In this study, we presented a new two-parameter model termed the Generalized XLindely distribution. This novel model is a combination of the exponential and the Two-Parameter lindley distributions. After exploring the statistical characterization of this model, we estimated its parameters using the maximum likelihood method and the Maximum Product of Spacings Method. The approximate confidence interval, based on a normal approximation is additionally calculated. We applied our model to real lifetime data sets to demonstrate its validity, and it was discovered that our distribution fits significantly better than other current distributions.
{"title":"APPLICATION OF THE GENERALISED XLINDLEY MODEL FOR RELIABILITY DATA","authors":"A. Ghouar, A. Yousfi, Z. Djeridi","doi":"10.37418/amsj.12.1.6","DOIUrl":"https://doi.org/10.37418/amsj.12.1.6","url":null,"abstract":"In this study, we presented a new two-parameter model termed the Generalized XLindely distribution. This novel model is a combination of the exponential and the Two-Parameter lindley distributions. After exploring the statistical characterization of this model, we estimated its parameters using the maximum likelihood method and the Maximum Product of Spacings Method. The approximate confidence interval, based on a normal approximation is additionally calculated. We applied our model to real lifetime data sets to demonstrate its validity, and it was discovered that our distribution fits significantly better than other current distributions.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122242584","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}
In this paper, we are concerned with the numerical solution of simplicial cone constrained convex quadratic optimization (SCQO) problems. A reformulation of the K.K.T optimality conditions of SCQOs as an equivalent linear complementarity problem with $mathcal{P}$-matrix ($mathcal{P}$-LCP) is considered. Then, a feasible full-Newton step interior-point algorithm (IPA) is applied for solving SCQO via $mathcal{P}$-LCP. For the completeness of the study, we prove that the proposed algorithm is well-defined and converges locally quadratic to an optimal of SCQOs. Moreover, we obtain the currently best well-known iteration bound for the algorithm with short-update method, namely,$ mathcal{O}(sqrt{n}logfrac{n}{epsilon })$. Finally, we present a various set of numerical results to show its efficiency.
{"title":"AN INTERIOR-POINT ALGORITHM FOR SIMPLICIAL CONE CONSTRAINED CONVEX QUADRATIC OPTIMIZATION","authors":"M. Khaldi, M. Achache","doi":"10.37418/amsj.12.1.5","DOIUrl":"https://doi.org/10.37418/amsj.12.1.5","url":null,"abstract":"In this paper, we are concerned with the numerical solution of simplicial cone constrained convex quadratic optimization (SCQO) problems. A reformulation of the K.K.T optimality conditions of SCQOs as an equivalent linear complementarity problem with $mathcal{P}$-matrix ($mathcal{P}$-LCP) is considered. Then, a feasible full-Newton step interior-point algorithm (IPA) is applied for solving SCQO via $mathcal{P}$-LCP. For the completeness of the study, we prove that the proposed algorithm is well-defined and converges locally quadratic to an optimal of SCQOs. Moreover, we obtain the currently best well-known iteration bound for the algorithm with short-update method, namely,$ mathcal{O}(sqrt{n}logfrac{n}{epsilon })$. Finally, we present a various set of numerical results to show its efficiency.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"32 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131377936","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}
In this paper, we show that the Diophantine equation $frac{1}{x}+frac{3}{y}+frac{5}{z}=frac{3}{4}$ has finitely many integral solutions in the positive integers $x,y$ and $z$.
