On Products and Line Graphs of Signed Graphs, their Eigenvalues and Energy

In this article we examine the adjacency and Laplacian matrices and their eigenvalues and energies of the general product (non-complete extended $p$-sum, or NEPS) of signed graphs. We express the adjacency matrix of the product in terms of the Kronecker matrix product and the eigenvalues and energy of the product in terms of those of the factor signed graphs. For the Cartesian product we characterize balance and compute expressions for the Laplacian eigenvalues and Laplacian energy. We give exact results for those signed planar, cylindrical and toroidal grids which are Cartesian products of signed paths and cycles. We also treat the eigenvalues and energy of the line graphs of signed graphs, and the Laplacian eigenvalues and Laplacian energy in the regular case, with application to the line graphs of signed grids that are Cartesian products and to the line graphs of all-positive and all-negative complete graphs.Comment: 30 page

Validity of very short answer versus single best answer questions for undergraduate assessment

Background Single Best Answer (SBA) questions are widely used in undergraduate and postgraduate medical examinations. Selection of the correct answer in SBA questions may be subject to cueing and therefore might not test the student’s knowledge. In contrast to this artificial construct, doctors are ultimately required to perform in a real-life setting that does not offer a list of choices. This professional competence can be tested using Short Answer Questions (SAQs), where the student writes the correct answer without prompting from the question. However, SAQs cannot easily be machine marked and are therefore not feasible as an instrument for testing a representative sample of the curriculum for a large number of candidates. We hypothesised that a novel assessment instrument consisting of very short answer (VSA) questions is a superior test of knowledge than assessment by SBA. Methods We conducted a prospective pilot study on one cohort of 266 medical students sitting a formative examination. All students were assessed by both a novel assessment instrument consisting of VSAs and by SBA questions. Both instruments tested the same knowledge base. Using the filter function of Microsoft Excel, the range of answers provided for each VSA question was reviewed and correct answers accepted in less than two minutes. Examination results were compared between the two methods of assessment. Results Students scored more highly in all fifteen SBA questions than in the VSA question format, despite both examinations requiring the same knowledge base. Conclusions Valid assessment of undergraduate and postgraduate knowledge can be improved by the use of VSA questions. Such an approach will test nascent physician ability rather than ability to pass exams

Measurement of radon gas concentration in water and soil samples in AL-Najaf governorate by using nuclear track detector (CR-39)

The radon gas concentration in environmental samples soil and water of selected regions in Al-Najaf governorate was measured by using alpha-emitters registrations which are emitted form radon gas in (CR-39) nuclear track detector. The first part is concerned with the determination of radon gas concentration in soil samples, results of measurements indicate that the highest average radon concentration in soil samples was found in (Al-Moalmen) region which was (100.0±7.0 Bq/m3), while the lowest average radon concentration was found in (Al-Askary) region which was (38.5±4.7 Bq/m3), with an average value of (64.23±14.9 Bq/m3) ,the results show that the radon gas concentrations in soil is below the allowed limit from (ICRP) agency which is (200 Bq/m3), while the radon exhalation rate (RER) ranged from (35.23-91.52 µBq/m2h), and average value which was (58.77±13.6 µBq/m2h). The second part is concerned with the determination of radon gas concentration in samples of tap water obtained from networks in dwellings in Al-Najaf governorate, the results indicate that the highest average radon concentration in water samples was found in (Meassan) region which was (0.59±0.08 Bq/L), while the lowest average radon concentration was found in (Al-Jamhorah) region which was (0.16±0.04 Bq/L), with an average value of (0.36±0.1 Bq/L), the present results show that the radon gas concentrations in tap water is below the allowed limit from (ICRP) agency which is (0.5994 Bq/L), while the radon exhalation rate (RER) ranged from (2.15-0.58 ?Sv/y), and average value which was (1.28±0.31 ?Sv/y)

Transpiration cooling of a heat generating porous plate

This investigation is a continuation of a thesis by T. S. Purewal. Several of the simplifying assumptions made by the above author are either ignored or the justifiability of such assumptions is probed into in order to obtain a more rigorous solution. Effects of the assorted grain size, non-Newtonian cooling, direction of coolant flow, thickness of the porous heat generating plate, specific heat of the coolant, and compressibility of the coolant are investigated in this thesis. Variation of maximum temperature of both coolant and the solid material for different types of heat source distribution are also studied. As the grain size decreases heat transfer area per unit volume increases considerably. It is also observed that the temperature difference between the solid and the coolant increases as the particle size increases. It is established that the assumption of Newtonian cooling does not introduce any error in the case of a porous plate formed by very small spheres. Expressions are also derived for maximum coolant and solid temperatures under uniform, linear, exponential and sinusoidal heat source distribution. The effect of thickness of the plate on heat distribution and on the temperature of the solid and the coolant have been mathematically expressed. The specific heat of coolant fluid does affect the temperature of the coolant. Specific heats of different fluids are not equal. Even for the same fluid specific heat generally varies with temperature. How these variations affect the coolant temperature was studied and equations for different categories of heat source distribution developed. Graphs based on such equations are presented. In the case of compressible fluids higher pressures are found to be advantageous. Advantages include lower percentage pressure drop, lower figure of merit and higher mass rate of flow for same linear velocity --Abstract, pages 2-3

