scholarly journals $\mu$-statistical convergence and the space of functions $\mu$-stat continuous on the segment

2021 ◽  
Vol 13 (2) ◽  
pp. 433-451
Author(s):  
S.R. Sadigova
Keyword(s):  
Banach Space ◽  
Borel Measure ◽  
Statistical Convergence ◽  
Continuous Functions ◽  
Statistical Limit ◽  
The Relationship

In this work, the concept of a point $\mu$-statistical density is defined. Basing on this notion, the concept of $\mu$-statistical limit, generated by some Borel measure $\mu\left(\cdot \right)$, is defined at a point. We also introduce the concept of $\mu$-statistical fundamentality at a point, and prove its equivalence to the concept of $\mu$-stat convergence. The classification of discontinuity points is transferred to this case. The appropriate space of $\mu$-stat continuous functions on the segment with sup-norm is defined. It is proved that this space is a Banach space and the relationship between this space and the spaces of continuous and Lebesgue summable functions is considered.

On the Classification of Biorthogonal Sequences

1974 ◽  
Vol 26 (3) ◽  
pp. 721-733 ◽  
Author(s):  
William H. Ruckle
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Separable Banach Space ◽  
Continuous Functions ◽  
Schauder Basis

The work of various authors (e.g. Frink [3] and Markushevitch [7]) suggests the possibility of studying complete biorthogonal sequences in Banach spaces as a generalization of orthogonal families of continuous functions. But except for the case where the complete biorthogonal sequence is a Schauder basis such studies have not led to a very rich theory. The main reason for this is that an arbitrary complete biorthogonal sequence is not likely to have many helpful properties. For instance, in every separable Banach space X one can find a complete biorthogonal sequence {ei, Ei} which is not one-summable.

scholarly journals Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms

2004 ◽  
Vol 2004 (55) ◽  
pp. 2937-2945 ◽  
Author(s):  
Yusuf Abu Muhanna ◽  
El-Bachir Yallaoui
Keyword(s):  
Banach Space ◽  
Composition Operator ◽  
Borel Measure ◽  
Absolutely Continuous ◽  
Borel Measures ◽  
Cauchy Transforms ◽  
Complex Borel Measure ◽  
Continuous Measures ◽  
The Relationship ◽  
Complex Borel Measures

The analytic self-map of the unit diskD,φis said to induce a composition operatorCφfrom the Banach spaceXto the Banach spaceYifCφ(f)=f∘φ∈Yfor allf∈X. Forz∈Dandα>0, the families of weighted Cauchy transformsFαare defined byf(z)=∫TKxα(z)dμ(x), whereμ(x)is complex Borel measure,xbelongs to the unit circleT, and the kernelKx(z)=(1−x¯z)−1. In this paper, we will explore the relationship between the compactness of the composition operatorCφacting onFαand the complex Borel measuresμ(x).

scholarly journals Statistical convergence of double sequences in fuzzy normed spaces

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 673-681 ◽  
Author(s):  
S.A. Mohiuddine ◽  
H. Şevli ◽  
M. Cancan
Keyword(s):  
Limit Point ◽  
General Class ◽  
Statistical Convergence ◽  
Cluster Point ◽  
Double Sequences ◽  
Normed Spaces ◽  
Statistical Cluster ◽  
Statistical Limit ◽  
Statistical Cluster Point ◽  
The Relationship

In this paper, we study the concepts of statistically convergent and statistically Cauchy double sequences in the framework of fuzzy normed spaces which provide better tool to study a more general class of sequences. We also introduce here statistical limit point and statistical cluster point for double sequences in this framework and discuss the relationship between them.

WEAKLY COMPACT HOMOMORPHISMS BETWEEN SMALL ALGEBRAS OF ANALYTIC FUNCTIONS

2001 ◽  
Vol 33 (6) ◽  
pp. 715-726 ◽  
Author(s):  
PABLO GALINDO ◽  
MIKAEL LINDSTRÖM
Keyword(s):  
Banach Space ◽  
Composition Operator ◽  
Analytic Functions ◽  
Approximation Property ◽  
Composition Operators ◽  
Continuous Functions ◽  
Weak Compactness ◽  
Weakly Compact ◽  
The Relationship ◽  
Uniformly Continuous

The weak compactness of the composition operator CΦ(f) = f ○ Φ acting on the uniform algebra of analytic uniformly continuous functions on the unit ball of a Banach space with the approximation property is characterized in terms of Φ. The relationship between weak compactness and compactness of these composition operators and general homomorphisms is also discussed.