{"title":"ON THE DIOPHANTINE EQUATION $frac{1}{x}+frac{3}{y}+frac{5}{z}=frac{3}{4}}$","authors":"Hunar Sherzad Taher","doi":"10.37418/amsj.12.1.4","DOIUrl":"https://doi.org/10.37418/amsj.12.1.4","url":null,"abstract":"In this paper, we show that the Diophantine equation $frac{1}{x}+frac{3}{y}+frac{5}{z}=frac{3}{4}$ has finitely many integral solutions in the positive integers $x,y$ and $z$.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"418 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115611385","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}
Let $ T in B(H)$ be a bounded linear operator on a complex Hilbert space $H$. For $ nin mathbb{N } $, an operator $ Tin B(H)$ is said to be n-normal if $ T^{n}T^{*}=T^{*}T^{n} $. In this paper we investigate a necessary and sufficient condition for the n-normality of $ ST $ and $ TS $, where $ S,T in B(H). $ As a consequence, we generalize Kaplansky theorem for normal operators to n-normal operators. Also, In this paper, we provide new characterizations of n-normal operators by certain conditions involving powers of Moore-Penrose inverse.
设$ T in B(H)$是复希尔伯特空间$H$上的一个有界线性算子。对于$ nin mathbb{n} $，如果$ T^{n}T^{*}=T^{*}T^{n} $，则表示运算符$ Tin B(H)$是n正态的。本文研究了$ ST $和$ TS $的n正态性的一个充分必要条件，其中$ S,T In B(H)。因此，我们将正常算子的Kaplansky定理推广到n-正常算子。此外，本文还利用涉及摩尔-彭罗斯逆幂的某些条件，给出了n正规算子的新的表征。
{"title":"ON THE CLASS OF $n$-NORMAL OPERATORS AND MOORE-PENROSE INVERSE","authors":"A. Elgues, S. Menkad","doi":"10.37418/amsj.12.1.1","DOIUrl":"https://doi.org/10.37418/amsj.12.1.1","url":null,"abstract":"Let $ T in B(H)$ be a bounded linear operator on a complex Hilbert space $H$. For $ nin mathbb{N } $, an operator $ Tin B(H)$ is said to be n-normal if $ T^{n}T^{*}=T^{*}T^{n} $. In this paper we investigate a necessary and sufficient condition for the n-normality of $ ST $ and $ TS $, where $ S,T in B(H). $ As a consequence, we generalize Kaplansky theorem for normal operators to n-normal operators. Also, In this paper, we provide new characterizations of n-normal operators by certain conditions involving powers of Moore-Penrose inverse.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121666960","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}
This paper deals with an inclusive review of the literature on fractio- nal-order chaotic systems and their applications in secure communications and synchronization schemes. The chaotic systems have gained more attention in the literature, which can be detected in different fields of science and engineering such as mechanical, chemical, biological, and physics. Furthermore, The fractional-order increases the degrees of complexity in chaotic systems behaviour, which leads to better degrees of security. This work can help the researchers in highlighting the most critical applications of the fractional-order chaotic systems that existed in the literature, which saves the trouble of searching and time.
{"title":"AN IN-DEPTH REVIEW LITERATURE OF FRACTIONAL-ORDER CHAOTIC SYSTEMS AND ITS APPLICATIONS IN SECURE TRANSMISSION SCHEMES","authors":"M. A. Atoussi, B. Nail, S. Saadi, M. Bettayeb","doi":"10.37418/amsj.12.1.2","DOIUrl":"https://doi.org/10.37418/amsj.12.1.2","url":null,"abstract":"This paper deals with an inclusive review of the literature on fractio- nal-order chaotic systems and their applications in secure communications and synchronization schemes. The chaotic systems have gained more attention in the literature, which can be detected in different fields of science and engineering such as mechanical, chemical, biological, and physics. Furthermore, The fractional-order increases the degrees of complexity in chaotic systems behaviour, which leads to better degrees of security. This work can help the researchers in highlighting the most critical applications of the fractional-order chaotic systems that existed in the literature, which saves the trouble of searching and time.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125003588","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}
We propose a scalable computational framework for the hybrid CPU-GPU implementation ofa traffic-induced and finite element-based air quality model. The hybrid computing paradigm we investigate consists in combining the CPU-based distributed-memory programming approach using Message Passing Interface (MPI) and a GPU programming model for the finite element numerical integration using Compute Unified Device Architecture (CUDA), a general purpose parallel computing platform released by NVIDIA Corporation and featured on its own GPUs. The scalability results obtained from numerical experiments on two major road traffic-induced air pollutants, namely the fine and inhalable particulate matter PM$_{2.5}$ and PM$_{10}$, are illustrated. These achievements, including speedup and efficiency analyses, support that this framework scales well up to 256 CPU cores used concurrently with GPUs from a hybrid computing system.
