://bit.ly/2RqoN3a]] >
//[[茨城大学水戸キャンパス:http://www.ibaraki.ac.jp/generalinfo/campus/mito/index.html]]
//＞教育学部＞D棟＞3階＞307号室
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* 専門分野 [#c0d0bf5c]
- 数学，解析学，非線形偏微分方程式論，特に非線形楕円型境界値問題
* キーワード [#x2917c95]
- 非線形楕円型境界値問題
- 正値解
- ロジスティック方程式
- 混合型非線形条件
- 非線形境界条件
- concave 及び concave-convex
- 漸近的解の形状
- 分岐理論
- 変分解析
- 位相的手法
- 人口動態論
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* 新着 [#c2805c09]
//&size(サイズ){インライン要素};
//
//
// --- 半角スペース
//----------------------------------------
// What's new !
//----------------------------------------
- 2020-01-25 &br;
- 2020-01-31 &br;
U.Kaufmann, H.Ramos Quoirin and K.Umezu, Uniqueness and sign properties of minimizers in a quasilinear indefinite problem, preprint.
- 2020-01-25 &br;
U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem II: local and global exactness results, preprint.
[[arXiv:2001.09315:https://arxiv.org/abs/2001.09315]]
- 2020-01-25 &br;
U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear Robin problem I: positivity, exact multiplicity, and existence of a subcontinuum, '''Annali di Matematica Pura ed Applicata''', (2020), accepted.
[[arXiv:1901.04019:https://arxiv.org/abs/1901.04019]]
- 2019-11-13 &br;
U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, '''Discrete and Continuous Dynamical Systems-A''', ''40''(2), (2020), 817--845.
//[[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]
[[10.3934/dcds.2020063:http://doi.org/10.3934/dcds.2020063]]
//- 2019-10-17 &br;
//U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, to appear in '''[[Discrete and Continuous Dynamical Systems - A:https://www.aimsciences.org/journal/1078-0947]]''', ''40''(2), (2020). //[[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]
//- 2019-08-30 &br;
//U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, accepted in '''[[Discrete and Continuous Dynamical Systems:https://www.aimsciences.org/journal/1078-0947]]'''. [[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]
- 2019-05-04 &br;
U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive solutions for indefinite concave-convex problems, '''Advanced Nonlinear Studies''', ''19''(2), (2019), 391--412.
[[10.1515/ans-2018-2027:https://doi.org/10.1515/ans-2018-2027]]
//- 2019-02-27 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, '''Advances in Nonlinear Analysis''', ''8''(1), (2019), 175--192.
//[[10.1515/anona-2016-0023:http://dx.doi.org/10.1515/anona-2016-0023]]
//- 2019-01-14 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Nonnegative solutions of an indefinite sublinear elliptic problem: positivity, exact multiplicity, and existence of a subcontinuum, preprint. //[[arXiv:1901.04019:https://arxiv.org/abs/1901.04019]]
// \href{https://arxiv.org/abs/1901.04019}{arXiv:1901.04019}
//- 2018-09-11 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive solutions for indefinite concave-convex problems, '''Advanced Nonlinear Studies''', (2018), published online. DOI: [[10.1515/ans-2018-2027:https://doi.org/10.1515/ans-2018-2027]]
//- 2018-07-27 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive solutions for indefinite concave-convex problems, accepted in [['''Advanced Nonlinear Studies''':https://www.degruyter.com/view/j/ans]]. //(arXiv:1710.07802) Downloadable //[[pdf:https://arxiv.org/pdf/1710.07802.pdf]]
//- 2018-02-27 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity,
//'''Nonlinear Differential Equations and Applications NoDEA''' (2018) ''25'':12.
////////////////////////////////////
//- 2018-02-11&br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity, accepted in [['''Nonlinear Differential Equations and Applications NoDEA''':http://bit.ly/2EhPkpD]].
// (arXiv:1705.07791) Downloadable [[pdf:https://arxiv.org/pdf/1705.07791.pdf]]
//
//- 2018-02-02 &br;
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative solutions set of an indefinite elliptic problem, '''Communications on Pure and Applied Analysis''', ''17''(3), (2018), 1255-1269. &size(13){&color(red){[[''pdf'':https://arxiv.org/pdf/1610.00964v3.pdf]] with corrected figures for the published version};};
// DOI: [[10.3934/cpaa.2018060:http://dx.doi.org/10.3934/cpaa.2018060]]
//(arXiv:1610.00964)
// Downloadable [[pdf:https://arxiv.org/pdf/1610.00964.pdf]]
////////////////////////////////////////////////////
//- 2017-12-16 &br;
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative solutions set of an indefinite elliptic problem, [['''Communications on Pure and Applied Analysis''':http://aimsciences.org/journal/1534-0392]], to be published in ''17''(3)(May 2018).
