Pub Date : 2023-05-28DOI: 10.12697/acutm.2023.27.10
Kalev Pärna, Mohammad Jamsher Ali
In this paper, we study a Lévy risk process consisting of Brownian component together with premiums and claims that are phase-type with many phases. Our aim is to approximate the probability of ruin without touching an upper barrier a. In line with this, the study demonstrates that the described Lévy risk process can essentially be replaced with a simpler risk process in which both premiums and claims are phase-type with just few phases.
{"title":"PH approximation of two-barrier ruin probability for Lévy risk having two-sided PH jumps","authors":"Kalev Pärna, Mohammad Jamsher Ali","doi":"10.12697/acutm.2023.27.10","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.10","url":null,"abstract":"In this paper, we study a Lévy risk process consisting of Brownian component together with premiums and claims that are phase-type with many phases. Our aim is to approximate the probability of ruin without touching an upper barrier a. In line with this, the study demonstrates that the described Lévy risk process can essentially be replaced with a simpler risk process in which both premiums and claims are phase-type with just few phases.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135896110","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}
Pub Date : 2023-05-28DOI: 10.12697/acutm.2023.27.06
Sejal Puvar, Rajendra G. Vyas
Introducing (ψ, ϕ) − Gb-Wardowski contraction for three maps, a common fixed point result is obtained for complete Gb-metric spaces. An application related to discontinuous activation function in neural network is also established.
{"title":"(ψ, ϕ)-Wardowski contraction for three maps in Gb-metric spaces","authors":"Sejal Puvar, Rajendra G. Vyas","doi":"10.12697/acutm.2023.27.06","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.06","url":null,"abstract":"Introducing (ψ, ϕ) − Gb-Wardowski contraction for three maps, a common fixed point result is obtained for complete Gb-metric spaces. An application related to discontinuous activation function in neural network is also established.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894866","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}
Pub Date : 2023-05-28DOI: 10.12697/acutm.2023.27.05
Milutin Obradović, Nikola Tuneski
In this paper we determine the upper bounds of the Hankel determinants of special type H2(3)(f) and H2(4)(f) for the general class of univalent functions and for the class U.
{"title":"Two types of the second Hankel determinant for the class U and the general class S","authors":"Milutin Obradović, Nikola Tuneski","doi":"10.12697/acutm.2023.27.05","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.05","url":null,"abstract":"In this paper we determine the upper bounds of the Hankel determinants of special type H2(3)(f) and H2(4)(f) for the general class of univalent functions and for the class U.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894862","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}
Pub Date : 2023-05-28DOI: 10.12697/acutm.2023.27.09
Simo Puntanen, Stephen Haslett, Jarkko Isotalo, Augustyn Markiewicz
We consider the partitioned linear model M12(V0) = { y, X1β1 + X2 β2, V0 } and the corresponding small model M1(V0) = { y, X1β1 , V0 } . We define the set V1/12 of nonnegative definite matrices V such that every representation of the best linear unbiased estimator, BLUE, of μ1 = X1β1 under M12(V0) remains BLUE under M12(V) . Correspondingly, we can characterize the set V1 of matrices V such that every BLUE of μ1 = X1β1 under M1(V0) remains BLUE under M1(V). In this paper we focus on the mutual relations between the sets V1 and V1/12 .
{"title":"Further remarks on permissible covariance structures for simultaneous retention of BLUEs in linear models","authors":"Simo Puntanen, Stephen Haslett, Jarkko Isotalo, Augustyn Markiewicz","doi":"10.12697/acutm.2023.27.09","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.09","url":null,"abstract":"We consider the partitioned linear model M12(V0) = { y, X1β1 + X2 β2, V0 } and the corresponding small model M1(V0) = { y, X1β1 , V0 } . We define the set V1/12 of nonnegative definite matrices V such that every representation of the best linear unbiased estimator, BLUE, of μ1 = X1β1 under M12(V0) remains BLUE under M12(V) . Correspondingly, we can characterize the set V1 of matrices V such that every BLUE of μ1 = X1β1 under M1(V0) remains BLUE under M1(V). In this paper we focus on the mutual relations between the sets V1 and V1/12 .","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135896103","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}
Pub Date : 2023-05-28DOI: 10.12697/acutm.2023.27.08
None Bhaskar Srivastava
The idea of this paper is to prove two general theorems using q-series and deduce some partial theta identities and false theta identities. Some of the identities of Ramanujan come as special cases.
本文的思想是利用q级数证明两个一般定理，并推导出一些偏恒等式和假恒等式。拉马努金的一些身份是特例。
{"title":"On the identities of Ramanujan – a q-series approach","authors":"None Bhaskar Srivastava","doi":"10.12697/acutm.2023.27.08","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.08","url":null,"abstract":"The idea of this paper is to prove two general theorems using q-series and deduce some partial theta identities and false theta identities. Some of the identities of Ramanujan come as special cases.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135896101","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}
Pub Date : 2023-05-28DOI: 10.12697/acutm.2023.27.07
Alvin Lepik
We show that a unitary surjective Morita context connecting two semigroups yields Galois connections between certain lattices of compatible relations whenever either semigroup has common weak local units. In the event both semigroups have common weak local units, we obtain mutually inverse lattice isomorphisms that preserve reflexivity, symmetricity and transitivity between the lattices of compatible relations on the semigroups.
