Saha, Sangeeta; Pal, Swadesh; Melnik, Roderick Nonlocal cooperative behaviour, psychological effects, and collective decision-making: an exemplification with predator-prey models. arXiv:2406.10713 Preprint, arXiv:2406.10713 [math.DS] (2024). BibTeX Cite \textit{S. Saha} et al., ``Nonlocal cooperative behaviour, psychological effects, and collective decision-making: an exemplification with predator-prey models'', Preprint, arXiv:2406.10713 [math.DS] (2024) Full Text: arXiv OA License
Akshayveer, Akshayveer; Buroni, Federico C; Melnik, Roderick; Rodriguez-Tembleque, Luis; Saez, Andres; Singh, Sundeep Computational modelling of complex multiphase behavior of environmentally-friendly materials for sustainable technological solutions. arXiv:2403.07826 Preprint, arXiv:2403.07826 [cond-mat.mtrl-sci] (2024). BibTeX Cite \textit{A. Akshayveer} et al., ``Computational modelling of complex multiphase behavior of environmentally-friendly materials for sustainable technological solutions'', Preprint, arXiv:2403.07826 [cond-mat.mtrl-sci] (2024) Full Text: arXiv OA License
Shaheen, Hina; Pal, Swadesh; Melnik, Roderick Astrocytic clearance and fragmentation of toxic proteins in Alzheimer’s disease on large-scale brain networks. (English) Zbl 1521.92042 Physica D 454, Article ID 133839, 13 p. (2023). MSC: 92C32 92B20 92C40 35Q92 PDFBibTeX XMLCite \textit{H. Shaheen} et al., Physica D 454, Article ID 133839, 13 p. (2023; Zbl 1521.92042) Full Text: DOI
Akshayveer; Buroni, Federico C; Melnik, Roderick; Rodriguez-Tembleque, Luis; Saez, Andres; Singh, Sundeep The influence of thermo-electromechanical coupling on the performance of lead-free BNT-type piezoelectric materials. arXiv:2312.15807 Preprint, arXiv:2312.15807 [cond-mat.mtrl-sci] (2023). BibTeX Cite \textit{Akshayveer} et al., ``The influence of thermo-electromechanical coupling on the performance of lead-free BNT-type piezoelectric materials'', Preprint, arXiv:2312.15807 [cond-mat.mtrl-sci] (2023) Full Text: arXiv OA License
Kravchenko, D. S.; Kustova, E. V.; Melnik, M. Yu. Modeling of state-to-state oxygen kinetics behind reflected shock waves. (English. Russian original) Zbl 1503.76083 Vestn. St. Petersbg. Univ., Math. 55, No. 3, 281-289 (2022); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 9(67), No. 3, 429-442 (2022). MSC: 76P05 76L05 76V05 76M20 PDFBibTeX XMLCite \textit{D. S. Kravchenko} et al., Vestn. St. Petersbg. Univ., Math. 55, No. 3, 281--289 (2022; Zbl 1503.76083); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 9(67), No. 3, 429--442 (2022) Full Text: DOI
Pal, Swadesh; Melnik, Roderick; Banerjee, Malay Pattern alternations induced by nonlocal interactions. arXiv:2208.03533 Preprint, arXiv:2208.03533 [math.DS] (2022). BibTeX Cite \textit{S. Pal} et al., ``Pattern alternations induced by nonlocal interactions'', Preprint, arXiv:2208.03533 [math.DS] (2022) Full Text: arXiv OA License
Prabhakar, Sanjay; Melnik, Roderick Berry phase and spin precession without magnetic fields in semiconductor quantum dots. (English) Zbl 1516.82090 Eur. Phys. J. B, Condens. Matter Complex Syst. 92, No. 12, Paper No. 263, 7 p. (2019). MSC: 82D37 PDFBibTeX XMLCite \textit{S. Prabhakar} and \textit{R. Melnik}, Eur. Phys. J. B, Condens. Matter Complex Syst. 92, No. 12, Paper No. 263, 7 p. (2019; Zbl 1516.82090) Full Text: DOI Link
Vekslerchik, V. E.; Pritula, G. M.; Melnik, S. S.; Usatenko, O. V. Correlation properties of the random linear high-order Markov chains. (English) Zbl 07568500 Physica A 528, Article ID 121477, 11 p. (2019). MSC: 82-XX 60J10 68P30 PDFBibTeX XMLCite \textit{V. E. Vekslerchik} et al., Physica A 528, Article ID 121477, 11 p. (2019; Zbl 07568500) Full Text: DOI arXiv
Selezneva, S. N.; Mel’nik, M. V.; Astakhova, A. V. Coloring of pseudocubic graphs in three colors. (English. Russian original) Zbl 1445.05042 Mosc. Univ. Comput. Math. Cybern. 43, No. 2, 82-88 (2019); translation from Vestn. Mosk. Univ., Ser. XV 2019, No. 2, 49-55 (2019). MSC: 05C15 05C07 05C85 PDFBibTeX XMLCite \textit{S. N. Selezneva} et al., Mosc. Univ. Comput. Math. Cybern. 43, No. 2, 82--88 (2019; Zbl 1445.05042); translation from Vestn. Mosk. Univ., Ser. XV 2019, No. 2, 49--55 (2019) Full Text: DOI
Mel’nik, S. A. Self-similar solutions of the Cauchy problem for a parabolic stochastic differential equation. (English. Russian original) Zbl 1427.35381 Differ. Equ. 55, No. 8, 1077-1083 (2019); translation from Differ. Uravn. 55, No. 8, 1111-1117 (2019). MSC: 35R60 35K10 35B40 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Differ. Equ. 55, No. 8, 1077--1083 (2019; Zbl 1427.35381); translation from Differ. Uravn. 55, No. 8, 1111--1117 (2019) Full Text: DOI
Melnik, S. S.; Usatenko, O. V. Entropy of high-order Markov chains beyond the pair correlations. (English) Zbl 1514.60082 Physica A 506, 208-216 (2018). MSC: 60J10 68P30 PDFBibTeX XMLCite \textit{S. S. Melnik} and \textit{O. V. Usatenko}, Physica A 506, 208--216 (2018; Zbl 1514.60082) Full Text: DOI arXiv
Utkin, Ivan S.; Melnik, O. E. Dynamics of explosive volcano degassing. (English. Russian original) Zbl 1397.35230 Proc. Steklov Inst. Math. 300, 182-188 (2018); translation from Tr. Mat. Inst. Steklova 300, 190-196 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35Q35 76S05 76N15 PDFBibTeX XMLCite \textit{I. S. Utkin} and \textit{O. E. Melnik}, Proc. Steklov Inst. Math. 300, 182--188 (2018; Zbl 1397.35230); translation from Tr. Mat. Inst. Steklova 300, 190--196 (2018) Full Text: DOI
Makhno, Sergei Ya.; Mel’nik, Sergei A. Stochastic differential equation in a random environment. (English. Russian original) Zbl 1391.60142 J. Math. Sci., New York 231, No. 1, 48-69 (2018); translation from Ukr. Mat. Visn. 14, No. 3, 370-398 (2017). MSC: 60H10 60K37 PDFBibTeX XMLCite \textit{S. Ya. Makhno} and \textit{S. A. Mel'nik}, J. Math. Sci., New York 231, No. 1, 48--69 (2018; Zbl 1391.60142); translation from Ukr. Mat. Visn. 14, No. 3, 370--398 (2017) Full Text: DOI
