Pub Date : 2023-11-10DOI: 10.15388/namc.2024.29.33604
Ignas Dapšys, Raimondas Čiegis, Vadimas Starikovičius
We investigate the ill-posedness of the inverse biosensor problem when the biosensor signals are corrupted by noise. To solve the problem, we employ feed-forward and convolutional neural networks. Computational experiments were performed with different levels of additive and multiplicative noises for the batch and flow injection analysis modes of the biosensor. Obtained results show that the largest errors of recovered concentrations are located on the edges of the training domain. We have found that the inverse problem is less ill-posed in the flow injection analysis mode and concentrations can be reliably recovered for higher levels of noise compared to the batch mode. This finding is confirmed by the application of the DIRECT global optimization method to the considered inverse biosensor problem.
{"title":"Applying artificial neural networks to solve the inverse problem of evaluating concentrations in multianalyte mixtures from biosensor signals","authors":"Ignas Dapšys, Raimondas Čiegis, Vadimas Starikovičius","doi":"10.15388/namc.2024.29.33604","DOIUrl":"https://doi.org/10.15388/namc.2024.29.33604","url":null,"abstract":"We investigate the ill-posedness of the inverse biosensor problem when the biosensor signals are corrupted by noise. To solve the problem, we employ feed-forward and convolutional neural networks. Computational experiments were performed with different levels of additive and multiplicative noises for the batch and flow injection analysis modes of the biosensor. Obtained results show that the largest errors of recovered concentrations are located on the edges of the training domain. We have found that the inverse problem is less ill-posed in the flow injection analysis mode and concentrations can be reliably recovered for higher levels of noise compared to the batch mode. This finding is confirmed by the application of the DIRECT global optimization method to the considered inverse biosensor problem.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.15388/namc.2024.29.33535
Artūras Acus, Adolfas Dargys
Closed form expressions for a logarithm of general multivector (MV) in basis-free form in real geometric algebras (GAs) Clp,q are presented for all n = p + q = 3. In contrast to logarithm of complex numbers (isomorphic to Cl0,1), 3D logarithmic functions, due to appearance of two double angle arc tangent functions, allow to include two sets of sheets characterized by discrete coefficients. Formulas for generic and special cases of individual blades and their combinations are provided.
在实几何代数(GAs) Clp,q中，对于所有n = p + q = 3，给出了无基形式的一般多向量(MV)的对数的封闭表达式。与复数的对数(同构于Cl0,1)相反，三维对数函数由于两个双角弧切函数的出现，允许包含两组以离散系数为特征的片。给出了单个叶片及其组合的一般和特殊情况的公式。
{"title":"Logarithm of multivector in real 3D Clifford algebras","authors":"Artūras Acus, Adolfas Dargys","doi":"10.15388/namc.2024.29.33535","DOIUrl":"https://doi.org/10.15388/namc.2024.29.33535","url":null,"abstract":"Closed form expressions for a logarithm of general multivector (MV) in basis-free form in real geometric algebras (GAs) Clp,q are presented for all n = p + q = 3. In contrast to logarithm of complex numbers (isomorphic to Cl0,1), 3D logarithmic functions, due to appearance of two double angle arc tangent functions, allow to include two sets of sheets characterized by discrete coefficients. Formulas for generic and special cases of individual blades and their combinations are provided.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135539750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.15388/namc.2024.29.33534
Subhadip Roy, Parbati Saha, Sumon Ghosh, Binayak S. Choudhury
In this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces.
{"title":"Fixed points of generalized cyclic contractions without continuity and application to fractal generation","authors":"Subhadip Roy, Parbati Saha, Sumon Ghosh, Binayak S. Choudhury","doi":"10.15388/namc.2024.29.33534","DOIUrl":"https://doi.org/10.15388/namc.2024.29.33534","url":null,"abstract":"In this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135474855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-07DOI: 10.15388/amc.2024.29.33550
Guang Yang, Guo-Cheng Wu, Hui Fu
A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function. From the Cauchy problem of the nth-order difference equation, new fractional-order sum and differences are presented. The propositions between each other and numerical schemes are derived. Finally, fractional linear difference equations are presented, and exact solutions are given by using a new discrete Mittag-Leffler function.
{"title":"Discrete fractional calculus with exponential memory: Propositions, numerical schemes and asymptotic stability","authors":"Guang Yang, Guo-Cheng Wu, Hui Fu","doi":"10.15388/amc.2024.29.33550","DOIUrl":"https://doi.org/10.15388/amc.2024.29.33550","url":null,"abstract":"A new fractional difference with an exponential kernel function is proposed in this study. First, a difference operator is defined by the exponential function. From the Cauchy problem of the nth-order difference equation, new fractional-order sum and differences are presented. The propositions between each other and numerical schemes are derived. Finally, fractional linear difference equations are presented, and exact solutions are given by using a new discrete Mittag-Leffler function.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135539598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-31DOI: 10.15388/namc.2023.28.33508
Kęstutis Kubilius
In this article, we are interested in fractional stochastic differential equations (FSDEs) with stochastic forcing, i.e., to FSDE we add a stochastic forcing term. The conditions for the existence and uniqueness of solutions of such equations are obtained, and the convergence rate of the implicit Euler approximation scheme for them is established. Such types of equations can be applied to the consideration of FSDEs with a permeable wall.
