This paper establishes an extreme $C^k$ reducibility theorem of quasi-periodic $SL(2, \mathbb {R})$ cocycles in the local perturbative region, revealing both the essence of Eliasson [Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation. Comm. Math. Phys. 146 (1992), 447–482], and Hou and You [Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems. Invent. Math. 190 (2012), 209–260] in respectively the non-resonant and resonant cases. By paralleling further the reducibility process with the almost reducibility, we are able to acquire the least initial regularity as well as the least loss of regularity for the whole Kolmogorov–Arnold–Moser (KAM) iterations. This, in return, makes various spectral applications of quasi-periodic Schrödinger operators wide open.

To date, a comprehensive understanding of the influence of the Prandtl number ($Pr$) on flow topology in turbulent Rayleigh–Bénard convection (RBC) remains elusive. In this study, we present an experimental investigation into the evolution of flow topology in quasi-two-dimensional turbulent RBC with $7.0 \leq Pr \leq 244.2$ and $2.03\times 10^{8} \leq Ra \leq 2.81\times 10^{9}$. Particle image velocimetry (PIV) measurements reveal the flow transitions from multiple-roll state to single-roll state with increasing $Ra$, and the transition is hindered with increasing $Pr$, i.e. the transitional Rayleigh number $Ra_t$ increases with $Pr$. We mapped out a phase diagram on the flow topology change on $Ra$ and $Pr$, and identified the scaling of $Ra_t$ on $Pr$: $Ra_t \sim Pr^{0.93}$ in the low $Pr$ range, and $Ra_t \sim Pr^{3.3}$ in the high $Pr$ range. The scaling in the low $Pr$ range is consistent with the model of balance of energy dissipation time and plume travel time that we proposed in our previous study, while the scaling in the high $Pr$ range implies a new governing mechanism. For the first time, the scaling of $Re$ on $Ra$ and $Pr$ is acquired through full-field PIV velocity measurement, $Re \sim Ra^{0.63}\,Pr^{-0.87}$. We also propose that increasing horizontal velocity promotes the formation of the large-scale circulation (LSC), especially for the high $Pr$ case. Our proposal was verified by achieving LSC through introducing horizontal driving force $Ra_H$ by tilting the convection cell with a small angle.

Pharmaceutical distribution routing problem is a key problem for pharmaceutical enterprises, since efficient schedules can enhance resource utilization and reduce operating costs. Meanwhile, it is a complicated combinatorial optimization problem. Existing research mainly focused on delivery route lengths or distribution costs minimization, while seldom considered customer priority and carbon emissions simultaneously. However, considering the customer priority and carbon emissions simultaneously will not only help to enhance customer satisfaction, but also help to reduce the carbon emissions. In this article, we consider the customer priority and carbon emission minimization simultaneously in the pharmaceutical distribution routing problem, the corresponding problem is named pharmaceutical distribution routing problem considering customer priority and carbon emissions. A corresponding mathematical model is formulated, the objectives of which are minimizing fixed cost, refrigeration cost, fuel consumption cost, carbon emission cost, and penalty cost for violating time windows. Moreover, a hybrid genetic algorithm (HGA) is proposed to solve the problem. The framework of the proposed HGA is genetic algorithm (GA), where an effective local search based on variable neighborhood search (VNS) is specially designed and incorporated to improve the intensification abilities. In the proposed HGA, crossover with adaptive probability and mutation with adaptive probability are utilized to enhance the algorithm performance. Finally, the proposed HGA is compared with four optimization algorithms, and experimental results have demonstrated the effectiveness of the HGA.

We demonstrate that a large class of discrete choice models of demand can be approximated by real analytic demand models. We obtain this result by combining (i) a novel real analytic property of the mixed logit and the mixed probit models with any distribution of random coefficients and (ii) an approximation property of finite mixtures of Gumbel and Gaussian distributions. To illustrate some of the implications of this result, we discuss how real analyticity facilitates nonparametric and semi-nonparametric identification, extrapolation to hypothetical counterfactuals, numerical implementation of demand inverses, and numerical implementation of the maximum likelihood estimator.

