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The blue color mechanism on sapphires from different gem deposits before and after heating under oxidizing atmosphere 不同宝石矿床的蓝宝石在氧化气氛下加热前后的蓝色机理
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-12-20 DOI: 10.1088/2399-6528/ad1762
Wanvisa Thengthong, S. Sakkaravej, Wiwat Wongkokua, C. Saiyasombat, N. Monarumit
The blue color of sapphire is commonly related to the amount of Fe and Ti impurities replacing Al3+ in Al2O3 structure. Generally, the color intensity on sapphires is related to the gem deposits including the basaltic-related and metamorphic-related ones. The color of sapphires has been changed after heating under oxidizing atmosphere. However, the explanation about the color mechanism from some previous research contradicted each other and it was still wondered. For this reason, this research is focused on the role of Fe and Ti oxidation states as well as the blue color mechanism on sapphires before and after heating under oxidizing atmosphere. In this study, the sapphire samples were collected from different gem deposits including basaltic-related sapphires from Kanchanaburi province, Thailand and metamorphic-related ones from Sri Lanka before and after heating at 1100°C under oxidizing atmosphere. As a result, the blue color on sapphires before heating can be described that a hole color center assigned to Fe3+-Ti4+ mixed acceptor states inside an energy band gap that could be received an electron from the valence band for charge-balancing after excitation. After heating, the basaltic-related sapphires turned from dark blue to light blue and the metamorphic-related ones turned from light blue to colorless because the Fe3+-Ti4+ mixed acceptor states were decreased because a hole color center was filled by an electron from oxygen during the heating process instead of an electron from the valence band. Therefore, it can be concluded that the blue color mechanism on sapphires before and after heating under oxidizing atmosphere can be explained by an energy band model involving the presence or absence of Fe3+-Ti4+ mixed acceptor states as well as a hole color center inside an energy band gap.
蓝宝石的蓝色通常与取代 Al2O3 结构中 Al3+ 的 Fe 和 Ti 杂质的含量有关。一般来说,蓝宝石的颜色强度与宝石矿床有关,包括玄武岩相关矿床和变质岩相关矿床。在氧化气氛下加热后,蓝宝石的颜色会发生变化。然而,之前的一些研究对颜色机理的解释相互矛盾,仍然令人疑惑。因此,本研究将重点放在氧化气氛下加热前后,Fe 和 Ti 氧化态的作用以及蓝宝石的蓝色机理上。在这项研究中,蓝宝石样品采集自不同的宝石矿床,包括泰国堪差那武里府的玄武岩相关蓝宝石和斯里兰卡的变质岩相关蓝宝石。因此,加热前蓝宝石上的蓝色可以描述为能带间隙内 Fe3+-Ti4+ 混合受体态的空穴色心,激发后可从价带获得电子以平衡电荷。加热后,玄武岩相关蓝宝石由深蓝色变为浅蓝色,而变质岩相关蓝宝石则由浅蓝色变为无色,这是因为在加热过程中,空穴色心被来自氧的电子填满,而不是被来自价带的电子填满,从而导致Fe3+-Ti4+混合受主态减少。因此,可以得出结论,在氧化气氛下加热前后蓝宝石的蓝色机理可以用能带模型来解释,该模型涉及能带间隙内是否存在 Fe3+-Ti4+ 混合受主态以及空穴色心。
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引用次数: 0
Classical relativistic electron-field dynamics: Hamiltonian approach to radiation reaction 经典相对论电子场动力学:辐射反应的哈密顿方法
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-12-13 DOI: 10.1088/2399-6528/ad1049
R F Álvarez-Estrada, I Pastor, L Roso, F Castejón
Motivated by the renewed interest due to the presently available extreme light sources, the dynamics of a single classical relativistic (spinless) extended electron interacting with a classical electromagnetic field (an incoming radiation and the field radiated by the electron) is revisited. The field is treated in Lorentz gauge, with the Lorentz condition. By assumption, there is a crucial finite cut-off kmax on the magnitude of any wavevector contributing to the field (preventing a point electron) and, for a simple formulation, the initial conditions for particle and fields are given in the infinitely remote past. In an infinite three-dimensional vacuum and in an inertial system, Hamilton’s dynamical equations for the particle and the complex field amplitudes acting as canonical variables (a's) yield an exact Lorentz force equation for the former, that includes the incoming radiation and an exact radiation reaction force FRR due to the field radiated by the electron. Uniform motion is obtained as a test of consistency. Based upon numerical computations, some approximations on FRR are given. A covariant formulation is also presented.
