and Applied Analysis 3 in the normal bundle T⊥M, and AN is the shape operator of the second fundamental form. Moreover, we have g ANX, Y g h X,Y ,N , 2.4 where g denotes the Riemannian metric onM as well as the metric induced onM. The mean curvature vector H on M is given by

Key points .................................................................................................................. 559 H

The eastern part of the Pamir Mountains, located in Central Asia, is characterized by great climatic continentality and aridity. Wetlands developed in this hostile region are restricted to spring areas, terraces of shallow lakes or floodplains along rivers, and provide diversified ecosystem services e.g. as water reservoirs, refugia for rare species and pastures for domestic cattle. These ecosy...

c o l o r e d l i g h t r e f l e c t i o n s p r o d u c e d b y h i s m o b i l e s . H i s s h o r t J a m e s E . D a v i s , " F i g u r e S t u d y , " p e n c i l o n p a p e r , 1 9 3 4 . f i l m s , a v e r a g i n g a b o u t t e n m i n u t e s i n l e n g t h , w e r e o f t e n a c c o m p a n i e d b y o r i g i n a l m u s i c , s o m e t i m e s c o m p o s e d a n d a r r a n g...

In this work, we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical-potential equalization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for the NDDO type of methods by Giese and York, has been shown to significantly emend minimal basis methods with respect to the response pr...

In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville) or a solution with increasing...