Abstract In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.
{"title":"Analysis and optimisation of a M/M/1/WV queue with Bernoulli schedule vacation interruption and customer’s impatience","authors":"Shakir Majid, A. Bouchentouf, Abdelhak Guendouzi","doi":"10.2478/ausm-2021-0023","DOIUrl":"https://doi.org/10.2478/ausm-2021-0023","url":null,"abstract":"Abstract In this investigation, we establish a steady-state solution of an infinite-space single-server Markovian queueing system with working vacation (WV), Bernoulli schedule vacation interruption, and impatient customers. Once the system becomes empty, the server leaves the system and takes a vacation with probability p or a working vacation with probability 1 − p, where 0 ≤ p ≤ 1. The working vacation period is interrupted if the system is non empty at a service completion epoch and the server resumes its regular service period with probability 1 − q or carries on with the working vacation with probability q. During vacation and working vacation periods, the customers may be impatient and leave the system. We use a probability generating function technique to obtain the expected number of customers and other system characteristics. Stochastic decomposition of the queueing model is given. Then, a cost function is constructed by considering different cost elements of the system states, in order to determine the optimal values of the service rate during regular busy period, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Further, by taking illustration, numerical experiment is performed to validate the analytical results and to examine the impact of different parameters on the system characteristics.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74676187","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}
Abstract We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.
{"title":"Fixed point and a Cantilever beam problem in a partial b-metric space","authors":"A. Tomar, M. Joshi, Venkatesh Bhatt","doi":"10.2478/ausm-2021-0032","DOIUrl":"https://doi.org/10.2478/ausm-2021-0032","url":null,"abstract":"Abstract We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77074362","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}
Abstract In this article, we consider a Lamé system with a delay term in the internal fractional feedback. We show the existence and uniqueness of solutions by means of the semigroup theory under a certain condition between the weight of the delay term in the fractional feedback and the weight of the term without delay. Furthermore, we show the exponential stability by the classical theorem of Gearhart, Huang and Pruss.
{"title":"Stability result of the Lamé system with a delay term in the internal fractional feedback","authors":"A. Benaissa, Soumia Gaouar","doi":"10.2478/ausm-2021-0021","DOIUrl":"https://doi.org/10.2478/ausm-2021-0021","url":null,"abstract":"Abstract In this article, we consider a Lamé system with a delay term in the internal fractional feedback. We show the existence and uniqueness of solutions by means of the semigroup theory under a certain condition between the weight of the delay term in the fractional feedback and the weight of the term without delay. Furthermore, we show the exponential stability by the classical theorem of Gearhart, Huang and Pruss.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76500944","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}
Abstract In this paper by using hereditary classes [6], we define the notion of γ -Lindelöf modulo hereditary classes called γℋ-Lindelöf and obtain several properties of γℋ-Lindelöf spaces.
摘要利用遗传类[6]，定义了γ -Lindelöf模遗传类γ h -Lindelöf的概念，得到了γ h -Lindelöf空间的若干性质。
{"title":"Generalizations of Lindelöf spaces via hereditary classes","authors":"A. Al-Omari, T. Noiri","doi":"10.2478/ausm-2021-0017","DOIUrl":"https://doi.org/10.2478/ausm-2021-0017","url":null,"abstract":"Abstract In this paper by using hereditary classes [6], we define the notion of γ -Lindelöf modulo hereditary classes called γℋ-Lindelöf and obtain several properties of γℋ-Lindelöf spaces.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85089278","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}
Abstract In the paper, Lp-harmonic addition, p-harmonic Blaschke addition and Lp-dual mixed volume are improved. A new p-harmonic Blaschke mixed quermassintegral is introduced. The relationship between p-harmonic Blaschke mixed volume and Lp-dual mixed volume is shown.
{"title":"The Lp-mixed quermassintegrals for 0 < p < 1","authors":"Chang-Jian Zhao, M. Bencze","doi":"10.2478/ausm-2021-0033","DOIUrl":"https://doi.org/10.2478/ausm-2021-0033","url":null,"abstract":"Abstract In the paper, Lp-harmonic addition, p-harmonic Blaschke addition and Lp-dual mixed volume are improved. A new p-harmonic Blaschke mixed quermassintegral is introduced. The relationship between p-harmonic Blaschke mixed volume and Lp-dual mixed volume is shown.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87613140","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}
S. Pirzada, B. Rather, Rezwan Ul Shaban, Merajuddin
Abstract For a simple connected graph G of order n having distance signless Laplacian eigenvalues ρ1Q≥ρ2Q≥⋯≥ρnQ rho _1^Q ge rho _2^Q ge cdots ge rho _n^Q , the distance signless Laplacian energy DSLE(G) is defined as DSLE(G)=∑i=1n| ρiQ-2W(G)n | DSLEleft( G right) = sumnolimits_{i = 1}^n {left| {rho _i^Q - {{2Wleft( G right)} over n}} right|} where W(G) is the Weiner index of G. We show that the complete split graph has the minimum distance signless Laplacian energy among all connected graphs with given independence number. Further, we prove that the graph Kk ∨ ( Kt∪ Kn−k−t), 1≤t≤⌊ n-k2 ⌋ 1 le t le leftlfloor {{{n - k} over 2}} rightrfloor has the minimum distance signless Laplacian energy among all connected graphs with vertex connectivity k.
