Search results for: calculus

Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Golden J. Zhang, Dongbao Zhou

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Darcy’s law is the fundamental theory in fluid dynamics and engineering applications. Although Darcy linearity was found to be valid for slow, viscous flow, non-linear and non-Darcian flow has been well documented under both small and large velocity fluid flow. Various classical models were proposed and used widely to quantify non-Darcian flow, including the well-known Forchheimer, Izbash, and Swartzendruber models. Applications, however, revealed limitations of these models. Here we propose a general model built upon the Caputo fractional derivative to quantify non-Darcian flow for various flows (laminar to turbulence).Real-world applications and model comparisons showed that the new fractional-derivative model, which extends the fractional model proposed recently by Zhou and Yang (2018), can capture the non-Darcian flow in the relatively small velocity in low-permeability deposits and the relatively high velocity in high-permeability sand. A scale effect was also identified for non-Darcian flow in fractured rocks. Therefore, fractional calculus may provide an efficient tool to improve classical models to quantify fluid dynamics in aquatic environments.

Keywords: fractional derivative, darcy’s law, non-darcian flow, fluid dynamics

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Authors: Falek Kamel

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Various approaches are usually used in the dynamic analysis of beams vibrating transversally. For this, numerical methods allowing the solving of the general eigenvalue problem are utilized. The equilibrium equations describe the movement resulting from the solution of a fourth-order differential equation. Our investigation is based on the finite element method. The findings of these investigations are the vibration frequencies obtained by the Jacobi method. Two types of the elementary mass matrix are considered, representing a uniform distribution of the mass along with the element and concentrated ones located at fixed points whose number is increased progressively separated by equal distances at each evaluation stage. The studied beams have different boundary constraints representing several classical situations. Comparisons are made for beams where the distributed mass is replaced by n concentrated masses. As expected, the first calculus stage is to obtain the lowest number of beam parts that gives a frequency comparable to that issued from the Rayleigh formula. The obtained values are then compared to theoretical results based on the assumptions of the Bernoulli-Euler theory. These steps are used for the second type of mass representation in the same manner.

Keywords: structural elements, beams vibrating, dynamic analysis, finite element method, Jacobi method

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Authors: Sadia Arshad, Yifa Tang, Dumitru Baleanu

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A fractional order mathematical model is proposed that incorporate CD8+ cells, natural killer cells, cytokines and tumor cells. The tumor cells growth in the absence of an immune response is modeled by logistic law as it was the simplest form for which predictions also agreed with the experimental data. Natural Killer Cells are our first line of defense. NK cells directly kill tumor cells through several mechanisms, including the release of cytoplasmic granules containing perforin and granzyme, expression of tumor necrosis factor (TNF) family members. The effect of the NK cells on the tumor cell population is expressed with the product term. Rational form is used to describe interaction between CD8+ cells and tumor cells. A number of cytokines are produced by NKs, including tumor necrosis factor TNF, IFN, and interleukin (IL-10). Source term for cytokines is modeled by Michaelis-Menten form to indicate the saturated effects of the immune response. Stability of the equilibrium points is discussed for biologically significant values of bifurcation parameters. We studied the treatment of fractional order system by investigating analytical conditions of tumor eradication. Numerical simulations are presented to illustrate the analytical results.

Keywords: cancer model, fractional calculus, numerical simulations, stability analysis

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Authors: Wafa Tourab, Abdessalem Babouri, Mohamed Nemamcha

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This work presents an experimental and theoretical characterization of electromagnetic environment in the vicinity of EL-HADJAR high voltage substation located in the eastern Algerian within a very high populated zone. There have been analyses on the effects of electromagnetic fields emanating from coupled multi-lines power systems on the health of the workers and people living in proximity of substations. An experimental investigation has been conducted around a circuit of two 220Kv lines running in parallel. The experimental results are validated by a flexible code of calculus developed in the environment Matlab. The implications of the results are discussed and are in very good agreement with the ICNIRP reference levels for occupational and non-occupational exposures. In a case of study, the separation between the two structures “S” is varied to demonstrate its influence on the electric and magnetic charges quantities generated by the circuit of lines proposed. It is found that increasing S decreases the electric and magnetic fields which occur at the center of the structure then reduces the coupling between lines. We concluded that the evaluation of the spacing between the phase conductors is of paramount interest in the preparation of the line’s implantation inside the electrical posts to reduce them radiations in the environment.