Kamaletdinov, A. Sh.; Kozhevnikova, L. M.; Melnik, L. Yu. Existence of solutions of anisotropic elliptic equations with variable exponents in unbounded domains. (English) Zbl 1394.35193 Lobachevskii J. Math. 39, No. 2, 224-235 (2018). MSC: 35J62 35J25 PDFBibTeX XMLCite \textit{A. Sh. Kamaletdinov} et al., Lobachevskii J. Math. 39, No. 2, 224--235 (2018; Zbl 1394.35193) Full Text: DOI
Melnyk, Sergei A.; Kharkhota, Anna A. Differential representation of a Samuelson model with a telegraph drift. (English) Zbl 1492.60085 Tatra Mt. Math. Publ. 69, 45-59 (2017). MSC: 60G10 60H10 PDFBibTeX XMLCite \textit{S. A. Melnyk} and \textit{A. A. Kharkhota}, Tatra Mt. Math. Publ. 69, 45--59 (2017; Zbl 1492.60085) Full Text: DOI
Kharkhota, Anna Aleksandrovna; Melnyk, Sergei Anatol’evich Estimation of parameters of the Samuelson model with telegraph drift. (English. Ukrainian original) Zbl 1414.91376 J. Math. Sci., New York 218, No. 1, 16-27 (2016); translation from Ukr. Mat. Visn. 12, No. 4, 557-572 (2015). MSC: 91G20 62F12 62P05 PDFBibTeX XMLCite \textit{A. A. Kharkhota} and \textit{S. A. Melnyk}, J. Math. Sci., New York 218, No. 1, 16--27 (2016; Zbl 1414.91376); translation from Ukr. Mat. Visn. 12, No. 4, 557--572 (2015) Full Text: DOI
Hurd, T. R.; Cellai, Davide; Melnik, Sergey; Shao, Quentin H. Double cascade model of financial crises. (English) Zbl 1396.91795 Int. J. Theor. Appl. Finance 19, No. 5, Article ID 1650041, 27 p. (2016). MSC: 91G50 05C80 PDFBibTeX XMLCite \textit{T. R. Hurd} et al., Int. J. Theor. Appl. Finance 19, No. 5, Article ID 1650041, 27 p. (2016; Zbl 1396.91795) Full Text: DOI arXiv
Mel’nik, S. A. Dynamics of solutions of the Cauchy problem for semilinear parabolic stochastic partial differential equations with power-law singularities. (English. Russian original) Zbl 1338.60162 Differ. Equ. 52, No. 1, 76-83 (2016); translation from Differ. Uravn. 52, No. 1, 78-85 (2016). MSC: 60H15 35R60 35K58 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Differ. Equ. 52, No. 1, 76--83 (2016; Zbl 1338.60162); translation from Differ. Uravn. 52, No. 1, 78--85 (2016) Full Text: DOI
Fennell, Peter G.; Melnik, Sergey; Gleeson, James P. The limitations of discrete-time approaches to continuous-time contagion dynamics. arXiv:1603.01132 Preprint, arXiv:1603.01132 [physics.soc-ph] (2016). BibTeX Cite \textit{P. G. Fennell} et al., ``The limitations of discrete-time approaches to continuous-time contagion dynamics'', Preprint, arXiv:1603.01132 [physics.soc-ph] (2016) Full Text: DOI arXiv OA License
Krejčí, Pavel; Lamba, Harbir; Melnik, Sergey; Rachinskii, Dmitrii Kurzweil integral representation of interacting Prandtl-Ishlinskii operators. (English) Zbl 1335.47043 Discrete Contin. Dyn. Syst., Ser. B 20, No. 9, 2949-2965 (2015). Reviewer: Leszek Gasiński (Kraków) MSC: 47J40 74C15 PDFBibTeX XMLCite \textit{P. Krejčí} et al., Discrete Contin. Dyn. Syst., Ser. B 20, No. 9, 2949--2965 (2015; Zbl 1335.47043) Full Text: DOI
Mel’nik, S. A. Comparison theorem for solutions of parabolic stochastic equations with an absorber. (English. Russian original) Zbl 1322.60118 Theory Probab. Math. Stat. 90, 161-173 (2015); translation from Teor. Jmovirn. Mat. Stat. 90, 142–154 (2014). MSC: 60H15 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Theory Probab. Math. Stat. 90, 161--173 (2015; Zbl 1322.60118); translation from Teor. Jmovirn. Mat. Stat. 90, 142--154 (2014) Full Text: DOI
Cojocaru, Monica G. (ed.); Kotsireas, Ilias S. (ed.); Makarov, Roman N. (ed.); Melnik, Roderick V. N. (ed.); Shodiev, Hasan (ed.) Interdisciplinary topics in applied mathematics, modeling and computational science. Selected papers based on the presentations at the 2nd conference, AMMCS 2013, Waterloo, Canada, August 26–30, 2013. (English) Zbl 1325.00049 Springer Proceedings in Mathematics & Statistics 117. Cham: Springer (ISBN 978-3-319-12306-6/hbk; 978-3-319-12307-3/ebook). xxiii, 555 p. (2015). MSC: 00B25 00A69 34-06 35-06 37-06 60-06 90-06 91-06 92-06 PDFBibTeX XMLCite \textit{M. G. Cojocaru} (ed.) et al., Interdisciplinary topics in applied mathematics, modeling and computational science. Selected papers based on the presentations at the 2nd conference, AMMCS 2013, Waterloo, Canada, August 26--30, 2013. Cham: Springer (2015; Zbl 1325.00049) Full Text: DOI
Melnik, Sergey; Porter, Mason A.; Mucha, Peter J.; Gleeson, James P. Dynamics on modular networks with heterogeneous correlations. (English) Zbl 1345.05110 Chaos 24, No. 2, 023106, 11 p. (2014). MSC: 05C90 05C80 90B15 PDFBibTeX XMLCite \textit{S. Melnik} et al., Chaos 24, No. 2, 023106, 11 p. (2014; Zbl 1345.05110) Full Text: DOI arXiv Link
Mel’nik, S. A. The dynamics of the mean mass of a solution of the stochastic porous media equation. (English. Ukrainian original) Zbl 1309.60068 Theory Probab. Math. Stat. 87, 153-161 (2013); translation from Teor. Jmovirn. Mat. Stat. 87, 136-143 (2012). MSC: 60H15 60F10 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Theory Probab. Math. Stat. 87, 153--161 (2013; Zbl 1309.60068); translation from Teor. Jmovirn. Mat. Stat. 87, 136--143 (2012) Full Text: DOI
Mel’nik, S. A. Triviality of totally conservative solutions of a stochastic partial differential equation with power-law nonlinearities. (English. Russian original) Zbl 1296.60169 Differ. Equ. 49, No. 10, 1290-1298 (2013); translation from Differ. Uravn. 49, No. 10, 1323-1331 (2013). MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Differ. Equ. 49, No. 10, 1290--1298 (2013; Zbl 1296.60169); translation from Differ. Uravn. 49, No. 10, 1323--1331 (2013) Full Text: DOI
