Pub Date : 2020-12-17DOI: 10.1556/012.2020.57.4.1481
S. Sophia, Babu Muthu Deepika
A fluid queueing system in which the fluid flow in to the buffer is regulated by the state of the background queueing process is considered. In this model, the arrival and service rates follow chain sequence rates and are controlled by an exponential timer. The buffer content distribution along with averages are found using continued fraction methodology. Numerical results are illustrated to analyze the trend of the average buffer content for the model under consideration. It is interesting to note that the stationary solution of a fluid queue driven by a queue with chain sequence rates does not exist in the absence of exponential timer.
{"title":"Stationary Solution of a Fluid Queue Driven by a Queue with Chain Sequence Rates and Controlled Input","authors":"S. Sophia, Babu Muthu Deepika","doi":"10.1556/012.2020.57.4.1481","DOIUrl":"https://doi.org/10.1556/012.2020.57.4.1481","url":null,"abstract":"A fluid queueing system in which the fluid flow in to the buffer is regulated by the state of the background queueing process is considered. In this model, the arrival and service rates follow chain sequence rates and are controlled by an exponential timer. The buffer content distribution along with averages are found using continued fraction methodology. Numerical results are illustrated to analyze the trend of the average buffer content for the model under consideration. It is interesting to note that the stationary solution of a fluid queue driven by a queue with chain sequence rates does not exist in the absence of exponential timer.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"15 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87769553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1556/012.2020.57.4.1479
Siwar Hkimi, H. Mejjaoli, S. Omri
We introduce the directional short-time Fourier transform for which we prove a new Plancherel’s formula. We also prove for this transform several uncertainty principles as Heisenberg inequalities, logarithmic uncertainty principle, Faris–Price uncertainty principles and Donoho–Stark’s uncertainty principles.
{"title":"Dispersion’s Uncertainty Principles Associated with the Directional Short-Time Fourier Transform","authors":"Siwar Hkimi, H. Mejjaoli, S. Omri","doi":"10.1556/012.2020.57.4.1479","DOIUrl":"https://doi.org/10.1556/012.2020.57.4.1479","url":null,"abstract":"We introduce the directional short-time Fourier transform for which we prove a new Plancherel’s formula. We also prove for this transform several uncertainty principles as Heisenberg inequalities, logarithmic uncertainty principle, Faris–Price uncertainty principles and Donoho–Stark’s uncertainty principles.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"64 2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89840588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1556/012.2020.57.4.1476
G. Cordeiro, T. Ramires, E. Ortega, R. R. Pescim
We define the extended beta family of distributions to generalize the beta generator pioneered by Eugene et al. [10]. This paper is cited in at least 970 scientific articles and extends more than fifty well-known distributions. Any continuous distribution can be generalized by means of this family. The proposed family can present greater flexibility to model skewed data. Some of its mathematical properties are investigated and maximum likelihood is adopted to estimate its parameters. Further, for different parameter settings and sample sizes, some simulations are conducted. The superiority of the proposed family is illustrated by means of two real data sets.
{"title":"The Extended Beta Generator of Distributions: Properties and Applications","authors":"G. Cordeiro, T. Ramires, E. Ortega, R. R. Pescim","doi":"10.1556/012.2020.57.4.1476","DOIUrl":"https://doi.org/10.1556/012.2020.57.4.1476","url":null,"abstract":"We define the extended beta family of distributions to generalize the beta generator pioneered by Eugene et al. [10]. This paper is cited in at least 970 scientific articles and extends more than fifty well-known distributions. Any continuous distribution can be generalized by means of this family. The proposed family can present greater flexibility to model skewed data. Some of its mathematical properties are investigated and maximum likelihood is adopted to estimate its parameters. Further, for different parameter settings and sample sizes, some simulations are conducted. The superiority of the proposed family is illustrated by means of two real data sets.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"86 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81533176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1556/012.2020.57.4.1474
M. Sablik, K. Stapor
We present the sufficient condition for a classical two-class problem from Fisher discriminant analysis has a solution. Actually, the solution was presented up to our knowledge with a necessary condition only. We use an extended Cauchy–Schwarz inequality as a tool.