//(arXiv:1610.00964) Downloadable //[[pdf:https://arxiv.org/pdf/1610.00964.pdf]]
////////////////////////////////////////////////////////////////
//- 2017-10-24 &br;
//U.Kaufmann, H.Ramos Quoirin and K.Umezu, Loop type subcontinua of positive solutions for indefinite concave-convex problems, preprint. //(arXiv:1710.07802) Downloadable [[pdf:https://arxiv.org/pdf/1710.07802.pdf]]
//////////////////////////////////
//- 2017-10-20 &br;
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative solutions set of an indefinite elliptic problem, [['''Communications on Pure and Applied Analysis''':https://www.aimsciences.org/journals/home.jsp?journalID=3]], to appear.
//(arXiv:1610.00964) Downloadable //[[pdf:https://arxiv.org/pdf/1610.00964.pdf]]
///////////////////////////////////
//- 2017-09-15 &br;
//U. Kaufmann, H. Ramos Quoirin and K. Umezu, A curve of positive solutions for an indefinite sublinear Dirichlet problem, preprint. //[[arXiv:1709.04822:https://arxiv.org/abs/1709.04822]]
////////////////////////////////////////////////////
//- 2017-08-08 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positivity results for indefinite sublinear elliptic problems via a continuity argument, '''Journal of Differential Equations''', ''263''(8), (2017), 4481-4502.
//DOI:
//[[10.1016/j.jde.2017.05.021:http://dx.doi.org/10.1016/j.jde.2017.05.021]]
// (arXiv:1610.07872)
// Downloadable [[pdf:https://arxiv.org/pdf/1610.07872.pdf]]
///////////////////////////////
//- 2017-07-10 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, '''Topological Methods in Nonlinear Analysis''', ''49''(2), (2017), 739-756. DOI: //[[10.12775/TMNA.2017.007:http://dx.doi.org/10.12775/TMNA.2017.007]]
// (arXiv:1703.04229) Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]
///////////////////////////////////////////////////////
//- 2017-06-29 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, '''Israel Journal of Mathematics''', ''220''(1), (2017), 103-160. DOI: [[10.1007/s11856-017-1512-0:http://dx.doi.org/10.1007/s11856-017-1512-0]]
// (arXiv:1603.04940). Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]
////////////////////////////////////////
//- 2017-05-23 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity, preprint.
// (arXiv:1705.07791) Downloadable [[pdf:https://arxiv.org/pdf/1705.07791.pdf]]
////////////////////////////////////////////////////
//- 2017-05-21 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positivity results for indefinite sublinear elliptic problems via a continuity argument, '''Journal of Differential Equations''', (2017), Articles in Press. DOI: [[10.1016/j.jde.2017.05.021:http://dx.doi.org/10.1016/j.jde.2017.05.021]]
// (arXiv:1610.07872) Downloadable //[[pdf:https://arxiv.org/pdf/1610.07872.pdf]]
///////////////////////////////
//- 2017-05-17 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, '''Topological Methods in Nonlinear Analysis''', (2017), online first. DOI: [[10.12775/TMNA.2017.007:http://dx.doi.org/10.12775/TMNA.2017.007]] (arXiv:1703.04229) Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]
/////////////////////////////////////
//- 2017-05-05 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, '''Israel Journal of Mathematics''', (2017), first online. DOI: [[10.1007/s11856-017-1512-0:http://dx.doi.org/10.1007/s11856-017-1512-0]]
//(arXiv:1603.04940). Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]
//--------------------------------------------------------------------
//- 2017-03-25 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, [['''Topological Methods in Nonlinear Analysis''':http://apcz.umk.pl/czasopisma/index.php/TMNA]], (2017), to appear (arXiv:1703.04229). Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]
//>''Abstract'' We proceed with the investigation of the problem $$-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} $$
//where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Dealing now with the case $b \geq 0$, $b \not \equiv 0$, we show the existence (and several properties) of a unbounded subcontinuum of positive solutions of $(P_\lambda)$. Our approach is based on {\it a priori} bounds, a regularisation procedure, and Whyburn's topological method.
//-------------------------------------------------------------
//- 2017-03-23 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, [['''Israel Journal of Mathematics''':http://www.springer.com/mathematics/journal/11856]], in press (arXiv:1603.04940). Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]
//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.
//>''Abstract'' We investigate the problem $$ -\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} $$ where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as $\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.
//----------------------------------------------------------------------
//- 2017-02-03 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, [['''Israel Journal of Mathematics''':http://www.springer.com/mathematics/journal/11856]], in press (arXiv:1603.04940). Downloadable [[pdf:https://arxiv.org/pdf/1603.04940.pdf]]
//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.
//>''Abstract'' We investigate the problem $$-\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} $$where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as $\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.
