INFINITE-DIMENSIONAL WIDTHS IN THE SPACES OF FUNCTION (Ⅰ)

Ⅰ. INTRODUCTION AND DEFINITIONLet r be a positive integer and p∈[1, +∞]. We consider the following Sobolev function classes over the real line R, Wpr（R）:={f∈Lp（R）: fr-1 is locally absolutely continuous on

An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation

Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical ＇σ/σx＇-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.

Invertibility of Infinite-Dimensional Hamiltonian Operators and Its Application to Plate Bending Equation

The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.

Spectral Description of a Class of Infinite-Dimensional Hamiltonian Operators and Its Application to Plane Elasticity Equations Without Body Force

In this paper,the results of spectral description and invertibility of upper triangle infinite-dimensionalHamiltonian operators with a diagonal domain are given.By the above results,it is proved that the infinite-dimensionalHamiltonian operator associated with plane elasticity equations without the body force is invertible,and the spectrumof which is non-empty and is a subset of R.

Method to measure tree-ring width,density,elemental composition,and stable carbon and oxygen isotopes using one sample

Tree-ring width(RW),density,elemental com-position,and stable carbon and oxygen isotope(δ^(13)C,δ^(18)O)are widely used as proxies to assess climate change,ecology,and environmental pollution;however,a specific pretreat-ment has been needed for each proxy.Here,we developed a method by which each proxy can be measured in the same sample.First,the sample is polished for ring width meas-urement.After obtaining the ring width data,the sample is cut to form a 1-mm-thick wood plate.The sample is then mounted in a vertical sample holder,and gradually scanned by an X-ray beam.Simultaneously,the count rates of the fluorescent photons of elements(for chemical characteriza-tion)and a radiographic grayscale image(for wood density)are obtained,i.e.the density and the element content are obtained.Then,cellulose is isolated from the 1-mm wood plate by removal of lignin,and hemicellulose.After producing this cellulose plate,cellulose subsamples are separated by knife under the microscope for inter-annual and intra-annual stable carbon and oxygen isotope(δ^(13)C,δ^(18)O)analysis.Based on this method,RW,density,elemental composition,δ^(13)C,and δ^(18)O can be measured from the same sample,which reduces sample amount and treatment time,and is helpful for multi-proxy comparison and combination research.

Realization of the Infinite-Dimensional 3-Algebras in the Calogero-Moser Model

We investigate realization of the infinite-dimensional 3-algebras in the classical Calogero-Moser model. In terms of the Lax matrix of the Calogero Moser model and the Nambu 3-brackets in which the variables are the coordinates qi, and canonically conjugate momenta pi and the coupling parameter β are an extra auxiliary phase-space parameter, we present the realization of the Virasoro-Witt, w∞ and SDi f f （T2） 3-algebras, respectively.

Relationship between Inter Canine Width and Inter Alar Width, Inter Commissural Width, and Inter Canthal Distance: A Pilot Study