{"title":"On graphs with minimal distance signless Laplacian energy","authors":"S. Pirzada, B. Rather, Rezwan Ul Shaban, Merajuddin","doi":"10.2478/ausm-2021-0028","DOIUrl":"https://doi.org/10.2478/ausm-2021-0028","url":null,"abstract":"Abstract For a simple connected graph G of order n having distance signless Laplacian eigenvalues ρ1Q≥ρ2Q≥⋯≥ρnQ rho _1^Q ge rho _2^Q ge cdots ge rho _n^Q , the distance signless Laplacian energy DSLE(G) is defined as DSLE(G)=∑i=1n| ρiQ-2W(G)n | DSLEleft( G right) = sumnolimits_{i = 1}^n {left| {rho _i^Q - {{2Wleft( G right)} over n}} right|} where W(G) is the Weiner index of G. We show that the complete split graph has the minimum distance signless Laplacian energy among all connected graphs with given independence number. Further, we prove that the graph Kk ∨ ( Kt∪ Kn−k−t), 1≤t≤⌊ n-k2 ⌋ 1 le t le leftlfloor {{{n - k} over 2}} rightrfloor has the minimum distance signless Laplacian energy among all connected graphs with vertex connectivity k.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72465582","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}
Abstract In the present paper we introduce the sequence spaces c0{ℳ, Λ , p, q}, c{ℳ, Λ, p, q} and l∞ {ℳ, Λ, p, q} defined by a Musielak-Orlicz function ℳ = (ℳk). We study some topological properties and prove some inclusion relations between these spaces.
{"title":"Some classes of sequence spaces defined by a Musielak-Orlicz function","authors":"S. Sharma","doi":"10.2478/ausm-2021-0031","DOIUrl":"https://doi.org/10.2478/ausm-2021-0031","url":null,"abstract":"Abstract In the present paper we introduce the sequence spaces c0{ℳ, Λ , p, q}, c{ℳ, Λ, p, q} and l∞ {ℳ, Λ, p, q} defined by a Musielak-Orlicz function ℳ = (ℳk). We study some topological properties and prove some inclusion relations between these spaces.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80956892","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}
H. Orhan, P. Mamatha, S. R. Swamy, N. Magesh, J. Yamini
Abstract In this paper we consider two subclasses of bi-univalent functions defined by the Horadam polynomials. Further, we obtain coefficient estimates for the defined classes.
{"title":"Certain classes of bi-univalent functions associated with the Horadam polynomials","authors":"H. Orhan, P. Mamatha, S. R. Swamy, N. Magesh, J. Yamini","doi":"10.2478/ausm-2021-0015","DOIUrl":"https://doi.org/10.2478/ausm-2021-0015","url":null,"abstract":"Abstract In this paper we consider two subclasses of bi-univalent functions defined by the Horadam polynomials. Further, we obtain coefficient estimates for the defined classes.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87605478","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}
Abstract In this paper, we investigate the existence of a positive solution to the third-order boundary value problem { -u‴(t)+k2u′(t)=φ(t)f(t,u(t),u′(t)), t>0u(0)=u′(0)=u′(+∞)=0, left{ matrix{- u'''left( t right) + {k^2}u'left( t right) = phi left( t right)fleft( {t,uleft( t right),u'left( t right)} right),,,,t > 0 hfill cr uleft( 0 right) = u'left( 0 right) = u'left( { + infty } right) = 0, hfill cr} right. where k is a positive constant, ϕ ∈ L1 (0;+ ∞) is nonnegative and does vanish identically on (0;+ ∞) and the function f : ℝ+ × (0;+ ∞) × (0;+ ∞) → ℝ+ is continuous and may be singular at the space variable and at its derivative.
{"title":"Positive solution for singular third-order BVPs on the half line with first-order derivative dependence","authors":"Abdelhamid Benmezaï, El-Djouher Sedkaoui","doi":"10.2478/ausm-2021-0006","DOIUrl":"https://doi.org/10.2478/ausm-2021-0006","url":null,"abstract":"Abstract In this paper, we investigate the existence of a positive solution to the third-order boundary value problem { -u‴(t)+k2u′(t)=φ(t)f(t,u(t),u′(t)), t>0u(0)=u′(0)=u′(+∞)=0, left{ matrix{- u'''left( t right) + {k^2}u'left( t right) = phi left( t right)fleft( {t,uleft( t right),u'left( t right)} right),,,,t > 0 hfill cr uleft( 0 right) = u'left( 0 right) = u'left( { + infty } right) = 0, hfill cr} right. where k is a positive constant, ϕ ∈ L1 (0;+ ∞) is nonnegative and does vanish identically on (0;+ ∞) and the function f : ℝ+ × (0;+ ∞) × (0;+ ∞) → ℝ+ is continuous and may be singular at the space variable and at its derivative.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83987631","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}
Abstract In this paper, we discuss tripotent1 elements in the finite ring ℍ/ℤp. We provide examples and establish conditions for tripotency. We follow similar methods used in [3] for idempotent elements in ℍ/ℤp.
{"title":"Tripotent elements in quaternion rings over ℤp","authors":"Michael Aristidou, Kidus Hailemariam","doi":"10.2478/ausm-2021-0004","DOIUrl":"https://doi.org/10.2478/ausm-2021-0004","url":null,"abstract":"Abstract In this paper, we discuss tripotent1 elements in the finite ring ℍ/ℤp. We provide examples and establish conditions for tripotency. We follow similar methods used in [3] for idempotent elements in ℍ/ℤp.","PeriodicalId":43054,"journal":{"name":"Acta Universitatis Sapientiae-Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73541900","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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