This paper is devoted to the problem of finding a local parametric representation of solutions to a nonlinear algebraic system in the neighborhood of singular points. At points where the Jacobian matrix becomes degenerate, the implicit function theorem cannot be applied directly. Therefore, a new Newton-Minkowski method is proposed, which combines the techniques of Newton polyhedra, Minkowski sums, and power geometry to study the local properties of the solution set. The effectiveness of the method in describing the local structure of solutions near singularities and obtaining explicit parametrizations is demonstrated through illustrative examples.
| Mualliflar | A S Soleev, Sh. Kurdashov |
|---|---|
| Jurnal | Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi |
| Nashriyot | Самарқанд давлат университети |
| ISSN | 2091-5446, 2181-1296 |
| Nashr sanasi | 2026-07-01 |
| Jild | 1 |
| Son | 3 |
| Betlar | 5-14 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.59251/2181-3973.2025.v1.138.1.3876 |
| Indeksga qo‘shilgan | 2026-09-02 |
DOI: 10.59251/2181-3973.2025.v1.138.1.3876 · Maqolaning asl sahifasi
| APA | A S Soleev, & Sh. Kurdashov (2026). FINDING THE LOCAL PARAMETRIC REPRESENTATION OF A FOUR-DIMENSIONAL NONLINEAR ALGEBRAIC SYSTEM IN THE NEIGHBORHOOD OF SMALL SINGULARITIES. Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 5-14. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3876 |
|---|---|
| GOST (OAK) | A S Soleev, Sh. Kurdashov FINDING THE LOCAL PARAMETRIC REPRESENTATION OF A FOUR-DIMENSIONAL NONLINEAR ALGEBRAIC SYSTEM IN THE NEIGHBORHOOD OF SMALL SINGULARITIES // Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi. – 2026. – T. 1, № 3. – P. 5-14. – DOI: 10.59251/2181-3973.2025.v1.138.1.3876. |
| MLA | A S Soleev, and Sh. Kurdashov. “FINDING THE LOCAL PARAMETRIC REPRESENTATION OF A FOUR-DIMENSIONAL NONLINEAR ALGEBRAIC SYSTEM IN THE NEIGHBORHOOD OF SMALL SINGULARITIES.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 5-14, 2026. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3876 |
| Chicago | A S Soleev, and Sh. Kurdashov. “FINDING THE LOCAL PARAMETRIC REPRESENTATION OF A FOUR-DIMENSIONAL NONLINEAR ALGEBRAIC SYSTEM IN THE NEIGHBORHOOD OF SMALL SINGULARITIES.” Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 5-14 (2026). https://doi.org/10.59251/2181-3973.2025.v1.138.1.3876 |
| Harvard | A S Soleev, and Sh. Kurdashov (2026) ‘FINDING THE LOCAL PARAMETRIC REPRESENTATION OF A FOUR-DIMENSIONAL NONLINEAR ALGEBRAIC SYSTEM IN THE NEIGHBORHOOD OF SMALL SINGULARITIES’, Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi, 1(3), 5-14. https://doi.org/10.59251/2181-3973.2025.v1.138.1.3876 |
| BibTeX | @article{assoleev2026,
title = {FINDING THE LOCAL PARAMETRIC REPRESENTATION OF A FOUR-DIMENSIONAL NONLINEAR ALGEBRAIC SYSTEM IN THE NEIGHBORHOOD OF SMALL SINGULARITIES},
author = {A S Soleev and Sh. Kurdashov},
journal = {Samarqand davlat universiteti ilmiy tadqiqotlar axborotnomasi},
year = {2026},
volume = {1},
number = {3},
pages = {5-14},
doi = {10.59251/2181-3973.2025.v1.138.1.3876},
url = {https://doi.org/10.59251/2181-3973.2025.v1.138.1.3876}
} |
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