Normalized Solutions to Nonautonomous Kirchhoff Equation

In this paper, we study the existence of normalized solutions to the following Kirchhoff equation with a perturbation: $$\left\{ \begin{aligned} &-\left(a+b\int _{\mathbb{R}^{N}}\left | \nabla u \right|^{2} dx\right)\Delta u+\lambda u=|u|^{p-2} u+h(x)\left |u\right |^{q-2}u, \quad \text{ in } \mathbb{R}^{N}, \\ &\int_{\mathbb{R}^{N}}\left|u\right|^{2}dx=c, \quad u \in H^{1}(\mathbb{R}^{N}), \end{aligned} \right.$$ where $1\le N\le 3, a,b,c>0, 1\leq q<2$, $\lambda \in \mathbb{R}$. We treat three cases. (i)When $2<p<2+\frac{4}{N},h(x)\ge0$, we obtain the existence of global constraint minimizers. (ii)When $2+\frac{8}{N}<p<2^{*},h(x)\ge0$, we prove the existence of mountain pass solution. (iii)When $2+\frac{8}{N}<p<2^{*},h(x)\leq0$, we establish the existence of bound state solutions.Comment: arXiv admin note: text overlap with arXiv:2301.07926 by other author

Existence of solutions for a Dirichlet problem with a p-Laplacian

AbstractSome theorems of existence of weak solutions are obtained for p-Laplacian equations with Dirichlet boundary conditions by using a critical point theorem

Normalized bound state solutions of fractional Schr\"{o}dinger equations with general potential

In this paper, we study a class of fractional Schr\"{o}dinger equation \begin{equation} \label{eq0} \left\{ \begin{aligned} &(-\Delta)^{s}u=\lambda u+a(x)|u|^{p-2}u,\\ &\int_{\mathbb{R}^{N}}|u|^{2}dx=c^{2},\ u\in H^{s}(\mathbb{R}^{N}), \end{aligned} \right. \end{equation} where $N>2s$, $s\in(0,1)$ and $p\in(2,2+4s/N), c>0$. $a(x)\in C(\mathbb{R}^{N},\mathbb{R})$ is a positive potential function. By using Fixed Point Theorem of Brouwer, barycenter function and variational method, we obtain the existence of normalized bound solutions for the problem

The CTNNBIP1-CLSTN1 fusion transcript regulates human neocortical development

Fusion transcripts or RNAs have been found in both disordered and healthy human tissues and cells; however, their physiological functions in the brain development remain unknown. In the analysis of deposited RNA-sequence libraries covering early to middle embryonic stages, we identify 1,055 fusion transcripts present in the developing neocortex. Interestingly, 98 fusion transcripts exhibit distinct expression patterns in various neural progenitors (NPs) or neurons. We focus on CTNNBIP1-CLSTN1 (CTCL), which is enriched in outer radial glial cells that contribute to cortex expansion during human evolution. Intriguingly, downregulation of CTCL in cultured human cerebral organoids causes marked reduction in NPs and precocious neuronal differentiation, leading to impairment of organoid growth. Furthermore, the expression of CTCL fine-tunes Wnt/β-catenin signaling that controls cortex patterning. Together, this work provides evidence indicating important roles of fusion transcript in human brain development and evolution

Serum Early Prostate Cancer Antigen (EPCA) Level and Its Association with Disease Progression in Prostate Cancer in a Chinese Population

BACKGROUND: Early prostate cancer antigen (EPCA) has been shown a prostate cancer (PCa)-associated nuclear matrix protein, however, its serum status and prognostic power in PCa are unknown. The goals of this study are to measure serum EPCA levels in a cohort of patients with PCa prior to the treatment, and to evaluate the clinical value of serum EPCA. METHODS: Pretreatment serum EPCA levels were determined with an ELISA in 77 patients with clinically localized PCa who underwent radical prostatectomy and 51 patients with locally advanced or metastatic disease who received primary androgen deprivation therapy, and were correlated with clinicopathological variables and disease progression. Serum EPCA levels were also examined in 40 healthy controls. RESULTS: Pretreatment mean serum EPCA levels were significantly higher in PCa patients than in controls (16.84 ± 7.60 ng/ml vs. 4.12 ± 2.05 ng/ml, P<0.001). Patients with locally advanced and metastatic PCa had significantly higher serum EPCA level than those with clinically localized PCa (22.93 ± 5.28 ng/ml and 29.41 ± 8.47 ng/ml vs. 15.17 ± 6.03 ng/ml, P = 0.014 and P<0.001, respectively). Significantly elevated EPCA level was also found in metastatic PCa compared with locally advanced disease (P < 0.001). Increased serum EPCA levels were significantly and positively correlated with Gleason score and clinical stage, but not with PSA levels and age. On multivariate analysis, pretreatment serum EPCA level held the most significantly predictive value for the biochemical recurrence and androgen-independent progression among pretreatment variables (HR = 4.860, P<0.001 and HR = 5.418, P<0.001, respectively). CONCLUSIONS: Serum EPCA level is markedly elevated in PCa. Pretreatment serum EPCA level correlates significantly with the poor prognosis, showing prediction potential for PCa progression

