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Fraction frenzy : fractions and decimals
\"Introduces the reader to fractions and decimals.\"-- Provided by publisher.
Book
Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation
There are two main interrelated goals of this paper. Firstly we investigate the sums
eBook
Meanings of savarṇana in Indian Arithmetic
In Indian mathematical texts the term savarnana \"reduction to the same color\" is usually found in the context of calculation for fractions. A number of explanations for the term have been offered in previous studies, but they slightly differ from each other. The Trišatībhāsva is an anonymous commentary on Srīdhara's Trišatī. In the present paper, I survey the meanings of savarnana in each text and the usage of it in the Trišatībhāsva.
Journal Article
Piece=part=portion : fractions=decimals=percents
Explains how in the language of mathematics, fractions, decimals and percents are three different ways of describing the same parts of things.
Book
The correlation of left atrial diameter with preserved ejection fraction, reduced ejection fraction, and mid‐range ejection fraction
Background In patients with heart failure, left atrial remodeling often occurs to varying degrees. Left atrial enlargement has been proved to be an important predictor of cardiovascular‐related adverse events. However, the relationship between left atrial diameter (LAD) with heart failure (HF) with preserved ejection fraction (HFpEF), reduced ejection fraction (HFrEF) and mid‐range ejection fraction (HFmrEF) remains unclear. Hypothesis We want to explore the correlation between left atrial diameter and HFpEF, HFmrEF, and HFrEF. Methods A total of 210 patients with heart failure who underwent hospitalization in Ningbo Medical Center Lihuili Hospital, Zhejiang, China, from January 1, 2020, to June 31, 2021, were reviewed. The basic demographic characteristics, blood test, and the related indexes of echocardiography of the subjects were collected and analyzed. Results There is a significant difference between HFpEF and HFrEF group in LAD (p = .007), and LAD is negatively correlated with left ventricular ejection fraction (LVEF) (p = .002, r = −.209). Conclusion LAD is negatively correlated with LVEF, which may predict the prevalence of HFrEF. We studied the data of 210 individuals with heart failure. There is a significant difference between HFpEF and HFrEF groups in LAD (p = .007). And LAD is negatively correlated with LVEF (p = .002, r = −.209), which may predict the prevalence of HFrEF.
Journal Article
Ready for fractions and decimals
\"Learn the basic fundamentals of adding, subtracting, multiplying and dividing using fractions and decimals\"--Provided by publisher.
Book
2 Definition of clinical stability following management of heart failure deterioration is suboptimal and benefits from focused echo evaluation
BackgroundHeart Failure (HF) decompensation is increasingly being managed in the outpatient setting. Following stabilisation, recurrent deterioration is frequently observed, presenting a challenge to physicians as accurate definition of clinical status is limited by the imprecise nature of clinical assessment. Therefore, the question arises as to whether clinical stability reflects true stability in resolved outpatient HF decompensation (HFD).AimsTo assess the clinical value of focused Doppler-Echocardiography (ECHO) in addition to clinical evaluation in defining stability following outpatient decompensation.MethodsThis is an interim analysis of an ongoing single-centre, observational study including all patients diagnosed with HFD in our HF clinic from December 2023-May 2025, defined as:A. ≥1 HF symptom or physical sign and ≥1 other feature of HFDORB. Patients not meeting these criteria but deemed to have HFD on the discretion of the treating physician. Both definitions require escalation in diuretic therapy.Upon stabilisation, ECHO analysis of volume status is carried out and assessed with persistent pressure/volume overload defined as an indirect measure of left ventricular filling pressure E/E’ ≥ 13 ± IVC respiratory variation < 50% (figure 1).Results248 patients are included in this study, of which 191 (77%) have been stabilised (table 1). ECHO assessment was completed in 137/191 and the following categories have been identified;A. Normal IVC and E/E’; 69/137(50%)B. Abnormal IVC/Normal E/E’; 39/137(29%)C. Normal IVC and elevated E/E’; 16/137(12%)D. Abnormal IVC and elevated E/E’; 13/137(9%ConclusionDetermination of clinical status post stabilisation is limited by the lack of sensitivity of clinical evaluation. The data reflects evidence of residual sub-clinical pressure/volume overload on ECHO, likely contributing to the risk of recurrence. ECHO analysis of volume status should be considered as a component of assessment in the evaluation of stability following HF decompensation.Abstract 2 Figure 1Breakdown of doppler-echocardiographic analysis of volume assessment upon stabilisation following outpatient heart failure decompensation. IVC = inferior vena cava; ECHO = doppler-echocardiographic[Image Omitted. See PDF.]Abstract 2 Table 1Selected baseline characteristics of patients. Values are reported as mean (S.D) or n (%) as appropriate. HFpEF = heart failure preserved ejection fraction; HFrEF = heart failure reduced ejection fraction; NT-proBNP HFD = NT-proBNP at the time of diagnosis of decompensated heart failure; NT-proBNP STABLE = NT-proBNP following resolved HFD when deemed stable[Image Omitted. See PDF.]
Journal Article
6-010 AI-driven global longitudinal strain and long-axis ejection fraction by cardiac MRI provide a better assessment to serially monitor heart function compared to manually derived short axis EF in breast cancer patients on trastuzumab
IntroductionTrastuzumab is associated with cardiotoxicity, necessitating interval cardiac monitoring. Our centre utilises cardiac magnetic resonance (CMR) measured ejection fraction (EF) for serial heart function assessment. This pilot study evaluated the accuracy and reliability of an AI-powered method using Global Longitudinal Strain (GLS) and long-axis EF (LA EF) compared to conventional volume-derived EF (SA EF) from CMR in patients undergoing Trastuzumab treatment for breast cancer.MethodsWe retrospectively analysed CMR imaging of five patients who had serial scans as per protocol between 2021–2024. AI-assisted software (Q Mass) generated GLS and LA EF from three long-axis views (4-chamber, 3-chamber, and 2-chamber), which were compared to SA EF derived manually from CMR, the gold standard for clinical decisions.ResultsFive patients underwent 34 scans during the monitoring period. Bland-Altman analysis showed a linear regression with no significant proportional bias between SA EF and LA EF (p = 0.377). GLS and SA EF demonstrated a strong inverse correlation (Spearman coefficient = 0.77, p < 0.0001) with a worsening GLS (i.e. becoming less negative) corresponding to a lower EF. ROC analysis indicated that GLS had a moderate ability to detect SA EF < 50% (AUC = 0.667).ConclusionEF derived by LA EF and SA EF methods showed consistent differences, supporting the reliability of AI-generated LA EF for serial LV function assessment. AI-based LA EF provides a rapid and reproducible monitoring method, reducing interobserver variability. While GLS and EF are strongly correlated, GLS shows moderate predictive ability for EF decline below 50%. Further studies are warranted to enhance its clinical utility.Conflict of InterestNone
Journal Article