{"title":"A SCALABLE HYBRID CPU-GPU COMPUTATIONAL FRAMEWORK FOR A FINITE ELEMENT-BASED AIR QUALITY MODEL","authors":"A. Samaké, M. Alassane, A. Mahamane, O. Diallo","doi":"10.37418/amsj.12.1.3","DOIUrl":"https://doi.org/10.37418/amsj.12.1.3","url":null,"abstract":"We propose a scalable computational framework for the hybrid CPU-GPU implementation ofa traffic-induced and finite element-based air quality model. The hybrid computing paradigm we investigate consists in combining the CPU-based distributed-memory programming approach using Message Passing Interface (MPI) and a GPU programming model for the finite element numerical integration using Compute Unified Device Architecture (CUDA), a general purpose parallel computing platform released by NVIDIA Corporation and featured on its own GPUs. The scalability results obtained from numerical experiments on two major road traffic-induced air pollutants, namely the fine and inhalable particulate matter PM$_{2.5}$ and PM$_{10}$, are illustrated. These achievements, including speedup and efficiency analyses, support that this framework scales well up to 256 CPU cores used concurrently with GPUs from a hybrid computing system.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128685323","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}
To ensure confidentiality and avoid humain attacks against our data, we exchange encryption and decryption keys. In our proposal scheme, we use the commutative properties of the product of circular matrices to create a common encryption key by applying the protocol of { it Diffie-Hellman} exchange through a classic channel. To raise the security level of our system we have introduced the sensibility of chaotic logistic maps in another exchange protocol which is the $BB84$ throuth a quantum channal.
{"title":"SHARING KEYS USING CIRCULANT MATRICES AND LOGISTIC MAPS THROUGH QUANTUM CHANNAL","authors":"A. Salah, B. Benzeghli, L. Noui","doi":"10.37418/amsj.11.12.13","DOIUrl":"https://doi.org/10.37418/amsj.11.12.13","url":null,"abstract":"To ensure confidentiality and avoid humain attacks against our data, we exchange encryption and decryption keys. In our proposal scheme, we use the commutative properties of the product of circular matrices to create a common encryption key by applying the protocol of { it Diffie-Hellman} exchange through a classic channel. To raise the security level of our system we have introduced the sensibility of chaotic logistic maps in another exchange protocol which is the $BB84$ throuth a quantum channal.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115556714","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}
In this paper, we deal with the fractional backward stochastic differential equations (F-BSDEs in short) with Hurst parameter $Hin (frac{1}{2},1)$ when the driver $g$ is weak monotone. Via an approximation theory, we derive the existence and uniqueness of solutions to F-BSDEs. The comparison theorem is also established.
