2023 - T. Osipchuk, M. Tkachuk , On weakly 1-convex sets in the plane ,
Proceedings of the International Geometry Center, 16(1), 42-49; DOI: 10.15673/tmgc.v16i1.2440
2022 - T. Osipchuk , On closed weakly m-convex sets ,
Proceedings of the International Geometry Center, 15(1), 50-65; DOI: 10.15673/tmgc.v15i1.2139
2022 - T. Osipchuk, Topological and Geometric Properties of the Set of 1-Nonconvexity
Points of a Weakly 1-Convex Set in the Plane,
Ukr. Math. J., 73, 1918–1936; DOI: 10.1007/s11253-022-02038-w
2022 - T. Osipchuk, Topological properties of closed weakly m-semiconvex sets ,
Journal of mathematical sciences, 260, 678–692; DOI: 10.1007/s10958-022-05719-w
2019 - T. Osipchuk , On semiconvexity of open sets with smooth boundary in the plane ,
Proceedings of the International Geometry Center, 12(4), 69–88; DOI: 10.15673/tmgc.v12i4.1710
2018 - T. Osipchuk, On system of balls with equal radii generating shadow at a point ,
Bulletin de la societe des sciences et des letters de Lodz, Vol. LXVIII, No 2, 77–84; DOI: 10.26485/0459-6854/2018/68.2/8
2017 - T. Osipchuk, M. Tkachuk, The problem of shadow for domains in Euclidean spaces ,
Journal of mathematical sciences, 224, 555–562; DOI: 10.1007/s10958-017-3435-z
2011 - T. Osipchuk, M. Tkachuk, The analytic criterion of linear convexity of the Hartogs domains
with smooth boundary in two dimensional quaternion space,
Ukr. Math. J., 63, 266–277. DOI: 10.1007/s11253-011-0503-2
2020 - T. Osipchuk, On topological properties of weakly m-convex sets,
Proceedings of IAMM, 34, P. 75–84 (in Ukrainian). DOI: 10.37069/1683-4720-2020-34-8
2018 - T. Osipchuk, Analytical properties of linearly convex domains
in complex and hypercomplex spaces, Current Research in Mathematics and Computer Sciences, II, 187-198.
2017 - T. Osipchuk, Some remarks on systems of balls generating shadow at point,
Proceedings of IAMM, 31, P. 109–116 (in Ukrainian).
2016 - T. Osipchuk, The problem of shadow for domains in the plane,
Proceedings of IAMM, 30, с. 100–105 (in Russian).
2015 - T. Osipchuk, M. Tkachuk, The problem of shadow for ellipsoid of revolution, Zb. Pr. Inst. Mat. NAN Ukr.,
12(3), P. 246-253 (in Russian).
2013 - T. Osipchuk, Analytical conditions of local linear convexity in the space
under the algebra of generalized quaternions, Zb. Pr. Inst. Mat. NAN Ukr.,
10(4-5), P. 301-305.
2012 - T. Osipchuk, Mathematical modeling of cortico-pontine projection, Zb. Pr. Inst. Mat. NAN Ukr.,
9(2), P. 265-269.
2010 - T. Osipchuk, M. Tkachuk, Yu. Zelinskii, The analytic conditions of local generalized
linear convexity in multy-dimensional Clifford spase, Zb. Pr. Inst. Mat. NAN Ukr.,
7(4), P. 393–401 (in Ukrainian).
2006 - T. Osipchuk,
The analytic conditions of local linear convexity in multy-dimensional quaternion space, Zb. Pr. Inst. Mat. NAN Ukr.,
2(3), P. 244-254 (in Ukrainian).
The notion of lineal convexity from the multidimensional complex space is generalized to the multidimensional hypercomplex spaces,
in particular, the spaces under the algebra of real quaternions, generalized real quaternions, and Clifford algebras. Necessary and sufficient conditions
of local lineal convexity of domains with smooth boundary in corresponding spaces are obtained in terms of nonnegativity and positivity of quadratic differential forms.
The shadow problem for a sphere is generalized and solved for arbitrary domains in the plane and in the three-dimensional real Euclidean space.
Namely, it is determined the minimum number of pairwise disjoint balls not containing some fixed point of a domain, with centers on the boundary of
the domain, and such that any line passing through the point intersects at least one of the balls.