Solving system of nonlinear integral equations by Newton-Kantorovich method

Newton-Kantorovich method is applied to obtain an approximate solution for a system of nonlinear Volterra integral equations which describes a large class of problems in ecology, economics, medicine and other fields. The system of nonlinear integral equations is reduced to find the roots of nonlinear integral operator. This nonlinear integral operator is solved by the Newton-Kantorovich method with initial guess and this procedure is continued by iteration method to find the unknown functions. Finally, numerical examples are provided to show the validity and the efficiency of the method presented

An approximate solution of two dimensional nonlinear Volterra integral equation using Newton-Kantorovich method

This paper studies the method for establishing an approximate solution of nonlinear two dimensional Volterra integral equations (NLTD-VIE). The Newton-Kantorovich (NK) suppositions are employed to modify NLTD-VIE to the sequence of linear two dimensional Volterra integral equation (LTD-VIE). The proper-ties of the two dimensional Gauss-Legenre (GL) quadrature fromula are used to abridge the sequence of LTD-VIE to the solution of the linear algebraic system. The existence and uniqueness of the approximate solution is demonstrated, and an illustrative example is provided to show the precision and authenticity of the method

One dimensional nonlinear integral operator with Newton–Kantorovich method

The Newton–Kantorovich method (NKM) is widely used to find approximate solutions for nonlinear problems that occur in many fields of applied mathematics. This method linearizes the problems and then attempts to solve the linear problems by generating a sequence of functions. In this study, we have applied NKM to Volterra-type nonlinear integral equations then the method of Nystrom type Gauss–Legendre quadrature formula (QF) was used to find the approximate solution of a linear Fredholm integral equation. New concept of determining the solution based on subcollocation points is proposed. The existence and uniqueness of the approximated method are proven. In addition, the convergence rate is established in Banach space. Finally illustrative examples are provided to validate the accuracy of the presented method

Peripartum cardiomyopathy: ten year experience at a tertiary care hospital in Pakistan.

Background: There is very little literature regarding peripartum cardiomyopathy from the Asian countries. We conducted this study to determine demographic details, clinical presentations, complications and recovery of left ventricular (LV) systolic function in peripartum cardiomyopathy (PPCMP) patients of Pakistani origin. Method: A ten year retrospective case series of PPCMP was conducted at the Aga Khan University Hospital. Patients were also followed up for six months after presentation, with special regard to improvement in the LV function. Results: Total 45 patients were included, 25 (55.5%) primigravida and 8 (17.7%) gravida 2 and the remaining 12 (26.6%) were multigravida. Fourteen patients (31.1%) presented during pregnancy and 31 (68.8%) after delivery. All patients presented with CHF and three (6.6%) were complicated with ventricular tachycardia (VT) at presentation. LV systolic dysfunction was present in 39 (86.66%) patients and RV dysfunction in 15 (33.3%) patients. Two patients had LV clot and thromboembolic stroke occurred in another 4 patients. All patients received standard treatment except three patients who had asthma and could not be given beta blockers. Echocardiogram was repeated after 6 month and in 32 (71.1%) patients LV functions recovered to normal. RV function improved in all except 2 (4.4%) patients. All patients were discharged in stable condition. Conclusion: Significant numbers of PPCMP patients, who had severe LV dysfunction at presentation recovered their LV functions at six month follow u

Cadmium Zinc Telluride (CZT) photon counting detector Characterisation for soft tissue imaging

The use of photon counting detection technology has resulted in significant X-ray imaging research interest in recent years. Computed Tomography (CT) scanners can benefit from photon-counting detectors, which are new technology with the potential to overcome key limitations of conventional CT detectors. Researchers are still studying the effectiveness and sensitivity of semiconductor detector materials in photon counting detectors for detecting soft tissue contrasts. This study aimed to characterize the performance of the Cadmium Zinc Telluride photon counting detector in identifying various tissues. An optimal frame rate per second (FPS) of CZT detector was evaluated by setting the X-ray tube voltage and current at 25 keV, 35 keV and 0.5 mA, 1.0 mA respectively by keeping the optimum FPS fixed, the detector energy thresholds were set in small steps from 15 keV to 35 keV and the Currents were set for X-ray tubes in ranges of 0.1 mA to 1.0 mA to find the relationship between voltage and current of the X-ray source and counts per second (CPS). The samples i.e., fat, liver, muscles, paraffin wax, and contrast media were stacked at six different thickness levels in a stair-step chamber made from Plexi-glass. X-ray transmission at six different thicknesses of tissue samples was also examined for five different energy (regions) thresholds (21 keV, 25 keV, 29 keV, 31 keV, and 45 keV) to determine the effect on count per second (CPS). In this study, 12 frames per second is found to be the optimum frame rate per second (FPS) based on the spectral response of an X-ray source and CPS has a linear relationship with X-ray tube current as well. It was also noted that A sample's thickness also affects its X-ray transmission at different energy thresholds. A high sensitivity and linearity of the detectors make them suitable for use in both preclinical and medical applications.Comment: 29 pages and 11 figure