Maximal Surfaces on Five-Dimensional Group Structures

2018 ◽  
Vol 59 (3) ◽  
pp. 442-457 ◽  
Author(s):  
M. B. Karmanova
1978 ◽  
Vol 125 (7) ◽  
pp. 549-565 ◽  
Author(s):  
V.G. Polevoi ◽  
S.M. Rytov

Author(s):  
Nobuo Uemura ◽  
Hiroshi Kasanuki ◽  
Mitsuo Umezu

Abstract Objective The developer and sponsor of new combination products in US needs to forecast which classification and designation to the regulatory scheme of drug, biological product, or device would be required for the new products by the Food and Drug Administration (FDA). To improve the predictability and acceptability of the designation of new combination products for innovators, developers, and sponsors, and to encourage the development and early access of new combination products, we proposed new visualization models of the designation pathway and group categorization. Method We searched the website of the FDA on 15 November, 2020 to identify the regulatory scheme of the FDA’s 129 capsular decision cases of device–drug and device–biologics combination products and other publicly available cases the FDA designated to the drug/biologic or device regulatory scheme. Results By introducing a new definition for primary intended use (PIU) by developers and sponsors extracted from the classification factors of primary mode of action (PMOA), we developed new visualization models of the designation pathway and two-dimensional group categorization. And applying these models to the cases the FDA designated, we proposed a new group categorization of combination products while focusing on the device component function. Conclusions The new visualization models with PIU and PMOA and the new group categorization focusing on the device component function proposed in this study may increase predictability and acceptability of the classification of newly developed combination products into the regulatory scheme of drug, biological product, and device, for innovators, developers, and sponsors.


2021 ◽  
Author(s):  
Yasuteru Mawatari ◽  
Muneki Oouchi ◽  
Yoshiaki Yoshida ◽  
Toshifumi Hiraoki ◽  
Masayoshi Tabata

2019 ◽  
Author(s):  
Jia Chen

Summary This paper studies the estimation of latent group structures in heterogeneous time-varying coefficient panel data models. While allowing the coefficient functions to vary over cross-sections provides a good way to model cross-sectional heterogeneity, it reduces the degree of freedom and leads to poor estimation accuracy when the time-series length is short. On the other hand, in a lot of empirical studies, it is not uncommon to find that heterogeneous coefficients exhibit group structures where coefficients belonging to the same group are similar or identical. This paper aims to provide an easy and straightforward approach for estimating the underlying latent groups. This approach is based on the hierarchical agglomerative clustering (HAC) of kernel estimates of the heterogeneous time-varying coefficients when the number of groups is known. We establish the consistency of this clustering method and also propose a generalised information criterion for estimating the number of groups when it is unknown. Simulation studies are carried out to examine the finite-sample properties of the proposed clustering method as well as the post-clustering estimation of the group-specific time-varying coefficients. The simulation results show that our methods give comparable performance to the penalised-sieve-estimation-based classifier-LASSO approach by Su et al. (2018), but are computationally easier. An application to a panel study of economic growth is also provided.


2004 ◽  
Vol 2004 (10) ◽  
pp. 487-534 ◽  
Author(s):  
M. B. Sheftel

We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence ont,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries and use them to construct infinite discrete sets of exact solutions of the studied equations. We find the interrelation between higher symmetries and recursion operators. Two-component systems are studied in more detail thann-component systems. As a special case, we consider Hamiltonian and semi-Hamiltonian systems of Tsarëv.


2017 ◽  
Vol 34 (8) ◽  
pp. 087701 ◽  
Author(s):  
Jing Shi ◽  
Yong Gao ◽  
Xiao-Li Wang ◽  
Si-Ning Yun

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