Integrability Formulas. Part II

In this article, we give several differentiation and integrability formulas of special and composite functions including trigonometric function, and polynomial function.Li Bo - Qingdao University of Science and Technology, ChinaMa Na - Qingdao University of Science and Technology, ChinaLiang Xiquan - Qingdao University of Science and Technology, ChinaCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Jarosław Kotowicz. The limit of a real function at infinity. Formalized Mathematics, 2(1):17-28, 1991.Xiquan Liang and Bing Xie. Inverse trigonometric functions arctan and arccot. Formalized Mathematics, 16(2):147-158, 2008, doi:10.2478/v10037-008-0021-3.Konrad Raczkowski. Integer and rational exponents. Formalized Mathematics, 2(1):125-130, 1991.Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998

Integrability Formulas. Part III

In this article, we give several differentiation and integrability formulas of composite trigonometric function.Li Bo - Qingdao University of Science and Technology, ChinaMa Na - Qingdao University of Science and Technology, ChinaCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Noboru Endou and Artur Korniłowicz. The definition of the Riemann definite integral and some related lemmas. Formalized Mathematics, 8(1):93-102, 1999.Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.Jarosław Kotowicz. Partial functions from a domain to the set of real numbers. Formalized Mathematics, 1(4):703-709, 1990.Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990.Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.Yasunari Shidama. The Taylor expansions. Formalized Mathematics, 12(2):195-200, 2004.Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Peng Wang and Bo Li. Several differentiation formulas of special functions. Part V. Formalized Mathematics, 15(3):73-79, 2007, doi:10.2478/v10037-007-0009-4.Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998

Antagonistic potential of fungi of the order Capnodiales causing sooty blotch and fly speck on apples

RATIONALE: Critical illness may be associated with increased bone turnover and loss of bone mineral density (BMD). Prospective evidence describing long-term changes in BMD after critical illness is needed to further define this relationship. OBJECTIVES: To measure the change in BMD and bone turnover markers (BTMs) in subjects 1 year after critical illness compared with population-based control subjects. METHODS: We studied adult patients admitted to a tertiary intensive care unit (ICU) who required mechanical ventilation for at least 24 hours. We measured clinical characteristics, BTMs, and BMD during admission and 1 year after ICU discharge. We compared change in BMD to age- and sex-matched control subjects from the Geelong Osteoporosis Study. MEASUREMENTS AND MAIN RESULTS: Sixty-six patients completed BMD testing. BMD decreased significantly in the year after critical illness at both femoral neck and anterior-posterior spine sites. The annual decrease was significantly greater in the ICU cohort compared with matched control subjects (anterior-posterior spine, -1.59%; 95% confidence interval, -2.18 to -1.01; P < 0.001; femoral neck, -1.20%; 95% confidence interval, -1.69 to -0.70; P < 0.001). There was a significant increase in 10-year fracture risk for major fractures (4.85 ± 5.25 vs. 5.50 ± 5.52; P < 0.001) and hip fractures (1.57 ± 2.40 vs. 1.79 ± 2.69; P = 0.001). The pattern of bone resorption markers was consistent with accelerated bone turnover. CONCLUSIONS: Critically ill individuals experience a significantly greater decrease in BMD in the year after admission compared with population-based control subjects. Their bone turnover biomarker pattern is consistent with an increased rate of bone loss

Reasons for referral to bone densitometry in men and women aged 20-49 years: population-based data.

INTRODUCTION: Osteoporosis poses a significant public health problem for ageing Australians. However, approximately 25 % of Australian adults aged 20-49 years have osteopenia, a precursor condition to osteoporosis. Despite this, little is known about bone density testing in this age group. METHODS: Reasons for referral to dual energy X-ray absorptiometry (DXA) were examined in 2,264 patients aged 20-49 years, referred in 2001-2010 to the Geelong Bone Densitometry Service, Geelong Hospital, Victoria. Referral reasons were determined from clinical indication codes derived from patient records. Age, sex and bone mineral density (BMD) T scores were ascertained for each patient. RESULTS: The most common reason for referral for women reflected glucocorticoid use, and for men reflected fracture. Compared to women, men were more likely to have been referred because of minimal trauma fracture or low BMD (41.7 versus 27.1 %, p < 0.001). No further differences were identified between the sexes, with similar numbers of referral observed for secondary osteoporosis, and monitoring of drug therapy. At the spine, and for all indications, men had a significantly greater BMD deficit compared to women (all p ≤ 0.002). After age adjustment, men who were tested due to fracture or glucocorticoid reasons had significantly greater BMD at the total hip (p ≤ 0.03). No further associations were seen after age adjustment between referral reason and BMD. CONCLUSIONS: Our study presents the first data examining reasons for referral to DXA among Australians aged 20-49 years. Understanding health service utilisation regarding bone health in young adults is fundamental to understanding future risk, informing effective public health messages and raising awareness of osteoporosis

