Pub Date : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.19
Delia Spiridon
Advances in the graphics processing unit (GPU) development led to the opportunity for software developers to increase the execution speed for their programs by massive parallelization of the algorithms using GPU programming. NVIDIA company developed an arhitecture for parallel computing named Compute Unified Device Architecture (CUDA) which includes a set of CUDA instructions and the hardware for parallel computing. Computational Physics is an interdisciplinary field which is in continuous progress and which studies, develops and optimizes numerical algorithms and computational techniques for their application in solving various physics problems. Computational Physics has applicability in all sub-branches of physics and related fields such as: biophysics, astrophysics, plasma physics, biomechanics, fluid physics, etc. Moreover, with the evolution of technology in the last few decades, this relatively new field has helped to quickly obtain results in these fields, facilitating the connection between theoretical and experimental physics. In this paper, some of the latest researches and results obtained in computational physics by using GPU computing with CUDA architecture are reviewed.
图形处理器（GPU）的发展为软件开发人员提供了通过使用 GPU 编程对算法进行大规模并行化来提高程序执行速度的机会。英伟达公司开发了一种用于并行计算的架构，名为 "计算统一设备架构"（CUDA），其中包括一套CUDA指令和用于并行计算的硬件。计算物理学是一个正在不断发展的跨学科领域，它研究、开发和优化数值算法和计算技术，并将其应用于解决各种物理问题。计算物理学适用于物理学的所有分支和相关领域，如：生物物理学、天体物理学、等离子体物理学、生物力学、流体物理学等。此外，随着过去几十年技术的发展，这一相对较新的领域有助于快速获得这些领域的成果，促进理论物理与实验物理之间的联系。本文回顾了利用 CUDA 架构 GPU 计算在计算物理学领域取得的一些最新研究和成果。
{"title":"Advances in CUDA for computational physics","authors":"Delia Spiridon","doi":"10.31926/but.mif.2023.3.65.2.19","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.19","url":null,"abstract":"Advances in the graphics processing unit (GPU) development led to the opportunity for software developers to increase the execution speed for their programs by massive parallelization of the algorithms using GPU programming. NVIDIA company developed an arhitecture for parallel computing named Compute Unified Device Architecture (CUDA) which includes a set of CUDA instructions and the hardware for parallel computing. Computational Physics is an interdisciplinary field which is in continuous progress and which studies, develops and optimizes numerical algorithms and computational techniques for their application in solving various physics problems. Computational Physics has applicability in all sub-branches of physics and related fields such as: biophysics, astrophysics, plasma physics, biomechanics, fluid physics, etc. Moreover, with the evolution of technology in the last few decades, this relatively new field has helped to quickly obtain results in these fields, facilitating the connection between theoretical and experimental physics. In this paper, some of the latest researches and results obtained in computational physics by using GPU computing with CUDA architecture are reviewed.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139174886","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.7
Iana M. Fudulu
The aim of this work is defined by the study of the plane deformation for micropolar isotropic materials in equilibrium theory, where, in addition to displacement and absolute temperature, the particles of the mentioned materials have pores and microrotations.The determined solution to the field equations helps us to study the effect of heat sources and pores on the deformation of the body, which deformation is studied later.
{"title":"Plane strain of isotropic micropolar bodies with pores","authors":"Iana M. Fudulu","doi":"10.31926/but.mif.2023.3.65.2.7","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.7","url":null,"abstract":"The aim of this work is defined by the study of the plane deformation for micropolar isotropic materials in equilibrium theory, where, in addition to displacement and absolute temperature, the particles of the mentioned materials have pores and microrotations.The determined solution to the field equations helps us to study the effect of heat sources and pores on the deformation of the body, which deformation is studied later.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"14 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139175942","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}
The article discusses one of the classic problems of macroeconomic dynamics, on which the neo-Keynesian theory of growth is based, so that the interaction between the multiplier and the accelerator. A new approach was proposed to develop a mathematical model of the dynamics of the mutual multiplier, which indicates the marginal propensity to save as a result of the GDP growth, and the accelerator, which reflects the growth of capital of the national income in the multiplier. The model is based on the hypothesis of non-linear dependence of the consumption on the amount of profit. This assumes that consumption growth is limited, i.e., a saturation effect occurs. In addition, the model took into account the delayed reaction of the accelerator to the influence of the multiplier. Under building the model, the considered processes were considered continuous in time. This made it possible to provide the mathematical model ”accelerator - multiplier” as a system of two differential equations of the first order. The application of the developed model to the analysis of the dynamic properties of the macroeconomic system makes it possible to evaluate the parameters at which the ”multiplier-accelerator” system enters a critical state. It has been proven that the conditions for the occurrence of self-oscillations depend on the critical value of the accelerator power. The presence of a two-fold limit cycle with corresponding ”soft” and ”hard” modes of birth (death) of the limit cycle was also founded. The applied usefulness of the model is that the choice of management decisions taking into account these results allow us preventing the occurrence of bifurcations and disasters in the process of evolution of the macroeconomic systems.