Dynamical alterations of brain function and gut microbiome in weight loss

ObjectiveIntermittent energy restriction (IER) is an effective weight loss strategy. However, little is known about the dynamic effects of IER on the brain-gut-microbiome axis.MethodsIn this study, a total of 25 obese individuals successfully lost weight after a 2-month IER intervention. FMRI was used to determine the activity of brain regions. Metagenomic sequencing was performed to identify differentially abundant gut microbes and pathways in from fecal samples.ResultsOur results showed that IER longitudinally reduced the activity of obese-related brain regions at different timepoints, including the inferior frontal orbital gyrus in the cognitive control circuit, the putamen in the emotion and learning circuit, and the anterior cingulate cortex in the sensory circuit. IER longitudinally reduced E. coli abundance across multiple timepoints while elevating the abundance of obesity-related Faecalibacterium prausnitzii, Parabacteroides distasonis, and Bacterokles uniformis. Correlation analysis revealed longitudinally correlations between gut bacteria abundance alterations and brain activity changes.ConclusionsThere was dynamical alteration of BGM axis (the communication of E. coli with specific brain regions) during the weight loss under the IER

Observation of the electromagnetic doubly OZI-suppressed decay J/ψ→ϕπ0J/\psi \rightarrow \phi \pi^{0}

Using a sample of $1.31$ billion $J/\psi$ events accumulated with the BESIII detector at the BEPCII collider, we report the observation of the decay $J/\psi \rightarrow \phi\pi^{0}$, which is the first evidence for a doubly Okubo-Zweig-Iizuka suppressed electromagnetic $J/\psi$ decay. A clear structure is observed in the $K^{+} K^{-}$ mass spectrum around 1.02 GeV/$c^2$, which can be attributed to interference between $J/\psi \rightarrow \phi\pi^{0}$ and $J/\psi \rightarrow K^{+}K^{-}\pi^{0}$ decays. Due to this interference, two possible solutions are found. The corresponding measured values of the branching fraction of $J/\psi \to \phi\pi^{0}$ are $[2.94 \pm 0.16\text{(stat.)} \pm 0.16\text{(syst.)}] \times 10^{-6}$ and $[1.24 \pm 0.33\text{(stat.)} \pm 0.30\text{(syst.)}] \times 10^{-7}$.Comment: 7 pages, 4 figures, published in Phys. Rev.

Challenges and recent advancements of functionalization of two-dimensional nanostructured molybdenum trioxide and dichalcogenides

Atomically-thin two-dimensional (2D) semiconductors are the thinnest functional semiconducting materials available today. Among them, both molybdenum trioxide and chalcogenides (MT&Ds) represent key components within the family of the different 2D semiconductors for various electronic, optoelectronic and electrochemical applications due to their unique electronic, optical, mechanical and electrochemical properties. However, despite great progress in research dedicated to the development and fabrication of 2D MT&Ds observed within the last decade, there are significant challenges affected their charge transport behavior, fabrication on a large scale as well as high dependence of the carrier mobility on thickness. In this article, we review the recent progress on the carrier mobility engineering of 2D MT&Ds and elaborate devised strategies dedicated to the optimization of MT&Ds properties. Specifically, the latest physical and chemical methods towards the surface functionalization and optimization of the major factors influencing the extrinsic transport at the electrode-2D semiconductor interface are discusse

Emerging technologies for the production of renewable liquid transport fuels from biomass sources enriched in plant cell walls

Plant cell walls are composed predominantly of cellulose, a range of non-cellulosic polysaccharides and lignin. The walls account for a large proportion not only of crop residues such as wheat straw and sugarcane bagasse, but also of residues of the timber industry and specialist grasses and other plants being grown specifically for biofuel production. The polysaccharide components of plant cell walls have long been recognized as an extraordinarily large source of fermentable sugars that might be used for the production of bioethanol and other renewable liquid transport fuels. Estimates place annual plant cellulose production from captured light energy in the order of hundreds of billions of tons. Lignin is synthesized in the same order of magnitude and, as a very large polymer of phenylpropanoid residues, lignin is also an abundant, high energy macromolecule. However, one of the major functions of these cell wall constituents in plants is to provide the extreme tensile and compressive strengths that enable plants to resist the forces of gravity and a broad range of other mechanical forces. Over millions of years these wall constituents have evolved under natural selection to generate extremely tough and resilient biomaterials. The rapid degradation of these tough cell wall composites to fermentable sugars is therefore a difficult task and has significantly slowed the development of a viable lignocellulose-based biofuels industry. However, good progress has been made in overcoming this so-called recalcitrance of lignocellulosic feedstocks for the biofuels industry, through modifications to the lignocellulose itself, innovative pre-treatments of the biomass, improved enzymes and the development of superior yeasts and other microorganisms for the fermentation process. Nevertheless, it has been argued that bioethanol might not be the best or only biofuel that can be generated from lignocellulosic biomass sources and that hydrocarbons with intrinsically higher energy densities might be produced using emerging and continuous flow systems that are capable of converting a broad range of plant and other biomasses to bio-oils through so-called 'agnostic' technologies such as hydrothermal liquefaction. Continued attention to regulatory frameworks and ongoing government support will be required for the next phase of development of internationally viable biofuels industries.Hwei-Ting Tan, Kendall R. Corbin and Geoffrey B. Finche