Maystrenko, A. A.; Melnik, S. S.; Pritula, G. M.; Usatenko, O. V. Bunches of random cross-correlated sequences. (English) Zbl 1278.82064 J. Phys. A, Math. Theor. 46, No. 39, Article ID 395002, 18 p. (2013). MSC: 82D30 82B44 PDFBibTeX XMLCite \textit{A. A. Maystrenko} et al., J. Phys. A, Math. Theor. 46, No. 39, Article ID 395002, 18 p. (2013; Zbl 1278.82064) Full Text: DOI arXiv
Belonenko, Mikhail B.; Zhukov, Alexander V.; Nemchenko, Konstantin É.; Prabhakar, Sanjay; Melnik, Roderick Echo effects on relativistic Landau levels in graphene and bigraphene as a manifestation of the quantum memory. (English) Zbl 1277.81037 Mod. Phys. Lett. B 26, No. 15, Article ID 1250094, 8 p. (2012). MSC: 81P68 PDFBibTeX XMLCite \textit{M. B. Belonenko} et al., Mod. Phys. Lett. B 26, No. 15, Article ID 1250094, 8 p. (2012; Zbl 1277.81037) Full Text: DOI
Melnik, Sergei A. Dynamics of nonself-similar solutions of the Dawson equation. (English. Ukrainian original) Zbl 1279.35127 J. Math. Sci., New York 175, No. 2, 150-160 (2011); translation from Ukr. Mat. Visn. 7, No. 3, 355-368 (2010). MSC: 35R60 60H15 PDFBibTeX XMLCite \textit{S. A. Melnik}, J. Math. Sci., New York 175, No. 2, 150--160 (2011; Zbl 1279.35127); translation from Ukr. Mat. Visn. 7, No. 3, 355--368 (2010) Full Text: DOI
Mel’nik, S. A. The comparison theorem for solutions of quasilinear parabolic SPDEs with weak sources. (Russian. English summary) Zbl 1240.35285 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2011, No. 1, 17-22 (2011). MSC: 35K59 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2011, No. 1, 17--22 (2011; Zbl 1240.35285)
Zgurovsky, Mikhail Z.; Mel’nik, Valery S.; Kasyanov, Pavlo O. Evolution inclusions and variation inequalities for earth data processing. II. Differential-operator inclusions and evolution variation inequalities for earth data processing. (English) Zbl 1213.47002 Advances in Mechanics and Mathematics 25. Berlin: Springer (ISBN 978-3-642-13877-5/hbk; 978-3-642-13878-2/ebook). xxv, 274 p. (2011). Reviewer: Boris Danilovich Gel’man (Voronezh) MSC: 47-02 34A60 34G20 34G25 47H04 47H05 47J20 47J22 49J35 49J53 86A10 PDFBibTeX XMLCite \textit{M. Z. Zgurovsky} et al., Evolution inclusions and variation inequalities for earth data processing. II. Differential-operator inclusions and evolution variation inequalities for earth data processing. Berlin: Springer (2011; Zbl 1213.47002) Full Text: DOI
Zgurovsky, Mikhail Z.; Mel’nik, Valery S.; Kasyanov, Pavlo O. Evolution inclusions and variation inequalities for Earth data Processing. I. Operator inclusions and variation inequalities for earth data processing. (English) Zbl 1213.47001 Advances in Mechanics and Mathematics 24. Berlin: Springer (ISBN 978-3-642-13836-2/hbk; 978-3-642-13837-9/ebook). xxx, 247 p. (2011). Reviewer: Boris Danilovich Gel’man (Voronezh) MSC: 47-02 34A60 34G20 34G25 47H04 47H05 47J20 47J22 49J35 49J53 86A10 PDFBibTeX XMLCite \textit{M. Z. Zgurovsky} et al., Evolution inclusions and variation inequalities for Earth data Processing. I. Operator inclusions and variation inequalities for earth data processing. Berlin: Springer (2011; Zbl 1213.47001) Full Text: DOI
Prabhakar, Sanjay; Takhtamirov, Eduard; Melnik, Roderick Mathematical models and numerical analysis of the conduction and valence band eigenenergy in cylindrical quantum dots. (English) Zbl 1335.81081 Mastorakis, Nikos (ed.) et al., Applied mathematics and informatics. European conference for the applied mathematics and informatics, Vouliagmeni, Athens, Greece, December 29–31, 2010. Athens: WSEAS Press (ISBN 978-960-474-260-8/hbk; 978-960-474-266-0/cd-rom). Applied Mathematics and Informatics, 201-206 (2010). MSC: 81Q37 65Z05 PDFBibTeX XMLCite \textit{S. Prabhakar} et al., in: Applied mathematics and informatics. European conference for the applied mathematics and informatics, Vouliagmeni, Athens, Greece, December 29--31, 2010. Athens: WSEAS Press. 201--206 (2010; Zbl 1335.81081)
Kasyanov, P. O.; Mel’nik, V. S.; Toscano, S. Solutions of Cauchy and periodic problems for evolution inclusions with multi-valued \(w_{\lambda_0}\)-pseudomonotone maps. (English) Zbl 1216.47093 J. Differ. Equations 249, No. 6, 1258-1287 (2010). Reviewer: Chuanzhi Bai (Huaian) MSC: 47J22 47H05 35B10 37L65 47H04 PDFBibTeX XMLCite \textit{P. O. Kasyanov} et al., J. Differ. Equations 249, No. 6, 1258--1287 (2010; Zbl 1216.47093) Full Text: DOI
Usatenko, O. V.; Apostolov, S. S.; Mayzelis, Z. A.; Melnik, S. S. Random-finite-valued dynamical systems: additive Markov approach. (English) Zbl 1189.82003 Kharkov Series in Physics and Mathematics 1. Cambridge: Cambridge Scientific Publishers (ISBN 978-1-904868-74-3). 176 p. (2010). MSC: 82-02 60-02 PDFBibTeX XMLCite \textit{O. V. Usatenko} et al., Random-finite-valued dynamical systems: additive Markov approach. Cambridge: Cambridge Scientific Publishers (2010; Zbl 1189.82003)
Mahapatra, D. Roy; Anand, S. V.; Sinha, N.; Melnik, R. V. N. Enhancing field emission from a carbon nanotube array by lateral control of electrodynamic force field. (English) Zbl 1170.82446 Mol. Simul. 35, No. 6-7, 512-519 (2009). MSC: 82D99 92C50 PDFBibTeX XMLCite \textit{D. R. Mahapatra} et al., Mol. Simul. 35, No. 6--7, 512--519 (2009; Zbl 1170.82446) Full Text: DOI
Kasyanov, Pavlo O.; Mel’nik, Valery S.; Piccirillo, Anna M. Local subdifferentials and multivariational inequalities in Banach and Fréchet spaces. (English) Zbl 1182.47047 Opusc. Math. 28, No. 3, 295-311 (2008). Reviewer: Dian K. Palagachev (Bari) MSC: 47J20 49J40 58E30 54C05 47H04 PDFBibTeX XMLCite \textit{P. O. Kasyanov} et al., Opusc. Math. 28, No. 3, 295--311 (2008; Zbl 1182.47047)
