Ultrahigh-brightness 50 MeV electron beam generation from laser wakefield acceleration in a weakly nonlinear regime

We propose an efficient scheme to produce ultrahigh-brightness tens of MeV electron beams by designing a density-tailored plasma to induce a wakefield in the weakly nonlinear regime with a moderate laser energy of 120 mJ.In this scheme,the second bucket of the wakefield can have a much lower phase velocity at the steep plasma density down-ramp than the first bucket and can be exploited to implement longitudinal electron injection at a lower laser intensity,leading to the generation of bright electron beams with ultralow emittance together with low energy spread.Three-dimensional particle-in-cell simulations are carried out and demonstrate that high-quality electron beams with a peak energy of 50 MeV,ultralow emittance of28 nm rad,energy spread of 1%,charge of 4.4 pC,and short duration less than 5 fs can be obtained within a 1-mm-long tailored plasma density,resulting in an ultrahigh six-dimensional brightness B6D,n of2×1017 A/m2/0.1%.By changing the density parameters,tunable bright electron beams with peak energies ranging from 5 to 70 MeV,a small emittance of B0.1 mm mrad,and a low energy spread at a few-percent level can be obtained.These bright MeV-class electron beams have a variety of potential applications,for example,as ultrafast electron probes for diffraction and imaging,in laboratory astrophysics,in coherent radiation source generation,and as injectors for GeV particle accelerators.

Local saliency consistency-based label inference for weakly supervised salient object detection using scribble annotations

Recently,weak supervision has received growing attention in the field of salient object detection due to the convenience of labelling.However,there is a large performance gap between weakly supervised and fully supervised salient object detectors because the scribble annotation can only provide very limited foreground/background information.Therefore,an intuitive idea is to infer annotations that cover more complete object and background regions for training.To this end,a label inference strategy is proposed based on the assumption that pixels with similar colours and close positions should have consistent labels.Specifically,k-means clustering algorithm was first performed on both colours and coordinates of original annotations,and then assigned the same labels to points having similar colours with colour cluster centres and near coordinate cluster centres.Next,the same annotations for pixels with similar colours within each kernel neighbourhood was set further.Extensive experiments on six benchmarks demonstrate that our method can significantly improve the performance and achieve the state-of-the-art results.

Negative Stiffness Mechanism on An Asymmetric Wave Energy Converter by Using A Weakly Nonlinear Potential Model

Salter's duck,an asymmetrical wave energy converter(WEC)device,showed high efficiency in extracting energy from 2D regular waves in the past;yet,challenges remain for fluctuating wave conditions.These can potentially be addressed by adopting a negative stiffness mechanism(NSM)in WEC devices to enhance system efficiency,even in highly nonlinear and steep 3D waves.A weakly nonlinear model was developed which incorporated a nonlinear restoring moment and NSM into the linear formulations and was applied to an asymmetric WEC using a time domain potential flow model.The model was initially validated by comparing it with published experimental and numerical computational fluid dynamics results.The current results were in good agreement with the published results.It was found that the energy extraction increased in the range of 6%to 17%during the evaluation of the effectiveness of the NSM in regular waves.Under irregular wave conditions,specifically at the design wave conditions for the selected test site,the energy extraction increased by 2.4%,with annual energy production increments of approximately 0.8MWh.The findings highlight the potential of NSM in enhancing the performance of asymmetric WEC devices,indicating more efficient energy extraction under various wave conditions.

Weakly Supervised Network with Scribble-Supervised and Edge-Mask for Road Extraction from High-Resolution Remote Sensing Images