K-MEANS CLUSTERING ALGORITHM BASED CLASSIFICATION OF SOIL FERTILITY IN NORTH WEST NIGERIA

2020 ◽  
Vol 4 (2) ◽  
pp. 780-787
Author(s):  
Ibrahim Hassan Hayatu ◽  
Abdullahi Mohammed ◽  
Barroon Ahmad Isma’eel ◽  
Sahabi Yusuf Ali
Keyword(s):  
Soil Fertility ◽  
Crop Yield ◽  
Clustering Algorithm ◽  
Soil Samples ◽  
North West ◽  
R Programming ◽  
Available Information ◽  
Northwest Region ◽  
The Relationship

Soil fertility determines a plant's development process that guarantees food sufficiency and the security of lives and properties through bumper harvests. The fertility of soil varies according to regions, thereby determining the type of crops to be planted. However, there is no repository or any source of information about the fertility of the soil in any region in Nigeria especially the Northwest of the country. The only available information is soil samples with their attributes which gives little or no information to the average farmer. This has affected crop yield in all the regions, more particularly the Northwest region, thus resulting in lower food production.  Therefore, this study is aimed at classifying soil data based on their fertility in the Northwest region of Nigeria using R programming. Data were obtained from the department of soil science from Ahmadu Bello University, Zaria. The data contain 400 soil samples containing 13 attributes. The relationship between soil attributes was observed based on the data. K-means clustering algorithm was employed in analyzing soil fertility clusters. Four clusters were identified with cluster 1 having the highest fertility, followed by 2 and the fertility decreases with an increasing number of clusters. The identification of the most fertile clusters will guide farmers on where best to concentrate on when planting their crops in order to improve productivity and crop yield.

Approximation in statistical sense to B -continuous functions by positive linear operators

2010 ◽  
Vol 47 (3) ◽  
pp. 289-298 ◽  
Author(s):  
Fadime Dirik ◽  
Oktay Duman ◽  
Kamil Demirci
Keyword(s):  
Compact Subset ◽  
Real Line ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Classical Version ◽  
Statistical Sense

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

DONG SON BRONZE DRUM - THE WORK OF THE LAC VIET PEOPLE

2018 ◽  
Author(s):  
Nguyen Van Hao
Keyword(s):  
Classification Criteria ◽  
Way Of Life ◽  
Tribal Identity ◽  
The Relationship

Bronze drums are widely distributed, broader than the range of a nation. Therefore, the identification of each kind of drum is a basic subject, should be concerned. In determining the tribal identity of the drum, the classification of drum is the key stage, the relationship between the objective of the classification and classification criteria is the relation as shape and shadow, if there is no right criteria then the result of division will be difficult to reach the desired goal. Likewise, the criterion of the pattern on the bronze drum brought to the affirmation is the Dong Son bronze drum of the Lac Viet people. And the parallel is the affirmation of the culture, way of life, residence of the nation created the drum.

scholarly journals Pituitary MRI characteristics in 297 acromegaly patients based on T2-weighted sequences

2015 ◽  
Vol 22 (2) ◽  
pp. 169-177 ◽  
Author(s):  
Iulia Potorac ◽  
Patrick Petrossians ◽  
Adrian F Daly ◽  
Franck Schillo ◽  
Claude Ben Slama ◽  
...  
Keyword(s):  
Large Population ◽  
Optic Chiasm ◽  
Research Priority ◽  
Maximal Diameter ◽  
Magnetic Resonance Imaging Mri ◽  
Multimodal Management ◽  
Mri Characteristics ◽  
Weighted Sequences ◽  
The Relationship

