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On Kolmogorov Complexity of Unitary Transformations in Quantum Computing 论量子计算中酉变换的Kolmogorov复杂度
Pub Date : 2021-10-10 DOI: 10.26634/jmat.11.2.19190
A. Kaltchenko
We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the context of quantum computing, it corresponds to the least possible amount of data to define and describe a quantum circuit or quantum computer program. Our Kolmogorov complexity of unitary transformation is built upon Kolmogorov "qubit complexity" of Berthiaume, W. Van Dam and S. Laplante via mapping from unitary transformations to unnormalized density operators, which are subsequently "purified" into unnormalized vectors in Hilbert space. We discuss the optimality of our notion of Kolmogorov complexity in a broad sense.
我们引入了酉变换的Kolmogorov复杂度的概念,它可以(粗略地)被理解为完全描述和重构给定的有限酉变换所需的最少信息量。在量子计算的背景下,它对应于尽可能少的数据量来定义和描述量子电路或量子计算机程序。我们的幺正变换的Kolmogorov复杂度是建立在Berthiaume, W. Van Dam和S. Laplante的Kolmogorov“量子比特复杂度”的基础上,通过将幺正变换映射到非规范化密度算子,然后将其“纯化”成Hilbert空间中的非规范化向量。我们从广义上讨论了Kolmogorov复杂性概念的最优性。
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引用次数: 0
Performance analysis of convolutional neural networks for image classification with appropriate optimizers 卷积神经网络图像分类性能分析与适当的优化器
Pub Date : 1900-01-01 DOI: 10.26634/jmat.12.1.19398
Danish Sana, Ul Rahman Jamshaid, Haider Gulfam
Optimizers in Convolutional Neural Networks play an important role in many advanced deep learning models. Studies on advanced optimizers and modifications of existing optimizers continue to hold significant importance in the study of machine tools and algorithms. There are a number of studies to defend and the selection of these optimizers illustrate some of the challenges on the effectiveness of these optimizers. Comprehensive analysis on the optimizers and alteration with famous activation function Rectified Linear Unit (ReLU) offered to protect effectiveness. Significance is determined based on the adjustment with the original Softmax and ReLU. Experiments were performed with Adam, Root Mean Squared Propagation (RMSprop), Adaptive Learning Rate Method (Adadelta), Adaptive Gradient Algorithm (Adagrad) and Stochastic Gradient Descent (SGD) to examine the performance of Convolutional Neural Networks for image classification using the Canadian Institute for Advanced Research dataset (CIFAR-10).
卷积神经网络中的优化器在许多高级深度学习模型中起着重要作用。对先进优化器和现有优化器的改进的研究在机床和算法的研究中仍然具有重要意义。有许多研究需要辩护,这些优化器的选择说明了这些优化器有效性的一些挑战。对优化器进行了综合分析,并对著名的激活函数整流线性单元(ReLU)进行了改造,以保证其有效性。通过与原始Softmax和ReLU的调整来确定意义。采用Adam、均方根传播(RMSprop)、自适应学习率方法(Adadelta)、自适应梯度算法(Adagrad)和随机梯度下降(SGD)进行实验,利用加拿大高级研究所数据集(CIFAR-10)检验卷积神经网络在图像分类中的性能。
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引用次数: 0
Analytic rayleigh wave speed formula in non-linear orthotropic material 非线性正交各向异性材料中的解析瑞利波速公式
Pub Date : 1900-01-01 DOI: 10.26634/jmat.11.1.18469
A. Rehman, Maqsood-Ul-Hassan
Analytic Rayleigh wave speed formula in nonlinear orthotropic medium is determined. Speed of Rayleigh waves in iodic acid, a specimen of non-linear orthotropic materials, is calculated and is compared with that of the speed in linear orthotropic iodic acid. In linear iodic acid, three distinct Rayleigh waves propagate with speeds 53.44 km/s, 80.94 km/s, and 125.37 km/s, respectively. While, in nonlinear iodic acid these three waves become coincident and only one Rayleigh wave seem to propagate with velocity 63.68 km/s.
建立了非线性正交各向异性介质中的解析瑞利波速公式。计算了非线性正交各向异性材料在碘酸中的瑞利波速,并与在线性正交各向异性碘酸中的瑞利波速进行了比较。在线性碘酸中,三种不同的瑞利波分别以53.44 km/s、80.94 km/s和125.37 km/s的速度传播。而在非线性碘酸中,这三种波是重合的,只有一个瑞利波以63.68 km/s的速度传播。
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引用次数: 0
2-HH NORM AND BIRKHOFF-JAMES ORTHOGONALITY IN NORMED SPACES 赋范空间中的2-hh范数和birkhoff-james正交性
Pub Date : 1900-01-01 DOI: 10.26634/jmat.8.3.16746
Prasad Ojha Bhuwan, Muni Bajracharya Prakash
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引用次数: 0
Common fixed-point theorems via notion of Pairwise Semi-Compatible Mappings and Occasionally Weakly Compatible Mappings (OWC) for six self-mappings in fuzzy metric spaces 由模糊度量空间中六个自映射的成对半相容映射和偶弱相容映射(OWC)的概念得到的公共不动点定理
Pub Date : 1900-01-01 DOI: 10.26634/jmat.12.1.19308
Singh T. Rakesh
The notion of occasionally weakly compatible mappings, and Semi compatible mappings in fuzzy metric space is discussed in this research. The paper investigates the Common fixed-point theorems in fuzzy metric spaces. By taking the property of commutativity of pair mappings, the pairwise semi-compatible mappings and occasionally weakly compatible mappings, satisfying constructive type condition for six self-mappings the common fixed-point theorems in fuzzy metric spaces were proved. The result improves and generalizes other similar results in the literature.
