We count how many ‘different’ Morse functions exist on the 2-sphere. There are several ways of declaring that two Morse functions f and g are ‘indistinguishable’ but we concentrate only on two natural equivalence relations: homological (when the regular sublevel sets f and g have identical Betti numbers) and geometric (when f is obtained from g via global, orientation-preserving changes of coor...

– We present a new theoretical analysis of the strongly suppressed F-and M-dependent Stark shifts of the Cs ground state hyperfine structure. Our treatment uses third order perturbation theory including off-diagonal hyperfine interactions not considered in earlier treatments. A numerical evaluation of the perturbation sum using bound states up to n=200 yields ground state tensor polarizabilitie...

An important tool in the field of topological data analysis is persistent homology (PH), which used to encode abstract representations at different resolutions form persistence barcode (PB). Normally, one will obtain PB from a digital image when using sublevel-set filtration method. In this work, we built more than representation single based on landmark selection method, known as local binary ...

Abstract In this paper, we present a geometric approach for computing the controlled invariant set of continuous-time control system. While problem is well studied in ellipsoidal case, family quite conservative constrained or switched linear systems. We reformulate invariance as an inequality its support function that valid any convex set. This produces novel algebraic conditions sets with poly...

Dynamic behavior analysis of electric motors is required in order to accurately evaluate the performance, energy consumption and pollution level of hybrid electric vehicles. Simulation tools for hybrid electric vehicles are divided into steady state and dynamic models. Tools with steady-state models are useful for system-level analysis whereas tools that utilize dynamic models give in-depth inf...

Variations in rock fragmentation are very likely to occur a sublevel-caving operation. This study conducted comprehensive test an iron ore mine monitor fragmentation. The results show clear trend variations from start end of production ring. These suggest increase coarse and oversized fragments with increasing material extraction the rings that can be linked increased overburden drill hole devi...