Keywords: low frequency, electromagnetic fields, electromagnetic coupling, high voltage power lines

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Authors: Chandra Prayaga, Aaron Wade, Lakshmi Prayaga, Gopi Shankar Mallu

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This paper presents the use of machine learning algorithms to predict the success of students in an introductory physics course. Data having 140 rows pertaining to the performance of two batches of students was used. The lack of sufficient data to train robust machine learning models was compensated for by generating synthetic data similar to the real data. CTGAN and CTGAN with Gaussian Copula (Gaussian) were used to generate synthetic data, with the real data as input. To check the similarity between the real data and each synthetic dataset, pair plots were made. The synthetic data was used to train machine learning models using the PyCaret package. For the CTGAN data, the Ada Boost Classifier (ADA) was found to be the ML model with the best fit, whereas the CTGAN with Gaussian Copula yielded Logistic Regression (LR) as the best model. Both models were then tested for accuracy with the real data. ROC-AUC analysis was performed for all the ten classes of the target variable (Grades A, A-, B+, B, B-, C+, C, C-, D, F). The ADA model with CTGAN data showed a mean AUC score of 0.4377, but the LR model with the Gaussian data showed a mean AUC score of 0.6149. ROC-AUC plots were obtained for each Grade value separately. The LR model with Gaussian data showed consistently better AUC scores compared to the ADA model with CTGAN data, except in two cases of the Grade value, C- and A-.

Keywords: machine learning, student success, physics course, grades, synthetic data, CTGAN, gaussian copula CTGAN

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Authors: Kong Ngai Pei

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The argument scheme approach to argumentation has two components. One is to identify the recurrent patterns of inferences used in everyday discourse. The second is to devise critical questions to evaluate the inferences in these patterns. Although this approach is intuitive and contains many insightful ideas, it has been noted to be not free of problems. One is that due to its disavowing the probability calculus, it cannot give the exact strength of an inference. In order to tackle this problem, thereby paving the way to a more complete normative account of argument strength, it has been proposed, the most promising way is to combine the scheme-based approach with Bayesian networks (BNs). This paper pursues this line of thought, attempting to combine three common schemes, Appeal to Ignorance, Composition, and Division, with BNs. In the first part, it is argued that most (if not all) formulations of the critical questions corresponding to these schemes in the current argumentation literature are incomplete and not very informative. To remedy these flaws, more thorough and precise formulations of these questions are provided. In the second part, how to use graphical idioms (e.g. measurement and synthesis idioms) to translate the schemes as well as their corresponding critical questions to graphical structure of BNs, and how to define probability tables of the nodes using functions of various sorts are shown. In the final part, it is argued that many misuses of these schemes, traditionally called fallacies with the same names as the schemes, can indeed be adequately accounted for by the BN models proposed in this paper.

Keywords: appeal to ignorance, argument schemes, Bayesian networks, composition, division

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Authors: Wanhyun Cho, Seongchae Seo, Soonja Kang

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In this work, we propose a variational technique for image contrast enhancement which utilizes global and local information around each pixel. The energy functional is defined by a weighted linear combination of three terms which are called on a local, a global contrast term and dispersion term. The first one is a local contrast term that can lead to improve the contrast of an input image by increasing the grey-level differences between each pixel and its neighboring to utilize contextual information around each pixel. The second one is global contrast term, which can lead to enhance a contrast of image by minimizing the difference between its empirical distribution function and a cumulative distribution function to make the probability distribution of pixel values becoming a symmetric distribution about median. The third one is a dispersion term that controls the departure between new pixel value and pixel value of original image while preserving original image characteristics as well as possible. Second, we derive the Euler-Lagrange equation for true image that can achieve the minimum of a proposed functional by using the fundamental lemma for the calculus of variations. And, we considered the procedure that this equation can be solved by using a gradient decent method, which is one of the dynamic approximation techniques. Finally, by conducting various experiments, we can demonstrate that the proposed method can enhance the contrast of colour images better than existing techniques.