The aim of this study was to determine the relationship between inter canine width (ICW) and inter alar width (IAW), inter commissural width (ICoW), and inter canthal distance (ICaD) in Bantu population. Materials and Methods: It was a pilot study included all participants who were aged at least 18 years, without a history of orthodontics treatment from Prosthodontics Department, Faculty of Dental Medicine, University of Kinshasa. The Ethics committee of the National Center of Research for Dental Sciences in DR Congo approved the study protocol (CNRSB 1504.218). The participants medical records were obtained from the interview and dental examination. Nature of the study was explained with participant information sheet, and an informed consent of all participants was obtained. The inclusion criteria were no missing maxillary and mandibular teeth, no diastema, and no anterior restorations, 18 years old before enrollment in the study. The exclusion criteria were inability to meet the above requirements, pregnancy, and refusal to participate in the study. The inter-canine width (ICW), inter alar width (IAW), inter canthal distance (ICaD) and inter-commissural width (ICoW) of each participant were measured with a digital Vernier caliper (Mitutoyo, UK Ltd.,) (0.01 mm) three times and the average value was recorded. The inter canthal distance (ICaD) was measured without applying pressure by bringing the recording parts of the caliper just in contact with the medial angle. The inter alar width (IAW) was marked with a fine marked pencil on the widest outer surface of the alae of the nose on either side or width. Those two points were measured without applying pressure by bringing the recording parts of the caliper just in contact with the outer surface. The participant was told to stop breathing shortly to avoid any change in shape of the nose. The inter-commissural width (ICoW) was determined by measuring the maxillary lip vermilion from commissure to commissure without the application of pressure on the tissue in the relaxed state. The inter-canine width (ICW) was measured indirectly using a dental floss. A dental floss was marked on one end prior to placement in the mouth. Using that point as reference, the dental floss was circumference along the curvature of the anterior dentition such that it passed along the contact point of all the teeth. The distal end of the canine teeth on both sides was then marked on the floss while it was stretched in the patients mouth. Floss was marked on both sides with the marker pencil. The distance between the two proximal contact points was measured and recorded. Data, analysis and validation were performed by the SPSS software (version 22.0, IBM SPSS Statistics, Chicago, IL, USA). Unpaired t-test was used, of Kolmogorov-Smirnov test. Analysis of variance (ANOVA) test was used to test for comparability between socio-demographic characteristics dental measurements. Pearsons correlation coefficients test was calculated to determine the relationship between facial and dental parameters. Significance was set at P 0.01. Results: Of 314 participants enrolled, 202 were included. The age ranged from 18 to 68 years, with a mean age of 40.62 12.99 years. Although the Pearsons correlation coefficients were negative. Ninety-three participants (46%) were men and one hundred and nine (54%) were women. The overall mean age was 40.62 12.99 years. Facial and dental measurements were greater in women than men with significant differences for ICW (p = 0.04). However, no significant difference was seen between men and women for IAW, ICaD and ICoW (p = 0.44, p = 0.23, p = 0.31 respectively). The correlation including Pearsons correlation coefficient and P-values for all participants is not demonstrated. Conclusion: Within the limitations of this study, the results suggest that IAW, ICaD and ICoW cannot be used as a preliminary method for determining the width of the maxillary for anterior teeth for edentulous patients.

Red cell distribution width/platelet ratio estimates the 3-year risk of decompensation in Metabolic Dysfunction-Associated Steatotic Liver Disease-induced cirrhosis

BACKGROUND For compensated advanced chronic liver disease(cACLD)patients,the first decompensation represents a dramatically worsening prognostic event.Based on the first decompensation event(DE),the transition to decompensated advanced chronic liver disease(dACLD)can occur through two modalities referred to as acute decompensation(AD)and non-AD(NAD),respectively.Clinically Significant Portal Hypertension(CSPH)is considered the strongest predictor of decompensation in these patients.However,due to its invasiveness and costs,CSPH is almost never evaluated in clinical practice.Therefore,recognizing noninvasively predicting tools still have more appeal across healthcare systems.The red cell distribution width to platelet ratio(RPR)has been reported to be an indicator of hepatic fibrosis in Metabolic Dysfunction-Associated Steatotic Liver Disease(MASLD).However,its predictive role for the decompensation has never been explored.AIM In this observational study,we investigated the clinical usage of RPR in predicting DEs in MASLD-related cACLD patients.METHODS Fourty controls and 150 MASLD-cACLD patients were consecutively enrolled and followed up(FUP)semiannually for 3 years.At baseline,biochemical,clinical,and Liver Stiffness Measurement(LSM),Child-Pugh(CP),Model for End-Stage Liver Disease(MELD),aspartate aminotransferase/platelet count ratio index(APRI),Fibrosis-4(FIB-4),Albumin-Bilirubin(ALBI),ALBI-FIB-4,and RPR were collected.During FUP,DEs(timing and modaities)were recorded.CSPH was assessed at the baseline and on DE occurrence according to the available Clinical Practice Guidelines.RESULTS Of 150 MASLD-related cACLD patients,43(28.6%)progressed to dACLD at a median time of 28.9 months(29 NAD and 14 AD).Baseline RPR values were significantly higher in cACLD in comparison to controls,as well as MELD,CP,APRI,FIB-4,ALBI,ALBI-FIB-4,and LSM in dACLD-progressing compared to cACLD individuals[all P<0.0001,except for FIB-4(P:0.007)and ALBI(P:0.011)].Receiving operator curve analysis revealed RPR>0.472 and>0.894 as the best cut-offs in the prediction respectively of 3-year first DE,as well as its superiority compared to the other non-invasive tools examined.RPR(P:0.02)and the presence of baseline-CSPH(P:0.04)were significantly and independently associated with the DE.Patients presenting baseline-CSPH and RPR>0.472 showed higher risk of decompensation(P:0.0023).CONCLUSION Altogether these findings suggest the RPR as a valid and potentially applicable non-invasive tool in the prediction of timing and modalities of decompensation in MASLD-related cACLD patients.

