scholarly journals On the Spectral Properties of the Weighted Mean Difference Operator Gu,v;Δ over the Sequence Space ℓ1

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
P. Baliarsingh ◽  
S. Dutta
Keyword(s):  
Sequence Space ◽  
Difference Operator ◽  
Point Spectrum ◽  
Weighted Mean Difference ◽  
Mean Difference ◽  
Weighted Mean ◽  
Residual Spectrum ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference

In the present work the generalized weighted mean difference operator Gu,v;Δ has been introduced by combining the generalized weighted mean and difference operator under certain special cases of sequences u=(uk) and v=(vk). For any two sequences u and v of either constant or strictly decreasing real numbers satisfying certain conditions the difference operator Gu,v;Δ is defined by (G(u,v;Δ)x)k=∑i=0k‍ukvi(xi-xi-1) with xk=0 for all k<0. Furthermore, we compute the spectrum and the fine spectrum of the operator Gu,v;Δ over the sequence space l1. In fact, we determine the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of this operator on the sequence space l1.

scholarly journals Some Spectral Aspects of the Operator over the Sequence Spaces and

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. Dutta ◽  
P. Baliarsingh
Keyword(s):  
Difference Operator ◽  
Main Idea ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Positive Real ◽  
Residual Spectrum ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference

The main idea of the present paper is to compute the spectrum and the fine spectrum of the generalized difference operator over the sequence spaces . The operator denotes a triangular sequential band matrix defined by with for , where or , ; the set nonnegative integers and is either a constant or strictly decreasing sequence of positive real numbers satisfying certain conditions. Finally, we obtain the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of the operator over the sequence spaces and . These results are more general and comprehensive than the spectrum of the difference operators , , , , and and include some other special cases such as the spectrum of the operators , , and over the sequence spaces or .

scholarly journals On the fine spectrum of the generalized difference operatorB(r,s)over the sequence spacesc0andc

2005 ◽  
Vol 2005 (18) ◽  
pp. 3005-3013 ◽  
Author(s):  
Bilâl Altay ◽  
Feyzı Başar
Keyword(s):  
Difference Operator ◽  
Sequence Spaces ◽  
Band Matrix ◽  
Fine Spectrum ◽  
Special Cases ◽  
The Difference ◽  
The Right

We determine the fine spectrum of the generalized difference operatorB(r,s)defined by a band matrix over the sequence spacesc0andc, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operatorΔ, and includes as other special cases the right shift and the Zweier matrices.

scholarly journals Fine Spectra of Upper Triangular Triple-Band Matrices over the Sequence Space ()

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Karaisa ◽  
Feyzi Başar
Keyword(s):  
Continuous Spectrum ◽  
Sequence Space ◽  
Point Spectrum ◽  
Band Matrices ◽  
Residual Spectrum ◽  
Approximate Point Spectrum ◽  
Fine Spectrum ◽  
The Matrix ◽  
Lower Triangular ◽  
Triple Band

The fine spectra of lower triangular triple-band matrices have been examined by several authors (e.g., Akhmedov (2006), Başar (2007), and Furken et al. (2010)). Here we determine the fine spectra of upper triangular triple-band matrices over the sequence space . The operator on sequence space on is defined by , where , with . In this paper we have obtained the results on the spectrum and point spectrum for the operator on the sequence space . Further, the results on continuous spectrum, residual spectrum, and fine spectrum of the operator on the sequence space are also derived. Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space and we give some applications.

