Reflected backward stochastic differential equations in an orthant

We consider RBSDE in an orthant with oblique reflection and with time and space dependent coefficients, viz. Z(t)=ε+∫tTb(s, Z(s))ds+∫tTR(s, Z(s))dY(s)-∫tT‹U(s), dB(s)›with Zi(·)≥0, Yi(·) nondecreasing and Yi(·) increasing only when Zi(·) =0, 1 ≤i ≤d. Existence of a unique solution is established under Lipschitz continuity of b, R and a uniform spectral radius condition onR. On the way we also prove a result concerning the variational distance between the 'pushing parts' of solutions of auxiliary one-dimensional problem

Large deviations: an introduction to 2007 Abel prize

2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan

On a stochastic model in insurance

Basic aspects of the classical Cramer-Lundberg insurance model are described

Hitting a boundary point by diffusions in the closed half space

It is proved that a nondegenerate diffusion process in the closed half space , where d >= 2, with Wentzell's boundary conditions does not hit any specified point on the boundary

On the gauge for the Neumann problem in the half space

We consider the gauge function G for the Neumann problem for 1/2Δ+q in the half space D = {(α, x) ∈ Rd : α > 0}, where q is independent of α and is periodic in x. It is shown that if G ≠ ∞, then G is a bounded continuous function on Cl(D). If H(x) = \int_0^{\infty }G(\alpha ,x)d\alpha ≠\∞ 8, it is shown that the corresponding Feynman-Kac semi-group decays exponentially

