Approximate solution for a class of hypersingular integral equations

AbstractA simple approximate method for solving a general hypersingular integral equation of the first kind with its kernel consisting of a hypersingular part and a regular part is developed here. The method is illustrated by considering some simple examples

Approximate solution of a class of singular integral equations of second kind

AbstractA simple method based on polynomial approximation of a function is employed to obtain approximate solution of a class of singular integral equations of the second kind. For a hypersingular integral equation of the second kind, this method avoids the complex function-theoretic method and produces the known exact solution to Prandtl's integral equation as a special case. For a particular singular integro-differential equation of the second kind, this also produces an approximate solution which compares favourably with numerical results obtained by various Galerkin methods. The convergence of the method for both the equations is also established

Proteomic and genetic approaches to identifying defence-related proteins in rice challenged with the fungal pathogen Rhizoctonia solani

Sheath blight, caused by the fungus Rhizoctonia solani, is a major disease of rice world-wide, but little is known about the host response to infection. The objective of this study was to identify proteins and DNA markers in resistant and susceptible rice associated with response to infection by R. solani. Replicated two-dimensional polyacrylamide gel electrophoresis experiments were conducted to detect proteins differentially expressed under inoculated and non-inoculated conditions. Tandem mass spectra analysis using electrospray ionization quadrupole-time of flight mass spectrometry (ESI Q-TOF MS) was carried out for protein identification with the NCBI non-redundant protein database. Seven proteins were increased after inoculation in both susceptible and resistant plants. Six of the seven proteins were identified with presumed antifungal, photosynthetic and proteolytic activities. An additional 14 proteins were detected in the response of the resistant line. Eleven of the 14 proteins were identified with presumed functions relating to antifungal activity, signal transduction, energy metabolism, photosynthesis, molecular chaperone, proteolysis and antioxidation. The induction of 3-β- hydroxysteroid dehydrogenase/isomerase was detected for the first time in resistant rice plants after pathogen challenge, suggesting a defensive role of this enzyme in rice against attack by R. solani. The chromosomal locations of four induced proteins were found to be in close physical proximity to genetic markers for sheath blight resistance in two genetic mapping populations. The proteomic and genetic results from this study indicate a complex response of rice to challenge by R. solani that involves simultaneous induction of proteins from multiple defence pathways. © 2006 Blackwell Publishing Ltd

The Influence of Number and Timing of Pregnancies on Breast Cancer Risk for Women With BRCA1 or BRCA2 Mutations

Background: Full-term pregnancy (FTP) is associated with a reduced breast cancer (BC) risk over time, but women are at increased BC risk in the immediate years following an FTP. No large prospective studies, however, have examined whether the number and timing of pregnancies are associated with BC risk for BRCA1 and BRCA2 mutation carriers. Methods: Using weighted and time-varying Cox proportional hazards models, we investigated whether reproductive events are associated with BC risk for mutation carriers using a retrospective cohort (5707 BRCA1 and 3525 BRCA2 mutation carriers) and a prospective cohort (2276 BRCA1 and 1610 BRCA2 mutation carriers), separately for each cohort and the combined prospective and retrospective cohort. Results: For BRCA1 mutation carriers, there was no overall association with parity compared with nulliparity (combined hazard ratio [HRc] ¼ 0.99, 95% confidence interval [CI] ¼ 0.83 to 1.18). Relative to being uniparous, an increased number of FTPs was associated with decreased BC risk (HRc¼ 0.79, 95% CI ¼ 0.69 to 0.91; HRc¼ 0.70, 95% CI ¼ 0.59 to 0.82; HRc¼ 0.50, 95% CI ¼ 0.40 to 0.63, for 2, 3, and 4 FTPs, respectively, Ptrend < .0001) and increasing duration of breastfeeding was associated with decreased BC risk (combined cohort Ptrend ¼ .0003). Relative to being nulliparous, uniparous BRCA1 mutation carriers were at increased BC risk in the prospective analysis (prospective hazard ration [HRp] ¼ 1.69, 95% CI ¼ 1.09 to 2.62). For BRCA2 mutation carriers, being parous was associated with a 30% increase in BC risk (HRc ¼ 1.33, 95% CI ¼ 1.05 to 1.69), and there was no apparent decrease in risk associated with multiparity except for having at least 4 FTPs vs. 1 FTP (HRc¼ 0.72, 95% CI ¼ 0.54 to 0.98). Conclusions: These findings suggest differential associations with parity between BRCA1 and BRCA2 mutation carriers with higher risk for uniparous BRCA1 carriers and parous BRCA2 carriers

Oral contraceptive use and ovarian cancer risk for BRCA1/2 mutation carriers: an international cohort study

International audienceBackground: Ovarian cancer risk in BRCA1 and BRCA2 mutation carriers has been shown to decrease with longer duration of oral contraceptive use. Although the effects of using oral contraceptives in the general population are well established (approximately 50% risk reduction in ovarian cancer), the estimated risk reduction in mutation carriers is much less precise because of potential bias and small sample sizes. In addition, only a few studies on oral contraceptive use have examined the associations of duration of use, time since last use, starting age, and calendar year of start with risk of ovarian cancer.Objective: This study aimed to investigate in more detail the associations of various characteristics of oral contraceptive use and risk of ovarian cancer, to provide healthcare providers and carriers with better risk estimates.Study design: In this international retrospective study, ovarian cancer risk associations were assessed using oral contraceptives data on 3989 BRCA1 and 2445 BRCA2 mutation carriers. Age-dependent-weighted Cox regression analyses were stratified by study and birth cohort and included breast cancer diagnosis as a covariate. To minimize survival bias, analyses were left truncated at 5 years before baseline questionnaire. Separate analyses were conducted for each aspect of oral contraceptive use and in a multivariate analysis, including all these aspects. In addition, the analysis of duration of oral contraceptive use was stratified by recency of use.Results: Oral contraceptives were less often used by mutation carriers who were diagnosed with ovarian cancer (ever use: 58.6% for BRCA1 and 53.5% BRCA2) than by unaffected carriers (ever use: 88.9% for BRCA1 and 80.7% for BRCA2). The median duration of use was 7 years for both BRCA1 and BRCA2 carriers who developed ovarian cancer and 9 and 8 years for unaffected BRCA1 and BRCA2 carriers with ovarian cancer, respectively. For BRCA1 mutation carriers, univariate analyses have shown that both a longer duration of oral contraceptive use and more recent oral contraceptive use were associated with a reduction in the risk of ovarian cancer. However, in multivariate analyses, including duration of use, age at first use, and time since last use, duration of oral contraceptive use proved to be the prominent protective factor (compared with 10 years [hazard ratio, 0.37; 95% confidence interval, 0.19-0.73]; Ptrend=.008). The inverse association between duration of use and ovarian cancer risk persisted for more than 15 years (duration of ≥10 years; BRCA1 15 years since last use [hazard ratio, 0.56; 95% confidence interval, 0.18-0.59]). Univariate results for BRCA2 mutation carriers were similar but were inconclusive because of limited sample size.Conclusion: For BRCA1 mutation carriers, longer duration of oral contraceptive use is associated with a greater reduction in ovarian cancer risk, and the protection is long term