Significant advancements have been achieved in road surface extraction based on high-resolution remote sensingimage processing. Most current methods rely on fully supervised learning, which necessitates enormous humaneffort to label the image. Within this field, other research endeavors utilize weakly supervised methods. Theseapproaches aim to reduce the expenses associated with annotation by leveraging sparsely annotated data, such asscribbles. This paper presents a novel technique called a weakly supervised network using scribble-supervised andedge-mask (WSSE-net). This network is a three-branch network architecture, whereby each branch is equippedwith a distinct decoder module dedicated to road extraction tasks. One of the branches is dedicated to generatingedge masks using edge detection algorithms and optimizing road edge details. The other two branches supervise themodel’s training by employing scribble labels and spreading scribble information throughout the image. To addressthe historical flaw that created pseudo-labels that are not updated with network training, we use mixup to blendprediction results dynamically and continually update new pseudo-labels to steer network training. Our solutiondemonstrates efficient operation by simultaneously considering both edge-mask aid and dynamic pseudo-labelsupport. The studies are conducted on three separate road datasets, which consist primarily of high-resolutionremote-sensing satellite photos and drone images. The experimental findings suggest that our methodologyperforms better than advanced scribble-supervised approaches and specific traditional fully supervised methods.

Macro-micro behaviors and failure mechanism of frozen weakly cemented mudstone

Understanding the mechanical properties and multiscale failure mechanism of frozen soft rock is an important prerequisite for the construction safety of tunnels,artificially frozen ground and other infrastructure in cold regions.In this study,the triaxial compression test are performed on mudstone in the weakly cemented soft rock strata in the mining area of western China,and the mechanical characteristics and failure mechanism of weakly cemented mudstone are systematically investigated under the combined action of freezing and loading.Furthermore,the quantitative relationship between the microstructural parameters and the macroscopic strength and deformation parameters is established based on fractal theory.Thus,the failure mechanism of frozen weakly cemented mudstone is revealed on both micro- and macro-scales.The results show that temperature and confining pressure significantly affects the elastic modulus and peak strength of weakly cemented mudstone.With decreasing temperature,the compressive strength increases,while the corresponding peak strain decreases gradually.On the deformation curve,the plastic deformation stage is shortened,and the brittle fracture feature at the post-peak stage is more prominent,and the elastic modulus correspondingly increases with decreasing temperature.Under low-temperature conditions,most of the weakly cemented mudstone undergoes microscopic shear failure along the main fracture surface.The micro-fracture morphology characteristics of weakly cemented mudstone under different temperatures are quantified via the fractal dimension,and an approximately exponential relationship can be obtained among the fractal dimension and the temperature,compressive strength and elastic modulus.

Influence of confined water on the limit support pressure of tunnel face in weakly water-rich strata

In the process of shield tunneling through soft soil layers,the presence of confined water ahead poses a significant threat to the stability of the tunnel face.Therefore,it is crucial to consider the impact of confined water on the limit support pressure of the tunnel face.This study employed the finite element method(FEM)to analyze the limit support pressure of shield tunnel face instability within a pressurized water-containing layer.Subsequently,a multiple linear regression approach was applied to derive a concise solution formula for the limit support pressure,incorporating various influencing factors.The analysis yields the following conclusions:1)The influence of confined water on the instability mode of the tunnel face in soft soil layers makes the displacement response of the strata not significant when the face is unstable;2)The limit support pressure increases approximately linearly with the pressure head,shield tunnel diameter,and tunnel burial depth.And inversely proportional to the thickness of the impermeable layer,soil cohesion and internal friction angle;3)Through an engineering case study analysis,the results align well with those obtained from traditional theoretical methods,thereby validating the rationality of the equations proposed in this paper.Furthermore,the proposed equations overcome the limitation of traditional theoretical approaches considering the influence of changes in impermeable layer thickness.It can accurately depict the dynamic variation in the required limit support pressure to maintain the stability of the tunnel face during shield tunneling,thus better reflecting engineering reality.