Melnik, V. S.; Valero, J. Addendum to: “On attractors of multivalued semi-flows and differential inclusions”. (Addendum to: “On attractors of multivalued semiflows and differential inclusions”.) (English) Zbl 1172.35331 Set-Valued Anal. 16, No. 4, 507-509 (2008). MSC: 35B40 35B41 37L05 58C06 PDFBibTeX XMLCite \textit{V. S. Melnik} and \textit{J. Valero}, Set-Valued Anal. 16, No. 4, 507--509 (2008; Zbl 1172.35331) Full Text: DOI
Kasyanov, Pavlo; Mel’nik, Valeriy; Piccirillo, Anna Maria On some approximations and main topological descriptions for special classes of Banach spaces with integrable derivatives. (English) Zbl 1164.46012 Methods Funct. Anal. Topol. 14, No. 3, 255-270 (2008). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 46E35 46E40 PDFBibTeX XMLCite \textit{P. Kasyanov} et al., Methods Funct. Anal. Topol. 14, No. 3, 255--270 (2008; Zbl 1164.46012)
Zhang, Suyang; Dai, Weizhong; Wang, Haojie; Melnik, Roderick V. N. A finite difference method for studying thermal deformation in a 3D thin film exposed to ultrashort pulsed lasers. (English) Zbl 1142.80004 Int. J. Heat Mass Transfer 51, No. 7-8, 1979-1995 (2008). Reviewer: Nina Shokina (Freiburg) MSC: 80M20 80A20 78A60 74S20 PDFBibTeX XMLCite \textit{S. Zhang} et al., Int. J. Heat Mass Transfer 51, No. 7--8, 1979--1995 (2008; Zbl 1142.80004) Full Text: DOI
Kasyanov, Pavlo; Melnik, Valery; Valero, José On the method of approximation for evolutionary inclusions of pseudomonotone type. (English) Zbl 1163.35413 Bull. Aust. Math. Soc. 77, No. 1, 115-143 (2008). Reviewer: Constantin Corduneanu (Arlington) MSC: 35K55 58C06 34A60 47H05 47J35 PDFBibTeX XMLCite \textit{P. Kasyanov} et al., Bull. Aust. Math. Soc. 77, No. 1, 115--143 (2008; Zbl 1163.35413) Full Text: DOI
Kas’yanov, P. O.; Mel’nik, V. S.; Toscano, L. Multivalued penalty method for evolution variational inequalities with \(\lambda_0\)-pseudomonotone multivalued maps. (English) Zbl 1268.49010 Nonlinear Oscil., N.Y. 10, No. 4, 487-517 (2007) and Nelinijni Kolyvannya 10, No. 4, 481-509 (2007). MSC: 49J40 47J20 PDFBibTeX XMLCite \textit{P. O. Kas'yanov} et al., Nonlinear Oscil., N.Y. 10, No. 4, 487--517 (2007; Zbl 1268.49010) Full Text: DOI
Melnik, S. A. The decomposition for solutions of parabolic stochastic Itô equations with gradient nonlinearities. (Russian) Zbl 1249.60144 Tr. Inst. Prikl. Mat. Mekh. 15, 126-135 (2007). MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{S. A. Melnik}, Tr. Inst. Prikl. Mat. Mekh. 15, 126--135 (2007; Zbl 1249.60144)
Melnik, Sergey The decomposition of a solution of the quasilinear stochastic parabolic equation with weak source. (English) Zbl 1199.60236 Theory Stoch. Process. 13(29), No. 3, 55-64 (2007). MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{S. Melnik}, Theory Stoch. Process. 13(29), No. 3, 55--64 (2007; Zbl 1199.60236)
Mel’nik, S. A. Fibering of solutions of Itô stochastic equations of the parabolic type with power-law nonlinearities. (English. Russian original) Zbl 1149.60043 Differ. Equ. 43, No. 10, 1434-1444 (2007); translation from Differ. Uravn. 43, No. 10, 1400-1409 (2007). Reviewer: Martin Ondreját (Praha) MSC: 60H15 35K55 35C05 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Differ. Equ. 43, No. 10, 1434--1444 (2007; Zbl 1149.60043); translation from Differ. Uravn. 43, No. 10, 1400--1409 (2007) Full Text: DOI
Mel’nik, T. A.; Vashchuk, P. S. Homogenization of a boundary value problem with mixed type of boundary conditions in a thick junction. (English. Russian original) Zbl 1140.35340 Differ. Equ. 43, No. 5, 696-703 (2007); translation from Differ. Uravn. 43, No. 5, 677-684 (2007). MSC: 35B27 35M10 35C20 PDFBibTeX XMLCite \textit{T. A. Mel'nik} and \textit{P. S. Vashchuk}, Differ. Equ. 43, No. 5, 696--703 (2007; Zbl 1140.35340); translation from Differ. Uravn. 43, No. 5, 677--684 (2007) Full Text: DOI
Kapustyan, O. V.; Melnik, V. S.; Valero, J. A weak attractor and properties of solutions for the three-dimensional Benard problem. (English) Zbl 1143.35013 Discrete Contin. Dyn. Syst. 18, No. 2-3, 449-481 (2007). Reviewer: A. Cichocka (Katowice) MSC: 35B41 35B40 35K55 35Q30 37B25 58C06 PDFBibTeX XMLCite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst. 18, No. 2--3, 449--481 (2007; Zbl 1143.35013) Full Text: DOI
Mel’nik, S. A. The stratification of solutions of the Ito’s nonlinear equations of the parabolic type with source. (Russian. English summary) Zbl 1119.35370 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2007, No. 1, 17-22 (2007). MSC: 35R60 60H15 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2007, No. 1, 17--22 (2007; Zbl 1119.35370)
Durante, T.; Mel’nyk, T. A.; Vashchuk, P. S. Asymptotic approximation for the solution of a boundary-value problem with varying type of boundary conditions in a thick two-level junction. (English) Zbl 1262.35177 Nonlinear Oscil., N.Y. 9, No. 3, 326-345 (2006) and Nelinijni Kolyvannya 9, No. 3, 336-355 (2006). MSC: 35Q05 35J25 35B27 PDFBibTeX XMLCite \textit{T. Durante} et al., Nonlinear Oscil., N.Y. 9, No. 3, 326--345 (2006; Zbl 1262.35177) Full Text: DOI Link
Kas’yanov, P. O.; Mel’nik, V. S.; Toscano, S. Periodic solutions of nonlinear evolution equations with \(W_{\lambda _0 } \)-pseudomonotone maps. (English) Zbl 1262.35212 Nonlinear Oscil., N.Y. 9, No. 2, 181-206 (2006) and Nelinijni Kolyvannya 9, No. 2, 187-212 (2006). MSC: 35R20 34G20 35A35 47N10 PDFBibTeX XMLCite \textit{P. O. Kas'yanov} et al., Nonlinear Oscil., N.Y. 9, No. 2, 181--206 (2006; Zbl 1262.35212) Full Text: DOI
Mel’nik, Sergeĭ A. The decomposition of the solution of a quasilinear stochastic equation of parabolic type. (Russian. English summary) Zbl 1152.60332 Ukr. Mat. Visn. 3, No. 2, 242-259 (2006); translation in Ukr. Math. Bull. 3, No. 2, 233-249(2006). MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Ukr. Mat. Visn. 3, No. 2, 242--259 (2006; Zbl 1152.60332); translation in Ukr. Math. Bull. 3, No. 2, 233--24 (2006)