In this study, a toroidal quartz ($20\overline{2}3$) crystal is designed for monochromatic X-ray imaging at 72.3°. The designed crystal produces excellent images of a laser-produced plasma emitting He-like Ti X-rays at 4.75 keV. Based on the simulations, the imaging resolutions of the spherical and toroidal crystals in the sagittal direction are found to be 15 and 5 μm, respectively. Moreover, the simulation results show that a higher resolution image of the source can be obtained by using a toroidal crystal. An X-ray backlight imaging experiment is conducted using 4.75 keV He-like Ti X-rays, a 3 × 3 metal grid, an imaging plate and a toroidal quartz crystal with a lattice constant of 2d = 0.2749 nm. The meridional and sagittal radii of the toroidal α-quartz crystal are 295.6 and 268.5 mm, respectively. A highly resolved image of the microgrid, with a spatial resolution of 10 μm, is obtained in the experiment. By using similar toroidal crystal designs, the application of a spatially resolved spectrometer with high-resolution X-ray imaging ability is capable of providing imaging data with the same magnification ratio in the sagittal and meridional planes.

We consider the fractional elliptic problem:where B1 is the unit ball in ℝN, N ⩾ 3, s ∈ (0, 1) and p > (N + 2s)/(N − 2s). We prove that this problem has infinitely many solutions with slow decay O(|x|−2s/(p−1)) at infinity. In addition, for each s ∈ (0, 1) there exists Ps > (N + 2s)/(N − 2s), for any (N + 2s)/(N − 2s) < p < Ps, the above problem has a solution with fast decay O(|x|2s−N). This result is the extension of the work by Dávila, del Pino, Musso and Wei (2008, Calc. Var. Partial Differ. Equ. 32, no. 4, 453–480) to the fractional case.

We determined the effects of a combination of C18 unsaturated fatty acids (C18-UFAs) consisting of oleic, linoleic, and linolenic acids on milk lipogenesis in bovine mammary epithelial cells (BMECs). By orthogonal experiments to determine cellular triacylglycerol (TAG) accumulation, a combination of 200 μmol/l C18 : 1, 50 μmol/l C18 : 2, and 2 μmol/l C18 : 3 was selected as C18-UFAs combination treatment, and culture in medium containing fatty acid-free bovine serum albumin was used as the control. The expression of genes related to milk lipid synthesis and intracellular FA composition was measured. The results showed that cytosolic TAG formation was higher under C18-UFAs treatment than under control treatment. The mRNA expression of acetyl-CoA carboxylase-α (ACACA), fatty acid synthase (FASN), and peroxisome proliferator-activated receptor gamma (PPARG) did not differ between treatments. The abundance of stearoyl-CoA desaturase (SCD) and acyl-CoA synthetase long-chain family member 1 (ACSL1) was higher, whereas that of sterol regulatory element binding transcription factor 1 (SREBF-1) was lower after C18-UFAs treatment compared to control treatment. The C16 : 0 and SFA content was decreased following C18-UFAs treatment compared to control treatment, while the cis-9 C18 : 1 and UFA content was increased. In conclusion, C18-UFAs could stimulate triglyceride accumulation, increase the cellular UFA concentration, and regulate lipogenic genes in BMECs.

The uncertainty and information asymmetry that surround initial public offering firms (IPOs) often introduce difficulties for potential investors to discern organizational value, thereby leading to ‘underpricing’. Using the signaling theory, we investigate the role of organizational reputation in the underpricing of IPOs. We analyze 463 initial public offerings in China from the period of 2010 to 2016 and find that being known for quality and generalized favorability dimensions of reputation are negatively related with underpricing on the first day of trading. In addition, we find that the negative effects of organizational reputation on underpricing are mediated by investor attention.