血清sTWEAK、Netrin-1联合APACHEⅡ评分对重型颅脑损伤患者术后预后不良的预测价值

目的探讨血清可溶性肿瘤坏死因子样凋亡弱诱导因子(sTWEAK)、神经轴突导向因子-1(Netrin-1)联合急性生理学与慢性健康状况评分系统Ⅱ(APACHEⅡ)评分对重型颅脑损伤患者术后预后不良的预测价值。方法选取2020年6月至2022年6月该院收治的120例重型颅脑损伤患者,根据术后30 d预后情况分为预后良好组和预后不良组。对比两组血清sTWEAK、Netrin-1水平及APACHEⅡ评分。采用单因素和多因素Logistic回归分析重型颅脑损伤患者术后预后不良的影响因素,并据以构建血清sTWEAK、Netrin-1及APACHEⅡ评分联合应用的预测模型,受试者工作特征(ROC)曲线分析血清sTWEAK、Netrin-1水平及APACHEⅡ评分对重型颅脑损伤患者术后预后不良的预测价值。结果预后不良组的重症监护室居住时间长于预后良好组,白蛋白水平、入院时格拉斯哥昏迷评分法评分和血清Netrin-1水平低于预后良好组,多发脑挫裂伤占比、机械通气占比、入院时APACHEⅡ评分和血清sTWEAK、血清肌酐、血尿素氮水平均高于预后良好组,差异有统计学意义(P<0.05)。多因素Logistic回归分析结果显示,多发脑挫裂伤、Netrin-1水平降低、入院时APACHEⅡ评分升高、sTWEAK水平升高为重型颅脑损伤患者术后预后不良的危险因素(P<0.05)。ROC曲线分析结果显示,血清sTWEAK、Netrin-1及APACHEⅡ评分3个指标单独及联合应用时曲线下面积及其95%CI分别为0.742(0.552~0.925)、0.731(0.488~0.963)、0.714(0.502~0.911)、0.882(0.795~0.947)。结论血清sTWEAK、Netrin-1联合APACHEⅡ评分对重型颅脑损伤患者术后预后不良具有较好的预测价值,可为临床治疗方案的制订提供参考。

自发性急性脑出血患者血浆sCD163/sTWEAK比值与预后的关系

目的探究自发性急性脑出血(ACH)患者血浆可溶性CD163(sCD163)/可溶性肿瘤坏死因子样凋亡弱诱导因子(sTWEAK)比值与预后的关系。方法纳入ACH患者90例作为病例组,根据格拉斯哥预后评分将病例组分为预后不良组(38例)和预后良好组(52例);另选取同期体检健康者45例为对照组。酶联免疫吸附试验检测血浆sCD163、sTWEAK水平并计算sCD163/sTWEAK比值。分析血浆sCD163、sTWEAK水平及sCD163/sTWEAK比值与临床资料的相关性;Logistic回归分析ACH患者预后不良的影响因素;受试者工作特征(ROC)曲线分析sCD163/sTWEAK比值对ACH患者预后不良的预测价值。结果病例组血浆sCD163、sTWEAK水平及sCD163/sTWEAK比值均显著高于对照组;预后良好组上述指标均低于预后不良组(P<0.05)。预后良好组血肿体积、美国国立卫生研究院卒中量表(NIHSS)评分、高血压及幕下出血比例均低于预后不良组,低密度脂蛋白胆固醇(LDL-C)高于预后不良组(P<0.05)。相关性分析表明,血浆sCD163、sTWEAK水平及sCD163/sTWEAK比值与出血部位、血肿体积、NIHSS评分、白细胞计数、血小板计数、中性粒细胞/淋巴细胞比值(NLR)呈正相关(P<0.05)。Logistic回归分析显示,sCD163/sTWEAK比值、出血部位、血肿体积、NIHSS评分为ACH患者预后不良的影响因素(P<0.05)。ROC曲线结果表明,sCD163/sTWEAK比值评估ACH患者预后不良的AUC为0.850,敏感度和特异度分别为86.84%和69.23%。结论sCD163/sTWEAK比值在ACH患者血浆中水平较高,并与预后不良有关,该值对此类患者的预后有一定预测价值。