//---------------------------------------------------------------------
//- 2016-12-02 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, '''Advances in Nonlinear Analysis''' (2016). online published. DOI: [[10.1515/anona-2016-0023:http://dx.doi.org/10.1515/anona-2016-0023]]
// スペース 半角   全角
//>''Abstract'' We investigate the problem $$\begin{cases}-\Delta u = |u|^{p-2}u & \mbox{in $\Omega$}, \\ \frac{\partial u}{\partial \n} = \lambda b(x)|u|^{q-2}u & \mbox{on $\partial \Omega$}, \end{cases} \leqno{(P_\lambda)}$$ where $1<q<2<p$, $\lambda>0$ and $b \in C^{1+\alpha} (\partial \Omega)$, for some $\alpha \in (0,1)$. We show that $\int_{\partial \Omega} b <0$ is a necessary and sufficient condition for the existence of nontrivial non-negative solutions of $(P_\lambda)$. Under the additional condition $b^+ \not \equiv 0$ we show that for $\lambda>0$ sufficiently small $(P_\lambda)$ has two nontrivial non-negative solutions which converge to zero in $C(\overline{\Omega})$ as $\lambda \to 0$. When $p<2^*$ we also provide the asymptotic profiles of these solutions.
//---------------------------------------------------------------
//- 2016-10-25 &br;
//U. Kaufmann, H. Ramos Quoirin, and K. Umezu, Positivity results for indefinite sublinear elliptic problems via a continuity argument, preprint (arXiv:1610.07872). Downloadable [[pdf:https://arxiv.org/pdf/1610.07872.pdf]]
//>''Abstract'' We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum principle does not apply to. Our approach is based on a continuity
//argument combined with variational techniques, the sub and supersolutions method and some a priori bounds. Both Dirichlet and Neumann homogeneous boundary conditions are considered. As a byproduct, we deduce some existence and uniqueness results. Finally, as an application, we derive some positivity results for indefinite concave-convex type problems.
////////////////
//- 2016-10-11 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, accepted in '''[[Advances in Nonlinear Analysis:https://www.degruyter.com/view/j/anona]]''' (2016).
//>''Abstract'' We investigate the problem $$\begin{cases}-\Delta u = |u|^{p-2}u & //\mbox{in $\Omega$}, \\ \frac{\partial u}{\partial \n} = \lambda b(x)|u|^{q-2}u & //\mbox{on $\partial \Omega$},
//\end{cases} \leqno{(P_\lambda)}
//$$
//where $1<q<2<p$, $\lambda>0$ and $b \in C^{1+\alpha} (\partial \Omega)$, for some $\alpha \in (0,1)$. We show that $\int_{\partial \Omega} b <0$ is a necessary and sufficient condition for the existence of nontrivial non-negative solutions of $(P_\lambda)$. Under the additional condition $b^+ \not \equiv 0$ we show that for $\lambda>0$ sufficiently small $(P_\lambda)$ has two nontrivial non-negative solutions which converge to zero in $C(\overline{\Omega})$ as $\lambda \to 0$. When $p<2^*$ we also provide the asymptotic profiles of these solutions.
//-----------------------------------------------------------------
//- 2016-09-01 &br;
//H.Ramos Quoirin and K.Umezu, A loop type component in the non-negative //solutions set of an indefinite elliptic problem, preprint. //(arXiv:1610.00964) Downloadable //[[pdf:https://arxiv.org/pdf/1610.00964.pdf]]
//>''Absract.'' We prove the existence of a loop type component of non-negative solutions for an indefinite elliptic equation with homogeneous Neumann boundary conditions. This result complements our previous work, where the existence of another loop type component was established in a different situation. Our proof combines local and global bifurcation theory, rescaling and regularising arguments, a priori bounds, and Whyburn's topological method.
////////
//- 2016-07-27 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite
//equation with a nonlinear boundary condition: existence, multiplicity and //asymptotic profiles, '''Calculus of Variations and PDEs''', (2016). //http://dx.doi.org/10.1007/s00526-016-1033-4
//>''Abstract.'' We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a positive parameter $\lambda$, which is inversely proportional to the diffusion rate. We establish several multiplicity results when the diffusion rate is large and analyze the asymptotic profiles and the stability properties of these steady states as the diffusion rate grows to infinity. In particular, our results show that in some cases bifurcation from zero and from infinity occur at $\lambda=0$. Our approach combines variational and bifurcation techniques.
//----------------------------------------------------------------------
//- 2016-07-18 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, [['''Topological Methods in Nonlinear Analysis''':http://apcz.umk.pl/czasopisma/index.php/TMNA]], in press (arXiv:1703.04229). Downloadable [[pdf:https://arxiv.org/pdf/1703.04229.pdf]]
//>''Abstract'' We proceed with the investigation of the problem $$-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} $$where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Dealing now with the case $b \geq 0$, $b \not \equiv 0$, we show the existence (and several properties) of a unbounded subcontinuum of positive solutions of $(P_\lambda)$. Our approach is based on {\it a priori} bounds, a regularisation procedure, and Whyburn's topological method.