Climatic implications in earlywood and latewood width indices of Chinese pine in north central China

Latewood width(LWW)indices of trees are considered a reliable proxy of summer precipitation in the Northern Hemisphere.However,the strong coupling and high correlation between earlywood width(EWW)and LWW indices often prevent registration of climate signals of the LWW index.In this study,328-year-long earlywood width and latewood width chronologies were developed from Chinese pine at two sites in the Hasi Mountains,north central China.The climate responses of these chronologies were analyzed and the LWW index used to derive sum-mer precipitation signals.Correlation analyses showed that LWW was particularly influenced by earlywood growth and recorded stronger climate signals of the previous year as EWW,rather than those of the current year with infrequent summer climate signals.However,after removing the effect of earlywood growth using a simple regression model,the adjusted LWW chronology(LWW_(adj))showed a strong relationship with July precipitation in dry years.This suggests that the LWW_(adj) chronology has the potential to be used to investigate long-term variability in summer precipitation in drought-limited regions.

A mechanically coupled MEMS filter with high-Q width extensional mode resonators

This work presents a novel radio frequency(RF)narrowband Si micro-electro-mechanical systems(MEMS)filter based on capacitively transduced slotted width extensional mode(WEM)resonators.The flexibility of the plate leads to multiple modes near the target frequency.The high Q-factor resonators of around 100000 enable narrow bandwidth filters with small size and simplified design.The 1-wavelength and 2-wavelength WEMs were first developed as a pair of coupled modes to form a passband.To reduce bandwidth,two plates are coupled with aλ-length coupling beam.The 79.69 MHz coupled plate filter(CPF)achieved a narrow bandwidth of 8.8 kHz,corresponding to a tiny 0.011%.The CPF exhibits an impressive 34.84 dB stopband rejection and 7.82 dB insertion loss with near-zero passband ripple.In summary,the RF MEMS filter presented in this work shows promising potential for application in RF transceiver front-ends.

Predictive value of red blood cell distribution width and hematocrit for short-term outcomes and prognosis in colorectal cancer patients undergoing radical surgery

BACKGROUND Previous studies have reported that low hematocrit levels indicate poor survival in patients with ovarian cancer and cervical cancer,the prognostic value of hematocrit for colorectal cancer(CRC)patients has not been determined.The prognostic value of red blood cell distribution width(RDW)for CRC patients was controversial.AIM To investigate the impact of RDW and hematocrit on the short-term outcomes and long-term prognosis of CRC patients who underwent radical surgery.METHODS Patients who were diagnosed with CRC and underwent radical CRC resection between January 2011 and January 2020 at a single clinical center were included.The short-term outcomes,overall survival(OS)and disease-free survival(DFS)were compared among the different groups.Cox analysis was also conducted to identify independent risk factors for OS and DFS.RESULTS There were 4258 CRC patients who underwent radical surgery included in our study.A total of 1573 patients were in the lower RDW group and 2685 patients were in the higher RDW group.There were 2166 and 2092 patients in the higher hematocrit group and lower hematocrit group,respectively.Patients in the higher RDW group had more intraoperative blood loss(P<0.01)and more overall complications(P<0.01)than did those in the lower RDW group.Similarly,patients in the lower hematocrit group had more intraoperative blood loss(P=0.012),longer hospital stay(P=0.016)and overall complications(P<0.01)than did those in the higher hematocrit group.The higher RDW group had a worse OS and DFS than did the lower RDW group for tumor node metastasis(TNM)stage I(OS,P<0.05;DFS,P=0.001)and stage II(OS,P=0.004;DFS,P=0.01)than the lower RDW group;the lower hematocrit group had worse OS and DFS for TNM stage II(OS,P<0.05;DFS,P=0.001)and stage III(OS,P=0.001;DFS,P=0.001)than did the higher hematocrit group.Preoperative hematocrit was an independent risk factor for OS[P=0.017,hazard ratio(HR)=1.256,95%confidence interval(CI):1.041-1.515]and DFS(P=0.035,HR=1.194,95%CI:1.013-1.408).CONCLUSION A higher preoperative RDW and lower hematocrit were associated with more postoperative complications.However,only hematocrit was an independent risk factor for OS and DFS in CRC patients who underwent radical surgery,while RDW was not.