注意缺陷多动障碍患儿血清ACE2,TWEAK和CCL5水平检测及诊断价值研究

目的 探究血清血管紧张素转换酶2(angiotensin-converting enzyme 2,ACE2),细胞因子肿瘤坏死因子样细胞凋亡弱诱导因子(tumor necrosis factor-like weak inducer of apoptosis,TWEAK)和CC趋化因子配体5(CC motif chemokine ligand 5,CCL5)水平在注意缺陷多动障碍(attention deficit hyperactivity disorder,ADHD)患儿诊断、病情严重程度评估中的价值。方法 选取2022年10月~2023年10月在河北省儿童医院就诊的125例ADHD患儿记为ADHD组,另选105例在河北省妇幼保健中心体检的健康儿童为对照组,根据临床总体印象严重程度量表(CGI-S)将患儿分为轻中度组(n=83)和重度组(n=42)。ELISA方法检测血清ACE2,TWEAK,CCL5,促黄体生成素(LH)和催乳素(PRL)水平,联合型瑞文测验(CRT)和Conners父母症状问卷(PSQ)对患儿认知和行为状况进行评分。Spearman相关性分析重度组血清ACE2,TWEAK,CCL5与CGI-S,CRT,PSQ评分的相关性;受试者工作特征(ROC)曲线分析ACE2,TWEAK,CCL5对ADHD及严重程度的诊断价值。结果 ADHD患儿血清ACE2(284.35±92.34 pg/ml),TWEAK(2.56±0.76 pg/ml)水平低于对照组(379.23±106.28 pg/ml,3.52±1.12 pg/ml),CCL5水平(7.36±2.37ng/ml)高于对照组(5.24±1.63 ng/ml),差异具有统计学意义(t=7.244,7.703,7.753,均P<0.05);重度组患儿CRT,血清ACE2,TWEAK水平低于轻中度组(t=5.318,6.686,6.490),而PSQ,CCL5水平较高于轻中度组(t=5.220,6.134),差异具有统计学意义(均P<0.05);Spearman相关性分析结果显示,重度组患儿血清ACE2,TWEAK水平与CGI-S,PSQ评分负相关(r=-0.432,-0.453;-0.421,-0.426,均P<0.001),与CRT评分呈正相关(r=0.427,0.418,均P<0.001);CCL5与CGI-S,PSQ评分呈正相关(r=0.421,0.433,均P<0.001),与CRT评分呈负相关(r=-0.446,P<0.001)。血清ACE2,TWEAK和CCL5诊断ADHD发生的AUC分别为0.814,0.803和0.807,三者联合诊断的AUC为0.945,优于各自单独诊断(Z=5.439,4.258,5.576,均P<0.001);血清ACE2,TWEAK,CCL5诊断重度ADHD的AUC分别为0.853,0.796和0.805,三者联合诊断的AUC为0.930,优于各自单独诊断(Z=2.604,3.851,3.567,均P<0.001)。结论 血清ACE2,TWEAK在ADHD患儿血清中低表达,而CCL5高表达,三者表达水平具有相关性,并且诊断ADHD发生和严重程度具有较高的价值。

Significant risk factors for intensive care unit-acquired weakness:A processing strategy based on repeated machine learning

BACKGROUND Intensive care unit-acquired weakness(ICU-AW)is a common complication that significantly impacts the patient's recovery process,even leading to adverse outcomes.Currently,there is a lack of effective preventive measures.AIM To identify significant risk factors for ICU-AW through iterative machine learning techniques and offer recommendations for its prevention and treatment.METHODS Patients were categorized into ICU-AW and non-ICU-AW groups on the 14th day post-ICU admission.Relevant data from the initial 14 d of ICU stay,such as age,comorbidities,sedative dosage,vasopressor dosage,duration of mechanical ventilation,length of ICU stay,and rehabilitation therapy,were gathered.The relationships between these variables and ICU-AW were examined.Utilizing iterative machine learning techniques,a multilayer perceptron neural network model was developed,and its predictive performance for ICU-AW was assessed using the receiver operating characteristic curve.RESULTS Within the ICU-AW group,age,duration of mechanical ventilation,lorazepam dosage,adrenaline dosage,and length of ICU stay were significantly higher than in the non-ICU-AW group.Additionally,sepsis,multiple organ dysfunction syndrome,hypoalbuminemia,acute heart failure,respiratory failure,acute kidney injury,anemia,stress-related gastrointestinal bleeding,shock,hypertension,coronary artery disease,malignant tumors,and rehabilitation therapy ratios were significantly higher in the ICU-AW group,demonstrating statistical significance.The most influential factors contributing to ICU-AW were identified as the length of ICU stay(100.0%)and the duration of mechanical ventilation(54.9%).The neural network model predicted ICU-AW with an area under the curve of 0.941,sensitivity of 92.2%,and specificity of 82.7%.CONCLUSION The main factors influencing ICU-AW are the length of ICU stay and the duration of mechanical ventilation.A primary preventive strategy,when feasible,involves minimizing both ICU stay and mechanical ventilation duration.