Puerarin for OVX-Induced Postmenopausal Osteoporosis in Murine Model: Systematic Review and Meta-Analysis

2020 ◽  
Vol 15 (1) ◽  
pp. 37-42 ◽  
Author(s):  
Xiaobin Yang ◽  
Haishi Zheng ◽  
Yuan Liu ◽  
Dingjun Hao ◽  
Baorong He ◽  
...  
Keyword(s):  
Systematic Review ◽  
Bone Mass ◽  
Postmenopausal Osteoporosis ◽  
Murine Model ◽  
Weighted Mean Difference ◽  
Meta Analysis ◽  
Mean Difference ◽  
Weighted Mean ◽  
Enhancing Effect ◽  
Searching Strategy

Aims/Background: Ovariectomy (OVX)-induced murine model is widely used for postmenopausal osteoporosis study. Our current study was conducted to systematically review and essentially quantified the bone mass enhancing effect of puerarin on treating OVX-induced postmenopausal osteoporosis in murine model. Methods: Literatures from PUBMED, EMBASE, and CNKI were involved in our searching strategy by limited the inception date to January 9th, 2019. Moreover, the enhancing effect of puerarin on bone mass compared to OVX-induced rats is evaluated by four independent reviewers. Finally, all the data were extracted, quantified and analyzed via RevMan, besides that in our current review study, we assessed the methodological quality for each involved study. Results: Based on the searching strategy, eight randomization studies were finally included in current meta-analysis and systematic review. According to the data analysis by RevMan, puerarin could improve bone mineral density (BMD); (eight studies, n=203; weighted mean difference, 0.05; 95% CI, 0.03-0.07; P<0.0001) using a random-effects model. There is no significant difference between puerarin and estrogen (seven studies, n=184; weighted mean difference, 0.00; 95% CI, -0.01 to 0.00; P=0.30). Conclusions: Puerarin showed upregulating effects on bone mass in OVX-induced postmenopausal osteoporosis in murine model. More studies of the effect of puerarin on bone density in OVX animals are needed.

scholarly journals Effect of Earthworm on Wound Healing: A Systematic Review and Meta-Analysis

2021 ◽  
Vol 12 ◽  
Author(s):  
Dong Wang ◽  
Zhen Ruan ◽  
Rongchao Zhang ◽  
Xuejing Wang ◽  
Ruihui Wang ◽  
...  
Keyword(s):  
Systematic Review ◽  
Wound Healing ◽  
Healing Rate ◽  
Weighted Mean Difference ◽  
Meta Analysis ◽  
Healing Process ◽  
Risk Of Bias ◽  
Mean Difference ◽  
Cochrane Library ◽  
Weighted Mean

Background: Earthworm, also called dilong (Chinese language), has been used as a traditional Chinese medicine for thousands of years. Recently, some scientists believe that earthworm extracts (EE) can promote wound healing. However, its effectiveness remains controversial. We conducted a meta-analysis to evaluate the effect of EE on wound healing based on the healing rate.Methods: We comprehensively reviewed literature that mentioned EE for wound healing in the PubMed, Cochrane Library, Embase, Web of Science, China National Knowledge Infrastructure (CNKI), VIP database for Chinese Technical Periodicals, and WanFang database that have been published until January 2021. We computed weighted mean difference (WMD) for analysis with RevMan 5.3 software in animal and human models groups. Two researchers independently selected studies and evaluated the risk of bias with the Cochrane Collaboration tool. The quality of the evidence was assessed with the Cochrane risk of bias tool. This study is registered on PROSPERO (CRD42020168400).Results: From 2,486 articles, we selected 16 studies for analysis. EE treatment was associated with improvements in wound healing performance based on wound healing rate (mouse model: weighted mean difference (WMD) = 3.55, 95% confidence interval (CI): 2.34–4.77, p &lt; 0.00001; rat model: WMD = 17.29, 95% CI: 5.75–28.82, p = 0.003; rabbit model: WMD = 19.29, 95% CI: 9.95–28.64, p &lt; 0.0001). Clinical studies also confirmed that EE could reduce healing time in hospital (WMD = −8.94, 95% CI: −17.75 to −0.14, p = 0.05).Conclusion: The results of this meta-analysis demonstrated the efficacy of EE on wound healing process. As a corollary, EE can be a useful natural product for wound healing drug development.Systematic Review Registration:https://www.crd.york.ac.uk/PROSPERO/display_record.php?RecordID=168400, identifier CRD42020168400.

