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 ua...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).展开更多
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 si...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).展开更多
In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study ...In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.展开更多
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...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.展开更多
<div style="text-align:justify;"> <strong>Introduction</strong><span "=""><span>: Ventricular non-compaction, a cardiomyopathy recently described as likely to be ...<div style="text-align:justify;"> <strong>Introduction</strong><span "=""><span>: 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. </span><b><span>Methodology</span></b><span>: This is a three</span></span><span>-</span><span>year</span><span> </span><span "=""><span>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. </span><b><span>Results</span></b><span>: 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. </span><b><span>Conclusion</span></b><span>: Tough ventricular non-compaction has been recently described</span></span><span>.</span><span> It is present in Togo. It displays many clinical manifestations and the prognosis is often guarded.</span> </div>展开更多
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 o...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.展开更多
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 diagno...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.展开更多
在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广...在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广和改进了相关文献(Attouch H,RiahiH.Stability results for Ekeland’s-variational principle and cone extremal solution;Huang X X.Stabilityin vector-valued and set-valued optimization)中的相应结果,并给出例子说明了所得结果的正确性。展开更多
基金The project supported in part by the National Natural Science Foundation of China(11801255)。
文摘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).
文摘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).
文摘In point set topology, it is well known that the Kuratowski 14-set problem is one of the most interesting results. In this note, we first give a brief survey of the Kuratowski’s theorem. In particular, we will study and investigate the structure of the boundary of a given subset in a topological space. Some new results and topics which are related to the theorem of Kuratowski are presented and discussed. Finally, we pose some open problems of Kuratowskitype.
基金supported by the Fundamental Research Funds for the Central Universities (CDJZR10100006)
文摘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.
文摘<div style="text-align:justify;"> <strong>Introduction</strong><span "=""><span>: 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. </span><b><span>Methodology</span></b><span>: This is a three</span></span><span>-</span><span>year</span><span> </span><span "=""><span>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. </span><b><span>Results</span></b><span>: 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. </span><b><span>Conclusion</span></b><span>: Tough ventricular non-compaction has been recently described</span></span><span>.</span><span> It is present in Togo. It displays many clinical manifestations and the prognosis is often guarded.</span> </div>
文摘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.
文摘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.
文摘在不需要紧性假设下,利用拟C-凸函数及回收锥的性质,建立了向量优化问题有效点集的稳定性,获得了一列目标函数和可行集均扰动情形下的向量优化问题与对应的向量优化问题有效点集的Painlevé-Kuratowski内收敛性结果。所得结果推广和改进了相关文献(Attouch H,RiahiH.Stability results for Ekeland’s-variational principle and cone extremal solution;Huang X X.Stabilityin vector-valued and set-valued optimization)中的相应结果,并给出例子说明了所得结果的正确性。