//---------------------------------------------------------------
//- 2016-06-05 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite
//equation with a nonlinear boundary condition: existence, multiplicity and asymptotic profiles, accepted in [['''Calculus of Variations and PDEs''':http://www.springer.com/mathematics/analysis/journal/526]].
//[[arXiv:1509.01753:http://arxiv.org/abs/1509.01753]]
//>''Abstract.'' We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a positive parameter $\lambda$, which is inversely proportional to the diffusion rate. We establish several multiplicity results when the diffusion rate is large and analyze the asymptotic profiles and the stability properties of these steady states as the diffusion rate grows to infinity. In particular, our results show that in some cases bifurcation from zero and from infinity occur at $\lambda=0$. Our approach combines variational and bifurcation techniques.
//-------------------------------------------------------------------
//- 2016-05-20 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, accepted in [['''Israel Journal of Mathematics''':http://www.springer.com/mathematics/journal/11856]]. //[[arXiv:1603.04940:http://arxiv.org/abs/1603.04940]]
//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.
//>''Abstract'' We investigate the problem
//$$-\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad //\frac{\partial u}{\partial \n} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} //$$
//where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as $\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.
//---------------------------------------------------------
//- 2016-04-22 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition II, preprint.
//>''Abstract'' We proceed with the investigation of the problem $$-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \n} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} $$
//where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), $1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Dealing now with the case $b \geq 0$, $b \not \equiv 0$, we show the existence (and several properties) of a unbounded subcontinuum of positive solutions of $(P_\lambda)$. Our approach is based on {\it a priori} bounds, a regularisation procedure, and Whyburn's topological method.
//------------------------------------------------------------------
//- 2016-03-17 &br;
//H. Ramos Quoirin and K. Umezu, An indefinite concave-convex equation under a Neumann boundary condition I, preprint. [[arXiv:1603.04940:http://arxiv.org/abs/1603.04940]]
//A loop type subcontinuum of non-negative solutions for an indefinite concave-convex equation, preprint.
//>''Abstract'' We investigate the problem
//$$-\Delta u = a(x)|u|^{p-2}u + \lambda b(x)|u|^{q-2}u \mbox{ in } \Omega, \quad //\frac{\partial u}{\partial \n} = 0 \mbox{ on } \partial \Omega, \leqno{(P_\lambda)} $$
//where $\Omega$ is a bounded smooth domain in $\R^N$ ($N \geq2$), //$1<q<2<p$, $\lambda \in \R$, and $a,b \in C^\alpha(\overline{\Omega})$ with $0<\alpha<1$. Under some indefinite type conditions on $a$ and $b$ we prove the existence of two nontrivial non-negative solutions for $|\lambda|$ small. We characterize then the asymptotic profiles of these solutions as //$\lambda \to 0$, which implies in some cases the positivity and ordering of these solutions for $|\lambda|$ even smaller. In addition, this asymptotic analysis suggests the existence of a loop type subcontinuum in the non-negative solutions set. We prove in some cases the existence of such subcontinuum via a bifurcation and topological analysis of a regularized version of $(P_\lambda)$.
//--------------------------------------------------------------------------
//- 2016-01-25 &br;
//H. Ramos Quoirin and K. Umezu, An elliptic equation with an indefinite sublinear boundary condition, preprint.
//>''Abstract'' We investigate the problem $$\begin{cases}-\Delta u = |u|^{p-2}u & //\mbox{in $\Omega$}, \\ \frac{\partial u}{\partial \n} = \lambda b(x)|u|^{q-2}u & //\mbox{on $\partial \Omega$},
//\end{cases} \leqno{(P_\lambda)}
//$$
//where $1<q<2<p$, $\lambda>0$ and $b \in C^{1+\alpha} (\partial \Omega)$, for some //$\alpha \in (0,1)$. We show that $\int_{\partial \Omega} b <0$
//is a necessary and sufficient condition for the existence of nontrivial non-negative solutions of $(P_\lambda)$. Under the additional condition $b^+ \not \equiv 0$ we show that for $\lambda>0$ sufficiently small $(P_\lambda)$ has two nontrivial non-negative solutions which converge to zero in $C(\overline{\Omega})$ as $\lambda \to 0$. When $p<2^*$ we also provide the asymptotic profiles of these solutions.
//--------------------------------------------------------------------
//- 2015-09-15 &br;
//H. Ramos Quoirin and K. Umezu, On a concave-convex elliptic problem with a nonlinear boundary condition, '''Annali di Matematica Pura ed Applicata''', (2015). http://dx.doi.org/10.1007/s10231-015-0531-x
//>''Abstract'' We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition (depending on a positive parameter $\lambda$), which provides a concave-convex nature to the problem. We establish a global multiplicity result for positive solutions in the spirit of Ambrosetti-Brezis-Cerami and obtain their asymptotic profiles as $\lambda \to 0$. Furthermore, we also analyse the case where the nonlinearity is concave. Our arguments are based on a bifurcation analysis, a comparison principle and variational techniques.