scholarly journals Impact of extended lymphadenectomy on morbidity, mortality, recurrence and 5-year survival after gastrectomy for cancer: meta-analysis of randomized clinical trials

2008 ◽  
Vol 23 (6) ◽  
pp. 520-530 ◽  
Author(s):  
Suzana Angélica Silva Lustosa ◽  
Humberto Saconato ◽  
Álvaro Nagib Atallah ◽  
Gaspar de Jesus Lopes Filho ◽  
Delcio Matos
Keyword(s):  
Hospital Mortality ◽  
Recurrent Disease ◽  
Weighted Mean Difference ◽  
Meta Analysis ◽  
Mean Difference ◽  
Weighted Mean ◽  
D3 Lymphadenectomy ◽  
Statistical Heterogeneity ◽  
Significant Difference ◽  
Significant Statistical Heterogeneity

PURPOSE: To compare morbidity, mortality, recurrence and 5-year survival between D1 and D2 or D3 for treatment of gastric cancer. METHODS: Systematic review and meta-analysis of RCTs. Metaview in RevMan 4.2.8 for analysis; statistical heterogeneity by Cochran's Q test (P<0.1) and I² test (P>50%). Estimates of effect were calculated using random effects model. RESULTS: D2 or D3 was associated with higher in-hospital mortality, with RR = 2.13, p=0.0004, 95% CI, 1.40 to 3.25, I²=0%, P=0.63; overall morbidity showed higher incidence in D2 or D3, RR = 1.98, p<0.00001, 95% CI, 1.64 to 2.38, I² = 33.9%, P=0.20; operating time showed longer duration in D2 or D3, weighted mean difference of 1.05, p<0.00001, 95% CI, 0.71 to 1.38, I² = 78.7%, P=0.03, with significant statistical heterogeneity; reoperation showed higher rate in D2 or D3, with RR = 2.33, p<0.0001, 95% CI, 1.58 to 3.44, I² = 0%, P=0.99; hospital stay showed longer duration in the D2 or D3, with weighted mean difference of 4.72, p<0.00001, 95% CI, 3.80 to 5.65, I² = 89.9%, P<0.00001; recurrence was analyzed showed lower rate in D2 or D3, with RR = 0.89, p=0.02, 95% CI, 0.80 to 0.98, I² = 71.0%, P = 0.03, with significant statistical heterogeneity; mortality with recurrent disease showed higher incidence in D1, with RR = 0.88, p=0.04, 95% CI, 0.78 to 0.99, I² =51.8%, P=0.10; 5-year survival showed no significant difference, with RR = 1.05, p=0.40, 95% CI, 0.93 to 1.19, I² = 49.1% and P=0.12. CONCLUSIONS: D2 or D3 lymphadenectomy procedure is followed by higher overall morbidity and higher in-hospital mortality; D2 or D3 lymphadenectomy shows lower incidence of recurrence and lower mortality with recurrent disease, when analysed altogether with statistical heterogeneity; D2 or D3 lymphadenectomy has no significant impact on 5-year survival.

scholarly journals Diagnostic Value of sST2 in Cardiovascular Diseases: A Systematic Review and Meta-Analysis

2021 ◽  
Vol 8 ◽  
Author(s):  
Tianyi Zhang ◽  
Chengyang Xu ◽  
Rui Zhao ◽  
Zhipeng Cao
Keyword(s):  
Myocardial Infarction ◽  
Cardiac Troponin ◽  
Weighted Mean Difference ◽  
Meta Analysis ◽  
Diagnostic Value ◽  
Mean Difference ◽  
Diagnostic Biomarker ◽  
Healthy Individuals ◽  
Weighted Mean ◽  
Standard Mean Difference

