Gaussian Type(高斯型)到底是什麼？
Gaussian Type 高斯型 - The effect of the presence of both uniform and Gaussian type of interface trap charge distributions on the electrical performance of the devices under consideration are considered in the TCAD simulation study. [1] In this model, the heavy rainfall is modeled as a series of discretized pulse load whose amplitude follows the non-Gaussian distribution; then, the nonlinear governing equation and corresponding Fokker Planck Kolmogorov (FPK) equation of membrane structures are derived and solved by the perturbation method, considering both the geometrical nonlinearity of structure and the non-Gaussian type of load; consequently, the analytical solutions of the probability density function (PDF), mean and standard deviation of displacement response can be obtained. [2] The antecedents of primary membership functions of IT2 FLSs are chosen as Gaussian type-2 primary membership functions with uncertain standard deviations. [3] Among them, it is defective to use the conventional 1-D average fiber length (AFL) as a pulp quality index because the AFL is insufficient to describe the 2-D probability density function (pdf) shaping of fiber length distribution (FLD) with non-Gaussian types. [4] To alleviate this issue, this contribution proposes a fully decoupled approach for a specific class of problems, namely minimization of the failure probability of a linear system subjected to an uncertain dynamic load of the Gaussian type, under the additional constraint that the design variables are integer-valued. [5] For fuzzification in the first two layers, Gaussian type-2 fuzzy membership functions with uncertainty in the mean, are exploited. [6] We present the numerical results for a Gaussian type of the pore shape function and provide the software to calculate the space field structure for other pore shape functions. [7] Let M be a non-doubling parabolic manifold with ends and L a non-negative self-adjoint operator on L2(M) which satisfies a suitable heat kernel upper bound named the upper bound of Gaussian type. [8] The model is based upon conservation of momentum in the context of actuator disc theory, and the assumption of a distribution of the double-Gaussian type for the velocity deficit in the wake. [9] It is widely reported that attributes of geologic formations often exhibit statistical scaling with probability distribution of non-Gaussian type. [10] The work carried out so far predominantly models MRI noise as a Gaussian type. [11] The Gaussian type of magnetic field profile is optimized with the peak magnetic field value of 10 T at cavity center and the beam compression ratio of 35. [12] Use is made of a standard integral model of the top-hat type, which can be reduced to one of the Gaussian type by a simple transformation. [13] ,The result shows that optimum ANFIS model indicating RMSE and R scores adequately near between 0 and 1, respectively, was obtained from parameter set of network algorithm with two input membership functions, Gaussian type of membership function and hybrid optimization method. [14] The three-term