Inorganic–organic hybrid high-dimensional polyoxotantalates and their structural transformations triggered by water

2019 ◽  
Vol 55 (78) ◽  
pp. 11735-11738 ◽  
Author(s):  
Zhong Li ◽  
Jing Zhang ◽  
Li-Dan Lin ◽  
Jin-Hua Liu ◽  
Xin-Xiong Li ◽  
...  
Keyword(s):  
Structural Transformations ◽  
High Dimensional ◽  
Organic Hybrid ◽  
New Family

In this work, novel dimeric polyoxotantalate (POTa) clusters {Cu(en)(Ta6O19)}2/{Cu(enMe)(Ta6O19)}2 were introduced as SBUs to construct a new family of extended POTa materials, including the first two 3D POTa frameworks and two 2D POTa layers.

Conditional Similarity Reduction Method and Complex Wave Excitations for a High-Dimensional Nonlinear System

2015 ◽  
Vol 70 (9) ◽  
pp. 739-744
Author(s):  
Fu-Zhong Lin ◽  
Song-Hua Ma
Keyword(s):  
Nonlinear System ◽  
Water Wave ◽  
Reduction Method ◽  
Solitary Wave Solution ◽  
High Dimensional ◽  
Similarity Reduction ◽  
New Family ◽  
Wave Solutions ◽  
Complex Wave ◽  
Novel Complex

AbstractWith the help of the conditional similarity reduction method, a new family of complex wave solutions with q=lx + my + kt + Γ(x, y, t) for the (2+1)-dimensional modified dispersive water-wave (MDWW) system are obtained. Based on the derived solitary wave solution, some novel complex wave localised excitations are investigated.

New Family of Lanthanide-Based Inorganic–Organic Hybrid Frameworks: Ln2(OH)4[O3S(CH2)nSO3]·2H2O (Ln = La, Ce, Pr, Nd, Sm; n = 3, 4) and Their Derivatives

2013 ◽  
Vol 52 (4) ◽  
pp. 1755-1761 ◽  
Author(s):  
Jianbo Liang ◽  
Renzhi Ma ◽  
Yasuo Ebina ◽  
Fengxia Geng ◽  
Takayoshi Sasaki
Keyword(s):  
Organic Hybrid ◽  
New Family

scholarly journals Functionalized phosphonates as building units for multi-dimensional homo- and heterometallic 3d–4f inorganic–organic hybrid-materials

2016 ◽  
Vol 45 (32) ◽  
pp. 12854-12861 ◽  
Author(s):  
C. Köhler ◽  
E. Rentschler
Keyword(s):  
Single Crystal ◽  
Hybrid Materials ◽  
Magnetic Measurements ◽  
Diphosphonic Acid ◽  
Single Crystal Diffraction ◽  
Organic Hybrid ◽  
New Family ◽  
Multifunctional Ligand

Using the multifunctional ligand H4L (2,2′-bipyridinyl-5,5′-diphosphonic acid), a new family of 0D-3D inorganic–organic hybrid-materials was prepared and characterized by single crystal diffraction and magnetic measurements.

scholarly journals High-Dimensional Separability for One- and Few-Shot Learning

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1090
Author(s):  
Alexander N. Gorban ◽  
Bogdan Grechuk ◽  
Evgeny M. Mirkes ◽  
Sergey V. Stasenko ◽  
Ivan Y. Tyukin
Keyword(s):  
Domain Adaptation ◽  
Cluster Structure ◽  
Principal Component ◽  
Component Analysis ◽  
High Dimensional ◽  
Separation Theorems ◽  
Mathematical Basis ◽  
Fine Grained ◽  
New Family ◽  
Fine Grained Structure

