A VIEWPOINT TO MEASURE OF NON-COMPACTNESS OF OPERATORS IN BANACH SPACES

This article is committed to deal with measure of non-compactness of operators in Banach spaces.Firstly,the collection C(X)(consisting of all nonempty closed bounded convex sets of a Banach space X endowed with the uaual set addition and scaler multiplication)is a normed semigroup,and the mapping J from C(X)onto F(Ω)is a fully order-preserving positively linear surjective isometry,whereΩis the closed unit ball of X^*and F(Ω)the collection of all continuous and w^*-lower semicontinuous sublinear functions on X^*but restricted toΩ.Furthermore,both EC=JC-JC and EK=JK-JK are Banach lattices and EK is a lattice ideal of EC.The quotient space EC/EK is an abstract M space,hence,order isometric to a sublattice of C(K)for some compact Haudorspace K,and(FQJ)C which is a closed cone is contained in the positive cone of C(K),where Q:EC→EC/EK is the quotient mapping and F:EC/EK→C(K)is a corresponding order isometry.Finally,the representation of the measure of non-compactness of operators is given:Let BX be the closed unit ball of a Banach space X,thenμ(T)=μ(T(BX))=||(F QJ)T(BX)||C(K),∀T∈B(X).

Left ventricular non-compaction presenting as cardio-embolic stroke

A 39-year-old male with no known comorbidities presented with sudden onset right-sided weakness.On examination,blood pressure was 128/79 mmHg,National Institutes of Health Stroke Scale score was 4 and there were no signs of heart failure.Emergent computerized tomography demonstrated an ischemic infarct of the left middle cerebral artery distribution and brain magnetic resonance imaging later confirmed it(Figure 1).

METRIC ENTROPY OF HOMEOMORPHISM ON NON-COMPACT METRIC SPACE

Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying T ＊｜X = T and T ＊x＊ = x＊. We show that their topological entropies satisfy hd（T, X） ≥ h（T ＊, X＊） if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space.

Ventricular Non-Compaction: About the First Cases Reported in Lomé(Togo)

Introduction: Ventricular non-compaction, a cardiomyopathy recently described as likely to be rare, belongs to the group of unclassified cardiomyopathy according to European Society of Cardiology. Few studies have been published on the ventricular non-compaction in sub-Saharan Africa. We aim to find out the various aspects, being diagnosis, therapeutic, in Togolese patients carrying the ventricular non-compaction. Methodology: This is a three-year prospective and descriptive study conducted from January 2017 to December 2019 in the two University Hospital of Lomé. Patients having echocardiographic criteria of ventricular non-compaction were included in our study. Results: 10 patients (6 men and 4 women) were diagnosed for ventricular non-compaction during the study period. The mean age of patients was 32.3 years. The most frequent clinical manifestation was heart failure (7 patients). The main electrocardiogram anomaly was left ventricle hypertrophy (9 patients). The preferential segments were: apical (9 cases), apicolateral (8 cases), and septoapical (7 cases). The average ratio of non-compaction/compaction was 3.31. The main complication was thromboembolic event (4 patients). Angiotensin converting enzyme inhibitors and beta-blockers were essentially the medicines used. After a three (3) year follow-up, two (2) of the patients died. Conclusion: Tough ventricular non-compaction has been recently described. It is present in Togo. It displays many clinical manifestations and the prognosis is often guarded.

A Case Report of Isolated Left Ventricular Non-Compaction Presenting with Congestive Heart Failure and Intramural Thrombus

Isolated left ventricular non-compaction is recently described as a rare form of cardiomyopathy that is associated with a heart failure, life threatening cardiac arrhythmia and thromboembolic complications. The diagnosis is based on echocardiography demonstration of spongy myocardium. Here we report a case of 74 years old female patient diagnosed as an isolated left ventricular non-compaction with congestive heart failure, intramural thrombus and hypertension. There is no specific treatment for LVNC;therapeutic measures are directed towards the patient’s symptom (heart failure, arrhythmia and thrombotic events) and consideration of an implantable cardioverter defibrillator and cardiac transplantation.

Do Antineoplastic Drugs Play an Additional Role in the Progression of Non-Compaction Cardiomyopathy? A Case Report

Non-compaction cardiomyopathy is a rare form of cardiomyopathy;its most common clinical manifestations are heart failure (HF), ventricular arrhythmia, thromboembolism, and sudden cardiac death. We report a rare case of a 63-year-old man with chest tightness, worsening lower leg edema, dyspnea, and decreased exercise tolerance. He had a medical history of gastric cancer treated with subtotal gastrectomy and post-operative chemotherapy with paclitaxel and fluorouracil three years ago. At that time, he was diagnosed with non-compaction cardiomyopathy, and the thickened and reticulated trabecular muscle was exclusively confined to left ventricular apex. Five months ago, he was admitted to our hospital with heart failure and treated for dilated cardiomyopathy, echocardiography revealed severe trabecular noncompact myocardium in both ventricles, which was confirmed by cardiac magnetic resonance imaging (CMR). It is generally accepted that non-compacted myocardium forms in the early embryonic stage, which raises a question in our case whether acquired factors, such as antineoplastic drugs, potentially accelerate the pathological progression of non-compaction cardiomyopathy. Considering there are disparities between current screening tools such as echocardiography and CMR regarding diagnostic criteria, multi-detector CT may be an alternative examination method that could provide a new perspective for diagnosis.