recursion coefficients for orthogonal polynomials with respect to Gautschi’s weight function wG(t;s)=ts(t−1−logt)e−t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w^{G}(t;s)=t^{s}(t-1-\log t){\mathrm {e}}^{-t}$\end{document} (s > − 1) on (0,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(0,\infty )$\end{document}, as well as the corresponding quadrature formulas of Gaussian type, are used in this method. [15] The pulses considered were sech, Gaussian, and super-Gaussian type. [16] The two acid hydrolysis procedures produced NCCs suspensions that exhibited a unimodal or bimodal pattern of the Gaussian type, but differed in their properties. [17] The basic idea in this method is to transform the series to an integral with respect to some weight function on $\RR_+$ and then to approximate such an integral by the appropriate quadrature formulas of Gaussian type. [18] All fluctuations are assumed as Gaussian type and isotropic. [19] The most effective method of numerical integration of repeated integrals was introduced mathematically [1], namely the modification of numerical integration methods of the Gaussian type for use on repeated integrals. [20]在 TCAD 模擬研究中考慮了均勻和高斯型界面陷阱電荷分佈對所考慮器件的電氣性能的影響。 [1] 在該模型中，強降雨被建模為一系列離散的脈衝載荷，其幅度服從非高斯分佈；然後，考慮結構的幾何非線性和非高斯型荷載，採用微擾法推導並求解了膜結構的非線性控制方程和對應的福克普朗克科爾莫哥洛夫（FPK）方程；因此，可以獲得位移響應的概率密度函數（PDF）、均值和標準差的解析解。 [2] IT2 FLSs的初級隸屬函數的前件被選擇為具有不確定標準偏差的高斯類型2初級隸屬函數。 [3] 其中，使用傳統的一維平均纖維長度（AFL）作為紙漿質量指標是有缺陷的，因為AFL不足以描述纖維長度分佈（FLD）的二維概率密度函數（pdf）整形非高斯類型。 [4] 為了緩解這個問題，本文針對特定類別的問題提出了一種完全解耦的方法，即在設計變量為整數的附加約束下，最小化承受高斯類型不確定動態載荷的線性系統的故障概率-值。 [5] 對於前兩層的模糊化，利用了均值不確定的高斯 2 型模糊隸屬函數。 [6] 我們給出了高斯型孔形函數的數值結果，並提供了計算其他孔形函數空間場結構的軟件。 [7] 令 M 是一個有端點的非倍增拋物線流形，L 是 L2(M) 上的一個非負自伴隨算子，它滿足一個合適的熱核上界，稱為高斯類型的上界。 [8] 該模型基於致動器盤理論背景下的動量守恆，以及尾流速度缺陷的雙高斯分佈假設。 [9] 據廣泛報導，地質構造的屬性通常表現出具有非高斯類型概率分佈的統計尺度。 [10] 迄今為止進行的工作主要將 MRI 噪聲建模為高斯類型。 [11] 高斯型磁場分佈經過優化，腔中心的峰值磁場值為 10 T，光束壓縮比為 35。 [12] 使用頂帽類型的標準積分模型，通過簡單的變換可以將其簡化為高斯類型之一。 [13] ,結果表明，從具有兩個輸入隸屬函數、高斯型隸屬函數和混合優化方法的網絡算法的參數集中，獲得了分別充分接近 0 和 1 之間的 RMSE 和 R 分數的最優 ANFIS 模型。 [14] 正交多項式關於 Gautschi 權重函數的三項遞歸係數 wG(t;s)=ts(t−1−logt)e−t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym } \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$w^{G}(t; s)=t^{s}(t-1-\log t){\mathrm {e}}^{-t}$\end{document} (s > − 1) on (0,∞)\documentclass[ 12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(0,\infty)$\end{document}，以及對應的高斯類型的求積公式，都用在這個方法中。 [15] 所考慮的脈衝是 sech、Gaussian 和 super-Gaussian 類型。 [16] 兩種酸水解程序產生的 NCCs 懸浮液呈現出高斯型的單峰或雙峰模式，但它們的性質不同。 [17] 該方法的基本思想是將級數轉換為關於 $\RR_+$ 上的某個權重函數的積分，然後通過適當的高斯類型求積公式逼近該積分。 [18] 所有波動都假定為高斯型和各向同性的。 [19] 重複積分的數值積分最有效的方法在數學上被介紹了[1]，即修改高斯類型的數值積分方法以用於重複積分。 [20]
Electron Gaussian Type