由于目前可用的极端光源再次引起人们的兴趣,我们重新探讨了单个经典相对论(无自旋)扩展电子与经典电磁场(入射辐射和电子辐射场)相互作用的动力学。该场以洛伦兹轨距和洛伦兹条件处理。根据假设,对场有贡献的任何波矢量(防止点电子)的大小都有一个关键的有限截断 kmax,而且,为了简单起见,粒子和场的初始条件是在无限遥远的过去给出的。在无限三维真空和惯性系中,粒子的汉密尔顿动力学方程和作为典型变量(a's)的复数场振幅产生了前者的精确洛伦兹力方程,其中包括入射辐射和电子辐射场产生的精确辐射反作用力 FRR。匀速运动是对一致性的检验。基于数值计算,给出了 FRR 的一些近似值。还提出了一种协变公式。
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引用次数: 0
A tale of analogies: a review on gravitomagnetic effects, rotating sources, observers and all that 一个类比的故事:对重力磁效应、旋转源、观察者和所有这些的回顾
Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-11-02 DOI: 10.1088/2399-6528/ad08cf
Matteo Luca Ruggiero, Davide Astesiano
Abstract Gravitoelectromagnetic analogies are somewhat ubiquitous in General Relativity, and they are often used to explain peculiar effects of Einstein's theory of gravity in terms of familiar results from classical electromagnetism. Perhaps, the best known of these analogy pertains to the similarity between the equations of electromagnetism and those of the linearized theory of General Relativity. But the analogy is somewhat deeper and ultimately rooted in the splitting of spacetime, which is preliminary to the definition of the measurement process in General Relativity.&#xD;In this paper we review the various approaches that lead to the introduction of a magnetic-like part of the gravitational interaction, briefly called textit{gravitomagnetic} and, then, we provide a survey of the recent developments both from the theoretical and experimental viewpoints.
引力电磁类比在广义相对论中几乎无处不在,它们经常被用来解释爱因斯坦引力理论的特殊效应,根据经典电磁学的熟悉结果。也许,这些类比中最著名的是电磁学方程和广义相对论线性化理论的相似之处。但是,这种类比在某种程度上更为深刻,并且最终植根于时空的分裂,这是广义相对论中测量过程定义的先决条件。在本文中,我们回顾了导致引入引力相互作用中类似磁性部分的各种方法,简称为textit{引力磁},然后,我们从理论和实验的角度对最近的发展进行了概述。
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引用次数: 2
A new method that automatically regularizes scattering amplitudes 一种自动正则化散射振幅的新方法
Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-10-24 DOI: 10.1088/2399-6528/ad0649
Nagabhushana Prabhu
Abstract We present a new regularization procedure called autoregularization.&#xD;The new procedure regularizes the divergences, encountered previously &#xD;in a scattering process, using the intrinsic scale of the process. We use &#xD;autoregularization to calculate the amplitudes of several scattering processes &#xD;in QED and compare the calculations with experimental measurements over a &#xD;broad range of center-of-momentum energies (~ MeV to > 200 GeV). The &#xD;calculated amplitudes are found to be in good agreement with experimental data. &#xD;To test autoregularization in a non-Abelian gauge theory, we calculate the &#xD;QCD coupling constant at 1-loop and show that, like the known regularization&#xD;schemes, autoregularization also predicts asymptotic freedom in QCD.&#xD;Finally, we show that the vacuum energy density of the free fields in the &#xD;Standard Model, calculated using autoregularization, is smaller than the&#xD;current estimate of the cosmic critical density.