Inverse Faraday effect of weakly relativistic full Poincaré beams in plasma

The inverse Faraday effect(IFE),which usually refers to the phenomenon in which a quasi-static axial magnetic field is self-generated when a circularly polarized beam propagates in a plasma,has rarely been studied for lasers with unconventional polarization states.In this paper,IFE is reconsidered for weakly relativistic full Poincarébeams,which can contain all possible laser polarization states.Starting from cold electron fluid equations and the conservation of generalized vorticity,a self-consistent theoretical model combining the nonlinear azimuthal current and diamagnetic current is presented.The theoretical results show that when such a laser propagates in a plasma,an azimuthally varying quasi-static axial magnetic field can be generated,which is quite different from the circularly polarized case.These results are qualitatively and quantitatively verified by three-dimensional particle-in-cell simulations.Our work extends the theoretical understanding of the IFE and provides a new degree of freedom in the design of magnetized plasma devices.

A robust & weak-nucleophilicity electrocatalyst with an inert response for chlorine ion oxidation in large-current seawater electrolysis

Seawater splitting into hydrogen,a promising technology,is seriously limited by the durability and tolerance of electrocatalysts for chlorine ions in seawater at large current densities due to chloride oxidation and corrosion.Here,we present a robust and weak-nucleophilicity nickel-iron hydroxide electrocatalyst with excellent selectivity for oxygen evolution and an inert response for chlorine ion oxidation which are key and highly desired for efficient seawater electrolysis.Such a weak-nucleophilicity electrocatalyst can well match with strong-nucleophilicity OH-compared with the weak-nucleophilicity Cl^(-),resultantly,the oxidation of OH-in electrolyte can be more easily achieved relative to chlorine ion oxidation,confirmed by ethylenediaminetetraacetic acid disodium probing test.Further,no strongly corrosive hypochlorite is produced when the operating voltage reaches about 2.1 V vs.RHE,a potential that is far beyond the thermodynamic potential of chlorine ion oxidatio n.This concept and approach to reasonably designing weaknucleophilicity electrocatalysts that can greatly avoid chlorine ion oxidation under alkaline seawater environments can push forward the seawater electrolysis technology and also accelerate the development of green hydrogen technique.

Tuning desolvation kinetics of in-situ weakly solvating polyacetal electrolytes for dendrite-free lithium metal batteries

The host structure of polymers significantly influences ion transport and interfacial stability of electrolytes,dictating battery cycle life and safety for solid-state lithium metal batteries.Despite promising properties of ethylene oxide-based electrolytes,their typical clamp-like coordination geometry leads to crowd solvation sheath and overly strong interactions between Li^(+)and electrolytes,rendering difficult dissociation of Li+and unfavorable solid electrolyte interface(SEI).Herein,we explore weakly solvating characteristics of polyacetal electrolytes owing to their alternately changing intervals between–O–coordinating sites in the main chain.Such structural asymmetry leads to unique distorted helical solvation sheath,and can effectively reduce Li^(+)-electrolyte binding and tune Li^(+)desolvation kinetics in the insitu formed polymer electrolytes,yielding anion-derived SEI and dendrite-free Li electrodeposition.Combining with photoinitiated cationic ring-opening polymerization,polyacetal electrolytes can be instantly formed within 5 min at the surface of electrode,with high segmental chain motion and well adapted interfaces.Such in-situ polyacetal electrolytes enabled more than 1300-h of stable lithium electrodeposition and prolonged cyclability over 200 cycles in solid-state batteries at ambient temperatures,demonstrating the vital role of molecular structure in changing solvating behavior and Li deposition stability for high-performance electrolytes.