//---------------------------------------------------------------------
//- 2015-09-09 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite equation with a nonlinear boundary condition: existence, multiplicity and asymptotic profiles, [[arXiv:1509.01753:http://arxiv.org/abs/1509.01753]]
//>''Abstract.'' We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a positive parameter $\lambda$, which is inversely proportional to the diffusion rate. We establish several multiplicity results when the diffusion rate is large and analyze the asymptotic profiles and the stability properties of these steady states as the diffusion rate grows to infinity. In particular, our results show that in some cases bifurcation from zero and from infinity occur at $\lambda=0$. Our approach combines variational and bifurcation techniques.
//--------------------------------------------------------------
//- 2015-08-25 &br;
//H. Ramos Quoirin and K. Umezu, On a concave-convex elliptic problem with a nonlinear boundary condition, to appear in '''Annali di Matematica Pura ed Applicata''' (2015).
//>''Abstract'' We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition (depending on a positive parameter $\lambda$), which provides a concave-convex nature to the problem. We establish a global multiplicity result for positive solutions in the spirit of Ambrosetti-Br\'ezis-Cerami and obtain their asymptotic profiles as $\lambda \to 0$. Furthermore, we also analyse the case where the nonlinearity is concave. Our arguments are based on a bifurcation analysis, a comparison principle and variational techniques.
//--------------------------------------------------------------------
//- 2015-07-08 &br;
//K. Taira and K. Umezu, Bifurcation for nonlinear elliptic boundary value problems IV, preprint.
//>''Abstract'' This paper is devoted to global static bifurcation theory for a class of '''degenerate''' boundary value problems for semilinear second-order elliptic differential operators, generalizing the authors' previous work. More precisely, we prove global bifurcation for positive solutions of a degenerate logistic like equation with a smooth linear combination of the Dirichlet and Neumann boundary conditions. In the proof we make use of the super-subsolution method to prove existence and uniqueness theorems of positive solutions of our semilinear elliptic boundary value problems. The approach here is based on the uniqueness of a bifurcation point and the uniqueness of a bifurcation solution curve.
//---------------------------------------------------------------------
//- 2015-05-06 &br;
//H. Ramos Quoirin and K. Umezu, On a concave-convex elliptic problem with a nonlinear boundary condition, preprint.
//>''Abstract'' We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition (depending on a positive parameter $\lambda$), which provides a concave-convex nature to the problem. We establish a global multiplicity result for positive solutions in the spirit of Ambrosetti-Br\'ezis-Cerami and obtain their asymptotic profiles as $\lambda \to 0$. Furthermore, we also analyse the case where the nonlinearity is concave. Our arguments are based on a bifurcation analysis, a comparison principle and variational techniques.
//---------------------------------------------------------------------
//- 2015-04-14 &br;
//H. Ramos Quoirin and K. Umezu, Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: A limiting case, '''J. Math. Anal. Appl.''' ''428'', (2015), 1265-1285. http://dx.doi.org/10.1016/j.jmaa.2015.04.005
//>''Abstract.'' We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. The direction of the bifurcation component at zero is also investigated. This paper treats a limiting case of our previous work (H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation, J. Differential Equations 257, (2014), 3935-3977.), where the case of sign-changing nonlinear boundary conditions is considered.
//------------------------------------------------------------------------
//- 2014-12-24 &br;
//H. Ramos Quoirin and K. Umezu, Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: A limiting case, submitted.
//>''Abstract.'' We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. The direction of the bifurcation component at zero is also investigated. This paper treats a limiting case of our previous work (H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation, J. Differential Equations 257, (2014), 3935-3977.), where the case of sign-changing nonlinear boundary conditions is considered.
//---------------------------------------------------------------------
//- 2014-10-01 &br;
//H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary conditions on the structure of the positive solutions set of a logistic equation, '''J. Differential Equations''' ''257'', (2014), 3935-3977.
//[[doi.org/10.1016/j.jde.2014.07.016:http://dx.doi.org/10.1016/j.jde.2014.07.016]]
//>''Abstract.'' We investigate a semilinear elliptic equation with a logistic nonlinearity and an indefinite nonlinear boundary condition, both depending on a parameter. Overall, we analyze the effect of the indefinite nonlinear boundary condition on the structure of the positive solution set. Based on variational and bifurcation techniques, our main results establish the existence of '''three''' nontrivial non-negative solutions for some values of the parameter, as well as their asymptotic behavior. These results suggest that the positive solution set contains an '''S-shaped component''' in some case, as well as a combination of a C-shaped and a S-shaped components, called a '''CS-shaped component''', in another case.