摘要本文提出了一种新的正则化方法,称为自正则化。该方法利用过程的固有尺度对先前在散射过程中遇到的散度进行正则化。我们使用 自正则化来计算QED中几个散射过程的振幅 并将计算结果与在 较宽的动量中心能量范围(~ MeV到>200 GeV)。计算得到的振幅与实验数据吻合较好。为了验证非阿贝尔规范理论中的自正则化,我们计算了1环处的QCD耦合常数,并证明,与已知的正则化方案一样,自正则化也预测了QCD中的渐近自由。最后,我们证明了使用自正则化计算的标准模型中自由场的真空能量密度小于目前对宇宙临界密度的估计。
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引用次数: 0
Computational assessment of Sn activities and integral excess free energy change for mixing in the Sn-Au-Cu ternary liquid alloys using the molecular interaction volume model 用分子相互作用体积模型计算Sn- au - cu三元液态合金混合过程中Sn活度和整体多余自由能变化
Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-10-13 DOI: 10.1088/2399-6528/ad035a
Sanjay Kumar Sah, Ishwar Koirala
Abstract The activities of Sn in the liquid solder ternary alloy Sn-Au-Cu at 900 K have been computed using the molecular interaction volume model (MIVM). The calculated values have been compared with the experimental data for three cross-sections, i.e., for three different ratios of aurum to copper (XAu:XCu) = 3:1, 1:1, and 1:3. In addition, the excess Gibbs free energy of mixing, ΔGEx, for these ternary liquid alloys has been determined using the same model parameters to assess their validity. The resulting values have then been compared with the corresponding experimental data found in the literature. The agreement between the theoretical and experimental results has been found to be satisfactory.
摘要:采用分子相互作用体积模型(MIVM)计算了锡在液态钎料三元合金Sn- au - cu中900 K时的活度。将计算值与实验数据进行了对比,即在三种不同的金铜比(XAu:XCu) = 3:1、1:1和1:3的情况下。此外,用相同的模型参数测定了这些三元液态合金的过量混合吉布斯自由能ΔGEx,以评估其有效性。然后将所得值与文献中相应的实验数据进行比较。理论与实验结果吻合较好。
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引用次数: 0
From newton to universal planck natural units – disentangling the constants of nature 从牛顿到普朗克自然单位——解开自然常数的纠缠
Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-10-05 DOI: 10.1088/2399-6528/ad0090
Andrew Wutke
Abstract This study exploits a historical gap in the evolution of metric systems that resulted from incomplete implementation of the “rationalization” concept published by Heaviside in 1893 and ignoring the suggestion of Maxwell in 1873 to use the simplest form of Newton’s gravitational law expression with no proportionality constant. Bridging this gap required deriving an experimental Rationalized Metric System (RMS) and a corresponding Universal Planck Natural Unit System (UPNUS) in [ LT ] units.The described solution combines Heaviside’s rationalization of Newton’s law and makes the unit of mass dimensions [L 3 T −2 ], as suggested by Maxwell. Consequently the modified Coulomb’s law, changes the unit of the electric charges to the same dimensions as those of the mass. The elimination of the kilogram and ampere has a disentangling effect on the dependencies among the constants of nature and opens new horizons. The new systems have the potential to become powerful exploratory tools in fundamental research and education because of the simplification of the relationships among physical quantities. Noteworthy highlights from analyzed examples include the following: The well-known expression for Stoney mass ( m S ) when converted to RMS units is reduced to the electron charge quantity, whereas traditional metric systems entangle the charge, speed of light, and gravitational constant, forming an entity in the dimension of mass, as first presented by Stoney in 1874. A well-substantiated conjecture is proposed, wherein the Stoney energy E S =m S c 2 is nothing but the long-sought, finite electric field energy of the electron, and the gravitational constant appears to be the limiting factor. In UPNUS, the most disentangled fundamental expression, apart from the Stoney mass, is the elementary charge ӗ as the function of the fine structure constant α and the Planck mass( m̆ P ̌): ӗ = m̆ P √α ≈1.073 476 with ӗ , m̆ P of [L 3 T −2 ] dimensions in Planck units, and m̆ P = 4π
摘要:本研究利用了公制系统发展的历史空白,这一空白是由于对Heaviside在1893年发表的“合理化”概念的不完全实现,以及忽视了麦克斯韦在1873年提出的使用牛顿万有引力定律最简单形式的无比例常数表达式的建议。弥合这一差距需要推导出一个实验性的合理化公制(RMS)和相应的[LT]单位普朗克自然单位制(UPNUS)。所描述的解结合了Heaviside对牛顿定律的合理化,并使质量维度的单位[L 3 T−2],正如麦克斯韦所建议的那样。因此,修正后的库仑定律将电荷的单位改为与质量的单位相同的尺寸。千克和安培的消除对自然界常数之间的依赖关系产生了解缠作用,并开辟了新的视野。由于简化了物理量之间的关系,新系统有可能成为基础研究和教育中强大的探索工具。从分析的例子中,值得注意的亮点包括:众所周知的斯通质量(m S)在转换为均方根单位时被简化为电子电荷量,而传统的公制系统将电荷、光速和引力常数纠缠在一起,形成一个质量维度的实体,这是斯通在1874年首次提出的。提出了一个充分证实的猜想,其中斯通能E S =m S c 2只不过是长期寻找的有限电子电场能量,而引力常数似乎是限制因素。在UPNUS中,除Stoney质量外,最解离的基本表达式是基本电荷δ作为精细结构常数α和普朗克质量(m > P _)的函数:δ = m > P√α≈1.073 476,其中δ, m > P为[L 3 T−2]普朗克单位,m > P = 4π