Refractory hyperparathyroidism with a T3 bony lesion-differential diagnoses

We report a case of severe hyperparathyroidism complicated by osteitis fibrosa cystica in an 83-year-old man post-myocardial infarction. The lesions were evident on magnetic resonance imaging only. A diagnosis of parathyroid carcinoma was considered due to clinical appearance of the parathyroid intraoperatively and the presence of an invasive T3 lesion mimicking metastatic disease. Differentiating parathyroid carcinoma from the benign causes at presentation can be difficult due to overlapping clinical, biochemical, radiological and histological features. The presence of bony lesions increases the diagnostic complexity of the case and demonstrates the challenges involved in the management of this disorder

Acute delirium in the setting of primary hypothyroidism: the role of thyroid hormone replacement therapy.

Psychiatric illness, mostly mania and psychosis, are reported to occur after rapid normalization of thyroid function in patients with primary hypothyroidism. It is generally believed that the gradual restoration of thyroid function may reduce the risk of psychiatric complications. This case report describes the occurrence of acute delirium in a 67-year-old man with primary hypothyroidism shortly after the initiation of thyroid hormone replacement. The use of low-dose thyroxine initially and persistent severe biochemical hypothyroidism on presentation with psychiatric symptoms illustrate that psychiatric illness can still occur despite unaggressive thyroid hormone replacement. A temporal relationship with the initiation of thyroxine and rapid recovery of mental state over 1 to 2 weeks differentiate this condition from hypothyroidism-related psychopathology, which tends to have a more prolonged course

All-Cause Mortality Risk in Australian Women with Impaired Fasting Glucose and Diabetes

AIMS: Impaired fasting glucose (IFG) and diabetes are increasing in prevalence worldwide and lead to serious health problems. The aim of this longitudinal study was to investigate the association between impaired fasting glucose or diabetes and mortality over a 10-year period in Australian women. METHODS: This study included 1167 women (ages 20-94 yr) enrolled in the Geelong Osteoporosis Study. Hazard ratios for all-cause mortality in diabetes, IFG, and normoglycaemia were calculated using a Cox proportional hazards model. RESULTS: Women with diabetes were older and had higher measures of adiposity, LDL cholesterol, and triglycerides compared to the IFG and normoglycaemia groups (all p < 0.001). Mortality rate was greater in women with diabetes compared to both the IFG and normoglycaemia groups (HR 1.8; 95% CI 1.3-2.7). Mortality was not different in women with IFG compared to those with normoglycaemia (HR 1.0; 95% CI 0.7-1.4). CONCLUSIONS: This study reports an association between diabetes and all-cause mortality. However, no association was detected between IFG and all-cause mortality. We also showed that mortality in Australian women with diabetes continues to be elevated and women with IFG are a valuable target for prevention of premature mortality associated with diabetes

FRAX (Aus) and falls risk: Association in men and women

Purpose: The WHO fracture risk prediction tool (FRAX&reg;) utilises clinical risk factors to estimate the probability of fracture over a 10-year period. Although falls increase fracture risk, they have not been incorporated into FRAX. It is currently unclear if FRAX captures falls risk and whether addition of falls would improve fracture prediction. We aimed to investigate the association of falls risk and Australian-specific FRAX. Methods: Clinical risk factors were documented for 735 men and 602 women (age 40-90. yr) assessed at follow-up (2006-2010 and 2000-2003, respectively) of the Geelong Osteoporosis Study. FRAX scores with and without BMD were calculated. A falls risk score was determined at the time of BMD assessment and self-reported incident falls were documented from questionnaires returned one year later. Multivariable analyses were performed to determine: (i) cross-sectional association between FRAX scores and falls risk score (Elderly Falls Screening Test, EFST) and (ii) prospective relationship between FRAX and time to a fall. Results: There was an association between FRAX (hip with BMD) and EFST scores (. &beta;=. 0.07, p&lt;. 0.001). After adjustment for sex and age, the relationship became non-significant (. &beta;=. 0.00, p=. 0.79). The risk of incident falls increased with increasing FRAX (hip with BMD) score (unadjusted HR 1.04, 95% CI 1.02, 1.07). After adjustment for age and sex, the relationship became non-significant (1.01, 95% CI 0.97, 1.05). Conclusions: There is a weak positive correlation between FRAX and falls risk score, that is likely explained by the inclusion of age and sex in the FRAX model. These data suggest that FRAX score may not be a robust surrogate for falls risk and that inclusion of falls in fracture risk assessment should be further explored