Research group in “Mathematics with applications”
The research in “Mathematics with applications”, is a unit of the MathInfo research center. Group members (based on their areas of research) usually aim to discuss mathematical problems that have real applications. To this end, they are working with several foreign partners on various projects. Nothing proves the effectiveness of the group better than the fact that members take part in many international research projects, present their results at several international conferences, and last but not least in recent years, the achieved results are published in Scimago-rated Q1 and D1 journals. The members of the group are members of the Department of Mathematics and Informatics of Sapientia Hungarian University of Translyvania, Faculty Of Technical And Human Sciences Târgu Mureş, which is why the joint work within the members of the group is almost daily.
Research topics: Calculus of Variations (Calculus of variations and optimal control; Geometric optimization, Partial differential equations of elliptic type, Geometrical analysis, Riemann, Finsler geometry) Geometric Function Theory (Classes of univalent functions, the study of integral operators defined between classes of univalent functions, Special functions, Inequalities between special functions, Geometric properties of special functions) Applied Algebraic Geometry (Infinite Discriminant, Euclidean distance degree and curvature) Discrete Mathematics and Graph Theory.
Members:
Csaba Farkas – research group coordinator, Zoltán Kása, Róbert Szász, Emil Horobet
Pál Kupán, Zsuzsanna Nagy, Boróka Olteán-Péter
Partner Instituion: Babeș-Bolyai University-Cluj Napoca, Petru Maior University-Tg. Mures,
Catania University, Catania, Italy, Technische Universität Berlin Institut für Mathematik, Max Planck Institute for Mathematics in the Sciences (MIS) in Leipzig
Projects:
1. 2021-2023 CNCSIS (National Research Center for Advanced Studies), Project title :Eigenvalues on curved spaces., PN-III-P4-ID-PCE-2020-1001 (PI. Alexandru Kristály, Member: Csaba Farkas).
2. 2017-2019 K.P.I., Sapientia Hungarian University of Transylvania, project title: Critical points from analysis to algebra I (PI Csaba Farkas, Member: Horobet Emil)
3. 2019-2020 K.P.I., Sapientia Hungarian University of Transylvania, project title: Critical points from analysis to algebra II (PI Csaba Farkas, Member: Horobet Emil)
4. 2018-2022 National Research, Development and Innovation Fund of Hungary, K_18, No. 127926.a Project title „Functional inequalities and elliptic PDEs: the influence of curvature”. (PI. Alexandru Kristály, Member: Csaba Farkas)
5. 2017 INDAM „Hardy-type inequality on non-compact Riemannian manifolds” (PI Csaba Farkas)
6. 2016 INDAM „Schrödinger equations with Hardy-type nonlinearity” (PI Csaba Farkas)
Selected list of publications (2016-present):
C. Farkas:
1. C. Farkas, P. Winkert, An existence result for singular Finsler double phase problems. J. DIFFERENTIAL EQUATIONS 286 (2021), 455–473.
2. C. Farkas, A. Kristály, Á. Mester, Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups, accepted CALC. VAR. PARTIAL DIFFERENTIAL EQUATIONS
3. F. Faraci, C. Farkas, On a critical Kirchhoff-type problem, NONLINEAR ANALYSIS, Volume 192, March 2020, 111679.
4. F. Faraci, C. Farkas, On an Open Question of Ricceri Concerning a Kirchhoff-Type Problem, MINIMAX THEORY AND ITS APPLICATIONS 04 (2019), No. 2.
5. F Faraci, C. Farkas, A characterization related to Schrödinger equations on Riemannian manifolds, COMM. CONT. MATH., acceptată, DOI: 10.1142/S02191997 18500608, 2018.
6. C. Farkas, Schrödinger-Maxwell systems on compact Riemannian manifolds. ELECTRON. J. QUAL. THEORY DIFFER. EQU. 2018, Paper No. 64, 18 pp.
7. F. Faraci, C. Farkas, Kristály Alexandru (Sándor), Multipolar Hardy inequalities on Riemannian manifolds, ESAIM: CONTROL OPTIM. AND CALC. OF VARIATIONS, 24 (2018), no. 2, 551–567.