Deep Learning Models Based on Weakly Supervised Learning and Clustering Visualization for Disease Diagnosis

The coronavirus disease 2019(COVID-19)has severely disrupted both human life and the health care system.Timely diagnosis and treatment have become increasingly important;however,the distribution and size of lesions vary widely among individuals,making it challenging to accurately diagnose the disease.This study proposed a deep-learning disease diagnosismodel based onweakly supervised learning and clustering visualization(W_CVNet)that fused classification with segmentation.First,the data were preprocessed.An optimizable weakly supervised segmentation preprocessing method(O-WSSPM)was used to remove redundant data and solve the category imbalance problem.Second,a deep-learning fusion method was used for feature extraction and classification recognition.A dual asymmetric complementary bilinear feature extraction method(D-CBM)was used to fully extract complementary features,which solved the problem of insufficient feature extraction by a single deep learning network.Third,an unsupervised learning method based on Fuzzy C-Means(FCM)clustering was used to segment and visualize COVID-19 lesions enabling physicians to accurately assess lesion distribution and disease severity.In this study,5-fold cross-validation methods were used,and the results showed that the network had an average classification accuracy of 85.8%,outperforming six recent advanced classification models.W_CVNet can effectively help physicians with automated aid in diagnosis to determine if the disease is present and,in the case of COVID-19 patients,to further predict the area of the lesion.

Weakly Supervised Abstractive Summarization with Enhancing Factual Consistency for Chinese Complaint Reports

A large variety of complaint reports reflect subjective information expressed by citizens.A key challenge of text summarization for complaint reports is to ensure the factual consistency of generated summary.Therefore,in this paper,a simple and weakly supervised framework considering factual consistency is proposed to generate a summary of city-based complaint reports without pre-labeled sentences/words.Furthermore,it considers the importance of entity in complaint reports to ensure factual consistency of summary.Experimental results on the customer review datasets(Yelp and Amazon)and complaint report dataset(complaint reports of Shenyang in China)show that the proposed framework outperforms state-of-the-art approaches in ROUGE scores and human evaluation.It unveils the effectiveness of our approach to helping in dealing with complaint reports.

Anion-Regulated Weakly Solvating Electrolytes for High-Voltage Lithium Metal Batteries

Development of advanced high-voltage electrolytes is key to achieving high-energy-density lithium metal batteries(LMBs).Weakly solvating electrolytes(WSE)can produce unique anion-driven interphasial chemistry via altering the solvating power of the solvent,but it is difficult to dissolve the majority of Li salts and fail to cycle at a cut-off voltage above 4.5 V.Herein,we present a new-type WSE that is regulated by the anion rather than the solvent,and the first realize stable cycling of dimethoxyethane(DME)at 4.6 V without the use of the“solvent-in-salt”strategy.The relationships between the degree of dissociation of salts,the solvation structure of electrolytes,and the electrochemical performance of LMBs were systematically investigated.We found that LiBF_(4),which has the lowest degree of dissociation,can construct an anion-rich inner solvation shell,resulting in anion-derived anode/cathode interphases.Thanks to such unusual solvation structure and interphasial chemistry,the Li-LiCoO_(2)full cell with LiBF_(4)-based WSE could deliver excellent rate performance(115 mAh g^(-1)at 10 C)and outstanding cycling stability even under practical conditions,including high loading(10.7 mg cm^(-2)),thin Li(50μm),and limited electrolyte(1.2μL mg^(-1)).

An Experimental Study on the Reinforcement of Weakly-Consolidated Shallow Formation in Deep Water Using an Epoxy Resin-Based Fluid

The mechanical properties of Portland cement differ from the weakly consolidated shallow formation in deep water.This results in undesired abrupt changes in the compressive strength and elastic modulus at the cement–formation interface.In this study,a water-borne epoxy resin was applied as a strengthening material to reinforce the weakly consolidated shallow formation and protect the cement sheath from potential failure.The mechanical properties of the unconsolidated clay were tested,including their changes with increases in the temperature and curing time.In addition,the effects of the seawater,cement slurry alkaline filtrate,and saltwater drilling fluid were evaluated.As confirmed by the results,the strengthening fluid was excellent at reinforcing the unconsolidated clay,with a compressive strength of 2.49 MPa(after curing for 7 days),even at a dosage of 5%.A cement slurry filtrate with a high pH was suitable to produce the required strengthening of the formation,especially its early age strength.It should also be pointed out that the used fluid exhibited good compatibility with the saltwater drilling fluid and seawater behaved well as a diluent for the strengthening fluid.

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

Measuring small longitudinal phase shifts via weak measurement amplification

Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.