Keywords: color image, contrast enhancement technique, variational approach, Euler-Lagrang equation, dynamic approximation method, EME measure

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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Authors: G. S. Androulakis, G. Deli, M. Kaisari, N. Mihos

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Teaching practices at the university level have changed and developed during the last decade. Implementation of inverted classroom method in secondary education consists of a well-formed basis for academic teachers. On the other hand, distance learning is a well-known field in education research and widespread as a method of teaching. Nonetheless, the new pandemic found many Universities all over the world unprepared, which made adaptations to new methods of teaching a necessity. In this paper, we analyze a model of an inverted university classroom in a distance learning context. Thus, the main purpose of our research is to investigate students’ difficulties as they transit to a new style of teaching and explore their learning development during a semester totally different from others. Our teaching experiment took place at the Business Administration department of the University of Patras, in the context of two courses: Calculus, a course aimed at first-year students, and Statistics, a course aimed at second-year students. Second-year students had the opportunity to attend courses in the university classroom. First-year students started their semester with distance learning. Using a comparative study of these two groups, we explored significant differences in students’ learning procedures. Focused group interviews, written tests, analyses of students’ dialogues were used in a mixed quantity and quality research. Our analysis reveals students’ skills, capabilities but also a difficulty in following, non-traditional style of teaching. The inverted classroom model, according to our findings, offers benefits in the educational procedure, even in a distance learning environment.

Keywords: distance learning, higher education, inverted classroom, mathematics teaching

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Authors: Vinayak Bassi, Rajpreet Singh

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Over the years, with the emergence of sophisticated computers and algorithms, finance has been quantified using computational prowess. Asset valuation has been one of the key components of quantitative finance. In fact, it has become one of the embryonic steps in determining risk related to a portfolio, the main goal of quantitative finance. This study comprises a drawing comparison between valuation output generated by two stochastic dynamic models, namely Black-Scholes and Dupire’s bi-dimensionality model. Both of these models are formulated for computing the valuation function for a portfolio of European options using Monte Carlo simulation methods. Although Monte Carlo algorithms have a slower convergence rate than calculus-based simulation techniques (like FDM), they work quite effectively over high-dimensional dynamic models. A fidelity gap is analyzed between the static (historical) and stochastic inputs for a sample portfolio of underlying assets. In order to enhance the performance efficiency of the model, the study emphasized the use of variable reduction methods and customizing random number generators to implement parallelization. An attempt has been made to further implement the Dupire’s model on a GPU to achieve higher computational performance. Furthermore, ideas have been discussed around the performance enhancement and bottleneck identification related to the implementation of options-pricing models on GPUs.

Keywords: monte carlo, stochastic models, computational finance, parallel programming, scientific computing

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Authors: Lamia Bourdache, Amar Djema

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The effect of non-Newtonian property (power law index n) on traveling waves of thin layer of power law fluid flowing over an inclined plane is investigated. For this, a simplified second-order two-equation model (SM) is used. The complete model is second-order four-equation (CM). It is derived by combining the weighted residual integral method and the lubrication theory. This is due to the fact that at the beginning of the instability waves, a very small number of waves is observed. Using a suitable set of test functions, second order terms are eliminated from the calculus so that the model is still accurate to the second order approximation. Linear, spatial, and temporal stabilities are studied. For travelling waves, a particular type of wave form that is steady in a moving frame, i.e., that travels at a constant celerity without changing its shape is studied. This type of solutions which are characterized by their celerity exists under suitable conditions, when the widening due to dispersion is balanced exactly by the narrowing effect due to the nonlinearity. Changing the parameter of celerity in some range allows exploring the entire spectrum of asymptotic behavior of these traveling waves. The (SM) model is converted into a three dimensional dynamical system. The result is that the model exhibits bifurcation scenarios such as heteroclinic, homoclinic, Hopf, and period-doubling bifurcations for different values of the power law index n. The influence of the non-Newtonian parameter on the nonlinear development of these travelling waves is discussed. It is found at the end that the qualitative characters of bifurcation scenarios are insensitive to the variation of the power law index.