8. F. Faraci, C. Farkas, New conditions for the existence of infinitely many solutions for a quasi-linear problem, PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, Vol. (2) 59, No 3, 2016, ISSN 0013-0915, pp. 655–669.
9. C. Farkas, A. Kristály, Schrödinger-Maxwell systems on Hadamard manifolds, NONLINEAR ANALYSIS REAL WORLD APPLICATIONS, Vol. 31, No 31, 2016, ISSN 1468-1218, pp. 473–491.
R. Szász:
1. R. Szász, The radius of starlikeness and the radius of convexity of the Γq function. BULL. MALAYS. MATH. SCI. SOC. 39 (2016), no. 4, 1647–1657.
2. M. Acu, Mugur, O. Engel, R. Szász, Preserving properties of the generalized Bernardi integral operator defined on a class of analytic functions with varying arguments. INDIAN J. MATH. 58 (2016)
3. Á. Baricz, H. Orhan, R. Szász, The radius of α-convexity of normalized Bessel functions of the first kind. COMPUT. METHODS FUNCT. THEORY 16 (2016), no. 1, 93–103.
4. E. Deniz, R. Szász, The radius of uniform convexity of Bessel functions. J. MATH. ANAL. APPL. 453 (2017), no. 1, 572–588.
5. M. Çağlar, E. Deniz, Erhan, R. Szász, Radii of α-convexity of some normalized Bessel functions of the first kind. RESULTS MATH. 72 (2017), no. 4, 2023–2035.
6. Á. Baricz, A. Szakál, R. Szász, Róbert; N. Yağmur, Radii of starlikeness and convexity of a product and cross-product of Bessel functions. RESULTS MATH. 73 (2018), no. 2, Paper No. 62, 34 pp.
7. K. Selvakumaran, R. Szász, Certain geometric properties of an integral operator involving Bessel functions. KYUNGPOOK MATH. J. 58 (2018), no. 3, 507–517.
8. R. Szász, On Brannan's conjecture. MEDITERR. J. MATH. 17 (2020), no. 1, Paper No. 38, 19 pp.
9. E. Deniz, M. Çağlar, R. Szász, The final step in a proof of Brannan's conjecture for β=1. J. MATH. ANAL. APPL. 487 (2020), no. 2, 124001, 5 pp.
E. Horobeț:
1. E. Horobeț, M. Weinstein, Offset Hypersurfaces and Persistent Homology of Algebraic Varieties, COMPUTER AIDED GEOMETRIC DESIGN, Volume 74 (2019), Pages 101767
2. A. Boralevi, J. Draisma, E. Horobeț, E. Robeva, Orthogonal and unitary tensor decomposition from an algebraic perspective, ISRAEL J. MATH., 222 (2017), 223-260
3. E. Horobeț, The Data Singular and the Data Isotropic Loci for Affine Cones, COMM. ALGEBRA, Volume 45 (2017), Issue 3,1177 – 1186
4. E. Horobeț, J. I. Rodriguez, The Maximum Likelihood Data Singular Locus, J. SYMBOLIC COMPUT., Volume 79 (2017), Part 1, 99–107
5. J. Draisma, E. Horobeț, The average number of critical rank-one approximations to a tensor, LINEAR MULTILINEAR ALGEBRA, Volume 64 (2016), Issue 12, 2494 - 2514
6. R. H. Eggermont, E. Horobeț, K. Kubjas, Algebraic boundary of matrices of nonnegative rank at most three, LINEAR ALGEBRA APPL., Volume 508 (2016), 62-80
7. E. Horobeț, An algorithm to construct the basic algebra of a skew group algebra, MATH. REP., 18(68), No. 3 (2016), 403-416
8. J. Draisma, E. Horobeț, G. Ottaviani, B. Sturmfels, R. R. Thomas, The Euclidean Distance Degree of an Algebraic Variety, FOUND. COMPUT. MATH., Volume 16, Issue 1(2016), 99-149
P. Kupán:
1. A.P., Kupán, Gy. Márton, R. Szász, A result regarding monotonicity of
the Gamma function, ACTA UNIVERSITATIS SAPIENTIAE, MATHEMATICA, 9/2, (2017), 291−302.
2. A.P. Kupán, About strong starlikeness conditions, FILOMAT, 32/6, (2018), 2035-2042.