The ALMA twenty-six arcmin2 survey of GOODS-S at one millimeter (ASAGAO) is a deep (1σ ∼ 61μJy/beam) and wide area (26 arcmin2) survey on a contiguous field at 1.2 mm. By combining with archival data, we obtained a deeper map in the same region (1σ ∼ 30μJy/beam−1, synthesized beam size 0.59″ × 0.53″), providing the largest sample of sources (25 sources at 5σ, 45 sources at 4.5σ) among ALMA blank-field surveys. The median redshift of the 4.5σ sources is 2.4. The number counts shows that 52% of the extragalactic background light at 1.2 mm is resolved into discrete sources. We create IR luminosity functions (LFs) at z = 1–3, and constrain the faintest luminosity of the LF at 2 < z < 3. The LFs are consistent with previous results based on other ALMA and SCUBA-2 observations, which suggests a positive luminosity evolution and negative density evolution.

Triploid and pentaploid breeding is of great importance in agricultural production, but it is not always easy to obtain double ploidy parents. However, in fishes, chromosome ploidy is diversiform, which may provide natural parental resources for triploid and pentaploid breeding. Both tetraploid and hexaploid exist in Schizothorax fishes, which were thought to belong to different subfamilies with tetraploid Percocypris fishes in morphology, but they are sister genera in molecule. Fortunately, the pentaploid hybrid fishes have been successfully obtained by hybridization of Schizothorax wangchiachii (♀, 2n = 6X = 148) × Percocypris pingi (♂, 2n = 4X = 98). To understand the genetic and morphological difference among the hybrid fishes and their parents, four methods were used in this study: morphology, karyotype, red blood cell (RBC) DNA content determination and inter-simple sequence repeat (ISSR). In morphology, the hybrid fishes were steady, and between their parents with no obvious preference. The chromosome numbers of P. pingi have been reported as 2n = 4X = 98. In this study, the karyotype of S. wangchiachii was 2n = 6X = 148 = 36m + 34sm + 12st + 66t, while that the hybrid fishes was 2n = 5X = 123 = 39m + 28sm + 5st + 51t. Similarly, the RBC DNA content of the hybrid fishes was intermediate among their parents. In ISSR, the within-group genetic diversity of hybrid fishes was higher than that of their parents. Moreover, the genetic distance of hybrid fishes between P. pingi and S.wangchiachii was closely related to that of their parental ploidy, suggesting that parental genetic material stably coexisted in the hybrid fishes. This is the first report to show a stable pentaploid F1 hybrids produced by hybridization of a hexaploid and a tetraploid in aquaculture.

Dyeing wastewater has caused serious environmental problems nowadays. In this work, nickel–phosphorus plating–titanium dioxide (Ni-P-TiO2) electroless plating polyimide (PI) fabric was fabricated as an excellent visible light response composite. First, polyaniline (PANI) was in situ polymerized on the surface of the PI fabric. Second, PANI reduced palladium ions to be active seeds for initiating electroless plating of Ni-P-TiO2 layer. Finally, the Ni-P-TiO2/PANI/PI fabric with all-in-one structure was prepared, which can effectively overcome the drawbacks of poor loading fastness and insensitivity to visible light response. It was characterized by scanning electron microscopy, energy-dispersive spectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy, thermogravimetric analysis, and ultraviolet–visible diffuse reflectance spectroscopy. The photocatalytic activity was evaluated by degrading reactive blue 19, methylene blue, and reactive red (M-3BE) under visible light irradiation. The results show that the degradation rates of the all three dyes were over 91% with robust cycle stability for repeated 5 cycles of use. The possible photocatalytic degradation mechanism of fabrics was also proposed based on free radical and hole removal experiments.

Orthocoelium streptocoelium is a common paramphistome species parasitizing the rumen and/or reticulum of small ruminants, leading to significant losses. This study first determined the complete mitochondrial (mt) genome of O. streptocoelium. The complete mt genome of O. streptocoelium was amplified, sequenced, assembled, analysed and then compared with those of other digeneans. The entire mt genome of O. streptocoelium is 13,800 bp in length, which is smaller than those of other digeneans except for Opisthorchis viverrini. This mt genome contains 12 protein-coding genes, 22 transfer RNA genes, two ribosomal RNA genes and two non-coding regions. The arrangement of the O. streptocoelium mt genome is the same as those of other digeneans except for Schistosoma haematobium and Schistosoma spindale. Phylogenetic analyses based on concatenated amino acid sequences of the 12 protein-coding genes representing 16 digeneans were conducted to assess the relationship of O. streptocoelium with other digeneans. The result indicated that O. streptocoelium is closely related to Paramphistomum cervi and Fischoederius elongates, which is in accordance with their relationships by taxonomy. This complete mt genome of O. streptocoelium enriched the mitochondrial genome data of paramphistomes and provided important molecular markers for diagnostics and studies of population variation, epidemiology, ecology and evolution of O. streptocoelium and other digeneans.

