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Series Solution Method for Solving Sequential Caputo Fractional Differential Equations 求解顺序卡普托分数阶微分方程的级数解法
AppliedMath Pub Date : 2023-10-20 DOI: 10.3390/appliedmath3040039
Aghalaya S. Vatsala, Govinda Pageni
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引用次数: 0
The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions 系数满足各种单调性条件的复多项式圆盘上的零个数
AppliedMath Pub Date : 2023-10-17 DOI: 10.3390/appliedmath3040038
Robert Gardner, Matthew Gladin
{"title":"The Number of Zeros in a Disk of a Complex Polynomial with Coefficients Satisfying Various Monotonicity Conditions","authors":"Robert Gardner, Matthew Gladin","doi":"10.3390/appliedmath3040038","DOIUrl":"https://doi.org/10.3390/appliedmath3040038","url":null,"abstract":"Motivated by results on the location of the zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström–Kakeya theorem and its recent generalizations), we impose similar conditions and give bounds on the number of zeros in certain regions. We do so by introducing a reversal in monotonicity conditions on the real and imaginary parts of the coefficients and also on their moduli. The conditions imposed are less restrictive than many of those in the current literature and hence apply to polynomials not covered by previous results. The results presented naturally apply to certain classes of lacunary polynomials. In particular, the results apply to certain polynomials with two gaps in their coefficients.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135994132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling 随机延迟微分方程:一种理解生物系统并应用于疾病建模的综合方法
AppliedMath Pub Date : 2023-10-09 DOI: 10.3390/appliedmath3040037
Oluwatosin Babasola, Evans Otieno Omondi, Kayode Oshinubi, Nancy Matendechere Imbusi
{"title":"Stochastic Delay Differential Equations: A Comprehensive Approach for Understanding Biosystems with Application to Disease Modelling","authors":"Oluwatosin Babasola, Evans Otieno Omondi, Kayode Oshinubi, Nancy Matendechere Imbusi","doi":"10.3390/appliedmath3040037","DOIUrl":"https://doi.org/10.3390/appliedmath3040037","url":null,"abstract":"Mathematical models have been of great importance in various fields, especially for understanding the dynamical behaviour of biosystems. Several models, based on classical ordinary differential equations, delay differential equations, and stochastic processes are commonly employed to gain insights into these systems. However, there is potential to extend such models further by combining the features from the classical approaches. This work investigates stochastic delay differential equations (SDDEs)-based models to understand the behaviour of biosystems. Numerical techniques for solving these models that demonstrate a more robust representation of real-life scenarios are presented. Additionally, quantitative roles of delay and noise to gain a deeper understanding of their influence on the system’s overall behaviour are analysed. Subsequently, numerical simulations that illustrate the model’s robustness are provided and the results suggest that SDDEs provide a more comprehensive representation of many biological systems, effectively accounting for the uncertainties that arise in real-life situations.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135093449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Terracini Loci for Maps 地图Terracini Loci
AppliedMath Pub Date : 2023-09-17 DOI: 10.3390/appliedmath3030036
Edoardo Ballico
{"title":"Terracini Loci for Maps","authors":"Edoardo Ballico","doi":"10.3390/appliedmath3030036","DOIUrl":"https://doi.org/10.3390/appliedmath3030036","url":null,"abstract":"Let X be a smooth projective variety and f:X→Pr a morphism birational onto its image. We define the Terracini loci of the map f. Most results are only for the case dimX=1. With this new and more flexible definition, it is possible to prove strong nonemptiness results with the full classification of all exceptional cases. We also consider Terracini loci with restricted support (solutions not intersecting a closed set B⊊X or solutions containing a prescribed p∈X). Our definitions work both for the Zariski and the euclidean topology and we suggest extensions to the case of real varieties. We also define Terracini loci for joins of two or more subvarieties of the same projective space. The proofs use algebro-geometric tools.","PeriodicalId":477867,"journal":{"name":"AppliedMath","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135259550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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