The shadow problem for balls with eaqual radii and centers freely plased in the real Euclidean space of the arbitrary
finite dimension is solved. That is, the minimum number of pairwise disjoint balls with eaqual radii, not containing some fixed point
of the space, and such that any line passing through the point intersects at least one of the balls is determined.
The topological and geometric properties of (weakly) m-convex and (weakly) m-semiconvex sets
in the real n-dimensional Euclidean space, m=1,2,...,n-1, are investigated.
2021 - 13th International ISAAC Congress,
2–6 August 2021, Ghent, Belgium (online).
2021 - International Conference of Young Mathematicians,
3-5 June 2021, Kyiv, Ukraine (online).
2021 - International Online Conference Algebraic and Geometric Methods of Analysis dedicate to the memory of Yuriy Trokhymchuk,
25-28 May 2021, Odesa, Ukraine (online).
2020 - 11th International Skorobohatko Mathematical Conference (ISMC-2020),
26-30 October 2020, Lviv, Ukraine (online).
2020 - Online Mini-courses in Mathematical Analysis 2020,
14-17 September 2020, Padua, Italy (online).
2018 - The IV Conference of Mathematics and Computer Science
"Congressio-Mathematica", 20-23 September 2018, Mierki, Poland.
2018 - International Workshop "Hypercomplex Seminar 2018: (Hyper)Complex Analysis in Differential Equations,
Geometry and Physical Applications", 22 – 29 July 2018, Będlewo, Poland.
2017 - International Workshop "Hypercomplex Seminar 2017: (Hyper)Complex and Harmonic Dynamical Modelling: Topology in Physics of
Dynamical Systems and Molecular Nanoengines" (30 years of the direct cooperation agreement Łódź
[University and Łódź Society of Sciences and Arts] – Kyiv [National Academy of Sciences of Ukraine])
, 22 – 29 July 2017, Będlewo, Poland.
2016 - XI Summer School "Algebra, Topology, Analysis", 1–14 August 2016, Odessa, Ukraine.
2015 - X Summer School "Algebra, Topology, Analysis", 3–15 August 2015, Odessa, Ukraine.
2015 - International Conference of Young Mathematicians, 3 – 6 June 2015, Institute of Mathematics of NASU, Kyiv, Ukraine.
2013 - Crimean International Mathematical Conference "CIMC-2013", 22 August - 4 October 2013, Sudak, Ukraine.
2013 - International Conference "Complex Analysis, Potential Theory and Applications"
, 19 - 23 August 2013, Kyiv, Ukraine.
2010 - Humboldt Kolleg "Mathematics and life sciences: possibilities, interlacements and limits" ,
5 - 8 August 2010, Kyiv, Ukraine.
2009 - International Workshop "Hypercomplex Seminar 2009: From Schauder Basis to Hypercomplex, Randers-Ingarden and Fractal Structures, and Nanostructures"
, 24 - 31 July 2009, Będlewo, Poland.
2009 - International Conference "Analytic Methods of Mechanics and Complex Analysis"
, 29 June - 5 July 2009, Kyiv, Ukraine.
2008 - International Workshop "Hypercomplex Seminar 2008: Foliation Modelling of Hypercomplex Crystal Geometry vs. Randers-Ingarden Structures and Fractals"
, 26 July - 2 August 2008, Będlewo, Poland.
2007 - International Conference "Complex analysis and wave processes in mechanics" within the framework of Bogolyubov Readings
, 19 August - 2 September 2007, Zhitomir, Ukraine.
2006 - International Workshop "Hypercomplex Seminar 2006: Applied Complex and Quaternionic Approximation vs. Finslerian Structures",
18 - 25 August 2006, Będlewo, Poland.
2006 - Mathematical School "The Winter International Diffiety School"
, 25 January - 5 February 2006, Kostroma, Russian.
2012 - Traineeship at the CMA, University of Oslo, in cooperation with NeSys, the Centre for Molecular Biology and Neuroscience,
University of Oslo, Norway (within the EU-financed project EUMSL (EU-Ukrainian Mathematicians for Life Sciences)) (May - August, 2012).
2010 - Assistance in organizing of Humboldt Kolleg "Mathematics and life sciences: possibilities,
interlacements and limits", August 5-8, 2010, Kyiv, Ukraine.