//------------------------------------------------------------------------
//- 2014-09-07 &br;
//H.Ramos Quoirin and K.Umezu, Positive steady states of an indefinite equation with a nonlinear boundary condition: existence, multiplicity and asymptotic profiles, preprint.
//>''Abstract.'' We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a positive parameter $\lambda$, which is inversely proportional to the diffusion rate. We establish several multiplicity results when the diffusion rate is large and analyze the asymptotic profiles and the stability properties of these steady states as the diffusion rate grows to infinity. In particular, our results show that in some cases bifurcation from zero and from infinity occur at $\lambda=0$. Our approach combines variational and bifurcation techniques.
//- 2014-08-22 &br;
//H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary //conditions on the structure of the positive solutions set of a logistic //equation, JDE(2014), //[[doi.org/10.1016/j.jde.2014.07.016:http://dx.doi.org/10.1016/j.jde.2014.07.016]]
//- 2014-08-12 &br;
//H.Ramos Quoirin and K.Umezu, The effect of indefinite nonlinear boundary //conditions on the structure of the positive solution set of a logistic //equation, JDE(2014), in press.
//- 2013-06-17 &br;
//K.Umezu, Global structure of supercritical bifurcation with turning points
//for the logistic elliptic equation with nonlinear boundary conditions, //'''Nonlinear Analysis''', ''89'', (2013), 250-266. //[[doi:10.1016/j.na.2013.05.011:http://dx.doi.org/10.1016/j.na.2013.05.011]]
//- 2013-05-23 &br;
//現在，茨城大学教育学部数学教育教室では &size(20){准教授（幾何学）
//の公//募}; をしております（締切2013年6月24日(消印有効)；
//2013年10//月1日採用予定）．公募条件等詳細は下記のリンク先をご参照
//ください．ご//応募くださいますよう，よろしくお願い申し上げます．
//&br;
//> http://www.ibaraki.ac.jp/employment/index.html
//Bifurcation approach to a logistic elliptic
//equation with a homogeneous incoming flux boundary condition,
//'''J. Differential Equations''', ''252'',(2012), 1146-1168. //[[doi:10.1016/j.jde.2011.08.043:http://dx.doi.org/10.1016/j.jde.2011.08.043]]
//
//
//&br;
//#hr
//&br;
///////////////////////////////////
// ''インデックス''
//#contents
///////////////////////////////
* 教育 [#ec614af7]
///////////////////////////////
//** [[学生用連絡ページ:http://math.edu.ibaraki.ac.jp/index.php?id=9]]（茨城大学教育学部数学教育教室） [#z1b12855]
/////////////////////////////////////////////////////////////////
** [[教務情報ポータル:https://idc.ibaraki.ac.jp/portal/]] [#ea2c2fc8]
//
//** 授業支援用e-ラーニングシステム [RENANDI] [#cb7261af]
//URL https://renandi.ipc.ibaraki.ac.jp/renandi/session.do（今年度限り．H30年度から新システムへ移行）
//- 平成29年度後期利用科目
//-- 解析学概論
//-- 解析学基礎
//-- 解析学A
// -- 解析学C
//-- 解析学の基礎II
//-- 解析学B
//-- 解析学C
///////////////////////////////