{"title":"Extended Cauchy–Schwarz Inequality and Its Application for the Two-Class Fisher Discriminant Analysis","authors":"M. Sablik, K. Stapor","doi":"10.1556/012.2020.57.4.1474","DOIUrl":"https://doi.org/10.1556/012.2020.57.4.1474","url":null,"abstract":"We present the sufficient condition for a classical two-class problem from Fisher discriminant analysis has a solution. Actually, the solution was presented up to our knowledge with a necessary condition only. We use an extended Cauchy–Schwarz inequality as a tool.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"376 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81787967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1556/012.2020.57.4.1480
B. M. Najmabadi, T. L. Shateri, G. Sadeghi
In this paper, we define an orthonormal basis for 2-*-inner product space and obtain some useful results. Moreover, we introduce a 2-norm on a dense subset of a 2-*-inner product space. Finally, we obtain a version of the Selberg, Buzano’s and Bessel inequality and its results in an A-2-inner product space.
{"title":"A Type of Orthonormal Bases on 2-*-Inner Product Spaces","authors":"B. M. Najmabadi, T. L. Shateri, G. Sadeghi","doi":"10.1556/012.2020.57.4.1480","DOIUrl":"https://doi.org/10.1556/012.2020.57.4.1480","url":null,"abstract":"In this paper, we define an orthonormal basis for 2-*-inner product space and obtain some useful results. Moreover, we introduce a 2-norm on a dense subset of a 2-*-inner product space. Finally, we obtain a version of the Selberg, Buzano’s and Bessel inequality and its results in an A-2-inner product space.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75236255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1556/012.2020.57.4.1475
G. Sofi, S. Ahanger, R. Gardner
In this paper, a relationship between the zeros and critical points of a polynomial p(z) is established. The relationship is used to prove Sendov’s conjecture in some special cases.
{"title":"Some Classes of Polynomials Satisfying Sendov’s Conjecture","authors":"G. Sofi, S. Ahanger, R. Gardner","doi":"10.1556/012.2020.57.4.1475","DOIUrl":"https://doi.org/10.1556/012.2020.57.4.1475","url":null,"abstract":"In this paper, a relationship between the zeros and critical points of a polynomial p(z) is established. The relationship is used to prove Sendov’s conjecture in some special cases.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"16 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74854730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-17DOI: 10.1556/012.2020.57.4.1477
Huan Wang
Let be a Schrödinger operator on the Heisenberg group , where is the sublaplacian on and the nonnegative potential V belongs to the reverse Hölder class with . Here is the homogeneous dimension of . Assume that is the heat semigroup generated by. The Lusin area integral and the Littlewood–Paley–Stein function associated with the Schrödinger operator are defined, respectively, bywhereandWhere is a parameter. In this article, the author shows that there is a relationship between and the operator and for any , the following inequality holds true:Based on this inequality and known results for the Lusin area integral , the author establishes the strong-type and weak-type estimates for the Littlewood–Paley–Stein function on . In this article, the author also introduces a class of Morrey spaces associated with the Schrödinger operator on . By using some pointwise estimates of the kernels related to the nonnegative potential V, the author establishes the boundedness properties of the operator acting on the Morrey spaces for an appropriate choice of . It can be shown that the same conclusions hold for the operator on generalized Morrey spaces as well.