Mel’nyk, T. A.; Vashchuk, P. S. Homogenization of the Neumann-Fourier problem in a thick two-level junction of type 3:2:1. (English) Zbl 1141.35328 J. Math. Phys. Anal. Geom. 2, No. 3, 318-337 (2006). MSC: 35B27 35J25 35C20 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{P. S. Vashchuk}, J. Math. Phys. Anal. Geom. 2, No. 3, 318--337 (2006; Zbl 1141.35328)
Kasyanov, P. O.; Mel’nik, V. S. Differential-operator inclusions in Banach spaces with \(\Omega_\lambda\)-pseudomonotone maps. (English) Zbl 1150.34525 Nonlinear Bound. Value Probl. 16, 46-68 (2006). MSC: 34G25 65L99 PDFBibTeX XMLCite \textit{P. O. Kasyanov} and \textit{V. S. Mel'nik}, Nonlinear Bound. Value Probl. 16, 46--68 (2006; Zbl 1150.34525)
Mel’nik, V. S. Topological methods in the theory of operator inclusions in Banach spaces. II. (Russian, English) Zbl 1125.47036 Ukr. Mat. Zh. 58, No. 4, 505-521 (2006); translation in Ukr. Math. J. 58, No. 4, 573-595 (2006). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47H04 35R70 47J05 47J20 49J35 49J53 PDFBibTeX XMLCite \textit{V. S. Mel'nik}, Ukr. Mat. Zh. 58, No. 4, 505--521 (2006; Zbl 1125.47036); translation in Ukr. Math. J. 58, No. 4, 573--595 (2006) Full Text: DOI
Mel’nik, T. A.; Vashchuk, P. S. Homogenization of boundary-value problem with alternate boundary conditions in a thick two-level junction. (Russian. English summary) Zbl 1120.35303 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 9, 27-35 (2006). MSC: 35B27 74K30 35J25 PDFBibTeX XMLCite \textit{T. A. Mel'nik} and \textit{P. S. Vashchuk}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 9, 27--35 (2006; Zbl 1120.35303)
Mel’nik, V. S. Topological methods in the theory of operator inclusions in Banach spaces. I. (Russian, English) Zbl 1096.47054 Ukr. Mat. Zh. 58, No. 2, 184-194 (2006); translation in Ukr. Math. J. 58, No. 2, 206-219 (2006). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47H04 PDFBibTeX XMLCite \textit{V. S. Mel'nik}, Ukr. Mat. Zh. 58, No. 2, 184--194 (2006; Zbl 1096.47054); translation in Ukr. Math. J. 58, No. 2, 206--219 (2006) Full Text: DOI
Kasyanov, P. O.; Mel’nik, V. S.; Piccirillo, A. M. On some theorems of compact embedding for Banach and locally convex spaces. (English) Zbl 1129.35490 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 5, 34-40 (2006). MSC: 35R45 34G25 34A60 PDFBibTeX XMLCite \textit{P. O. Kasyanov} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 5, 34--40 (2006; Zbl 1129.35490)
Kasyanov, P. O.; Mel’nik, V. S.; Piccirillo, A. M. On the Schauder basis in some Banach spaces. (English) Zbl 1129.35489 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 4, 31-35 (2006). MSC: 35R45 34G25 34A60 PDFBibTeX XMLCite \textit{P. O. Kasyanov} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 4, 31--35 (2006; Zbl 1129.35489)
Mel’nyk, T. A.; Vaschuk, P. S. Averaging of a boundary-value problem with variation of the type of boundary conditions in a thick two-level junction. (Ukrainian) Zbl 1150.35360 Nelinijni Kolyvannya 8, No. 2, 241-257 (2005). Reviewer: E. Ya. Smirnov (St. Petersburg) MSC: 35J05 35J25 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{P. S. Vaschuk}, Neliniĭni Kolyvannya 8, No. 2, 241--257 (2005; Zbl 1150.35360) Full Text: DOI
Kasyanov, P. O.; Melnik, V. S. On subdifferential mappings in Banach and Fréchet spaces. (Russian. English summary) Zbl 1104.49018 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2005, No. 12, 23-27 (2005). MSC: 49J52 49J50 PDFBibTeX XMLCite \textit{P. O. Kasyanov} and \textit{V. S. Melnik}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2005, No. 12, 23--27 (2005; Zbl 1104.49018)
Ficici, Sevan; Melnik, Ofer; Pollack, Jordan Selection in coevolutionary algorithms and the inverse problem. (English) Zbl 1121.91312 Tumer, Kagan (ed.) et al., Collectives and the design of complex systems. New York, NY: Springer (ISBN 0-387-40165-2/hbk). 277-294 (2004). MSC: 91A22 PDFBibTeX XMLCite \textit{S. Ficici} et al., in: Collectives and the design of complex systems. New York, NY: Springer. 277--294 (2004; Zbl 1121.91312)
Zgurovsky, M. Z.; Mel’nik, V. S. Nonlinear analysis and control of physical processes and fields. With a preface by Roman Voranka. (English) Zbl 1056.93002 Data and Knowledge in a Changing World. Berlin: Springer (ISBN 3-540-14019-0/hbk). xiv, 508 p. (2004). Reviewer: A. Akutowicz (Berlin) MSC: 93-02 93C25 46N10 93C10 93B28 93C20 80A32 80A20 35Q30 47J05 46T30 47J35 49J45 49J52 47J20 47J25 47H05 49J27 49K27 49J40 PDFBibTeX XMLCite \textit{M. Z. Zgurovsky} and \textit{V. S. Mel'nik}, Nonlinear analysis and control of physical processes and fields. With a preface by Roman Voranka. Berlin: Springer (2004; Zbl 1056.93002)
Melnik, Sergey Generic model management. Concepts and algorithms. (English) Zbl 1049.68048 Lecture Notes in Computer Science 2967. Berlin: Springer (ISBN 3-540-21980-3/pbk). xix, 238 p. (2004). MSC: 68P01 68-02 68P05 PDFBibTeX XMLCite \textit{S. Melnik}, Generic model management. Concepts and algorithms. Berlin: Springer (2004; Zbl 1049.68048) Full Text: DOI
Kapustyan, Alexei V.; Melnik, Valery S.; Valero, José Attractors of multivalued dynamical processes generated by phase-field equations. (English) Zbl 1063.37070 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 7, 1969-1983 (2003). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37L30 37C70 35B41 35K55 35K85 35R70 PDFBibTeX XMLCite \textit{A. V. Kapustyan} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 7, 1969--1983 (2003; Zbl 1063.37070) Full Text: DOI
Valero, J.; Kapustyan, O. V.; Carballo, T.; Langa, J.; Mel’nyk, V. S. On global attractors from “\(-\infty\)” of multivalued dynamical processes in topological spaces. (Ukrainian. English summary) Zbl 1026.37063 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 3, 7-10 (2003). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37L30 47H20 54C60 54H20 PDFBibTeX XMLCite \textit{J. Valero} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 3, 7--10 (2003; Zbl 1026.37063)