{"title":"Fractional SDEs with stochastic forcing: Existence, uniqueness, and approximation","authors":"Kęstutis Kubilius","doi":"10.15388/namc.2023.28.33508","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33508","url":null,"abstract":"In this article, we are interested in fractional stochastic differential equations (FSDEs) with stochastic forcing, i.e., to FSDE we add a stochastic forcing term. The conditions for the existence and uniqueness of solutions of such equations are obtained, and the convergence rate of the implicit Euler approximation scheme for them is established. Such types of equations can be applied to the consideration of FSDEs with a permeable wall.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-28DOI: 10.15388/namc.2023.28.33507
Andrius Grigutis, Arvydas Karbonskis, Jonas Šiaulys
In ruin theory, the net profit condition intuitively means that the sizes of the incurred random claims are on average less than the premiums gained between the successive interoccurrence times. The breach of the net profit condition causes guaranteed ruin in few but simple cases when both the claims’ interoccurrence time and random claims are degenerate. In this work, we give a simplified argumentation for the unavoidable ruin when the incurred claims are on average equal to the premiums gained between the successive interoccurrence times. We study the discrete-time risk model with N ∈ N periodically occurring independent distributions, the classical risk model, also known as the Cramér–Lundberg risk process, and the more general Sparre Andersen model.
在破产理论中，净利润条件直观地意味着随机索赔的规模平均小于连续发生时间之间获得的保费。在索赔发生时间和随机索赔均退化的情况下，在少数但简单的情况下，违反净利润条件导致保证破产。在这项工作中，我们给出了一个简化的论证不可避免的破产，当发生的索赔平均等于在连续的相互发生时间之间获得的保费。我们研究了N∈N周期性独立分布的离散时间风险模型、经典风险模型(也称为cram r - lundberg风险过程)和更一般的Sparre Andersen模型。
{"title":"Ruin probability for renewal risk models with neutral net profit condition","authors":"Andrius Grigutis, Arvydas Karbonskis, Jonas Šiaulys","doi":"10.15388/namc.2023.28.33507","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33507","url":null,"abstract":"In ruin theory, the net profit condition intuitively means that the sizes of the incurred random claims are on average less than the premiums gained between the successive interoccurrence times. The breach of the net profit condition causes guaranteed ruin in few but simple cases when both the claims’ interoccurrence time and random claims are degenerate. In this work, we give a simplified argumentation for the unavoidable ruin when the incurred claims are on average equal to the premiums gained between the successive interoccurrence times. We study the discrete-time risk model with N ∈ N periodically occurring independent distributions, the classical risk model, also known as the Cramér–Lundberg risk process, and the more general Sparre Andersen model.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136231814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider an optimal control problem for a differential inclusion of the Carathéodory type affine with respect to the control with a coercive cost functional on a semiaxis and with fast oscillating time-dependent coefficients. We prove that, when the small parameter converges to zero, the solution to this problem tends to some solution of the optimal control problem with averaged coefficients, where the averaging we understand in the sense of the Kuratowski upper limit.
{"title":"Asymptotic analysis of optimal control problems on the semiaxes for Carathéodory differential inclusions with fast oscillating coefficients","authors":"Sergey Dashkovskiy, Oleksiy Kapustyan, Olena Kapustian, Tetyana Zhuk","doi":"10.15388/namc.2023.28.33435","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33435","url":null,"abstract":"We consider an optimal control problem for a differential inclusion of the Carathéodory type affine with respect to the control with a coercive cost functional on a semiaxis and with fast oscillating time-dependent coefficients. We prove that, when the small parameter converges to zero, the solution to this problem tends to some solution of the optimal control problem with averaged coefficients, where the averaging we understand in the sense of the Kuratowski upper limit.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.15388/namc.2023.28.33475
Lijun Pan, Jianqiang Hu, Jinde Cao
This paper generalizes Razumikhin-type theorem and Krasovskii stability theorem of impulsive stochastic delay systems. By proposing uniformly stable function (USF) in the form of impulse as a new tool, some properties about USF and some novel pth moment decay theorems are derived. Based on these new theorems, the stability theorems of impulsive stochastic linear delay system are acquired via the Razumikhin method and the Krasovskii method. The obtained results enhance the elasticity of the impulsive gain by comparing the previous results. Finally, numerical examples are given to demonstrate the effectiveness of theoretical results.
{"title":"Razumikhin and Krasovskii stability of impulsive stochastic delay systems via uniformly stable function method","authors":"Lijun Pan, Jianqiang Hu, Jinde Cao","doi":"10.15388/namc.2023.28.33475","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33475","url":null,"abstract":"This paper generalizes Razumikhin-type theorem and Krasovskii stability theorem of impulsive stochastic delay systems. By proposing uniformly stable function (USF) in the form of impulse as a new tool, some properties about USF and some novel pth moment decay theorems are derived. Based on these new theorems, the stability theorems of impulsive stochastic linear delay system are acquired via the Razumikhin method and the Krasovskii method. The obtained results enhance the elasticity of the impulsive gain by comparing the previous results. Finally, numerical examples are given to demonstrate the effectiveness of theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.15388/namc.2023.28.33472
Zhenhai Liu, Nikolaos S. Papageorgiou
We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we assume that the perturbation changes sign. We prove a multiplicity result producing two positive smooth solutions when the coefficient function in the singular term is small in the L∞-norm.
{"title":"Singular anisotropic equations with a sign-changing perturbation","authors":"Zhenhai Liu, Nikolaos S. Papageorgiou","doi":"10.15388/namc.2023.28.33472","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33472","url":null,"abstract":"We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we assume that the perturbation changes sign. We prove a multiplicity result producing two positive smooth solutions when the coefficient function in the singular term is small in the L∞-norm.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-27DOI: 10.15388/namc.2023.28.33436
Ishak Altun, İlker Gençtürk, Ali Erduran
In this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Prešić-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example.
{"title":"Prešić-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations","authors":"Ishak Altun, İlker Gençtürk, Ali Erduran","doi":"10.15388/namc.2023.28.33436","DOIUrl":"https://doi.org/10.15388/namc.2023.28.33436","url":null,"abstract":"In this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Prešić-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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