Keywords: inclined plane, nonlinear stability, non-Newtonian, thin film

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Authors: Barenten Suciu

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Classical matrix calculus and Routh-Hurwitz stability conditions, applied to the snake-like motion of the conical wheel axle, lead to the conclusion that the hunting mode is inherently unstable, and its natural frequency is a complex number. In order to analytically solve such a complicated vibration model, either the inertia terms were neglected, in the model designated as geometrical, or restrictions on the creep coefficients and yawing diameter were imposed, in the so-called dynamical model. Here, an alternative solution is proposed to solve the hunting mode, based on the observation that the bullet train wheel axle is equipped with cylindrical wheels. One argues that for such wheel treads, the geometrical hunting is irrelevant, since its natural frequency becomes nil, but the dynamical hunting is significant since its natural frequency reduces to a real number. Moreover, one illustrates that the geometrical simplification of the wheel causes the stabilization of the hunting mode, since the characteristic quartic equation, derived for conical wheels, reduces to a quadratic equation of positive coefficients, for cylindrical wheels. Quite simple analytical expressions for the damping ratio and natural frequency are obtained, without applying restrictions into the model of contact. Graphs of the time-depending hunting lateral perturbation, including the maximal and inflexion points, are presented both for the critically-damped and the over-damped wheel axles.

Keywords: bullet train, creep, cylindrical wheels, damping, dynamical hunting, stability, vibration analysis

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Authors: Yasir Karabacak

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Objective: The aim of periodontal therapy is to control and eliminate inflammation in order halt disease progression. The initial periodontal therapy (IPT) including scaling and root planing (SRP) can control periodontal disease in most cases of periodontitis; also maintaining good oral hygiene by the patient is fundamental. The aim of this case report is to present IPT and to present 3-month follow-up results in a patient with periodontitis. Materials and Methods IPT of a 63-year-old non-smoker male with generalized periodontitis is presented. The patient had no history of systemic disease. The intraoral examination reveals marked gingival inflammation as well as plaque accumulation and significant calculus deposits. On radiographic examination, severe bone loss was evident. The patient was diagnosed with generalized advanced periodontitis. Initial periodontal therapy including oral hygiene instructions and quadrant-based SRP under local anesthesia was performed using hand and ultrasonic instruments. No antibiotics were prescribed. The patient was recalled 4 weeks after IPT. Results Favorable clinical improvement was obtained. Gingival inflammation was resolved significantly. A reduction of the mean probing depth from 2.4 mm at baseline to 1.9 mm was observed. The patient presented with a good standard of oral hygiene. The plaque scores decreased from 54.0% at baseline to 17.0%. In addition, the percentage of sites with bleeding on probing decreased from 80.0% at baseline to 44.0%. The patient was scheduled for maintenance therapy every three months. Conclusion: The level of oral hygiene has a great impact on periodontal treatment outcome and supports periodontal therapy properly.

Keywords: initial periodontal, therapy and follow-up in a periodontitis, patient, a case report