OsDA1 positively regulates grain width in rice

The size and shape of rice grains influence their yield and commercial value.We investigated the role of OsDA1,a rice homolog of the Arabidopsis DA1 gene,in regulating grain size and shape.OsDA1 was highly expressed in young spikelets and glumes.Its overexpression led to enlarged seeds with increased width and decreased length/width ratio(LWR)and knocking out OsDA1 reduced grain width and increased grain length and LWR.A R310K point mutation in the DA1-like domain is a potential target for breeding for increased grain width and length.OsDA1 interacted with TCP gene-family proteins to regulate grain size and shape.Our findings deepen our understanding of the molecular mechanisms underlying grain size regulation and provide useful information for improving grain yield.

Application of neutrophil-lymphocyte ratio and red blood cell distribution width in diabetes mellitus complicated with heart failure

BACKGROUND Accumulating clinical evidence has shown that diabetes mellitus(DM)is a serious risk factor for cardiovascular disorders and an important factor for adverse cardiovascular events.AIM To explore the value of the combined determination of the neutrophil-lymphocyte ratio(NLR)and red blood cell distribution width(RDW)in the early diagnosis and prognosis evaluation of DM complicated with heart failure(HF).METHODS We retrospectively analyzed clinical data on 65 patients with type 2 DM(T2DM)complicated with HF(research group,Res)and 60 concurrent patients with uncomplicated T2DM(control group,Con)diagnosed at Zhejiang Provincial People’s Hospital between January 2019 and December 2021.The NLR and RDW values were determined and comparatively analyzed,and their levels in T2DM+HF patients with different cardiac function grades were recorded.The receiver operating characteristic(ROC)curves were plotted to determine the NLR and RDW values(alone and in combination)for the early diagnosis of HF.The correlation between NLR and RDW with the presence or absence of cardiac events was also investigated.RESULTS Higher NLR and RDW levels were identified in the Res vs the Con groups(P<0.05).The NLR and RDW increased gradually and synchronously with the deterioration of cardiac function in the Res group,with marked differences in their levels among patients with grade II,III,and IV HF(P<0.05).ROC curve analysis revealed that NLR combined with RDW detection had an area under the curve of 0.915,a sensitivity of 76.9%,and a specificity of 100%for the early diagnosis of HF.Furthermore,HF patients with cardiac events showed higher NLR and RDW values compared with HF patients without cardiac events.CONCLUSION NLR and RDW were useful laboratory indicators for the early diagnosis of DM complicated with HF,and their joint detection was beneficial for improving diagnostic efficiency.Additionally,NLR and RDW values were directly proportional to patient outcomes.

Enhancing predictive accuracy in hypertriglyceridemia-induced acute pancreatitis:Role of red cell distribution width and prospective studies

This letter addresses the study titled“Red cell distribution width:A predictor of the severity of hypertriglyceridemia-induced acute pancreatitis”by Lv et al published in the World Journal of Experimental Medicine.The study offers a valuable analysis of red cell distribution width(RDW)as a predictive marker for persistent organ failure in patients with hypertriglyceridemia-induced acute pancreatitis.The study results suggest that RDW,combined with the Bedside Index for Severity in Acute Pancreatitis score,could enhance the predictive accuracy for severe outcomes.Further investigation into the role of RDW in different severities of acute pancreatitis is recommended.Additionally,the need for large-scale and multicenter prospective studies to validate these findings is emphasized.

