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Natural Radioactivity and Dose Assessment for Brands of Chemical and Organic Fertilizers Used in Saudi Arabia  [PDF]
W. R. Alharbi
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.43047
Abstract:

The activity concentration of naturally occurring radionuclides 40K, 226Ra and 232Th have been measured in different brands of fertilizer samples in Saudi Arabia using sodium iodide gamma spectrometry. The results of measurements showed that the mean (ranges) of specific activities for 226Ra, 232Th and 40K activities in the nitrogen, phosphorus and potassium fertilizers are 64 (35.8 - 120.7), 17 (3.2 - 56.8) and 2453 (744.9 - 4227.1) Bq/kg, respectively. With respect to organic fertilizers under investigation, the average radioactivity of 226Ra, 232Th and 40K are 42, 10 and 333 BqKg

Intrinsic Location Parameter of a Diffusion Process
R. W. R. Darling
Mathematics , 1998,
Abstract: For nonlinear functions f of a random vector Y, E[f(Y)] and f(E[Y]) usually differ. Consequently the mathematical expectation of Y is not intrinsic: when we change coordinate systems, it is not invariant.This article is about a fundamental and hitherto neglected property of random vectors of the form Y = f(X(t)), where X(t) is the value at time t of a diffusion process X: namely that there exists a measure of location, called the "intrinsic location parameter" (ILP), which coincides with mathematical expectation only in special cases, and which is invariant under change of coordinate systems. The construction uses martingales with respect to the intrinsic geometry of diffusion processes, and the heat flow of harmonic mappings. We compute formulas which could be useful to statisticians, engineers, and others who use diffusion process models; these have immediate application, discussed in a separate article, to the construction of an intrinsic nonlinear analog to the Kalman Filter. We present here a numerical simulation of a nonlinear SDE, showing how well the ILP formula tracks the mean of the SDE for a Euclidean geometry.
Geometrically Intrinsic Nonlinear Recursive Filters I: Algorithms
R. W. R. Darling
Mathematics , 1998,
Abstract: The Geometrically Intrinsic Nonlinear Recursive Filter, or GI Filter, is designed to estimate an arbitrary continuous-time Markov diffusion process X subject to nonlinear discrete-time observations. The GI Filter is fundamentally different from the much-used Extended Kalman Filter (EKF), and its second-order variants, even in the simplest nonlinear case, in that: (i) It uses a quadratic function of a vector observation to update the state, instead of the linear function used by the EKF. (ii) It is based on deeper geometric principles, which make the GI Filter coordinate-invariant. This implies, for example, that if a linear system were subjected to a nonlinear transformation f of the state-space and analyzed using the GI Filter, the resulting state estimates and conditional variances would be the push-forward under f of the Kalman Filter estimates for the untransformed system - a property which is not shared by the EKF or its second-order variants. The noise covariance of X and the observation covariance themselves induce geometries on state space and observation space, respectively, and associated canonical connections. A sequel to this paper develops stochastic differential geometry results - based on "intrinsic location parameters", a notion derived from the heat flow of harmonic mappings - from which we derive the coordinate-free filter update formula. The present article presents the algorithm with reference to a specific example - the problem of tracking and intercepting a target, using sensors based on a moving missile. Computational experiments show that, when the observation function is highly nonlinear, there exist choices of the noise parameters at which the GI Filter significantly outperforms the EKF.
Geometrically Intrinsic Nonlinear Recursive Filters II: Foundations
R. W. R. Darling
Mathematics , 1998,
Abstract: This paper contains the technical foundations from stochastic differential geometry for the construction of geometrically intrinsic nonlinear recursive filters. A diffusion X on a manifold N is run for a time interval T, with a random initial condition. There is a single observation consisting of a nonlinear function of X(T), corrupted by noise, and with values in another manifold M. The noise covariance of X and the observation covariance themselves induce geometries on M and N, respectively. Using these geometries we compute approximate but coordinate-free formulas for the "best estimate" of X(T), given the observation, and its conditional variance. Calculations are based on use of Jacobi fields and of "intrinsic location parameters", a notion derived from the heat flow of harmonic mappings. When any nonlinearity is present, the resulting formulas are not the same as those for the continuous-discrete Extended Kalman Filter. A subsidiary result is a formula for computing approximately the "exponential barycenter" of a random variable S on a manifold, i.e. a point z such that the inverse image of S under the exponential map at z has mean zero in the tangent space at z.
Fluid Limits of Pure Jump Markov Processes: a Practical Guide
R. W. R. Darling
Mathematics , 2002,
Abstract: A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be used to build parsimonious models of large random or pseudo-random systems.
The Repeated Solicitation Model
R. W. R. Darling
Mathematics , 1998,
Abstract: This paper presents a probabilistic analysis of what we call the "repeated solicitation model". To give a specific context, suppose B is a direct marketing company with a list of S sales prospects. At epoch 1, B sends a solicitation to every prospect on the list, and elicits X(1) replies. The company deletes the respondents from the list, and at epoch 2 sends a solicitation to the other prospects, of whom X(2) respond, and so on. This continues until an epoch n such that X(n) = 0, which we call epoch T, and then B makes no further solicitations. We seek (a) the probability distribution of T; (b) the distribution of the total number of respondents; (c) the expected total number of solicitations. All three quantities are explicitly computed, assuming that (i) prospects' response times are independent, and (ii) S is Poisson distributed.