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Authors: Andre F. A. Cyrino

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Knowing that the technological advance is the focus on the efficient extraction of energy from wind, and therefore in the design of wind turbine structures, this work aims the study of the fluid-structure interaction of an idealized wind turbine. The blade was studied as a beam attached to a cylindrical Hub with rotation axis pointing the air flow that passes through the rotor. Using the calculus of variations and the finite difference method the blade will be simulated by a discrete number of nodes and the aerodynamic forces were evaluated. The study presented here was written on Matlab and performs a numeric simulation of a simplified model of windmill containing a Hub and three blades modeled as Euler-Bernoulli beams for small strains and under the constant and uniform wind. The mathematical approach is done by Hamilton’s Extended Principle with the aerodynamic loads applied on the nodes considering the local relative wind speed, angle of attack and aerodynamic lift and drag coefficients. Due to the wide range of angles of attack, a wind turbine blade operates, the airfoil used on the model was NREL SERI S809 which allowed obtaining equations for Cl and Cd as functions of the angle of attack, based on a NASA study. Tridimensional flow effects were no taken in part, as well as torsion of the beam, which only bends. The results showed the dynamic response of the system in terms of displacement and rotational speed as the turbine reached the final speed. Although the results were not compared to real windmills or more complete models, the resulting values were consistent with the size of the system and wind speed.

Keywords: blade aerodynamics, fluid–structure interaction, wind turbine aerodynamics, wind turbine blade

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Authors: Lina Wu, Ye Li, Jia Liu

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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series

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Authors: Sujeet Poudyal

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Introduction: After Holmium:yttrium-aluminum-garnet (Ho: YAG) laser has revolutionized the management of urolithiasis, the introduction of Thulium fibre laser (TFL) has already challenged Ho:YAG laser due to its multiple commendable properties. Nevertheless, there are only few studies comparing TFL and holmium laser in Retrograde Intrarenal Surgery(RIRS). Therefore, this study was carried out to compare the efficacy and safety of thulium fiber laser (TFL) and holmium laser in RIRS. Methods: This prospective comparative study, which included all patients undergoing laser lithotripsy (RIRS) for proximal ureteric calculus and nephrolithiasis from March 2022 to March 2023, consisted of 63 patients in Ho:YAG laser group and 65 patients in TFL group. Stone free rate, operative time, laser utilization time, energy used, and complications were analysed between the two groups. Results: Mean stone size was comparable in TFL (14.23±4.1 mm) and Ho:YAG (13.88±3.28 mm) group, p-0.48. Similarly, mean stone density in TFL (1269±262 HU) was comparable to Ho:YAG (1189±212 HU), p-0.48. There was significant difference in lasing time between TFL (12.69±7.41 mins) and Ho:YAG (20.44±14 mins), p-0.012). TFL group had operative time of 43.47± 16.8 mins which was shorter than Ho:YAG group (58±26.3 mins),p-0.005. Both TFL and Ho:YAG groups had comparable total energy used(11.4±6.2 vs 12±8 respectively, p-0.758). Stone free rate was 87%for TFL, whereas it was 79.5% for Ho:YAG, p-0.25). Two cases of sepsis and one ureteric stricture were encountered in TFL, whereas three cases suffered from sepsis apart from one ureteric stricture in Ho:YAG group, p-0.62). Conclusion: Thulium Fibre Laser has similar efficacy as Holmium: YAG Laser in terms of safety and stone free rate. However, due to better stone ablation rate in TFL, it can become the game changer in management of urolithiasis in the coming days.

Keywords: retrograde intrarenal surgery, thulium fibre laser, holmium:yttrium-aluminum-garnet (ho:yag) laser, nephrolithiasis

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Authors: Sameer Jung Karki, Gokhan Saygili

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The allowable bearing capacity of foundation systems is determined by applying a factor of safety to the ultimate bearing capacity. Conventional ultimate bearing capacity calculations routines are based on deterministic input parameters where the nonuniformity and inhomogeneity of soil and site properties are not accounted for. Hence, the laws of mathematics like probability calculus and statistical analysis cannot be directly applied to foundation engineering. It’s assumed that the Factor of Safety, typically as high as 3.0, incorporates the uncertainty of the input parameters. This factor of safety is estimated based on subjective judgement rather than objective facts. It is an ambiguous term. Hence, a probabilistic analysis of the bearing capacity of an isolated footing on a clayey soil is carried out by using the Monte Carlo Simulation method. This simulated model was compared with the traditional discrete model. It was found out that the bearing capacity of soil was found higher for the simulated model compared with the discrete model. This was verified by doing the sensitivity analysis. As the number of simulations was increased, there was a significant % increase of the bearing capacity compared with discrete bearing capacity. The bearing capacity values obtained by simulation was found to follow a normal distribution. While using the traditional value of Factor of safety 3, the allowable bearing capacity had lower probability (0.03717) of occurring in the field compared to a higher probability (0.15866), while using the simulation derived factor of safety of 1.5. This means the traditional factor of safety is giving us bearing capacity that is less likely occurring/available in the field. This shows the subjective nature of factor of safety, and hence probability method is suggested to address the variability of the input parameters in bearing capacity equations.

