We study the regularity of minima scalar variational integrals $p$-growth, $1<p<\infty$, in Heisenberg group and prove H\"older continuity horizontal gradient minima.

Computational results are described of interactions between nucleic acid bases and of searching for local minima of the interaction energy. As the bases are the elementary units of genetic material, their interactions are important for understanding the molecular mechanisms of genetic processes. The results allow us to reveal three different types of energy minima, which are responsible for var...

Aims. Using a reconstruction of sunspot numbers stretching over multiple millennia, we analyze the statistics of the occurrence of grand minima and maxima and set new observational constraints on long-term solar and stellar dynamo models. Methods. We present an updated reconstruction of sunspot number over multiple millennia, from C data by means of a physics-based model, using an updated model...

During rest, the human brain performs essential functions such as memory maintenance, which are associated with resting-state brain networks (RSNs) including the default-mode network (DMN) and frontoparietal network (FPN). Previous studies based on spiking-neuron network models and their reduced models, as well as those based on imaging data, suggest that resting-state network activity can be c...

This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, and global weak sharp minima for such problems and establish their complete characterizations in the case of convex problems on finite-dimensio...

Baud-rate blind equalization algorithms may converge to undesirable stable equi-libria due to diierent reasons. One is the use of FIR lter as an equalizer. It is proved in this paper that this kind of local minima exist for all blind equalization algorithms. The local minima generated by this mechanism are thus called unavoidable local minima. The other one is due to the cost function adopted b...

This study theoretically evaluated interactions between spherical colloids and rough surfaces in three-dimensional space using Derjaguin-Landau-Verwey- Overbeek (DLVO) energy/force map and curve. The rough surfaces were modeled as a flat surface covered by hemispherical protrusions. A modified Derjaguin approach was employed to calculate the interaction energies and forces. Results show that mo...

The Griewank function is commonly used to test the ability of different solution procedures to find local optima. It is important to know the exact number of minima of the function to support its use as a test function. However, to the best of our knowledge, no attempts have been made to analytically derive the number of minima. Because of the complex nature of the function surface, a numerical...

* Correspondence: [email protected] Department of Mathematics, School of Science, Shandong University of Technology, Zibo, 255049, China Full list of author information is available at the end of the article Abstract In this paper, we study the concept of weak sharp minima using two different approaches. One is transforming weak sharp minima to an optimization problem; another is using conju...

We show that molecular dynamics based moves in the minima hopping method are more efficient than saddle point crossing moves. For binary systems we incorporate identity exchange moves in a way that allows one to avoid the generation of high energy configurations. Using this modified minima hopping method, we re-examine the binary Lennard-Jones benchmark system with up to 100 atoms and we find a...