{"title":"From newton to universal planck natural units – disentangling the constants of nature","authors":"Andrew Wutke","doi":"10.1088/2399-6528/ad0090","DOIUrl":"https://doi.org/10.1088/2399-6528/ad0090","url":null,"abstract":"Abstract This study exploits a historical gap in the evolution of metric systems that resulted from incomplete implementation of the “rationalization” concept published by Heaviside in 1893 and ignoring the suggestion of Maxwell in 1873 to use the simplest form of Newton’s gravitational law expression with no proportionality constant. Bridging this gap required deriving an experimental Rationalized Metric System (RMS) and a corresponding Universal Planck Natural Unit System (UPNUS) in [ LT ] units.The described solution combines Heaviside’s rationalization of Newton’s law and makes the unit of mass dimensions [L 3 T −2 ], as suggested by Maxwell. Consequently the modified Coulomb’s law, changes the unit of the electric charges to the same dimensions as those of the mass. The elimination of the kilogram and ampere has a disentangling effect on the dependencies among the constants of nature and opens new horizons. The new systems have the potential to become powerful exploratory tools in fundamental research and education because of the simplification of the relationships among physical quantities. Noteworthy highlights from analyzed examples include the following: The well-known expression for Stoney mass ( m S ) when converted to RMS units is reduced to the electron charge quantity, whereas traditional metric systems entangle the charge, speed of light, and gravitational constant, forming an entity in the dimension of mass, as first presented by Stoney in 1874. A well-substantiated conjecture is proposed, wherein the Stoney energy E S =m S c 2 is nothing but the long-sought, finite electric field energy of the electron, and the gravitational constant appears to be the limiting factor. In UPNUS, the most disentangled fundamental expression, apart from the Stoney mass, is the elementary charge ӗ as the function of the fine structure constant α and the Planck mass( m̆ P ̌): ӗ = m̆ P √α ≈1.073 476 with ӗ , m̆ P of [L 3 T −2 ] dimensions in Planck units, and m̆ P = 4π","PeriodicalId":47089,"journal":{"name":"Journal of Physics Communications","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135483931","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
Decoding of imagined speech electroencephalography neural signals using transfer learning method 用迁移学习方法解码想象语音脑电图神经信号
Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-09-01 DOI: 10.1088/2399-6528/ad0197
Nrushingh Charan Mahapatra, Prachet Bhuyan
Abstract The use of brain-computer interfaces to produce imagined speech from brain waves has the potential to assist individuals with difficulty producing speech or communicating silently. The decoding of covert speech has been observed to have limited efficacy due to the diverse nature of the associated measured brain waves and the limited number of covert speech databases. As a result, traditional machine learning algorithms for learning and inference are challenging, and one of the real alternatives could be to leverage transfer of learning. The main goals of this research were to create a new deep learning (DL) framework for decoding imagined speech electroencephalography (EEG) signals tasks using transfer learning and to transfer the model learning of the source task of an imagined speech EEG dataset to the model training on the target task of another imagined speech EEG dataset, essentially the cross-task learning transfer of discriminative characteristics of the source task to the target task of imagined speech. The experiment was carried out using two distinct open-access EEG datasets, FEIS and KaraOne, that recorded the imagined speech classes of neural signals from multiple individuals. The target FEIS model and the target KaraOne model for multiclass classification exhibit overall accuracy of 89.01% and 82.35%, respectively, according to the proposed transfer learning. The experiment results indicate that the cross-task deep transfer learning design reliably classifies the imagined speech EEG signals by applying the source task learning to the target task learning. The findings suggest the feasibility of a consistent strategy for classifying multiclass imagined speech with transfer learning, which could thereby open up the possibility of future investigation into cross-task imagined speech classification knowledge usability for generalization of new imagined speech prompts.