Responses of GH-secreting adenomas to multimodal management of acromegaly vary widely between patients. Understanding the behavioral patterns of GH-secreting adenomas by identifying factors predictive of their evolution is a research priority. The aim of this study was to clarify the relationship between the T2-weighted adenoma signal on diagnostic magnetic resonance imaging (MRI) in acromegaly and clinical and biological features at diagnosis. An international, multicenter, retrospective analysis was performed using a large population of 297 acromegalic patients recently diagnosed with available diagnostic MRI evaluations. The study was conducted at ten endocrine tertiary referral centers. Clinical and biochemical characteristics, and MRI signal findings were evaluated. T2-hypointense adenomas represented 52.9% of the series, were smaller than their T2-hyperintense and isointense counterparts (P<0.0001), were associated with higher IGF1 levels (P=0.0001), invaded the cavernous sinus less frequently (P=0.0002), and rarely caused optic chiasm compression (P<0.0001). Acromegalic men tended to be younger at diagnosis than women (P=0.067) and presented higher IGF1 values (P=0.01). Although in total, adenomas had a predominantly inferior extension in 45.8% of cases, in men this was more frequent (P<0.0001), whereas in women optic chiasm compression of macroadenomas occurred more often (P=0.0067). Most adenomas (45.1%) measured between 11 and 20 mm in maximal diameter and bigger adenomas were diagnosed at younger ages (P=0.0001). The T2-weighted signal differentiates GH-secreting adenomas into subgroups with particular behaviors. This raises the question of whether the T2-weighted signal could represent a factor in the classification of acromegalic patients in future studies.

scholarly journals POS1456-HPR THE SERUM IRON LEVEL MIGHT BE USEFUL IN DETERMINING THE SEVERITY OF MALNUTRITION IN PATIENTS WITH RHEUMATOID ARTHRITIS

2021 ◽  
Vol 80 (Suppl 1) ◽  
pp. 1012.2-1012
Author(s):  
Y. Matsumoto ◽  
Y. Sugioka ◽  
M. Tada ◽  
T. Okano ◽  
K. Mamoto ◽  
...  
Keyword(s):  
Grip Strength ◽  
Serum Iron ◽  
Roc Analysis ◽  
Severe Malnutrition ◽  
Inflammatory Condition ◽  
Research Support ◽  
Chugai Pharmaceutical ◽  
The Relationship ◽  
Nutritional Indicator