{"title":"Non-linear model of the macroeconomic system dynamics: multiplier-accelerator","authors":"∗. OleksandrDOROKHOV, Irina Lebedeva, Lyudmyla Malyarets, Anatoly Voronin","doi":"10.31926/but.mif.2023.3.65.2.16","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.16","url":null,"abstract":"The article discusses one of the classic problems of macroeconomic dynamics, on which the neo-Keynesian theory of growth is based, so that the interaction between the multiplier and the accelerator. A new approach was proposed to develop a mathematical model of the dynamics of the mutual multiplier, which indicates the marginal propensity to save as a result of the GDP growth, and the accelerator, which reflects the growth of capital of the national income in the multiplier. The model is based on the hypothesis of non-linear dependence of the consumption on the amount of profit. This assumes that consumption growth is limited, i.e., a saturation effect occurs. In addition, the model took into account the delayed reaction of the accelerator to the influence of the multiplier. Under building the model, the considered processes were considered continuous in time. This made it possible to provide the mathematical model ”accelerator - multiplier” as a system of two differential equations of the first order. The application of the developed model to the analysis of the dynamic properties of the macroeconomic system makes it possible to evaluate the parameters at which the ”multiplier-accelerator” system enters a critical state. It has been proven that the conditions for the occurrence of self-oscillations depend on the critical value of the accelerator power. The presence of a two-fold limit cycle with corresponding ”soft” and ”hard” modes of birth (death) of the limit cycle was also founded. The applied usefulness of the model is that the choice of management decisions taking into account these results allow us preventing the occurrence of bifurcations and disasters in the process of evolution of the macroeconomic systems.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"41 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139176015","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.10
N. Minculete, Moradi Moradi
This paper aims to present several new properties of geometrically convex functions similar to some those known properties for convex functions. Finally, we show some improvements of Young’s inequality.
{"title":"On geometrically convex functions with some applications","authors":"N. Minculete, Moradi Moradi","doi":"10.31926/but.mif.2023.3.65.2.10","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.10","url":null,"abstract":"This paper aims to present several new properties of geometrically convex functions similar to some those known properties for convex functions. Finally, we show some improvements of Young’s inequality.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"158 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139173391","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.3
∗. GunjanAGRAWAL, Vijay Gupta
We deal here with the (p, q)-variant of the Post-Widder operators of semiexponential type. By using the basic properties of post-quantum properties, we calculate the moments of these operators and obtain some direct findings for such (p, q)-semi-exponential Post-Widder operators.
{"title":"(p,q)-Post-Widder operators of semi exponential type","authors":"∗. GunjanAGRAWAL, Vijay Gupta","doi":"10.31926/but.mif.2023.3.65.2.3","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.3","url":null,"abstract":"We deal here with the (p, q)-variant of the Post-Widder operators of semiexponential type. By using the basic properties of post-quantum properties, we calculate the moments of these operators and obtain some direct findings for such (p, q)-semi-exponential Post-Widder operators.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"22 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139173523","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.8
Sorin G. Gal
Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas. These include Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorems based on Hermite interpolation on two double knots.
由于正线性算子的 Voronovskaya 型经典渐近定理实际上是基于泰勒公式，而泰勒公式是拉格朗日-赫米特插值公式的一种非常特殊的情况，因此在最近的论文 Gal [3] 中，我基于其他拉格朗日-赫米特插值公式得到了半离散定量 Voronovskaya 型定理。这些公式包括两个和三个单结的拉格朗日插值公式，以及两个结（一个单结，另一个双结）的赫米特插值公式。在本文中，我们基于两个双结上的赫米特插值，得到了一个半离散的定量沃罗诺夫斯卡亚式定理。
{"title":"Semi-discrete Voronovskaya-type theorem for positive linear operators based on Hermite interpolation with two double knots","authors":"Sorin G. Gal","doi":"10.31926/but.mif.2023.3.65.2.8","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.8","url":null,"abstract":"Since the classical asymptotic theorems of Voronovskaya-type for positive and linear operators are in fact based on the Taylor’s formula which is a very particular case of Lagrange-Hermite interpolation formula, in the recent paper Gal [3], I have obtained semi-discrete quantitative Voronovskaya-type theorems based on other Lagrange-Hermite interpolation formulas. These include Lagrange interpolation on two and three simple knots and Hermite interpolation on two knots, one simple and the other one double. In the present paper we obtain a semi-discrete quantitative Voronovskaya-type theorems based on Hermite interpolation on two double knots.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"21 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139175666","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.2
A.-M. Acu, G. Motronea, I. Rasa
The divided differences of Bernstein polynomials were investigated by Alexandru Lupas in 1995. We extend the results of that investigation. Moreover, we establish new relations between them and the theory of dual functionals.