Biomarkers such as B-type natriuretic peptide (BNP), N-terminal pro-BNP (NT-proBNP), cardiac troponin (cTn), and CK-MB contribute significantly to the diagnosis of cardiovascular disease (CVD). Recent studies have demonstrated that suppression of tumorigenicity 2 (ST2) is associated with CVD, but a meta-analysis of ST2 levels in different CVDs has yet to be conducted. Therefore, the present study aimed to investigate soluble ST2 (sST2) levels in patients with ischemic heart disease (IHD), myocardial infarction (MI), and heart failure (HF). A total of 1,425 studies were searched across four databases, of which 16 studies were included in the meta-analysis. The Newcastle–Ottawa Quality Assessment Scale (NOS) values of all 16 studies were ≥7. The meta-analysis results indicated that the sST2 level was not correlated with IHD (standard mean difference [SMD] = 0.58, 95% confidence interval [95% CI] = 0.00 to 1.16, p = 0.05) or MI (weighted mean difference [WMD] = 0.17, 95% CI = −0.22 to 0.55, p = 0.40) but was significantly associated with HF (WMD = 0.21, 95% CI = 0.04 to 0.38, p = 0.02; I2 = 99%, p &lt; 0.00001). sST2 levels did not differ significantly between patients with IHD or MI and healthy individuals; however, we believe that ST2 could be used as an auxiliary diagnostic biomarker of HF.

scholarly journals Spectrum and fine spectrum of generalized second order forward difference operator Δuvw2 $\Delta _{uvw}^2 $ on sequence space l1

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
B. L. Panigrahi ◽  
P. D. Srivastava
Keyword(s):  
Sequence Space ◽  
Difference Operator ◽  
Second Order ◽  
Fine Spectrum ◽  
Forward Difference

AbstractThe purpose of this paper is to determine spectrum and fine spectrum of newly introduced operator

scholarly journals Comparison of total and activity energy expenditure estimates from physical activity questionnaires and doubly labelled water: a systematic review and meta-analysis

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Mohammad Sharifzadeh ◽  
Minoo Bagheri ◽  
John R. Speakman ◽  
Kurosh Djafarian
Keyword(s):  
Physical Activity ◽  
Energy Expenditure ◽  
Weighted Mean Difference ◽  
Meta Analysis ◽  
Mean Difference ◽  
Weighted Mean ◽  
Doubly Labelled Water ◽  
Significant Difference ◽  
Activity Questionnaires ◽  
Activity Energy

Abstract Physical activity questionnaires (PAQ) could be suitable tools in free-living people for measures of physical activity, total and activity energy expenditure (TEE and AEE). This meta-analysis was performed to determine valid PAQ for estimating TEE and AEE using doubly labelled water (DLW). We identified data from relevant studies by searching Google Scholar, PubMed and Scopus databases. This revealed thirty-eight studies that had validated PAQ with DLW and reported the mean differences between PAQ and DLW measures of TEE (TEEDLW − TEEPAQ) and AEE (AEEDLW − AEEPAQ). We assessed seventy-eight PAQ consisting of fifty-nine PAQ that assessed TEE and thirty-five PAQ that examined AEE. There was no significant difference between TEEPAQ and TEEDLW with a weighted mean difference of –243·3 and a range of –841·4 to 354·6 kJ/d, and a significant weighted mean difference of AEEDLW – AEE PAQ 414·6 and a range of 78·7–750·5. To determine whether any PAQ was a valid tool for estimating TEE and AEE, we carried out a subgroup analysis by type of PAQ. Only Active-Q, administered in two seasons, and 3-d PA diaries were correlated with TEE by DLW at the population level; however, these two PAQ did not demonstrate an acceptable limit of agreement at individual level. For AEE, no PAQ was correlated with DLW either at the population or at the individual levels. Active-Q and 3-d PA diaries were identified as the only valid PAQ for TEE estimation. Further well-designed studies are needed to verify this result and identify additional valid PAQ.

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