** [[定期試験問題]] [#zba36d52]
/////////////////////////
** [[ノート]] [#c96b06ba]
///////////////////////////////
** 担当授業 [#ldaffb8c]
*** 令和2年度 [#a2f572c3]
- 後期
- 前期
- 通年
-- 卒業研究ゼミ（6名）3/3開始
-- 修士M1ゼミ（3名）
*** 2019年度 [#g6ff0783]
- 後期
-- 解析学基礎 -- 点列の収束，ε-N法，ε-δ法，連続性の概念，一様性，リーマン和，定積分可能性，関数の多項式近似，級数展開
-- 解析学B -- 2変数関数の微分法，極値問題，陰関数定理，重積分，累次積分，変数変換の公式，広義積分
-- 解析学続論(4Q) -- 関数列，関数項級数（輪読）
-- 小学校算数基礎 -- 算数的活動（輪読）
-- 数学科の内容と実践（分担）
-- 教職実践演習（分担）
//-- iOPクォーター活動 -- [[「How to prove it」:https://amzn.to/2E3Axmv]] の輪読
--（大学院）解析学演習 -- 生物モデル，力学モデル，常微分方程式（輪読）
--（大学院）算数科授業設計（分担）
- 前期
-- 解析学概論 -- 関数とグラフ，関数の微分，導関数，初等関数の定義と性質，微分の応用，定積分，不定積分，微積分学の基本定理
-- 解析学A -- 広義積分，無限級数，ユークリッド空間の距離，2変数関数，偏微分，全微分，方向微分
-- 小学校算数実践（分担）-- 変化と関係
-- 統計学入門(1Q) -- データの分析
--（大学院）解析学特論 -- 距離空間，連続関数空間，陰関数定理，ベールのカテゴリー定理
--（大学院）算数総合研究（分担）
- 通年
-- 卒業研究ゼミ(5名) -- 2/28開始．常微分方程式論と力学系 [[常微分方程式論(朝倉書店):http://amzn.to/2jo16GR]]
--- 卒論題目「力学系における解の安定性解析」
//-- 修士M1ゼミ(1名) -- フーリエ解析
-- 修士M2ゼミ(1名) -- フーリエ解析
--- 修論題目「フーリエ解析とその応用」
*** 平成30年度 [#wd0da917]
- 後期
-- 解析学基礎 -- 点列の収束，ε-N法，ε-δ法，連続性の概念，一様性，リーマン和，定積分可能性，関数の多項式近似，級数展開
-- 解析学B -- 2変数関数の微分法，極値問題，陰関数定理，重積分，累次積分，変数変換の公式，広義積分
-- 解析学D(4Q) -- 微分方程式のトピックから（輪読）
-- 小学校算数基礎 -- 算数的活動（集団討論＆発表）
-- 教職実践演習（分担）
-- iOPクォーター活動 -- [[「How to prove it」:https://amzn.to/2E3Axmv]] の輪読
--（大学院）解析学演習 -- 生物モデル，常微分方程式（輪読）
- 前期
-- 解析学概論 -- 関数とグラフ，関数の微分，導関数，初等関数の定義と性質，微分の応用，定積分，不定積分，微積分学の基本定理
-- 解析学A -- 広義積分，無限級数，ユークリッド空間の距離，2変数関数，偏微分，全微分，方向微分
-- 解析学C -- 常微分方程式，常微分方程式系の解法と理論（輪読）
-- 統計学入門(2Q) -- 予想統計（教科書「[[意味がわかる統計学（ベレ出版）:https://amzn.to/2DY6APw]]」）
--（大学院）解析学特論 -- ベクトル値関数の微分，不動点定理，陰関数定理，有限次元版分岐理論（[[モースの補題:http://bit.ly/2ufukzh]]の応用）
--（大学院）算数総合研究（分担）-- 水の放出，割合，比例，1次関数，ベルヌーイの定理，常微分方程式
- 通年
-- 卒業研究ゼミ(4名) -- 3/1開始，[[ルベーグ積分(森北出版):http://amzn.to/2EwCHb6]]
--- 卒論題目「測度論的積分〜ルベーグの視点〜」
-- 修士M1ゼミ(1名) -- フーリエ解析
-- 修士M2ゼミ(1名) -- 安定性解析，分岐理論
--- 修論題目「常微分方程式の安定性解析と分岐理論」
////////////////////////////////////
*** 平成29年度 [#s6612cef]
- 後期
-- 解析学基礎（解析学の基礎II）-- 点列の収束，ε-N法，ε-δ法，連続性の概念，一様性，リーマン和，関数の多項式近似，級数展開
-- 解析学B -- 2変数関数の微分法の応用，極値問題，陰関数定理，重積分，累次積分，変数変換の公式
-- 解析学D(4Q) -- 力学と微分方程式（輪読）
-- 教職実践演習（分担）
--（大学院）応用数理学演習 -- 振動解析，[[Modelling with Ordinary Differential Equations(CRC):http://amzn.to/2ew38mR]] (輪読)
- 前期
-- 解析学概論（解析学の基礎I）-- 関数とグラフ，関数の微分，導関数，微分の応用，定積分，不定積分，微積分学の基本定理
-- 解析学A -- 広義積分，無限級数，2変数関数，偏微分，全微分，方向微分
-- 解析学C -- 線形常微分方程式，方程式系の解法と理論（輪読）
-- 大学入門ゼミ
-- ことばの力
--（大学院）応用数理学特論 -- 連続関数の空間とその応用
--（大学院）数学総合研究（分担）-- 常微分方程式の線形安定性
- 通年
-- 卒業研究ゼミ(5名) -- 2/28 開始，[[常微分方程式論(朝倉書店):http://amzn.to/2jo16GR]]
--- 卒論題目「線形微分方程式と境界値問題」
-- 修士M1ゼミ(1名) -- 常微分方程式の定性理論
////////////////////////////////////////////
*** 平成28年度 [#qe9e925d]
- 後期
-- 解析学の基礎II -- 点列の収束，ε-N法，ε-δ法，連続の概念
-- 解析学B -- 2変数関数の微分法の応用，重積分の概念
-- 解析学D -- 線形常微分方程式の解法，数理モデル
-- 身近な数学（教養；分担）-- データの分析
-- 教職実践演習（分担）