Keywords: bearing capacity, factor of safety, isolated footing, montecarlo simulation

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Authors: Martin Hofmann, Diego Stutzer, Thomas Niederhauser, Juergen Burger

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Dental biofilm is the main etiologic factor for caries, periodontal and peri-implant infections. In addition to the risk of tooth loss, periodontitis is also associated with an increased risk of systemic diseases such as atherosclerotic cardiovascular disease and diabetes. For this reason, dental hygienists use ultrasonic scalers for prophylactic and periodontal care of the teeth. However, the current instruments are limited to their dimensions and operating frequencies. The innovative design of a planar ultrasonic transducer introduces a new type of dental scalers. The flat titanium-based design allows the mass to be significantly reduced compared to a conventional screw-mounted Langevin transducer, resulting in a more efficient and controllable scaler. For the development of the novel device, multi-physics finite element analysis was used to simulate and optimise various design concepts. This process was supported by prototyping and electromechanical characterisation. The feasibility and potential of a planar ultrasonic transducer have already been confirmed by our current prototypes, which achieve higher performance compared to commercial devices. Operating at the desired resonance frequency of 28 kHz with a driving voltage of 40 Vrms results in an in-plane tip oscillation with a displacement amplitude of up to 75 μm by having less than 8 % out-of-plane movement and an energy transformation factor of 1.07 μm/mA. In a further step, we will adapt the design to two additional resonance frequencies (20 and 40 kHz) to obtain information about the most suitable mode of operation. In addition to the already integrated characterization methods, we will evaluate the clinical efficiency of the different devices in an in vitro setup with an artificial biofilm pocket model.

Keywords: ultrasonic instrumentation, ultrasonic scaling, piezoelectric transducer, finite element simulation, dental biofilm, dental calculus

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Authors: Avinash Nayak, Debopam Das

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The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

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Authors: Wedad Albalawi

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The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

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Authors: S. Vaibhav Kant Sahu, Surabhi Bipin Seth

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Human well-being has multiple constituents including the basic material for a good life, freedom and choice, health, good social relations, and security. Poverty is also multidimensional and has been defined as the pronounced deprivation of well-being. Dhurwa tribe of Bastar (India) have symbiotic relation with nature, it provisions ecosystem service such as food, fuel and fiber; regulating services such as climate regulation and non-material benefits such as spiritual or aesthetic benefits and they are managing their forest from ages. The demand for ecosystem services is now so great that trade-off among services become rule. Aim of study to explore evidences for linkages between ecosystem services and well-being of indigenous community, how much it helps them in poverty reduction and interaction between them. Objective of study was to find drivers of change and evidence concerning link between ecosystem, human development and sustainability, evidence in decision making does it opt for multi sectoral objectives. Which means human well-being as the central focus for assessment, while recognizing that biodiversity and ecosystems also have intrinsic value. Ecosystem changes that may have little impact on human well-being over days or weeks may have pronounced impacts over years or decades; so assessments needed to be conducted at spatial and temporal scales under social, political, economic scales to have high-resolution data. Researcher used framework developed by Millennium ecosystem assessment; since human action now directly or unknowingly virtually alter ecosystem. Researcher used ethnography study to get primary qualitative data, secondary data collected from panchayat office. The responses were transcribed and translated into English, as interview held in Hindi and local indigenous language. Focus group discussion were held with group of 10 women at Tiriya village. Researcher concluded with well-being is not just gap between ecosystem service supply but also increases vulnerability. Decision can have consequences external to the decision framework these consequences are called externalities because they are not part of the decision-making calculus.