{"title":"Some Galois connections arising from Morita contexts of semigroups","authors":"Alvin Lepik","doi":"10.12697/acutm.2023.27.07","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.07","url":null,"abstract":"We show that a unitary surjective Morita context connecting two semigroups yields Galois connections between certain lattices of compatible relations whenever either semigroup has common weak local units. In the event both semigroups have common weak local units, we obtain mutually inverse lattice isomorphisms that preserve reflexivity, symmetricity and transitivity between the lattices of compatible relations on the semigroups.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135894871","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}
Pub Date : 2023-05-27DOI: 10.12697/acutm.2023.27.03
Bedia Merih Özçetin, Mustafa Düldül
In this paper, we study the intersection problem of two surfaces in which at least one surface is given by its implicit equation in Euclidean n-space. We first obtain the curvatures of the transversal intersection curve of two implicit surfaces. Later, the intersection problem is studied for a parametric surface and an implicit surface in n-dimensional Euclidean space. Finally, we present examples as applications of the given methods.
{"title":"Implicit-implicit and parametric-implicit surface intersections in Euclidean n-space","authors":"Bedia Merih Özçetin, Mustafa Düldül","doi":"10.12697/acutm.2023.27.03","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.03","url":null,"abstract":"In this paper, we study the intersection problem of two surfaces in which at least one surface is given by its implicit equation in Euclidean n-space. We first obtain the curvatures of the transversal intersection curve of two implicit surfaces. Later, the intersection problem is studied for a parametric surface and an implicit surface in n-dimensional Euclidean space. Finally, we present examples as applications of the given methods.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135951042","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}
Pub Date : 2023-05-27DOI: 10.12697/acutm.2023.27.04
Teerapat Srichan
It is a classical result that the probability that two positive integers n, m ≤ x are relatively prime tends to 1/ζ(2) = 6/π2 as x → ∞. In this paper, the same result is still true when n and m are restricted to sub-sequences, i.e. Piatetski–Shapiro sequence, Beatty sequence and the floor function set.
{"title":"On the distribution of the greatest common divisor of the elements in integral part sets","authors":"Teerapat Srichan","doi":"10.12697/acutm.2023.27.04","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.04","url":null,"abstract":"It is a classical result that the probability that two positive integers n, m ≤ x are relatively prime tends to 1/ζ(2) = 6/π2 as x → ∞. In this paper, the same result is still true when n and m are restricted to sub-sequences, i.e. Piatetski–Shapiro sequence, Beatty sequence and the floor function set.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135950871","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}
Pub Date : 2023-05-26DOI: 10.12697/acutm.2023.27.01
Deeba Afzal, Muhammad Jibril Sahir
In this research article, we investigate reverse Radon's inequality, reverse Bergström's inequality, the reverse weighted power mean inequality, reverse Schlömilch's inequality, reverse Bernoulli's inequality and reverse Lyapunov's inequality with Specht's ratio on time scales. We also present reverse Rogers--Holder's inequality with logarithmic mean and Specht's ratio on time scales. The time scale dynamic inequalities unify and extend some continuous inequalities and their corresponding discrete and quantum versions.
{"title":"Specht's ratio and logarithmic mean in time scale dynamic inequalities and their retrospective variants","authors":"Deeba Afzal, Muhammad Jibril Sahir","doi":"10.12697/acutm.2023.27.01","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.01","url":null,"abstract":"In this research article, we investigate reverse Radon's inequality, reverse Bergström's inequality, the reverse weighted power mean inequality, reverse Schlömilch's inequality, reverse Bernoulli's inequality and reverse Lyapunov's inequality with Specht's ratio on time scales. We also present reverse Rogers--Holder's inequality with logarithmic mean and Specht's ratio on time scales. The time scale dynamic inequalities unify and extend some continuous inequalities and their corresponding discrete and quantum versions.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134922728","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}
Pub Date : 2023-05-26DOI: 10.12697/acutm.2023.27.02
Nasir Sohail, Abdullahi Umar
A semigroup S is called left ample if it can be embedded in the symmetric inverse semigroup IX of partial bijections of a non-empty set X such that the image of S is closed under the unary operation α → αα⁻¹, where α⁻¹ is the inverse of α in IX. Right ample semigroups are defined dually. A semigroup is called ample if it is both left and right ample. A monoid is (left, right) ample if it is (left, right) ample as a semigroup. We observe that the dominion of an ample subsemigroup of IX coincides with the inverse subsemigroup of IX generated by it. We then determine the dominions of certain submonoids of In, the symmetric inverse semigroup over a finite chain 1<2<⋯
{"title":"On dominions of certain ample monoids","authors":"Nasir Sohail, Abdullahi Umar","doi":"10.12697/acutm.2023.27.02","DOIUrl":"https://doi.org/10.12697/acutm.2023.27.02","url":null,"abstract":"A semigroup S is called left ample if it can be embedded in the symmetric inverse semigroup IX of partial bijections of a non-empty set X such that the image of S is closed under the unary operation α → αα⁻¹, where α⁻¹ is the inverse of α in IX. Right ample semigroups are defined dually. A semigroup is called ample if it is both left and right ample. A monoid is (left, right) ample if it is (left, right) ample as a semigroup. We observe that the dominion of an ample subsemigroup of IX coincides with the inverse subsemigroup of IX generated by it. We then determine the dominions of certain submonoids of In, the symmetric inverse semigroup over a finite chain 1<2<⋯<n.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134922590","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}
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