Valero, J.; Carballo, T.; Langa, J.; Mel’nyk, V. S. Attractors of nonautonomous and stochastic differential inclusions. (Ukrainian. English summary) Zbl 1026.37062 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 2, 7-14 (2003). Reviewer: I.O.Parasyuk (Kyïv) MSC: 37L30 37H10 34G25 54C60 35R70 47H04 47H20 35R60 60H15 PDFBibTeX XMLCite \textit{J. Valero} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2003, No. 2, 7--14 (2003; Zbl 1026.37062)
Do, Hong-Hai; Melnik, Sergey; Rahm, Erhard Comparison of schema matching evaluations. (English) Zbl 1027.68793 Chaudhri, Akmal B. (ed.) et al., Web, web-services, and database systems. NODe 2002 web- and database-related workshops, Erfurt, Germany, October 7-10, 2002. Revised papers. Berlin: Springer. Lect. Notes Comput. Sci. 2593, 221-237 (2003). MSC: 68U99 68U35 PDFBibTeX XMLCite \textit{H.-H. Do} et al., Lect. Notes Comput. Sci. 2593, 221--237 (2003; Zbl 1027.68793) Full Text: Link
Caraballo, T.; Langa, J. A.; Melnik, V. S.; Valero, J. Pullback attractors of nonautonomous and stochastic multivalued dynamical systems. (English) Zbl 1018.37048 Set-Valued Anal. 11, No. 2, 153-201 (2003). Reviewer: Victor Sharapov (Volgograd) MSC: 37L55 35B41 35K55 35K57 PDFBibTeX XMLCite \textit{T. Caraballo} et al., Set-Valued Anal. 11, No. 2, 153--201 (2003; Zbl 1018.37048) Full Text: DOI
Mel’nyk, S. A. Dynamics of non self-similar solutions of Cauchy problem for some parabolic type stochastic equations with polynomial nonlinearities. (Ukrainian, English) Zbl 1050.60066 Teor. Jmovirn. Mat. Stat. 67, 117-121 (2002); translation in Theory Probab. Math. Stat. 67, 129-134 (2003). Reviewer: N. M. Zinchenko (Kyïv) MSC: 60H15 PDFBibTeX XMLCite \textit{S. A. Mel'nyk}, Teor. Ĭmovirn. Mat. Stat. 67, 117--121 (2002; Zbl 1050.60066); translation in Theory Probab. Math. Stat. 67, 129--134 (2003)
Kapustyan, A. V.; Melnik, V. S.; Valero, J. Attractors of multivalued dynamical processes in topological space with inverse time. (English) Zbl 1048.37070 Nonlinear Bound. Value Probl. 12, 103-107 (2002). MSC: 37L30 35B41 PDFBibTeX XMLCite \textit{A. V. Kapustyan} et al., Nonlinear Bound. Value Probl. 12, 103--107 (2002; Zbl 1048.37070)
Melnik, Sergey; Garcia-Molina, Hector Divide-and-Conquer algorithm for computing set containment joins. (English) Zbl 1054.68799 Jensen, Christian S. (ed.) et al., Advances in database technology - EDBT 2002. 8th international conference on extending database technology, Prague, Czech Republic, March 25-27, 2002. Proceedings. Berlin: Springer (ISBN 3-540-43324-4). Lect. Notes Comput. Sci. 2287, 427-444 (2002). MSC: 68U99 68P15 PDFBibTeX XMLCite \textit{S. Melnik} and \textit{H. Garcia-Molina}, Lect. Notes Comput. Sci. 2287, 427--444 (2002; Zbl 1054.68799) Full Text: Link
Zgurovskij, M. Z.; Mel’nik, V. S. The Ky Fan inequality and operator inclusions in Banach spaces. (English. Russian original) Zbl 1046.49007 Cybern. Syst. Anal. 38, No. 2, 208-220 (2002); translation from Kibern. Sist. Anal. 2002, No. 2, 70-85 (2002). Reviewer: Nikolaos G. Yannakakis (Athens) MSC: 49J40 49J53 47J05 35R70 49J52 PDFBibTeX XMLCite \textit{M. Z. Zgurovskij} and \textit{V. S. Mel'nik}, Cybern. Syst. Anal. 38, No. 2, 208--220 (2002; Zbl 1046.49007); translation from Kibern. Sist. Anal. 2002, No. 2, 70--85 (2002) Full Text: DOI
Tikhonenko, N. Ya.; Mel’nik, A. S. Existence and properties of solutions of singular integro-differential equations on the real line. (English. Russian original) Zbl 1030.45005 Differ. Equ. 38, No. 9, 1298-1304 (2002); translation from Differ. Uravn. 38, No. 9, 1218-1224 (2002). Reviewer: V.Lakshmikantham (Melbourne/Florida) MSC: 45J05 45E05 PDFBibTeX XMLCite \textit{N. Ya. Tikhonenko} and \textit{A. S. Mel'nik}, Differ. Equ. 38, No. 9, 1298--1304 (2002; Zbl 1030.45005); translation from Differ. Uravn. 38, No. 9, 1218--1224 (2002) Full Text: DOI
Mel’nik, S. A. Estimates for the solution of the Cauchy problem for a stochastic differential equation of parabolic type with power-law nonlinearities (a strong source). (English. Russian original) Zbl 1030.60050 Differ. Equ. 38, No. 6, 847-854 (2002); translation from Differ. Uravn. 38, No. 6, 802-808 (2002). Reviewer: Wiesław Kotarski (Sosnowiec) MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Differ. Equ. 38, No. 6, 847--854 (2002; Zbl 1030.60050); translation from Differ. Uravn. 38, No. 6, 802--808 (2002) Full Text: DOI
Mel’nik, S. A. Upper and lower bounds of solution of the Cauchy problem for stochastic differential parabolic type equation with power nonlinearities (weak source). (English. Russian original) Zbl 1019.60061 Ukr. Math. J. 54, No. 1, 76-84 (2002); translation from Ukr. Mat. Zh. 54, No. 1, 63-70 (2002). Reviewer: Mikhail Moklyachuk (Kyïv) MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Ukr. Mat. Zh. 54, No. 1, 63--70 (2002; Zbl 1019.60061); translation from Ukr. Mat. Zh. 54, No. 1, 63--70 (2002) Full Text: DOI
Mel’nik, V. S.; Mizernyĭ, V. N.; Solonukha, O. V. A lower weak solution of a problem of the optimization of a time-dependent system with distributed parameters. (Russian) Zbl 1494.49016 Sergienko, I. V., Komp’yuterna matematyka. Optymizatsiya obchyslen’. Tom 2. Kiev: Natsional’naya Akademiya Nauk Ukrainy, Institut Kibernetiki im. V. M. Glushkova. 251-262 (2001). MSC: 49K20 49J20 PDFBibTeX XMLCite \textit{V. S. Mel'nik} et al., in: Komp'yuterna matematyka. Optymizatsiya obchyslen'. Tom 2. Kiev: Natsional'naya Akademiya Nauk Ukrainy, Institut Kibernetiki im. V. M. Glushkova. 251--262 (2001; Zbl 1494.49016)