Martensitic transformation and magnetic entropy change in Co substituted Ni50Mn35−xCoxSn15 (x = 0, 1.0, 1.5, 2.0, and 3.0) Heusler alloys have been investigated by X-ray powder diffraction analysis, differential scanning calorimetry, and magnetic measurements. X-ray diffraction analysis reveals that the Ni50Mn35−xCoxSn15 alloys have L21 Heusler structure at room temperature. The phase decomposition of the sample with x = 3.0, after annealing 48 h at 1173 K, is confirmed by both X-ray powder diffraction analysis and energy-dispersive x-ray spectroscopy in scanning electron microscopy. With the increase of the Co content from 0 to 2.0, the martensitic transformation temperature TM increases from 185 to 245 K, which is in good agreement with the rule of valence electron concentration e/a-dependence of TM. The magnetic entropy change ∆SM is investigated in the vicinity of the martensitic transformation.

Due to α radioactive decay Pu is vulnerable to aging. The behavior of He in Pu is the foundation for understanding Pu self-radiation damage aging. Molecular dynamics technique is performed to investigate the behavior of defects, the interaction between He and defects, the processes of initial nucleation and growth of He bubble and the dependence of He bubble on the macroscopical properties of Pu. Modified embedded atom method, Morse pair potential and the Lennard-Jones pair potential are used for describing the interactions of Pu-Pu, Pu-He and He-He, respectively. The main calculated results show that He atoms can combine with vacancies to form Hevacancy cluster (i.e., the precursor of He bubble) during the process of self-radiation as a result of high binding energy of an interstitial He atom to vacancy; He bubble’s growth can be dominated by the mechanism of punching out of dislocation loop; the swelling induced by He bubble is very small; grain boundaries give rise to an energetically more favorable zone for the interstitial He atom and self-interstitial atom accumulation than for vacancy accumulation; the process of He release can be identified as the formation of release channel induced by the cracking of He bubble and surface structure.

The distribution of alloying elements and the corresponding structural evolution of Mn–Sb alloys in magnetic field gradients were investigated in detail. It was found that a high magnetic field gradient could control the distribution of solute element in the alloys during the solidification process and therefore resulted in the coexistence of both primary MnSb and Sb phases or the aggregation of the primary MnSb with a continuous change in morphology. The positions where these primary phases located depended on the direction of field gradient. The control of the solute element distribution by a high magnetic field gradient was realized through the magnetic buoyancy force that could drive the migration of Mn element in the melt, originating from the difference in the magnetic susceptibility between Mn and Sb. The effectiveness of this control depends on the alloy composition, specimen dimension, cooling rate, and |BdB/dz| value.

Mn-90.8 wt%Sb alloys were solidified without and with high magnetic fields to investigate the effects of high magnetic fields on the structure evolution of the alloys. It was found that there were only MnSb/Sb eutectics without any primary phase in the alloy at 0 T, whereas a small amount of primary MnSb dendrites appeared in the MnSb/Sb eutectic matrix when the magnetic flux density was 4.4 T. In magnetic fields of 6.6, 8.8, and 11.5 T, both of two primary phases, i.e., MnSb and Sb, occurred in the matrix. In addition, the volume fraction of these two primary phases increased with increasing magnetic flux density. In magnetic fields of 8.8 and 11.5 T, primary MnSb dendrites aligned parallel to the magnetic field direction and gathered at the edge of the specimens. In contrast, primary Sb dendrites gathered in the center region of the specimens.