Palmar Dermatoglyphics in Oral Leukoplakia and Oral Squamous Cell Carcinoma

This study deals with the evaluation of difference in Palmar dermatoglyphics of Oral Leukoplakia, Oral Squamous cell carcinoma and control group. This study was conducted between April 2010 to May 2011 in the department of Oral Medicine and Radiology of Ragas Dental College and Hospital, Dr. Rai Memorial Medical and Cancer Centre, Chennai. A case control study was conducted in which 90 subjects were selected. The study subjects were categorized into three groups: Group I consist of 30 healthy individual with the habit of smoking but no evident lesions; Group II, 30 patients suffering from Oral leukoplakia; Group III, 30 patients suffering from oral cancer. Patients only with the habit of smoking were included in the study, in control group smoking tobacco of any form; more than 10 numbers for more than 10 years were included in the study. Individuals with the habit of chewing and with the habit of both smoking and chewing and individuals with dermatological diseases or disorders or syndromes which affects the palmar region were excluded from the study. The patients were made to sit comfortably on a dental chair. Sterile hand gloves were used during examination of the patient. Clinical diagnosis was made and patients who showed characteristic features of Leukoplakia, Oral Cancer and control group were prepared for sample collection. Subjects were asked to wash their hands with soap water, so as to remove any oil or dirt. The glass platen of the scanner is cleaned thoroughly to remove the dust. Then the patient was asked to place the right hand on the top of the glass platen and instruction given to the patient not to move the hand or not to press the hand hardly against the glass platen. The image is previewed in the laptop screen using the scan Gear starter software then the image of the hand was scanned at 300dpi. The same procedure was repeated for the left hand and the thumb fingers then the images were stored in the laptop. The finger and palm prints were analysed qualitatively and quantitatively using Photoshop 8.0 software. The qualitative analysis done include, finger print patterns and palmar patterns. The quantitative analysis done include, total finger ridge count, ab count and atd angles. 1. In the present study all the 90 individuals are males (100%). As per the inclusion criteria only persons with smoking habits were included in the study. Hence the study result shows that the females with the habit of smoking are nil. 2. The age of the subjects included in the study ranges between 35-70 years. Among the 30 in control group, 2(6.7%) were less than 40 years, 8(26.6%%) were between 41-50 yrs, 14(46.6%) were between 51-60 years and 6(20.1%) were above 61 years. Among the 30 in oral leukoplakia group, 4(13.3%) were between 41-50 years, 18(60%) were between 51-60, and 8(26.7%) were above60 years. Among the 30 in oral cancer group, 1(3.3%) was between 41-50 years, 20(66.7%) were between 51-60 years, 9(30%) were above 60 years. The p value is ≤0.018 which is statistically significant. This shows the positive correlation between the age and the occurrence of disease. 3. The distribution of habits was grouped as smoking only and smoking plus alcohol consumption. In controls, 30% had the habit of only smoking and 70% had the habit of smoking plus alcohol consumption. In oral leukoplakia patients, 10% had the habit of only smoking and 90% had the habit of smoking plus alcohol consumption. In OSCC patients, 6.6% had the habit of only smoking and 93.4% had the habit of smoking plus alcohol consumption. The p value is ≤0.026 which is significant. This shows a positive correlation between alcohol usage and the occurrence of disease. 4. In our study when arches were compared between the three groups, controls had less frequency of arches (2.3%) when compared to oral leukoplakia patients (6.0%) and OSCC patients (5.6%). When loops were compared controls had less frequency of loops (27.3%) when compared to oral leukoplakia patients (58.6%) and OSCC patients (61.7%). When whorls were compared controls had increased frequency of whorls (27.3%) when compared to oral leukoplakia patients (58.6%) and OSCC patients (61.7%). The p value was ≤0.001 which is highly significant. 5. When the hypothenar pattern in the right hand was compared 24(80%) in control, 23(76.6%) in oral leukoplakia patients and 22(73.3%) in OSCC patients had pattern. When hypothenar pattern in the left hand was compared 23 (76.6%) in control, 25(83.3%) in oral leukoplakia patients and 25(83.3%) in OSCC patients and had pattern. The p value is ≤0.912 which is insignificant. 6. When the thenar I1 pattern in the right hand was compared 25(83.3%) in control, 23(76.6%) in oral leukoplakia patients and 25(83.3%) in OSCC patients had pattern. When thenar I1 pattern in the left hand was compared 26(86.6%) in control, 27(90%) in oral leukoplakia patients and 26 (86.6%) in OSCC patients had pattern. The p value is ≤0.993 which is insignificant. 7. When the thenar I2 pattern in the right hand was compared 13(43.3%) in control, 14(46.6%) in oral leukoplakia patients and 13(43.3%) in OSCC patients had pattern. When thenar I2 pattern in the left hand was compared 10(33.3%) in control, 11(36.6%) in oral leukoplakia patients and 10(36.6%) in OSCC patients had pattern. The p value is ≤0.985 which is insignificant. 8. When thenar I3 pattern in the right hand was compared 11(36.6%) in control, 8(26.6%) in oral leukoplakia patients and 8(26.6%) in OSCC patients had pattern. When thenar I3 pattern in the left hand was compared 10(33.3%) in control, 9(30%) in oral leukoplakia patients and 7(23.3%) in OSCC patients had pattern. The p value is ≤0.926 which is insignificant. 9. When the thenar I4 pattern in the right hand was compared 9(30%) in control, 13(43.3%) in oral leukoplakia patients and 14(46.6%) in OSCC patients had pattern. When thenar I4 pattern in the left hand was compared 13(43.3%) in control, 13(43.3%) in oral leukoplakia patients and 13 (43.3%) in OSCC patients had pattern. The p value is ≤0.724 which is insignificant. 10. In our study no significant difference observed when comparing the total finger ridge count between the groups. In controls the mean value was 168.7 and standard deviation was 35.36. In oral leukoplakia patients the mean value was 158.87 and standard deviation was 39.18. In OSCC patients the mean value was 165.7 and standard deviation was 37.95. The p value is ≤0.457 which is insignificant. 11. In our study there is no significant difference observed when comparing the ab count on right hand. In controls the mean value was 39.27 and standard deviation was 6.198. In oral leukoplakia patients the mean value was 39.10 and standard deviation was 5.195. In OSCC patients the mean value was 37.43 and standard deviation was 5.811. The p value is ≤0.397 which is insignificant. 12. There was no significant difference observed when comparing the ab count of left hand in all the three groups. In controls the mean value was 40.37 and standard deviation was 6.76. In oral leukoplakia patients the mean value was 39.67 and standard deviation was 4.97. In OSCC patients the mean value was 37.47 and standard deviation was 5.12. The p value is ≤0.121 which is insignificant. 13. In our study the atd angle of right hand is decreased in oral leukoplakia and OSCC patients when compared to controls. In controls the mean value was 40.53 and standard deviation was 3.026. In oral leukoplakia patients the mean value was 35.73 and standard deviation was 4.093. In OSCC patients the mean value was 34.53 and standard deviation was 2.063. The p value is 0.000 which is highly significant. The p value between controls and oral leukoplakia patients is 0.000 which is highly significant. The p value between controls and OSCC patients is 0.000 which is highly significant. The p value between oral leukoplakia patients and OSCC patients is ≤0.312 which is insignificant. 14. In our study the atd angle of left hand is decreased in oral leukoplakia and OSCC patients when compared to controls. In controls the mean value was 41.03 and standard deviation was 3.079. In oral leukoplakia patients the mean value was 36.57 and standard deviation was 3.971. In OSCC patients the mean value was 34.40 and standard deviation was 2.111. The p value is ≤0.001 which is highly significant. The p value between controls and oral leukoplakia patients is ≤0.001 which is highly significant. The p value between controls and OSCC patients is ≤0.001 which is highly significant. The p value between oral leukoplakia patients and group III is ≤0.025 which is significant. Thus there is an increased frequency of arches and loops in oral leukoplakia and OSCC patients when compared with controls. In case of controls whorl pattern is predominant. Decreased atd angle in case of oral leukoplakia and OSCC patients when compared with controls. The palmar pattern will not change after birth. This shows the genetic susceptibility in persons who develops oral leukoplakia and OSCC. Using these parameters, the persons has the habit of smoking and similar pattern can be identified at the earliest and preventive measures can be instituted in the susceptible individuals

Reliance on Direct and Mediated Contact and Public Policies Supporting Outgroup Harm

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/133624/1/jcom12234.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/133624/2/jcom12234_am.pd

Reflecting diffusions

Probabilistic models of diffusion processes with 'reflecting boundary conditions' are discussed; the domains considered can be nonsmooth