{"title":"Morrey Spaces Related to Schrödinger Operators with Certain Nonnegative Potentials and Littlewood–Paley–Stein Functions on the Heisenberg groups","authors":"Huan Wang","doi":"10.1556/012.2020.57.4.1477","DOIUrl":"https://doi.org/10.1556/012.2020.57.4.1477","url":null,"abstract":"Let be a Schrödinger operator on the Heisenberg group , where is the sublaplacian on and the nonnegative potential V belongs to the reverse Hölder class with . Here is the homogeneous dimension of . Assume that is the heat semigroup generated by. The Lusin area integral and the Littlewood–Paley–Stein function associated with the Schrödinger operator are defined, respectively, bywhereandWhere is a parameter. In this article, the author shows that there is a relationship between and the operator and for any , the following inequality holds true:Based on this inequality and known results for the Lusin area integral , the author establishes the strong-type and weak-type estimates for the Littlewood–Paley–Stein function on . In this article, the author also introduces a class of Morrey spaces associated with the Schrödinger operator on . By using some pointwise estimates of the kernels related to the nonnegative potential V, the author establishes the boundedness properties of the operator acting on the Morrey spaces for an appropriate choice of . It can be shown that the same conclusions hold for the operator on generalized Morrey spaces as well.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"29 1","pages":"465-507"},"PeriodicalIF":0.7,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78953705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that if a non-degenerate PL map f : N → M lifts to a topological embedding in then it lifts to a PL embedding in there. We also show that if a stable smooth map Nn → Mm, m ≥ n, lifts to a topological embedding in , then it lifts to a smooth embedding in there.
{"title":"Lifting Generic Maps to Embeddings. Triangulation and Smoothing","authors":"S. A. Melikhov","doi":"10.1556/012.2022.01523","DOIUrl":"https://doi.org/10.1556/012.2022.01523","url":null,"abstract":"We show that if a non-degenerate PL map f : N → M lifts to a topological embedding in \u0000 \u0000 then it lifts to a PL embedding in there. We also show that if a stable smooth map Nn\u0000 → Mm, m ≥ n, lifts to a topological embedding in \u0000 \u0000 , then it lifts to a smooth embedding in there.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"56 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82214945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-20DOI: 10.1556/012.2020.57.3.1466
C. M. D. Fonseca, V. Kowalenko, L. Losonczi
This survey revisits Jenő Egerváry and Otto Szász’s article of 1928 on trigonometric polynomials and simple structured matrices focussing mainly on the latter topic. In particular, we concentrate on the spectral theory for the first type of the matrices introduced in the article, which are today referred to as k-tridiagonal matrices, and then discuss the explosion of interest in them over the last two decades, most of which could have benefitted from the seminal article, had it not been overlooked.
{"title":"Ninety years of k-tridiagonal matrices","authors":"C. M. D. Fonseca, V. Kowalenko, L. Losonczi","doi":"10.1556/012.2020.57.3.1466","DOIUrl":"https://doi.org/10.1556/012.2020.57.3.1466","url":null,"abstract":"This survey revisits Jenő Egerváry and Otto Szász’s article of 1928 on trigonometric polynomials and simple structured matrices focussing mainly on the latter topic. In particular, we concentrate on the spectral theory for the first type of the matrices introduced in the article, which are today referred to as k-tridiagonal matrices, and then discuss the explosion of interest in them over the last two decades, most of which could have benefitted from the seminal article, had it not been overlooked.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"114 1","pages":"298-311"},"PeriodicalIF":0.7,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79240122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-20DOI: 10.1556/012.2020.57.3.1470
Sung Guen Kim
For n,m≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of and , where is the space of n-linear forms on with the supremum norm, and is the subspace of consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of and , respectively. We show that ext ⊂ ext , which answers the question in [32]. We show that every extreme point of the unit balls of and is exposed, correspondingly. We also show thatand which answers the questions in [31].
{"title":"The unit balls of ℒ(nl∞m) and ℒs(nl∞m)","authors":"Sung Guen Kim","doi":"10.1556/012.2020.57.3.1470","DOIUrl":"https://doi.org/10.1556/012.2020.57.3.1470","url":null,"abstract":"For n,m≥ 2 this paper is devoted to the description of the sets of extreme and exposed points of the closed unit balls of and , where is the space of n-linear forms on with the supremum norm, and is the subspace of consisting of symmetric n-linear forms. First we classify the extreme points of the unit balls of and , respectively. We show that ext ⊂ ext , which answers the question in [32]. We show that every extreme point of the unit balls of and is exposed, correspondingly. We also show thatand which answers the questions in [31].","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"22 1","pages":"267-283"},"PeriodicalIF":0.7,"publicationDate":"2020-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88106371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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