The Infrared (IR) and Raman spectra of various interstitial carbon defects in silicon are computed at the quantum mechanical level by using an all electron Gaussian type basis set, the hybrid B3LYP functional and the supercell approach, as implemented in the CRYSTAL code (Dovesi et al. [1] The vibrational features of eight interstitial nitrogen related defects in silicon have been investigated at the first principles quantum mechanical level by using a periodic supercell approach, a hybrid functionals, an all electron Gaussian type basis set and the Crystal code. [2] The vibrational infrared (IR) and Raman spectra of seven substitutional defects in bulk silicon are computed, by using the quantum mechanical CRYSTAL code, the supercell scheme, an all electron Gaussian type basis set and the B3LYP functional. [3]矽中各種間隙碳缺陷的紅外 (IR) 和拉曼光譜通過使用全電子高斯型基組、混合 B3LYP 泛函和超級單元方法在量子力學水平上計算，如在 CRYSTAL 代碼中實現的 (Dovesi et人。 [1] 通過使用周期性超級單元方法、混合泛函、全電子高斯型基組和晶體代碼，在第一原理量子力學水平上研究了矽中八種間隙氮相關缺陷的振動特徵。 [2] 通過使用量子力學 CRYSTAL 代碼、超級電池方案、全電子高斯型基組和 B3LYP 泛函，計算了體矽中七個替代缺陷的振動紅外 (IR) 和拉曼光譜。 [3]
gaussian type orbital 高斯型軌道
The kinds of SUG are sampled from small molecules, and the Gaussian type orbitals (GTOs) only for core- and hydrogen atoms of each SUG are scaled in the SUG environment. [1] It regroups the expression in terms of primitive Gaussian type orbitals (GTOs) with identical angular momentum types and nuclei centers. [2] In this study, first-principles periodic calculations with localized Gaussian type orbitals within a hybrid density functional theory approach were performed to study the electronic, structural, thermodynamic, and transport properties of InxGa1−xN nitride alloys. [3] An implementation of the Hartree-Fock Roothaan with six expansion terms of Gaussian Type Orbitals (GTO-6G) is described and used to study the Helium atom’s ground state accurately. [4] The kinds of SUG are sampled from small molecules, and the s-type Gaussian type orbitals (GTOs) only for core- and hydrogen atoms of each SUG are floated in the SUG environment. [5] The accuracy of the method is demonstrated by evaluating integrals involving integrands containing Gaussian Type Orbitals and Yukawa potentials, on the atomic sites, as well as spherical Bessel functions centered on the master grid. [6] The coefficients of the same-spin and opposite-spin correlation energies and the Gaussian type orbitals (GTO) polarization exponents of the 6-31G** basis set are simultaneously optimized in order to minimize the energy differences with respect to the coupled-cluster with single, double and perturbative triples excitations [CCSD(T)] reference interaction energies, extrapolated to a complete basis set. [7] A methodology implemented to compute photoionization cross sections beyond the electric dipole approximation using Gaussian type orbitals for the initial state and plane waves for the final state is applied to molecules of various sizes. [8] In the present work, an extensive and detailed theoretical investigation is reported on the thermomechanical, electronic and thermodynamic properties of zinc-blende (sphalerite, zb-ZnS) and rock-salt zinc sulfide (rs-ZnS) over a wide range of pressure, by means of ab initio Density Functional Theory, Gaussian type orbitals and the well known B3LYP functional. [9] A methodology is developed to compute photoionization cross sections beyond the electric dipole approximation from response theory, using Gaussian type orbitals and plane waves for the initial and final states, respectively. [10] For electronic charge density, relativistic atomic natural orbitals based on Gaussian type orbitals were selected. [11]SUG 的種類是從小分子中取樣的，並且僅針對每個 SUG 的核心和氫原子的高斯型軌道 (GTO) 在 SUG 環境中進行縮放。 [1] 它根據具有相同角動量類型和核中心的原始高斯型軌道 (GTO) 重新組合表達式。 [2] 在這項研究中，在混合密度泛函理論方法中使用局部高斯型軌道進行第一性原理週期性計算，以研究 InxGa1-xN 氮化物合金的電子、結構、熱力學和傳輸特性。 [3] 描述了具有六個高斯型軌道 (GTO-6G) 擴展項的 Hartree-Fock Roothaan 實現，並用於準確研究氦原子的基態。 [4] SUG 的種類是從小分子中取樣的，每個 SUG 的核心和氫原子的 s 型高斯型軌道 (GTO) 都漂浮在 SUG 環境中。 [5] 該方法的準確性通過評估涉及在原子位點上包含高斯型軌道和 Yukawa 勢的被積函數的積分以及以主網格為中心的球形貝塞爾函數來證明。 [6] 同時優化了 6-31G** 基組的同自旋和相反自旋相關能的係數和高斯型軌道 (GTO) 極化指數，以最小化與耦合簇的能量差異單、雙和微擾三重激發 [CCSD(T)] 參考相互作用能量，外推到一個完整的基組。 [7] 一種用於計算超出電偶極子近似的光電離橫截面的方法，該方法使用初始狀態的高斯型軌道和最終狀態的平面波，應用於各種尺寸的分子。 [8] 在目前的工作中，對閃鋅礦（閃鋅礦，zb-ZnS）和岩鹽硫化鋅（rs-ZnS）在很寬的壓力範圍內的熱機械、電子和熱力學性質進行了廣泛而詳細的理論研究，通過從頭算密度泛函理論、高斯型軌道和眾所周知的 B3LYP 泛函。 [9] 開發了一種方法來計算超出響應理論的電偶極子近似的光電離橫截面，分別使用初始和最終狀態的高斯型軌道和平面波。 [10] 對於電子電荷密度，選擇了基於高斯型軌道的相對論原子自然軌道。 [11]
gaussian type basi 高斯型基
The algorithm which we study is the evaluation of tail integrals between Gaussian type basis functions for the R‐matrix method, a task that arises in the study of scattering of low energy electrons by molecular targets. [1] The Infrared (IR) and Raman spectra of various interstitial carbon defects in silicon are computed at the quantum mechanical level by using an all electron Gaussian type basis set, the hybrid B3LYP functional and the supercell approach, as implemented in the CRYSTAL code (Dovesi et al. [2] The vibrational features of eight interstitial nitrogen related defects in silicon have been investigated at the first principles quantum mechanical level by using a periodic supercell approach, a hybrid functionals, an all electron Gaussian type basis set and the Crystal code. [3] The vibrational infrared (IR) and Raman spectra of seven substitutional defects in bulk silicon are computed, by using the quantum mechanical CRYSTAL code, the supercell scheme, an all electron Gaussian type basis set and the B3LYP functional. [4] Three alternative strategies for the calculation of the IR intensity of crystalline systems, as determined by Born charges, have been implemented in the Crystal code, using a Gaussian type basis set. [5] In this article we present an effective approach to calculate quantum chemical two-electron integrals over basis sets consisting of Gaussian type basis functions on GPU. [6]我們研究的算法是評估 R 矩陣方法的高斯型基函數之間的尾積分，這是研究分子目標對低能電子的散射的一項任務。 [1] 矽中各種間隙碳缺陷的紅外 (IR) 和拉曼光譜通過使用全電子高斯型基組、混合 B3LYP 泛函和超級單元方法在量子力學水平上計算，如在 CRYSTAL 代碼中實現的 (Dovesi et人。 [2] 通過使用周期性超級單元方法、混合泛函、全電子高斯型基組和晶體代碼，在第一原理量子力學水平上研究了矽中八種間隙氮相關缺陷的振動特徵。 [3] 通過使用量子力學 CRYSTAL 代碼、超級電池方案、全電子高斯型基組和 B3LYP 泛函，計算了體矽中七個替代缺陷的振動紅外 (IR) 和拉曼光譜。 [4] 晶體系統的紅外強度計算的三種替代策略，由玻恩電荷確定，已在晶體代碼中實施，使用高斯型基組。 [5] 在本文中，我們提出了一種有效的方法來計算由 GPU 上的高斯型基函數組成的基組上的量子化學二電子積分。 [6]
gaussian type membership
ANN consists of a three-layer feed-forward back-propagation network with a 3-5-1 architecture and ANFIS consists of [4 4 4] Gaussian type membership functions. [1] The Gaussian type membership functions are used and its parameters are generated from the training dataset. [2]ANN 由具有 3-5-1 架構的三層前饋反向傳播網絡組成，而 ANFIS 由 [4 4 4] 高斯型隸屬函數組成。 [1] 使用高斯型隸屬函數，其參數由訓練數據集生成。 [2]