-- （大学院）応用数理学演習 -- [[Modelling with Ordinary Differential Equations(CRC):http://amzn.to/2ew38mR]] (輪読)
//
- 前期
-- 解析学の基礎I -- 関数とグラフ，関数の微分，導関数，微分の応用，定積分，不定積分，微積分学の基本定理
-- 解析学A -- 広義積分，無限級数，2変数関数，偏微分，全微分，方向微分
-- 解析学C -- 複素関数の微積分
//-- ことばの力 -- 4クラス担当
-- （大学院）応用数理学特論 -- 関数列の収束，関数解析の導入，常微分方程式の解の一意存在
-- （大学院）数学総合研究（分担）-- 成長と崩壊及び振動の数理，線形化安定性について，ヴォルテラの原理
//
- 通年
-- 卒業研究ゼミ(3名) -- 2/16 開始，[[ポストモダン解析学(丸善出版):http://amzn.to/1NFvQHi]]
--- 卒論題目「現代の解析学入門」
-- 自主ゼミ -- [[関数解析(岩波基礎数学選書):http://amzn.to/2lh0PV8]]
//////////////////////////////////
*** 平成27年度 [#qe9e925d]
- 後期
//
-- 解析学の基礎II -- 1変数関数の微分法とその応用，定積分，不定積分
-- 解析学B -- 2変数関数の微分法の応用，重積分の概念
-- 解析学D -- 常微分法方程式の解法（輪読学習）
-- 身近な数学（分担）-- 微分法をとらえる
-- 教職実践演習（分担）
//-- （大学院）応用数理学演習
//
- 前期
//
-- 解析学の基礎I -- 関数の微分，一変数関数，導関数，実数，収束，連続性
-- 解析学A -- 広義積分，無限級数，二変数関数，偏微分，全微分，方向微分
-- 解析学C -- 複素数，一次変換
-- ことばの力 -- 4クラス担当
// -- （大学院）応用数理学特論
// -- （大学院）数学総合研究（分担）
//
- 通年
-- 卒業研究ゼミ(4名) -- 2/17 開始，力学系入門（「[[Hirsch・Smale・Devaney 力学系入門:http://amzn.to/2nGuUA5]]」第２章から）
--- 卒論題目「力学系的視点からみる連立微分方程式系の解法」
////////////////////////////////
//*** 平成26年度 [#o0a18c16]
//- 後期
//
//-- 解析学の基礎II -- 一変数関数の微分の応用，積分法
//-- 解析学B -- 多項式近似，極値問題，重積分
//-- 解析学D -- 常微分方程式の基礎 (輪読)
//-- 身近な数学（分担）-- 行列と社会の数理，推移行列の基礎，投入産出の分析（テキスト「[[社会のなかの数理(九州大学出版会):http://amzn.to/2EJuL6e]]」）
//-- 教職実践演習（分担）
//-- （大学院）応用数理学演習 -- 常微分方程式のトピックから -ラプラス変換とその応用-（輪読）
//
//- 前期
//
//-- 解析学の基礎I -- 実数，数列，一変数関数，連続性，導関数
//-- 解析学A -- 広義積分，無限級数，2変数関数，偏微分，全微分
//-- 解析学C -- 複素数の微積分（テキスト「[[複素関数の基礎(サイエンス社):http://amzn.to/2EqvrzE]]」）
//-- ことばの力 -- 4クラス担当
//-- （大学院）応用数理学特論 -- 現象の数理モデル
//-- （大学院）数学総合研究（分担）-- 写像について
//- 通年
//-- 4年ゼミ(3名) -- [[微分方程式で数学モデルを作ろう(日本評論社):http://amzn.to/2C0ey9M]] 2/27開始
//--- 卒論題目「微分方程式を用いた数学モデルの考察」
// -- オフィスアワー 水曜2講時
///////////////////////////////////////////////
*** [[担当授業倉庫]] [#v89e0de7]
/////////////////////////////////////
// #hr
/////////////////////////////////////
* 研究 [#yfcfff5b]
//** [[内容:http://umeken.sakura.ne.jp/ibrk-u/research/research12_0112.html]] [#lf786755]
** List of Publications [#c84bb276]
** 講演リスト [#lde47d30]
** [[その他]] [#h77c7a85]
//////////////////////////////////////////
//** リンク [#w82bd548]
//*** [[MathSciNet:http://www.ams.org/mathscinet/]] Mathematical Reviews on the web, AMS [#q8e43499]
//*** [[MR Lookup:http://www.ams.org/mrlookup]] A Reference Tool for Linking, AMS [#c592cf0a]
//&br;
//#hr
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//&br;
[[過去のページ]]
//&br;
#hr
&br;
//&size(15){梅津健一郎（うめづ けんいちろう）}; &br; 茨城大学教育学部数学教育教室・教授 &br;
//〒310-8512 水戸市文京2-1-1 茨城大学教育学部数学教育教室 &br;
//Email: &ref(emailaddr.png,nolink);
//&br;
//
//研究室：教育学部 D307 &br;
//
//アクセス：[[茨城大学水戸キャンパス:http://www.ibaraki.ac.jp/generalinfo/campus/mito/index.html]]＞教育学部＞D棟＞3階＞307号室
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