{"title":"Bernstein polynomials and dual functionals","authors":"A.-M. Acu, G. Motronea, I. Rasa","doi":"10.31926/but.mif.2023.3.65.2.2","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.2","url":null,"abstract":"The divided differences of Bernstein polynomials were investigated by Alexandru Lupas in 1995. We extend the results of that investigation. Moreover, we establish new relations between them and the theory of dual functionals.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"107 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139173901","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.15
V. Chauhan, P.K. Srivastava
The optimal management and utilization of natural resources is eventually important, due to increase in the consumption of natural resources and in view of this, the main aim of fisheries is to maintain the marine organisms at levels that produces maximum sustainable yield (MSY). In this study, the one step numerical approximations schemes are developed to find the solution of such bioeconomic fisheries models whose analytical solution is not possible. In the proposed work, the explicit Runge-Kutta scheme based on fourth order tetra geometric mean is established and this method solve fishery management models of Schaefer and Gordon-Schaefer. The models analyze bioeconomic growth rate, carrying capacity, total and marginal costs and revenues. In solving, the models through proposed tetra geometric mean Runge-Kutta method, it is obtained that the method is easy to implement. The results obtained are much better as compared to other methods when compared in terms of errors and central processing unit (CPU) time.
{"title":"Tetra geoemtric mean Runge-Kutta analysis of bioeconomic fisheries model","authors":"V. Chauhan, P.K. Srivastava","doi":"10.31926/but.mif.2023.3.65.2.15","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.15","url":null,"abstract":"The optimal management and utilization of natural resources is eventually important, due to increase in the consumption of natural resources and in view of this, the main aim of fisheries is to maintain the marine organisms at levels that produces maximum sustainable yield (MSY). In this study, the one step numerical approximations schemes are developed to find the solution of such bioeconomic fisheries models whose analytical solution is not possible. In the proposed work, the explicit Runge-Kutta scheme based on fourth order tetra geometric mean is established and this method solve fishery management models of Schaefer and Gordon-Schaefer. The models analyze bioeconomic growth rate, carrying capacity, total and marginal costs and revenues. In solving, the models through proposed tetra geometric mean Runge-Kutta method, it is obtained that the method is easy to implement. The results obtained are much better as compared to other methods when compared in terms of errors and central processing unit (CPU) time.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"301 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139172709","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.13
Maria Talpau Dumitru
In this paper we define a new third-order modulus of smoothness and we prove the conservation by Stancu operators of the Lipschitz classes defined with this modulus.
{"title":"On a third-order modulus of smoothness","authors":"Maria Talpau Dumitru","doi":"10.31926/but.mif.2023.3.65.2.13","DOIUrl":"https://doi.org/10.31926/but.mif.2023.3.65.2.13","url":null,"abstract":"In this paper we define a new third-order modulus of smoothness and we prove the conservation by Stancu operators of the Lipschitz classes defined with this modulus.","PeriodicalId":505295,"journal":{"name":"Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science","volume":"263 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139174889","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 : 2023-12-18DOI: 10.31926/but.mif.2023.3.65.2.11
∗. AndreeaNISTOR-S¸ERBAN, Dorina R ˘ aducanu
In this paper we consider a class of functions Mα(φ) defined by subordination, consisting of functions f ∈ A satisfying the condition (1 −α) zf′(z)/ f(z) + α (1 + zf′′(z)/ f′(z) )≺ φ(z), z ∈ U. In the study of univalent functions, estimates on the Taylor coefficients are usually given. Another significant problem deals with the estimates of logarithmic coefficients. For the class S of univalent functions no sharp bounds for the modulus of the individual logarithmic coefficients are known if n ≥ 3. For different subclasses of S the results are not better and in most cases only th e first three initial coefficients of log f(z)/z are considered. For the class Mα(φ) we obtain upper bounds for the logarithmic coefficients γn, n ∈ {1, 2, 3} and also for Γn, n ∈ {1, 2, 3}, the logarithmic coefficients of the inverse of Mα(φ). Connections with previous known results are pointed out.
在本文中，我们考虑一类由从属定义的函数 Mα(φ)，它由满足条件 (1 -α) zf′(z)/ f(z) + α (1 + zf′(z)/ f′(z) )≺ φ(z)、z∈ U 的函数 f∈ A 组成。在研究一元函数时，通常会给出泰勒系数的估计值。另一个重要问题涉及对数系数的估计。对于单值函数 S 类，如果 n ≥ 3，单个对数系数的模数没有明确的界限。对于 S 的不同子类，结果也不尽相同，大多数情况下只考虑 log f(z)/z 的前三个初始系数。对于 Mα(φ)类，我们得到了对数系数 γn, n∈ {1, 2, 3} 的上界，也得到了 Mα(φ)逆的对数系数 Γn, n∈ {1, 2, 3} 的上界。指出了与之前已知结果的联系。
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