Keywords: Bastar, Dhurwa tribe, ecosystem services, millennium ecosystem assessment, sustainability

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Authors: Peter Akayuure

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Geometry is considered an important strand in mathematics due to its wide-ranging utilitarian value and because it serves as a building block for understanding other aspects of undergraduate mathematics, including algebra and calculus. Matters regarding students’ geometric thinking have therefore long been pursued by mathematics researchers and educators globally via different theoretical lenses, curriculum reform efforts, and innovative instructional practices. However, so far, studies remain inconclusive about the instructional platforms that effectively promote geometric thinking. At the University of Education, Winneba, an undergraduate geometry course was designed and delivered on UEW Learning Management System (LMS) using Moodle platform. This study utilizes van Hiele’s theoretical lens to examine the entry and exit’s geometric thinking behaviours of prospective teachers who took the undergraduate geometry course in the LMS platform. The study was a descriptive survey that involved an intact class of 280 first-year students enrolled to pursue a bachelor's in mathematics education at the university. The van Hiele’s Geometric thinking test was used to assess participants’ entry and exit behaviours, while semi-structured interviews were used to obtain data for triangulation. Data were analysed descriptively and displayed in tables and charts. An Independent t-test was used to test for significant differences in geometric thinking behaviours between those who entered the university with a diploma certificate and with senior high certificate. The results show that on entry, more than 70% of the prospective teachers operated within the visualization level of van Hiele’s geometric thinking. Less than 20% reached analysis and abstraction levels, and no participant reached deduction and rigor levels. On exit, participants’ geometric thinking levels increased markedly across levels, but the difference from entry was not significant and might have occurred by chance. The geometric thinking behaviours of those enrolled with diploma certificates did not differ significant from those enrolled directly from senior high school. The study recommends that the design principles and delivery of undergraduate geometry course via LMS should be structured and tackled using van Hiele’s geometric thinking levels to serve as means of bridging the existing learning gaps of undergraduate students.

Keywords: geometric thinking, van Hiele’s, UEW learning management system, undergraduate geometry

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Authors: Edwin Calderon-Mendoza, Patrick Schweitzer, Serge Weber

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Series arc faults appear frequently and unpredictably in low voltage distribution systems. Many methods have been developed to detect this type of faults and commercial protection systems such AFCI (arc fault circuit interrupter) have been used successfully in electrical networks to prevent damage and catastrophic incidents like fires. However, these devices do not allow series arc faults to be located on the line in operating mode. This paper presents a location algorithm for series arc fault in a low-voltage indoor power line in an AC 230 V-50Hz home network. The method is validated through simulations using the MATLAB software. The fault location method uses electrical parameters (resistance, inductance, capacitance, and conductance) of a 49 m indoor power line. The mathematical model of a series arc fault is based on the analysis of the V-I characteristics of the arc and consists basically of two antiparallel diodes and DC voltage sources. In a first step, the arc fault model is inserted at some different positions across the line which is modeled using lumped parameters. At both ends of the line, currents and voltages are recorded for each arc fault generation at different distances. In the second step, a fault map trace is created by using signature coefficients obtained from Kirchhoff equations which allow a virtual decoupling of the line’s mutual capacitance. Each signature coefficient obtained from the subtraction of estimated currents is calculated taking into account the Discrete Fast Fourier Transform of currents and voltages and also the fault distance value. These parameters are then substituted into Kirchhoff equations. In a third step, the same procedure described previously to calculate signature coefficients is employed but this time by considering hypothetical fault distances where the fault can appear. In this step the fault distance is unknown. The iterative calculus from Kirchhoff equations considering stepped variations of the fault distance entails the obtaining of a curve with a linear trend. Finally, the fault distance location is estimated at the intersection of two curves obtained in steps 2 and 3. The series arc fault model is validated by comparing current registered from simulation with real recorded currents. The model of the complete circuit is obtained for a 49m line with a resistive load. Also, 11 different arc fault positions are considered for the map trace generation. By carrying out the complete simulation, the performance of the method and the perspectives of the work will be presented.