This work is driven by a practical question: corrections of Artificial Intelligence (AI) errors. These corrections should be quick and non-iterative. To solve this problem without modification of a legacy AI system, we propose special `external’ devices, correctors. Elementary correctors consist of two parts, a classifier that separates the situations with high risk of error from the situations in which the legacy AI system works well and a new decision that should be recommended for situations with potential errors. Input signals for the correctors can be the inputs of the legacy AI system, its internal signals, and outputs. If the intrinsic dimensionality of data is high enough then the classifiers for correction of small number of errors can be very simple. According to the blessing of dimensionality effects, even simple and robust Fisher’s discriminants can be used for one-shot learning of AI correctors. Stochastic separation theorems provide the mathematical basis for this one-short learning. However, as the number of correctors needed grows, the cluster structure of data becomes important and a new family of stochastic separation theorems is required. We refuse the classical hypothesis of the regularity of the data distribution and assume that the data can have a rich fine-grained structure with many clusters and corresponding peaks in the probability density. New stochastic separation theorems for data with fine-grained structure are formulated and proved. On the basis of these theorems, the multi-correctors for granular data are proposed. The advantages of the multi-corrector technology were demonstrated by examples of correcting errors and learning new classes of objects by a deep convolutional neural network on the CIFAR-10 dataset. The key problems of the non-classical high-dimensional data analysis are reviewed together with the basic preprocessing steps including the correlation transformation, supervised Principal Component Analysis (PCA), semi-supervised PCA, transfer component analysis, and new domain adaptation PCA.

scholarly journals A New Family of Bimetallic Framework Materials Showing Reversible Structural Transformations

2009 ◽  
Vol 9 (7) ◽  
pp. 3104-3110 ◽  
Author(s):  
Olha Sereda ◽  
Fritz Stoeckli ◽  
Helen Stoeckli-Evans ◽  
Oleg Dolomanov ◽  
Yaroslav Filinchuk ◽  
...  
Keyword(s):  
Structural Transformations ◽  
Framework Materials ◽  
New Family

From 1D Chain to 3D Network: A New Family of Inorganic–Organic Hybrid Semiconductors MO3(L)x (M = Mo, W; L = Organic Linker) Built on Perovskite-like Structure Modules

2013 ◽  
Vol 135 (46) ◽  
pp. 17401-17407 ◽  
Author(s):  
Xiao Zhang ◽  
Mehdi Hejazi ◽  
Suraj J. Thiagarajan ◽  
William R. Woerner ◽  
Debasis Banerjee ◽  
...  
Keyword(s):  
Organic Hybrid ◽  
New Family ◽  
3D Network ◽  
1D Chain ◽  
Hybrid Semiconductors ◽  
Organic Linker

scholarly journals Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

2021 ◽  
Vol 2 (6) ◽  
Author(s):  
Weinan E ◽  
Martin Hutzenthaler ◽  
Arnulf Jentzen ◽  
Thomas Kruse
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Algorithms ◽  
High Dimensional ◽  
Heat Equations ◽  
Partial Differential ◽  
New Family ◽  
Dimensional Approximation ◽  
Analytical Tools ◽  
Semilinear Parabolic

AbstractWe introduce a new family of numerical algorithms for approximating solutions of general high-dimensional semilinear parabolic partial differential equations at single space-time points. The algorithm is obtained through a delicate combination of the Feynman–Kac and the Bismut–Elworthy–Li formulas, and an approximate decomposition of the Picard fixed-point iteration with multilevel accuracy. The algorithm has been tested on a variety of semilinear partial differential equations that arise in physics and finance, with satisfactory results. Analytical tools needed for the analysis of such algorithms, including a semilinear Feynman–Kac formula, a new class of seminorms and their recursive inequalities, are also introduced. They allow us to prove for semilinear heat equations with gradient-independent nonlinearities that the computational complexity of the proposed algorithm is bounded by $$O(d\,{\varepsilon }^{-(4+\delta )})$$ O ( d ε - ( 4 + δ ) ) for any $$\delta \in (0,\infty )$$ δ ∈ ( 0 , ∞ ) under suitable assumptions, where $$d\in {{\mathbb {N}}}$$ d ∈ N is the dimensionality of the problem and $${\varepsilon }\in (0,\infty )$$ ε ∈ ( 0 , ∞ ) is the prescribed accuracy. Moreover, the introduced class of numerical algorithms is also powerful for proving high-dimensional approximation capacities for deep neural networks.

Sign in / Sign up

Export Citation Format

Share Document