Melnik, V. S.; Vakulenko, A. N. Topological method in the theory of operator inclusions with densely defined mappings in Banach spaces. (English) Zbl 1067.47063 Nonlinear Bound. Value Probl. 11, 132-145 (2001). Reviewer: Alexander A. Kovalevsky (Donetsk) MSC: 47H04 47H05 47J25 PDFBibTeX XMLCite \textit{V. S. Melnik} and \textit{A. N. Vakulenko}, Nonlinear Bound. Value Probl. 11, 132--145 (2001; Zbl 1067.47063)
Zgurovskij, M. Z.; Mel’nik, V. S. Penalty method for variational inequalities with multivalued mappings. III. (English. Russian original) Zbl 1041.49014 Cybern. Syst. Anal. 37, No. 2, 203-213 (2001); translation from Kibern. Sist. Anal. 2001, No. 2, 70-83 (2001). MSC: 49J40 49J20 65K10 PDFBibTeX XMLCite \textit{M. Z. Zgurovskij} and \textit{V. S. Mel'nik}, Cybern. Syst. Anal. 37, No. 2, 203--213 (2001; Zbl 1041.49014); translation from Kibern. Sist. Anal. 2001, No. 2, 70--83 (2001) Full Text: DOI
Mel’nik, S. A. Evolution of solution of the Cauchy problem for a stochastic combustion equation with a weak source. (Russian. English summary) Zbl 0986.60052 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 12, 31-34 (2001). MSC: 60H15 PDFBibTeX XMLCite \textit{S. A. Mel'nik}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 12, 31--34 (2001; Zbl 0986.60052)
Mel’nyk, S. A. The dynamics of solutions of the Cauchy problem for a parabolic type stochastic equation with power nonlinearities (the stochastic term is linear). (English. Ukrainian original) Zbl 0998.60023 Theory Probab. Math. Stat. 64, 129-137 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 110-117 (2001). Reviewer: N.M.Zinchenko (Kyïv) MSC: 60F10 62F05 PDFBibTeX XMLCite \textit{S. A. Mel'nyk}, Teor. Ĭmovirn. Mat. Stat. 64, 110--117 (2001; Zbl 0998.60023); translation from Teor. Jmovirn. Mat. Stat. 64, 110--117 (2001)
Valero, J.; Mel’nik, V. S. Attractors of non-autonomous evolution inclusions in infinite-dimensional spaces. (Russian. English summary) Zbl 0983.35152 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 10, 7-12 (2001). MSC: 35R70 37L30 47H04 PDFBibTeX XMLCite \textit{J. Valero} and \textit{V. S. Mel'nik}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2001, No. 10, 7--12 (2001; Zbl 0983.35152)
Gorr, G. V.; Mel’nik, A. S. On three invariant parities for the equations of solid body dynamics. (Russian. English summary) Zbl 1054.70504 Visn. Khark. Univ., Ser. Mat. Prykl. Mat. Mekh. 514, No. 50, 91-98 (2001). MSC: 70E17 70E05 PDFBibTeX XMLCite \textit{G. V. Gorr} and \textit{A. S. Mel'nik}, Visn. Khark. Univ., Ser. Mat. Prykl. Mat. Mekh. 514, No. 50, 91--98 (2001; Zbl 1054.70504)
Valero, J.; Mel’nik, V. S. On global attractors of nonautonomous evolution inclusions in Banach spaces. (English. Russian original) Zbl 1090.34579 Dokl. Math. 62, No. 3, 394-397 (2000); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 375, No. 6, 730-733 (2000). MSC: 34G25 34A60 37L30 PDFBibTeX XMLCite \textit{J. Valero} and \textit{V. S. Mel'nik}, Dokl. Math. 62, No. 3, 730--733 (2000; Zbl 1090.34579); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 375, No. 6, 730--733 (2000)
Mel’nik, V. S. Multivariational inequalities and operator inclusions in Banach spaces with mappings of the class \((S)_{+}\). (English. Russian original) Zbl 0987.47045 Ukr. Math. J. 52, No. 11, 1724-1736 (2000); translation from Ukr. Mat. Zh. 52, No. 11, 1513-1523 (2000). MSC: 47J20 47H04 49J40 PDFBibTeX XMLCite \textit{V. S. Mel'nik}, Ukr. Mat. Zh. 52, No. 11, 1513--1523 (2000; Zbl 0987.47045); translation from Ukr. Mat. Zh. 52, No. 11, 1513--1523 (2000) Full Text: DOI
Zgurovskij, M. Z.; Mel’nik, V. S. Penalty method for variational inequalities with multivalued mappings. I. (English. Russian original) Zbl 1039.49015 Cybern. Syst. Anal. 36, No. 4, 520-530 (2000); translation from Kibern. Sist. Anal. 2000, No. 4, 57-69 (2000). Reviewer: Dian K. Palagachev (Bari) MSC: 49J40 47J20 65K10 PDFBibTeX XMLCite \textit{M. Z. Zgurovskij} and \textit{V. S. Mel'nik}, Cybern. Syst. Anal. 36, No. 4, 520--530 (2000; Zbl 1039.49015); translation from Kibern. Sist. Anal. 2000, No. 4, 57--69 (2000) Full Text: DOI
Zgurovskij, M. Z.; Mel’nik, V. S. Penalty method for variational inequalities with multivalued mappings. II. (English. Russian original) Zbl 1040.49014 Cybern. Syst. Anal. 36, No. 5, 667-677 (2000); translation from Kibern. Sist. Anal. 2000, No. 5, 41-53 (2000). Reviewer: Dian K. Palagachev (Bari) MSC: 49J40 47J20 65K10 PDFBibTeX XMLCite \textit{M. Z. Zgurovskij} and \textit{V. S. Mel'nik}, Cybern. Syst. Anal. 36, No. 5, 667--677 (2000; Zbl 1040.49014); translation from Kibern. Sist. Anal. 2000, No. 5, 41--53 (2000) Full Text: DOI
Mel’nik, R. S.; Patsahan, O. V. Vapor-liquid critical-point properties of a symmetric binary fluid mixture. (English. Russian original) Zbl 1112.76482 Theor. Math. Phys. 124, No. 2, 1145-1156 (2000); translation from Teor. Mat. Fiz. 124, No. 2, 339-352 (2000). MSC: 76T10 35Q35 82D15 PDFBibTeX XMLCite \textit{R. S. Mel'nik} and \textit{O. V. Patsahan}, Theor. Math. Phys. 124, No. 2, 1145--1156 (2000; Zbl 1112.76482); translation from Teor. Mat. Fiz. 124, No. 2, 339--352 (2000) Full Text: DOI arXiv
Mel’nyk, T. A.; Nazarov, S. A. Asymptotic analysis of the Neumann problem on the junction of a body and thin heavy rods. (English. Russian original) Zbl 0988.74043 St. Petersbg. Math. J. 12, No. 2, 317-351 (2001); translation from Algebra Anal. 12, No. 2, 188-238 (2000). MSC: 74K30 74G10 35P20 35Q72 PDFBibTeX XMLCite \textit{T. A. Mel'nyk} and \textit{S. A. Nazarov}, St. Petersbg. Math. J. 12, No. 2, 1 (2000; Zbl 0988.74043); translation from Algebra Anal. 12, No. 2, 188--238 (2000)
Melnik, Valery S.; Valero, José On global attractors of multivalued semiprocesses and nonautonomous evolution inclusions. (English) Zbl 1063.35040 Set-Valued Anal. 8, No. 4, 375-403 (2000). MSC: 35B41 35K55 35K90 35B40 35R70 35K85 PDFBibTeX XMLCite \textit{V. S. Melnik} and \textit{J. Valero}, Set-Valued Anal. 8, No. 4, 375--403 (2000; Zbl 1063.35040) Full Text: DOI