利用脑机接口从脑电波中产生想象的语音,有可能帮助有说话困难或无声交流困难的个体。由于相关测量脑电波的多样性和隐蔽语音数据库的数量有限,已经观察到隐蔽语音的解码效果有限。因此,用于学习和推理的传统机器学习算法具有挑战性,而真正的替代方案之一可能是利用学习迁移。本研究的主要目标是创建一个新的深度学习(DL)解码框架想象演讲脑电图(EEG)信号的任务使用学习和转移到传输源的模型学习任务的想象演讲脑电图数据集对模型训练的目标任务想象的另一次讲话中,脑电图数据集,本质上cross-task学习迁移的区别的特征源任务目标任务的想象演讲。实验使用两个不同的开放获取脑电图数据集,FEIS和KaraOne,记录了来自多个个体的神经信号的想象语音类别。根据所提出的迁移学习,目标FEIS模型和目标KaraOne模型的多类分类总体准确率分别为89.01%和82.35%。实验结果表明,跨任务深度迁移学习设计通过将源任务学习应用于目标任务学习,对想象语音脑电信号进行了可靠的分类。研究结果表明,采用迁移学习对多类想象语音进行统一分类的策略是可行的,从而为未来研究跨任务想象语音分类知识的可用性以推广新的想象语音提示开辟了可能性。
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引用次数: 0
Sublattice imbalance of states in graphene nanoflakes 石墨烯纳米片中亚晶格状态的不平衡
Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-09-01 DOI: 10.1088/2399-6528/ad0022
H Yorikawa
Abstract The energy states of π -electrons in a graphene nanoflake obtained from graphene, a well-known bipartite lattice or honeycomb lattice of carbon atoms, are studied using the tight-binding method. It is reported that the sublattice imbalance Δ N of the entire graphene nanoflake including vacancy clusters, which characterizes the electronic states, consists of those of the outer and inner edges. In nonzero-energy states, the electrons are evenly distributed between the sublattices A and B, regardless of the value of Δ N . In contrast, zero-energy states are ∣Δ N ∣-fold degenerate states where the electrons are unevenly distributed on either sublattice A or sublattice B. Occasionally, large or specific graphene nanoflakes have substantial zero-energy states, which are mixed states of the nonzero-energy states and zero-energy states.
摘要利用紧密结合方法研究了石墨烯纳米片中π电子的能态。石墨烯是碳原子的二部晶格或蜂窝晶格。据报道,包含空位团簇的整个石墨烯纳米片的亚晶格不平衡Δ N由外边缘和内边缘的亚晶格不平衡组成,这是表征电子态的特征。在非零能态中,电子均匀地分布在亚晶格A和B之间,与Δ N的值无关。相比之下,零能态是∣Δ N∣折叠简并态,其中电子不均匀地分布在亚晶格A或亚晶格b上。偶尔,大型或特定的石墨烯纳米片具有大量的零能态,它们是非零能态和零能态的混合态。
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引用次数: 0
Neoclassical models of charged particles 带电粒子的新古典模型
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-08-11 DOI: 10.1088/2399-6528/acefa6
F. De Zela
Classical electrodynamics (CED) has achieved great success in its domain of application, but despite this success, it has remained a theory that lacks complete self-consistency. It is worthwhile trying to make CED a self-consistent theory, because many important phenomena lie within its scope, and because modern field theories have been modelled on it. Alternative approaches to CED might help finding a definite formulation, and they might also lead to the prediction of new phenomena. Here we report two main results. The first one derives from standard CED. It is shown that the motion of a charged particle is ruled not only by the Lorentz equation, but also by equations that are formally identical to Maxwell equations. The latter hold for a velocity field and follow as a strict logical consequence of Hamilton’s action principle for a single particle. We construct a tensor with the velocity field in the same way as the electromagnetic tensor is constructed with the four potential. The two tensors are shown to be proportional to one another. As a consequence, and without leaving the realm of standard CED, one can envision new phenomena for a charged particle, which parallel those involving electromagnetic fields. The second result refers to a field-free approach to CED. This approach confirms the simultaneous validity of Maxwell-like and Lorentz equations as rulers of charged particle motion.