An unusual combination of left atrial myxoma and left ventricular non-compaction cardiomyopathy in a male patient:A Casereport

Left atrialmyxoma is a common primary cardiac tumor that is accompanied by organic heart diseases.But left atrial myxoma coexistent with left ventricular non-compaction(LVNC)is extremely rare.A young male patient with left atrial myxoma and LVNC was reported in this study.A 25-year-old manpresented to the emergency department with sudden shortness of breath and syncope,accompanied by fever and cough.He had a history ofacute ischemic strokeone year before hospitalization.Echocardiography revealed that the endocardium of the left ventricle was not smooth with raised muscle trabeculae and deep recesses.There was an oval-shaped strong echo mass with a pedicle in the left atrium attached to the atrial septum.Tumor resection was operated during extracorporeal circulation.Pathological results confirmed left atrium myxoma.In this case report,the patient had heart failure and an ischemic stroke likely of cardiogenic origin.He underwenttumor resection and started on therapeutic anticoagulation.Left atrial myxoma and LVNC are associated with poor outcomes.Early diagnosis and prompt treatment are crucial.

凸棱非平面聚晶金刚石齿的破岩机理及在含砾地层中的应用

为提高聚晶金刚石复合片(PDC)钻头在含砾、软硬交错等不均质地层中的抗冲击性能,开展了凸棱非平面PDC齿的研究。通过仿真和室内实验对比分析了凸棱非平面齿与常规平面齿的破岩机理。与平面齿相比,凸棱非平面齿与岩石的接触应力分布更均匀,切削破岩过程中的载荷波动幅度明显更小,切削稳定性更高。凸棱齿特殊的非平面结构改变了切削齿与岩石的互作用方式,在不均质地层得到成功应用。

盐渍土既有高速铁路路基压实质量检测

高速铁路路基填料压实标准主要通过压实系数、地基系数、动态变形模量等指标进行控制。对于既有路基,在不破坏路基的条件下,路基内部的控制指标难以有效测试。为评价某海外项目既有路基内部填料压实情况,最大程度减少对既有路基工程的扰动破坏,通过试验段建立了动力触探试验(DPT)锤击数与实测压实系数、地基系数、动态变形模量的拟合关系式,并将其应用于该项目全线路基内部压实质量检测。结果表明:应用该拟合关系式能够避免对既有路基的破坏,节约工期,取得了较好的经济效益。

Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure

In this paper, we show that every infinite dimensional Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure. Therefore, it resolves a long-standing question.

Isolated non-compaction of ventricular myocardium in a victim of the Wenchuan earthquake with crush syndrome and acute renal failure

Non-compaction of the ventricular myocardium （NVM） is a rare congenital genetic heart defect that was initially reported 17 years ago by means of autopsy; few cases have been published since then. It has been classified as the primary inherited cardiomyopathy by the American Heart Association Scientific Statement in 2006 under contemporary definitions and classification of cardiomyopathies. It is caused by an arrested development of muscle fiber compaction, a process that normally takes place dunng early embryogenesls, which is characterized by numerous sinusoids or trabeculae that are excessive in number and abnormal in prominence and by deep intratrabecular recesses covered by endothelium that exhibits continuity with ventricular endocardium. It usually involves one and/or more segments of the left ventricle, while the clinical manifestations are highly variable,

On the variational principle for the topological pressure for certain non-compact sets

Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous map.We assume that the dynamical system satisfies g-almost product property and the uniform separation property.We compute the topological pressure of saturated sets under these two conditions.If the uniform separation property does not hold,we compute the topological pressure of the set of generic points.We give an application of these results to multifractal analysis and finally get a conditional variational principle.

A class of Kazdan-Warner typed equations on non-compact Riemannian manifolds

In this paper,we discuss a Kazdan-Warner typed equation on certain non-compact Rie- mannian manifolds.As an application,we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles over certain non-compact K(?)hler manifolds.

Erratum to: Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure

[1, Theorem 4.4] states that every infinite dimensional Banach space admits a homogenous measure of noncompactness not equivalent to the Hausdorff measure. Howevere, there is a gap in the proof. In fact,we found that [1, Lemma 4.3] is not true. In this erratum, we give a corrected proof of [1, Theorem 4.4].