本文研究了一类具有赫斯特参数$H In (frac{1}{2}，1)$的分数阶倒向随机微分方程(简称F-BSDEs)，当驱动器$g$为弱单调时。利用近似理论，我们得到了F-BSDEs解的存在唯一性。并建立了比较定理。
{"title":"EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR FRACTIONAL BSDES WITH WEAK MONOTONICITY COEFFICIENTS","authors":"Mostapha Abdelouahab Saouli","doi":"10.37418/amsj.11.12.12","DOIUrl":"https://doi.org/10.37418/amsj.11.12.12","url":null,"abstract":"In this paper, we deal with the fractional backward stochastic differential equations (F-BSDEs in short) with Hurst parameter $Hin (frac{1}{2},1)$ when the driver $g$ is weak monotone. Via an approximation theory, we derive the existence and uniqueness of solutions to F-BSDEs. The comparison theorem is also established.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"225 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115742667","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}
Examination of thermal and solutal energy with sophisticated guesstimate of thermal radiation bearing. Conveyance portents in Maxwell fluid pour thru the gain of Cattaneo-Christov double diffusion theory is fulfilled in this artefact. Unsteady 2D flow of Maxwell fluid with variable thermal conductivity over the stretching cylinder with thermal emission and heat source/sink is deliberated here. We verbalize the partial differential equations (PDEs) under particular molds for the governing physical tricky of heat and mass transportation in Maxwell fluid by using double diffusion of Cattaneo-Christov model rather than classical Fourier's and Fick's law. Numerical technique $4^{text {th }}$ order Runge-Kutta method is employed for the solution of ordinary differential reckonings (ODEs) which are obtained from governing PDEs under the apt resemblance transformations. In the interpretation of acquired fallouts, we beheld that for fitting upshots the tenets of unsteadiness constraint should be less than one. The higher tenets of Maxwell parameter deteriorations the flow field but increase the energy transport in the fluid flow. Both temperature and attentiveness scatterings in Maxwell liquid deterioration for sophisticated tenets of thermal and attentiveness relaxation time constraint. Alike, trifling thermal conductivity constraint also augments the temperature field. Auxiliary, the rate of heat transfer deteriorations.
{"title":"THERMAL RADIATION IMPACT AND CATTANEO-CHRISTOV THEORY FOR UNSTEADY FLOW OF MAXWELL FLUID OVER STRETCHED CYLINDER WITH INCONSISTENT HEAT SOURCE/SINK","authors":"M. Sreedhar Babu","doi":"10.37418/amsj.11.12.10","DOIUrl":"https://doi.org/10.37418/amsj.11.12.10","url":null,"abstract":"Examination of thermal and solutal energy with sophisticated guesstimate of thermal radiation bearing. Conveyance portents in Maxwell fluid pour thru the gain of Cattaneo-Christov double diffusion theory is fulfilled in this artefact. Unsteady 2D flow of Maxwell fluid with variable thermal conductivity over the stretching cylinder with thermal emission and heat source/sink is deliberated here. We verbalize the partial differential equations (PDEs) under particular molds for the governing physical tricky of heat and mass transportation in Maxwell fluid by using double diffusion of Cattaneo-Christov model rather than classical Fourier's and Fick's law. Numerical technique $4^{text {th }}$ order Runge-Kutta method is employed for the solution of ordinary differential reckonings (ODEs) which are obtained from governing PDEs under the apt resemblance transformations. In the interpretation of acquired fallouts, we beheld that for fitting upshots the tenets of unsteadiness constraint should be less than one. The higher tenets of Maxwell parameter deteriorations the flow field but increase the energy transport in the fluid flow. Both temperature and attentiveness scatterings in Maxwell liquid deterioration for sophisticated tenets of thermal and attentiveness relaxation time constraint. Alike, trifling thermal conductivity constraint also augments the temperature field. Auxiliary, the rate of heat transfer deteriorations.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114767718","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}
In this paper, we characterize the four derived sequences obtained by the symbolic approach to the quadratic decomposition of Appll sequences. Moreover, we prove that the two monic polynomial sequences associated to such quadratic decomposition are also Appell sequences.
{"title":"SYMBOLIC APPROACH TO THE QUADRATIC DECOMPOSITION OF APPELL SEQUENCES","authors":"S. Mekhalfa, M. Bouras","doi":"10.37418/amsj.11.12.9","DOIUrl":"https://doi.org/10.37418/amsj.11.12.9","url":null,"abstract":"In this paper, we characterize the four derived sequences obtained by the symbolic approach to the quadratic decomposition of Appll sequences. Moreover, we prove that the two monic polynomial sequences associated to such quadratic decomposition are also Appell sequences.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129930700","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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