Kogut, P. I.; Melnik, V. S. On weak compactness of bounded sets in Banach and locally convex spaces. (English. Russian original) Zbl 0963.46014 Ukr. Math. J. 52, No. 6, 837-846 (2000); translation from Ukr. Mat. Zh. 52, No. 6, 731-739 (2000). Reviewer: A.N.Kochubei (Kyïv) MSC: 46B50 46A50 46N10 49J20 PDFBibTeX XMLCite \textit{P. I. Kogut} and \textit{V. S. Melnik}, Ukr. Mat. Zh. 52, No. 6, 731--739 (2000; Zbl 0963.46014); translation from Ukr. Mat. Zh. 52, No. 6, 731--739 (2000) Full Text: DOI
Melnik, Roderick (ed.); Oliveira, Suely (ed.); Stewart, David (ed.) New methods in applied and computational mathematics. Proceedings of the 1st NEMACOM workshop, Hervey Bay, Queensland, Australia, July 9, 1998. (English) Zbl 0952.00038 Proceedings of the Centre for Mathematics and its Applications, Australian National University. 38. Canberra: Australian National University, Centre for Mathematics and its Applications. iv, 105 p. (2000). MSC: 00B25 65-06 68-06 PDFBibTeX XMLCite \textit{R. Melnik} (ed.) et al., New methods in applied and computational mathematics. Proceedings of the 1st NEMACOM workshop, Hervey Bay, Queensland, Australia, July 9, 1998. Canberra: Australian National University, Centre for Mathematics and its Applications (2000; Zbl 0952.00038) Full Text: Euclid
Mel’nik, V. S. On topological degree to some class of multivalued mappings and its applications. (English) Zbl 0979.47044 Nonlinear Bound. Value Probl. 9, 120-125 (1999). Reviewer: N.A.Britov (Donetsk) MSC: 47H11 47H07 47H04 PDFBibTeX XMLCite \textit{V. S. Mel'nik}, Nonlinear Bound. Value Probl. 9, 120--125 (1999; Zbl 0979.47044)
Melnik, A. S. A solution of generalized equations of rigid body dynamics. (Russian) Zbl 1076.70501 Tr. Inst. Prikl. Mat. Mekh. 4, 113-119 (1999). Reviewer: A. M. Kovalev (Donetsk) MSC: 70E17 70E40 PDFBibTeX XMLCite \textit{A. S. Melnik}, Tr. Inst. Prikl. Mat. Mekh. 4, 113--119 (1999; Zbl 1076.70501)
Kapustyan, A. V.; Mel’nik, V. S. Global attractors of multivalued semidynamical systems and their approximations. (English. Russian original) Zbl 0962.37010 Dokl. Math. 59, No. 3, 415-418 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 366, No. 4, 445-448 (1999). MSC: 37C70 54H20 37B25 35B41 PDFBibTeX XMLCite \textit{A. V. Kapustyan} and \textit{V. S. Mel'nik}, Dokl. Math. 59, No. 3, 445--448 (1999; Zbl 0962.37010); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 366, No. 4, 445--448 (1999)
Vasil’kevich, S. I.; Mel’nik, V. S.; Slastikov, V. V. On the global attractors of multivalued semiprocesses. (Russian. English summary) Zbl 0947.54020 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No. 7, 12-17 (1999). Reviewer: I.O.Parasyuk (Kyïv) MSC: 54H20 37C70 34A60 PDFBibTeX XMLCite \textit{S. I. Vasil'kevich} et al., Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1999, No. 7, 12--17 (1999; Zbl 0947.54020)
Valero, Kh. K.; Mel’nik, V. S. Attractors of set-valued semidynamic systems generated by evolution inclusions. (English. Russian original) Zbl 0973.37049 Dokl. Math. 58, No. 1, 49-52 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 361, No. 3, 295-299 (1998). Reviewer: Peter Poláčik (Bratislava) MSC: 37L30 35B40 37L05 35R70 37B25 PDFBibTeX XMLCite \textit{Kh. K. Valero} and \textit{V. S. Mel'nik}, Dokl. Math. 58, No. 1, 295--299 (1998; Zbl 0973.37049); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 361, No. 3, 295--299 (1998)
Mel’nik, V. S. The theory of topological degree of set-valued maps. (English. Russian original) Zbl 0968.47027 Dokl. Math. 58, No. 1, 42-45 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 361, No. 2, 164-167 (1998). Reviewer: Marco Biroli (Monza) MSC: 47H11 47H04 58C30 PDFBibTeX XMLCite \textit{V. S. Mel'nik}, Dokl. Math. 58, No. 1, 164--167 (1998; Zbl 0968.47027); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 361, No. 2, 164--167 (1998)
Kapustyan, A. V.; Mel’nik, V. S. Global attractors of multivalued semidynamical systems and their approximations. (English. Russian original) Zbl 0995.37011 Cybern. Syst. Anal. 34, No. 5, 719-725 (1998); translation from Kibern. Sist. Anal. 1998, No. 5, 102-111 (1998). Reviewer: O.Ninnemann (Berlin) MSC: 37B25 34D45 54C60 54H20 PDFBibTeX XMLCite \textit{A. V. Kapustyan} and \textit{V. S. Mel'nik}, Cybern. Syst. Anal. 34, No. 5, 719--725 (1998; Zbl 0995.37011); translation from Kibern. Sist. Anal. 1998, No. 5, 102--111 (1998) Full Text: DOI
Mel’nik, V. S.; Kogut, P. I. On one class of extremum problems for nonlinear operator systems. (English. Russian original) Zbl 0951.49010 Cybern. Syst. Anal. 34, No. 6, 894-904 (1998); translation from Kibern. Sist. Anal. 1998, No. 6, 121-132 (1998). Reviewer: Igor Bock (Bratislava) MSC: 49J27 90C48 49N60 PDFBibTeX XMLCite \textit{V. S. Mel'nik} and \textit{P. I. Kogut}, Cybern. Syst. Anal. 34, No. 6, 894--904 (1998; Zbl 0951.49010); translation from Kibern. Sist. Anal. 1998, No. 6, 121--132 (1998) Full Text: DOI
Melnik, S. A. Asymptotics of automodel solutions for some stochastic combustion equations. (Russian) Zbl 0933.80006 Visn. Donetsk. Univ., Ser. A, Pryrod. Nauky 2, 26-31 (1998). MSC: 80A25 37H10 60H10 PDFBibTeX XMLCite \textit{S. A. Melnik}, Visn. Donetsk. Univ., Ser. A, Pryrod. Nauky 2, 26--31 (1998; Zbl 0933.80006)
Kapustyan, A. V.; Mel’nik, V. S. Attractors of multivalued semidynamical systems and their approximations. (Russian) Zbl 0927.54043 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1998, No. 10, 21-25 (1998). Reviewer: I.O.Parasyuk (Kyïv) MSC: 54H20 37C70 34A60 PDFBibTeX XMLCite \textit{A. V. Kapustyan} and \textit{V. S. Mel'nik}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 1998, No. 10, 21--25 (1998; Zbl 0927.54043)