Crack Width Comparison between ACI 318, Eurocode 2 and GB 50010 for Flexural RC Members

Comparative research on different countries’ structural design codes holds great importance and can gain valuable insights: Awareness of Design Levels, Identifying Code Deficiencies and Optimizing Designs. The crack width of concrete structure is an important design aspect of the civil design. The four highly recognized and widely used crack width theories are systematically summarized. Based on the mentioned theories and project practices, American code ACI system, Eurocode 2 1992-1 and Chinese code GB 50010 have different crack width control requirement and calculation methods. The crack width control method based on ACI system code has evolved from the Z-factor method to the steel bar spacing control method which is simple and easy to be adopted for engineering. Meanwhile, the ACI 224.1R also gives a direct crack width calculation method consistent with the steel bar spacing control method. The Eurocode 2 and GB 50010 based on the bond-slip & no-slip theory consider much more affecting factors than ACI for predicting crack width. Taking the crack width calculation of Tunnel 5 intake as an example, the crack widths of the structure are calculated according to ACI system code, Eurocode 2 and GB 50010 respectively, the results show that the crack width results in various codes are not much different. The EN 1992-1 and GB 50010 results are almost the same which are less than the ACI 224.1Rresults.

The Prognostic Value of Red Cell Distribution Width in Critically Ill Cerebral Infarction Patients:A Retrospective Cohort Study

Objective:Red blood cell distribution width(RDW)has been utilized as a prognostic indicator for mortality risk assessment in cardiovascular and cerebrovascular patients.Nevertheless,the prognostic significance of RDW in critically ill patients with cerebral infarction is yet to be investigated.The objective of this study is to examine the association between RDW and the risk of all-cause mortality in cerebral infarction patients admitted to the intensive care unit(ICU).Method:A retrospective cohort study was conducted using the Medical Information Mart for Intensive Care IV 2.2(MIMIC-IV)intensive care dataset for data analysis.The main results were the all-cause mortality rates at 3 and 12 months of follow-up.Cumulative curves were plotted using the Kaplan-Meier method,and Cox proportional hazards analysis was used to examine the relationship between RDW and mortality rates in critically ill cerebral infarction patients.Results:The findings indicate that RDW serves as a significant prognostic factor for mortality risk in critically ill stroke patients,specifically at the 3 and 12-month follow-up periods.The observed correlation between increasing RDW levels and higher mortality rates among cerebral infarction patients further supports the potential utility of RDW as a predictive indicator.Conclusion:RDW emerges as an independent predictor of mortality risk during the 3 and 12-month follow-up periods for critically ill patients with cerebral infarction.

Equal Width波方程的精确行波解与波的动态模拟(英文)

继Abdulkadir Dogan用Galar方法求解Equal Width波方程得到一些数值解之后,我们利用动力系统分支理论再次求解了这个方程。确定了存在光滑的孤立波和周期波解的参数条件。给出了一些精确的解析行波解。同时,给出了这些行波解的动态模拟图。

Equal Width波方程的各种椭圆函数周期解和孤子解

结合齐次平衡法和F-展开法,并利用Riccati方程的结果,直接给出了Equal Width波方程的各种椭圆函数周期解.当椭圆函数的模m分别趋于1和0时,利用这些椭圆函数周期解,得到了Equal Width波方程的各种孤子解和三角函数周期解,其解的数量超过了已有文献.

用EXP-函数法求Equal Width波方程的精确解

利用EXP-函数法,再次研究了Equal Width波方程的精确解,获得了与现有文献中的解的结构不相同的新类型的精确解。本文的孤子解,比一些文献中的双曲函数解的结构更具一般性,从而大大丰富了相关文献中关于Equal Width波方程的解的类型。

利用EXP-函数展开法求解Modified Equal Width波方程的精确解

本文将利用EXP-函数展开法,再次研究了Modified Equal Width波方程的精确解,获得了一些与现有文献中的解的结构不相同的新类型的精确解.本文的孤子解的波形图,与一些文献中的数值解的波形图相比,基本一致,进一步验证了这些文献中的数值解的有效性.