碱激发矿渣混凝土密实性超声无损检测法及其影响因素

研究了碱激发矿渣混凝土水胶比、模数、碱当量及粗骨料含量对其抗压强度、超声波速的影响,并通过分析混凝土配合比参数与密度、弹性模量、孔隙率之间的关系来揭示超声波速的变化机理。结果表明:不同配合比参数的碱激发矿渣混凝土超声波速与弹性模量成正比,与密度、孔隙率成反比,在超声无损检测过程中可将碱激发矿渣混凝土近似作为均质性实体材料进行建模计算,发现其超声波速与抗压强度呈线性关系。基于理论分析与试验结果建立了碱激发矿渣混凝土的密实性计算模型,可以为检测碱激发矿渣混凝土密实性作参考。

Whole-exome sequencing reveals twovariants in thegene in two Chinese patients with left ventricular non-compaction cardiomyopathy

Importance:Pathogenic variants in theRBM20 gene are associated with aggressive dilated cardiomyopathy(DCM).Recently,RBM20 was found to be associated with left ventricular non-compaction cardiomyopathy(LVNC).Thus far,only five families with LVNC have been reported to carry variants inRBM20.It remains unknown whether the variants inRBM20 associated with DCM can also cause LVNC.Objective:To elucidate the causativeRBM20 variant in two unrelated patients with both LVNC and DCM,and to identify the clinical characteristics associated with variants inRBM20.Methods:Trio whole-exome sequencing(WES)was performed.Variants were filtered and classified in accordance with the guidelines of the American College of Medical Genetics and Genomics(ACMG).Results:We identified two distinctde novo variants inRBM20(one per patient)in these two patients with LVNC.Both variants have been reported in patients with DCM,without the LVNC phenotype.Patient 1 was an 11-year-old girl who had DCM,LVNC,and heart failure;the ratio of noncompacted-to-compacted myocardium was 2.7:1.Ade novo heterozygous variant c.1907G>A(p.Arg636His)in exon 9 was identified in this patient.Patient 2 was a 13-year-old boy who had clinical phenotypes identical to those of Patient 1;the ratio of noncompacted-to-compacted myocardium was 3.2:1 in this patient.WES revealed ade novo heterozygous variant c.1909A>G(p.Ser637Gly)in exon 9.Both variants were previously characterized as pathogenic,and our study classified them as pathogenic variants based on the ACMG guidelines.Interpretation:We found that two patients with LVNC had variants inRBM20.Our results extended the clinical spectrum of the twoRBM20 variants and illustrated that the same variant inRBM20 can cause DCM,with or without the LVNC phenotype.

Note on families of semistable curves over P^1 with 4 singular fibers whose Jacobian are non-compact

Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.

On a Measure of Non-compactness for Some Classical Operators

The measure of non-compactness is estimated from below for various operators, including the Hardy-Littlewood maximal operator, the fractional maximal operator and the Hilbert transform, all acting between weighted Lebesgue spaces. The identity operator acting between weighted Lebesgue spaces and also between the counterparts of these spaces with variable exponents is similarly analysed. These results enable the lack of compactness of such operators to be quantified.

A rare case of isolated right ventricular non-compaction Cardiomyopathy

INTRODUCTION Isolated ventricular non-compaction is a rare congenital cardiomyopathy occurs due to arrest of normal myocardial development during embryogenesis. It is mainly diagnosed by echocar- diography through the appearance of characteristic prominent myocardial trabeculation and deep inter-trabecular spaces. Heart failore,

无核密度测试技术在SMA-10磨耗层碾压质量控制中的应用

SMA-10路面拥有良好的骨架嵌挤结构和足够的胶浆填充,具有优良的抗车辙、抗水损害、耐久性能,越来越多地应用于高速公路磨耗层和养护罩面层的铺筑。但在碾压环节容易出现过度碾压导致表面碎石被压碎,油膜脱落,不仅影响抗滑性能,甚至容易造成外界水分侵入导致路面水损害。为提高SMA-10沥青混合料的施工质量,以广东省粤西地区茂湛高速项目为依托,采用无核密度仪对碾压工艺开展试验研究。结果表明:影响SMA-10混合料压实度的主要因素包含压实组合、压实遍数和碾实温度,正常施工条件下碾压6遍(静压2.5遍+振动碾压3.5遍)即可达到规范要求的压实度,温度在下限状态下需适当增加振动碾压遍数;随着碾压遍数增加,压实度呈现先递增后平缓的规律,路表碎石棱角破损突出。建议对SMA-10路面施工,全面做好各阶段的温保措施,针对不同项目的SMA-10混合料的设计情况,采用无核密度仪获得压实曲线,作为SMA-10混合料精准碾压的控制手段。