External Representations in the Teaching and Learning of Introductory Chemistry  [PDF]
James R. Cox, Bethany W. Jones
Creative Education (CE) , 2011, DOI: 10.4236/ce.2011.25067
Abstract: This manuscript describes the role that external representations, such as diagrams and sketches, can play in organizing and learning concepts presented in a one-semester chemistry course (general, organic and biochemistry) designed for nursing students. Although external representations are typically found in chemistry textbooks and instructor-drawn notes, students are usually not taught or prompted to use various types of external representations to promote learning. Representations created by an instructor and a student are discussed to highlight effective ways to foster student participation in creating various diagrams. In addition, a student provides a perspective on the educational value of creating external representations and the roles of visual thinking and creativity in learning introductory chemistry. Although the model for this approach has been an introductory chemistry course, this approach can be widely applied across disciplines.
A Case Report of Mesenteric Panniculitis and Primary Sjögren’s Syndrome  [PDF]
R. L. Batten, W. F. Ng
Open Journal of Rheumatology and Autoimmune Diseases (OJRA) , 2013, DOI: 10.4236/ojra.2013.34036
Abstract: Mesenteric Panniculitis is a benign fibro-inflammatory process involving adipose tissue of the mesentery. It is characterised by fat necrosis, chronic inflammation and fibrosis, causing thickening and shortening of the mesentery. Patients may present with localised abdominal pain, abdominal mass, intestinal obstruction and ischaemic colitis. We report a case of mesenteric panniculitis causing abdominal pain in a patient with active Primary Sjogren’s Syndrome. The rarity of this case makes it of interest. We review the current literature on mesenteric panniculitis and its association with connective tissue disease and inflammatory conditions. A 64-year-old Caucasian male presented in 1994 with dry mouth. A diagnosis of Primary Sjogren’s Syndrome (PSS) was made on salivary gland biopsy. In 2010 he presented with an exacerbation of his eye symptoms, muscle pain and fatigue. He complained of abdominal pain and night sweating, but denied any weight loss or change in bowel habit. There was no significant past medical history other than PSS. On examination he had a small right submandibular node and mild synovitis at the right proximal interphalangeal joint and carpometacarpal joint. Examination of the abdomen showed marked umbilical tenderness but no organomegally. Blood tests at this time showed an active inflammation: CRP of 61 (NR < 5 mg/L), ESR 39 (NR < 20 mm/s), strongly positive ENA Ro and La. IgG was elevated at 18.6 (NR 5.8-15.4), Complement was low at 0.17 (NR 0.18-0.6). An abdominal ultrasound scan demonstrated a 6 × 3 ×3 cmarea of diffuse homogenous fat encasing some mesenteric vessels in the area of focal tenderness. CT abdomen and pelvis showed oedematous mesenteric fat and lymph nodes in the jejunal small bowel mesentery, consistent with mesenteric panniculitis. Laparoscopic biopsy was discussed with the surgical team, but was felt not indicated as risk outweighed potential benefit. The patient was treated with a 9-week reducing course of oral steroids. His abdominal symptoms resolved although CT abdomen showed little improvement in mesenteric panniculitis. A review of the literature suggests that currently there is no standard treatment and management should be guided by
On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
W. W. Koczkodaj,R. Szwarc
Computer Science , 2013, DOI: 10.3233/FI-2014-1055
Abstract: We examine the notion of inconsistency in pairwise comparisons and propose an axiomatization which is independent of any method of approximation or the inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It has been proven that the eigenvalue-based inconsistency (proposed as a part of AHP) is incorrect.
Removal of Copper Ions from Acid Mine Drainage Wastewater Using Ion Exchange Technique: Factorial Design Analysis  [PDF]
R. W. Gaikwad, R. S. Sapkal, V. S. Sapkal
Journal of Water Resource and Protection (JWARP) , 2010, DOI: 10.4236/jwarp.2010.211117
Abstract: A factorial experimental design method was used to examine the “Cu2+” removal from acid mine drainage wastewater by ion exchange technique. Ion Exchange technique is preferred because of reduced sludge generation compared to conventional treatment techniques and better decontamination efficiency from highly diluted solutions. Factorial design of experiments is employed to study the effect of four factors pH (3, 5, and 6), flow rate (5, 10, 15 L/hr), resin bed height (20, 40 and 60 cm) and initial concentration of the metal (100, 150 and 200 mgl-1) at three levels. The efficiency of metal removal was determined after 100 min of treatment. Main effects and interaction effects of the four factors were analyzed using statistical techniques. A regression model was recommended and it was found to fit the experimental data very well. The results were analyzed statistically using the Student’s t-test, analysis of variance, F-test and lack of fit to define most important process variables affecting the percentage “Cu2+” removal. In this study , pH was thus found to be the most important variable.
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