经典电动力学(CED)在其应用领域取得了巨大的成功,但尽管如此,它仍然是一个缺乏完全自洽性的理论。使其成为一个自洽理论是值得尝试的,因为许多重要的现象都在它的范围之内,而且现代场论都是以它为模型的。对CED的替代方法可能有助于找到一个明确的公式,它们也可能导致对新现象的预测。这里我们报告两个主要结果。第一个来源于标准CED。结果表明,带电粒子的运动不仅由洛伦兹方程决定,而且也由形式上与麦克斯韦方程相同的方程决定。后者适用于速度场,并遵循汉密尔顿作用原理对单个粒子的严格逻辑推论。我们用速度场构造一个张量就像用四势构造电磁张量一样。这两个张量是成比例的。因此,在不离开标准CED领域的情况下,人们可以设想带电粒子的新现象,这些现象与涉及电磁场的现象相似。第二个结果指的是一种无字段的CED方法。这种方法证实了麦克斯韦方程和洛伦兹方程同时作为带电粒子运动的标尺的有效性。
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引用次数: 0
On the comparison of diversity of parts of a distribution 关于分布各部分多样性的比较
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-07-20 DOI: 10.1088/2399-6528/ace952
R. Rajaram, N. Ritchey, B. Castellani
The literature on diversity measures, regardless of the metric used (e.g., Gini-Simpson index, Shannon entropy) has a notable gap: not much has been done to connect these measures back to the shape of the original distribution, or to use them to compare the diversity of parts of a given distribution and their relationship to the diversity of the whole distribution. As such, the precise quantification of the relationship between the probability of each type p i and the diversity D in non-uniform distributions, both among parts of a distribution as well as the whole, remains unresolved. This is particularly true for Hill numbers, despite their usefulness as ‘effective numbers’. This gap is problematic as most real-world systems (e.g., income distributions, economic complexity indices, rankings, ecological systems) have unequal distributions, varying frequencies, and comprise multiple diversity types with unknown frequencies that can change. To address this issue, we connect case-based entropy, an approach to diversity we developed, to the shape of a probability distribution; allowing us to show that the original probability distribution g 1, the case-based entropy curve g 2 and the c {1,k} versus the c{1,k}*lnA{1,k} curve g 3, which we call the slope of diversity, are one-to-one (or injective), i.e., a different probability distribution g 1 gives a different curve for g 2 and g 3. Hence, a different permutation of the original probability distribution g 1(that leads to a different shape) will uniquely determine the graphs g 2 and g 3. By proving the injective nature of our approach, we will have established a unique way to measure the degree of uniformity of parts as measured by D P /c P for a given part P of the original probability distribution, and also have shown a unique way to compute the D P /c P for various shapes of the original distribution and (in terms of comparison) for different curves.
关于多样性度量的文献,无论使用何种度量(例如,Gini Simpson指数、Shannon熵),都有一个显著的差距:没有做太多工作将这些度量与原始分布的形状联系起来,也没有用它们来比较给定分布部分的多样性及其与整个分布多样性的关系。因此,在非均匀分布中,每种类型的概率pi和多样性D之间的关系的精确量化,在分布的部分之间以及在整个分布之间,仍然没有解决。Hill数尤其如此,尽管它们作为“有效数”很有用。这种差距是有问题的,因为大多数现实世界的系统(例如,收入分配、经济复杂性指数、排名、生态系统)具有不平等的分布、不同的频率,并且包括具有未知频率的多种多样性类型,这些频率可能会发生变化。为了解决这个问题,我们将基于案例的熵(我们开发的一种多样性方法)与概率分布的形状联系起来;允许我们证明原始概率分布g1、基于事例的熵曲线g2和c{1,k}与c{1、k}*lnA{1,k}曲线g3(我们称之为多样性斜率)是一对一的(或内射的),即,不同的概率分布g1为g2和g3给出不同的曲线。因此,原始概率分布g1的不同排列(导致不同形状)将唯一地确定图g2和g3。通过证明我们的方法的内射性质,我们将建立一种独特的方法来测量由原始概率分布的给定部分P的D P/c P测量的部分的均匀度,并且还展示了一种计算原始分布的各种形状和(在比较方面)不同曲线的D P/c P的独特方法。
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