本文讨论了模糊度量空间中偶弱相容映射和半相容映射的概念。研究了模糊度量空间中的一般不动点定理。利用对映射的交换性,对半相容映射和偶弱相容映射满足六个自映射的构造型条件,证明了模糊度量空间中的公共不动点定理。该结果改进并推广了文献中其他类似结果。
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引用次数: 0
Mathematical Modelling of EOR Methods 提高采收率方法的数学建模
Pub Date : 1900-01-01 DOI: 10.26634/jmat.11.2.19034
Rao Kotini Tirumala, Singh Aman
The choice of appropriate and affordable procedures to boost oil recovery is usually recognized as one of the main challenges in reservoir development due to the huge demand for crude oil. Reservoir flow simulators are valuable tools for understanding and forecasting fluid flow in complex systems. The goal of this study is to run a mathematical model to evaluate the performance of various oil recovery methods, as well as to validate the model's accuracy with simulated field data. Thereby, the results of this developed model indicate that the model is approximately matched with the simulated field data. Enhanced oil recovery typically refers to chemical, miscible, thermal, and microbial processes. A system of nonlinear partial differential equations composed of Darcy's and mass conservation equations governs the model. The system is then numerically solved using the IMPEC (Implicit Pressure and Explicit Concentration) scheme by a finite difference method. We chose this approach because the experimental approaches are not only time consuming, but also costly. As a result, mathematical models could aid in the understanding of a reservoir and how such processes can be optimized to maximize oil recovery while lowering production costs. This paper provides a brief overview of mathematical modelling of various enhanced oil recovery methods, focusing on developing a generalized framework and describing some of the key challenges and opportunities.
由于对原油的巨大需求,选择合适且价格合理的方法来提高原油采收率通常被认为是油藏开发的主要挑战之一。油藏流动模拟器是了解和预测复杂系统中流体流动的重要工具。本研究的目的是运行数学模型来评估各种采油方法的性能,并通过模拟现场数据验证模型的准确性。因此,该模型的计算结果表明,该模型与现场模拟数据基本吻合。提高采收率通常指的是化学、混相、热和微生物过程。由达西方程和质量守恒方程组成的非线性偏微分方程组控制模型。然后用有限差分法对系统进行了数值求解,采用了隐式压力和显式浓度格式。我们之所以选择这种方法,是因为实验方法不仅耗时,而且成本高。因此,数学模型可以帮助理解储层,以及如何优化这些过程,以最大限度地提高采收率,同时降低生产成本。本文简要概述了各种提高采收率方法的数学建模,重点是建立一个通用的框架,并描述了一些关键的挑战和机遇。
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引用次数: 0
A STUDY TO PREDICT EID AL-FITR DAY IN OMAN USING MARKOV CHAIN TECHNIQUE 利用马尔科夫链技术预测阿曼开斋节的研究
Pub Date : 1900-01-01 DOI: 10.26634/JMAT.8.1.16233
Razeeuddin Mohammed, Kumar B. V. Senthil
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引用次数: 0
SOME TOPOLOGICAL PROPERTIES OF THE SPECTRUM OF PRIME D-FILTERS OF DISTRIBUTIVE LATTICES 分布格的素数d滤波器谱的一些拓扑性质
Pub Date : 1900-01-01 DOI: 10.26634/jmat.10.1.18165
A. Phaneendrakumar, M. Sambasivarao, K. Sobhanbabu
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引用次数: 0
TANGENT HYPERBOLIC NANOFLUID BOUNDARY LAYERNONLINEAR FLOW IN DOUBLY STRATIFIED ACROSS ASTRETCHING PERMEABLE CYLINDER:A BUONGIORNO MODEL 切线双曲纳米流体边界层在双分层中非线性流动:一个buongiorno模型
Pub Date : 1900-01-01 DOI: 10.26634/jmat.10.2.18321
G. Dharmaiah, K. Balamurugan
{"title":"TANGENT HYPERBOLIC NANOFLUID BOUNDARY LAYER\u0000NONLINEAR FLOW IN DOUBLY STRATIFIED ACROSS A\u0000STRETCHING PERMEABLE CYLINDER:\u0000A BUONGIORNO MODEL","authors":"G. Dharmaiah, K. Balamurugan","doi":"10.26634/jmat.10.2.18321","DOIUrl":"https://doi.org/10.26634/jmat.10.2.18321","url":null,"abstract":"","PeriodicalId":297202,"journal":{"name":"i-manager’s Journal on Mathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127523090","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}
引用次数: 0
IN SERIES CONNECTED RCL-ELEMENTS LOADED ON LOSSY TRANSMISSION LINES WITHOUT THE HEAVISIDE'S CONDITION 在无重载条件下,负载在有损耗传输线上的串联rcl元件
Pub Date : 1900-01-01 DOI: 10.26634/jmat.8.2.16649
G. Vasil, Sofia Bulgaria Geology “St. I. Rilski”
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引用次数: 0
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i-manager’s Journal on Mathematics
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