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This brief review summarizes recent theoretical and experimental results which predict and establish the existence of quantum droplets (QDs), i.e., robust two- and three-dimensional (2D and 3D) self-trapped states in Bose-Einstein condensates (BECs), which are stabilized by effective self-repulsion induced by quantum fluctuations around the mean-field (MF) states [alias the Lee-Huang-Yang (LHY) effect]. The basic models are presented, taking special care of the dimension crossover, 2D → 3D. Recently reported experimental results, which exhibit stable 3D and quasi-2D QDs in binary BECs, with the inter-component attraction slightly exceeding the MF self-repulsion in each component, and in single-component condensates of atoms carrying permanent magnetic moments, are presented in some detail. The summary of theoretical results is focused, chiefly, on 3D and quasi-2D QDs with embedded vorticity, as the possibility to stabilize such states is a remarkable prediction. Stable vortex states are presented both for QDs in free space, and for singular but physically relevant 2D modes pulled to the center by the inverse-square potential, with the quantum collapse suppressed by the LHY effect. [ABSTRACT FROM AUTHOR]

We study exponential stability of superstable systems in Hilbert spaces under perturbations. Formulas to calculate or to estimate the exponential growth bound of the perturbed systems are derived via which sufficient conditions on exponential stability are established. The obtained results are applied to a partial differential equation governing the vibration of a smart beam made of self-straining material. Several numerical simulations are given. [ABSTRACT FROM AUTHOR]

We study the interactions of moving discrete solitons in waveguide arrays with two types of point defects that are constructed by varying either the local linear coupling or local waveguide propagation constant at the center of the waveguide array. A broad discrete soliton is kicked toward the defect and interacts with it. Transmission, reflection, scattering, and trapping during the interaction between the soliton and the defect occur depending on the parameters. The detailed behavior of the soliton dynamics is analyzed numerically. A transmission window in the parameter domain is found and the behavior of this window for different parameters is studied. The dynamics of the soliton in the transmission window is found to have chaotic features under certain circumstances and the causes of these phenomena are identified and discussed. [ABSTRACT FROM AUTHOR]

Entrepreneurial learning is a hot issue in studies on entrepreneurship. In this paper, we reviewed the current researches on entrepreneurial learning from the perspectives of behaviorism, pragmatism, cognitive constructivism, humanism, and systematic theory in order to acquire an integrated understanding of the studies on entrepreneurial learning conducted from a multi-dimensional perspective. On this basis, we analyzed the purpose, subject, channel and process of entrepreneurial learning to reveal its essential contents. Finally, we pointed out the future directions of entrepreneurial learning from the following three aspects: the definition, the research methodology, and the sinicization of entrepreneurial learning. [ABSTRACT FROM AUTHOR]

Cotton (Gossypium spp.) is a vital global source of renewable fiber and ranks among the world's most important cash crops. While extensive nuclear genomic data of Gossypium has been explored, the organellar genomic resources of allotetraploid cotton, remain largely untapped at the population level. The plastid genome (plastome) is well suited for studying plant species relationships and diversity due to its nonrecombinant uniparental inheritance. Here, we conducted de novo assembly of 336 Gossypium plastomes, mainly from domesticated cultivars, and generated a pan‐plastome level resource for population structure and genetic diversity analyses. The assembled plastomes exhibited a typical quadripartite structure and varied in length from 160 103 to 160 597 bp. At the species level, seven allotetraploid species were resolved into three clades, where Gossypium tomentosum and Gossypium mustelinum formed an early diverging clade rooted by diploids, followed by splitting two sister clades of Gossypium darwinii–Gossypium barbadense and Gossypium hirsutum–Gossypium ekmanianum–Gossypium stephensii. Within the G. hirsutum clade the resolution of cultivated accessions was less polyphyletic with landrace and wild accessions than in G. barbadense suggesting some selection on plastome in the domestication of this adaptable species of cotton. The nucleotide diversity of G. hirsutum was higher than that of G. barbadense. We specifically compared the plastomes of G. hirsutum and G. barbadense to find mutational hotspots within each species as potential molecular markers. These findings contribute a valuable resource for exploring cotton evolution as well as in the breeding of new cotton cultivars and the preservation of wild and cultivated germplasm. [ABSTRACT FROM AUTHOR]

We investigate the nonlinear modes in a rotating double well potential with 풫풯 symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably exist by given certain parameter settings. The multistable area between these modes are studied numerically and the bistable and tristable areas are delimited. With different input trial wavefunctions, five types of solitary wave modes are identified. We found that the rotating of the potential can significantly affect the power flow of the fundamental harmonic mode, whose effect is absent for the other modes. [ABSTRACT FROM AUTHOR]