Background:The Global Leadership Initiative on Malnutrition (GLIM) criteria, the first international criteria for diagnosis of malnutrition, was released in 2018 [1]. Patients with rheumatoid arthritis (RA) are thought to be prone to malnutrition due to decreased food intake and increased muscle catabolism caused by chronic inflammation or pain. However, there has been no report to assess the nutritional status of RA patients in accordance with the GLIM criteria. In addition, commonly used blood nutrient indicators such as albumin might not be appropriate as nutritional indicators for RA because these values are affected by inflammation.Objectives:This study aims to examine the rates of malnutrition in RA patients according to GLIM criteria, and the relationship between blood nutrient indicators and the severity of malnutrition.Methods:In this study, we conducted a cross-sectional survey of 135 female RA patients in 2020. According to the GLIM criteria, patients were considered to be malnourished if patients had one of the following phenotypic: (1) low body mass index, (2) non-volitional weight loss, (3) reduced muscle mass, and one of the following etiologic: (1) reduced food intake or assimilation, (2) disease burden/inflammatory condition. Reduced muscle mass was evaluated by measuring calf circumference, and inflammatory condition was evaluated by Disease Activity Score (DAS) 28. In accordance with the GLIM criteria, the severity of malnutrition was judged as three levels: no problem, moderate, and severe malnutrition. Albumin, transthyretin, transferrin, retinol binding protein, zinc, iron, ceruloplasmin, and total cholesterol were assessed as blood nutrition indicators. Also grip strength was assessed. We compared each nutritional indicator among the three groups according to the severity of malnutrition using age-adjusted analysis of covariance, and examined the relationship between each nutritional indicator and the severity of malnutrition using receiver operating characteristic (ROC) analysis.Results:In RA patients, 20% were classified as severe malnutrition, and 40% were moderate or more. Serum iron levels were significantly lower in the severe malnutrition group compared to the no problem group (p = 0.001). In ROC analysis, serum iron, zinc, albumin, and grip strength (area under curve; AUC; 0.680, 0.696, 0.636, 0.790, respectively) were significant parameters for classification of moderate and severe malnutrition. Serum iron and grip strength (AUC for respective parameters were 0.741, 0.747) were significant parameters for classification of severe malnutrition.Conclusion:Evaluation based on the GLIM criteria showed that about 40% of RA patients were under moderate or severe malnutrition. It was suggested that serum iron and grip strength might be useful to predict the severity of malnutrition.References:[1]Cederholm T, Jensen GL, Correia MITD, Gonzalez MC, Fukushima R, Higashiguchi T, et al. GLIM criteria for the diagnosis of malnutrition – A consensus report from the global clinical nutrition community. Clinical Nutrition 2019; 38: 1-9.Acknowledgements:We thank to Tomoko Nakatsuka, and the Center for Drug & Food Clinical Evaluation, Osaka City University Hospital, for management and collection of the study data. We also thank to study participants.Disclosure of Interests:Yoshinari Matsumoto Grant/research support from: Yamada Research Grant, Yuko Sugioka: None declared, Masahiro Tada: None declared, Tadasi Okano Speakers bureau: AbbVie, Asahikasei, Astellas Pharma Inc, Ayumi Pharmaceutical, Bristol-Myers Squibb, Chugai Pharmaceutical, Daiich Sankyo, Eisai, Janssen, Lilly, Mitsubishi Tanabe Pharma Corporation, Novartis Pharma, Ono Pharmaceutical, Pfizer, Sanofi, Takeda Pharmaceutical, Teijin Pharma and UCB, Grant/research support from: AbbVie, Eisai, Mitsubishi Tanabe Pharma Corporation and Nipponkayaku, Kenji Mamoto: None declared, Kentaro Inui Speakers bureau: Daiichi Sankyo Co. Ltd., Mitsubishi Tanabe Pharma, Janssen Pharmaceutical K.K., Astellas Pharma Inc., Takeda Pharmaceutical Co. Ltd., Ono Pharmaceutical Co. Ltd., Abbvie GK, Pfizer Inc., Eisai Co., Ltd., Chugai Pharmaceutical Co., Ltd, Grant/research support from: anssen Pharmaceutical K.K., Astellas Pharma Inc., Sanofi K.K., Abbvie GK, Takeda Pharmaceutical Co. Ltd., QOL RD Co. Ltd., Mitsubishi Tanabe Pharma, Ono Pharmaceutical Co. Ltd., Eisai Co., Ltd., Daiki Habu: None declared, Tatsuya Koike Speakers bureau: AbbVie, Astellas Pharma Inc, Bristol-Myers Squibb, Chugai Pharmaceutical, Eisai, Janssen, Lilly, Mitsubishi Tanabe Pharma Corporation, MSD, Ono Pharmaceutical, Pfizer, Roche, Takeda Pharmaceutical, Teijin Pharma, and UCB, Grant/research support from: AbbVie, Astellas Pharma Inc, Bristol-Myers Squibb, Chugai Pharmaceutical, Eisai, Janssen, Lilly, Mitsubishi Tanabe Pharma Corporation, MSD, Ono Pharmaceutical, Pfizer, Roche, Takeda Pharmaceutical, Teijin Pharma, and UCB

scholarly journals Formation of an Export-Oriented Agricultural Economy and Regional Open Innovations

2021 ◽  
Vol 7 (1) ◽  
pp. 32
Author(s):  
Victor L. Shabanov ◽  
Marianna Ya Vasilchenko ◽  
Elena A. Derunova ◽  
Andrey P. Potapov
Keyword(s):  
Agricultural Economy ◽  
Institutional Management ◽  
Agricultural Exports ◽  
Modeling Methodology ◽  
Fixed Assets ◽  
Analysis Application ◽  
The Impact ◽  
The Relationship

The aim of the work is to find relevant indicators for assessing the relationship between investments in fixed assets in agriculture, gross output of the industry, and agricultural exports using tools for modeling the impact of innovation and investment development on increasing production and export potential in the context of the formation of an export-oriented agricultural economy. The modeling methodology and the proposed estimating and forecasting tools for diagnosing and monitoring the state of sectoral and regional innovative agricultural systems are used to analyze the relationship between investments in fixed assets in agriculture, gross output of the industry, and agricultural exports based on the construction of the classification of Russian regions by factors that aggregate these features to diagnose incongruence problems and to improve institutional management in regional innovative export-oriented agrosystems. Based on the results of the factor analysis application, an underestimated role of indicators of investment in agriculture, the intensity and efficiency of agricultural production, were established. Based on the results of the cluster analysis, the established five groups of regions were identified, with significant differences in the level of investment in agriculture, the volume of production of the main types of agricultural products, and the export and exported food. The research results are of practical value for use in improving institutional management when planning reforms and transformations of regional innovative agrosystems.

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