Keywords: indoor power line, fault location, fault map trace, series arc fault

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Authors: M. J. Ponnambalam

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Physics Outreach in Jamaica has nearly tripled the number of students doing Introductory Calculus-based Physics at the University of the West Indies (UWI, Mona) within 5 years, and thus has shown the importance of Physics Teaching & Learning in Informal Settings. In 1899, the first president of the American Physical Society called Physics, “the science above all sciences.” Sure enough, exactly one hundred years later, Time magazine proclaims Albert Einstein, “Person of the Century.” Unfortunately, Physics seems to be losing that glow in this century. Many countries, big and small, are finding it difficult to attract bright young minds to pursue Physics. At UWI, Mona, the number of students in first year Physics dropped to an all-time low of 81 in 2006, from more than 200 in the nineteen eighties, spelling disaster for the Physics Department! The author of this paper launched an aggressive Physics Outreach that same year, aimed at conveying to the students and the general public the following messages: i) Physics is an exciting intellectual enterprise, full of fun and delight. ii) Physics is very helpful in understanding how things like TV, CD player, car, computer, X-ray, CT scan, MRI, etc. work. iii) The critical and analytical thinking developed in the study of Physics is of inestimable value in almost any field. iv) Physics is the core subject for Science and Technology, and hence of national development. Science Literacy is a ‘must’ for any nation in the 21st century. Hence, the Physics Outreach aims at reaching out to every person, through every possible means. The Outreach work is split into the following target groups: i) Universities, ii) High Schools iii) Middle Schools, iv) Primary Schools, v) General Public, and vi) Physics teachers in High Schools. The programmes, tools and best practices are adjusted to suit each target group. The feedback from each group is highly positive. e.g. In February 2014, the author conducted in 3 Primary Schools the Interactive Show on ‘Science Is Fun’ to stimulate 290 students’ interest in Science – with lively and interesting demonstrations and experiments in a highly interactive way, using dramatization, story-telling and dancing. The feedback: 47% found the Show ‘Exciting’ and 51% found it ‘Interesting’ – totaling an impressive 98%. When asked to describe the Show in their own words, the leading 4 responses were: ‘Fun’ (26%), ‘Interesting’ (20%), ‘Exciting’ (14%) and ‘Educational’ (10%) – confirming that ‘fun’ & ‘education’ can go together. The success of Physics Outreach in Jamaica verifies the following words of Chodos, Associate Executive Officer of the American Physical Society: “If we could get members to go to K-12 schools and levitate a magnet or something, we really think these efforts would bring great rewards.”

Keywords: physics education, physics popularization, UWI, Jamaica

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Authors: Wedad Albalawi

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The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

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Authors: Lisa Kasmer

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Teachers’ instructional decisions shape the structure and content of mathematics lessons and influence the mathematics that students are given the opportunity to learn. Therefore, it is important to better understand how teachers make instructional decisions and thus find new ways to help practicing and future teachers give their students a more effective and robust learning experience. Understanding the relationship between teachers’ instructional decisions and their goals, resources, and orientations (beliefs) is important given the heightened focus on geometric transformations in the middle school mathematics curriculum. This work is significant as the development and support of current and future teachers need more effective ways to teach geometry to their students. The following research questions frame this study: (1) As middle school mathematics teachers plan and enact instruction related to teaching transformations, what thinking processes do they engage in to make decisions about teaching transformations with or without a coordinate system and (2) How do the goals, resources and orientations of these teachers impact their instructional decisions and reveal about their understanding of teaching transformations? Teachers and students alike struggle with understanding transformations; many teachers skip or hurriedly teach transformations at the end of the school year. However, transformations are an important mathematical topic as this topic supports students’ understanding of geometric and spatial reasoning. Geometric transformations are a foundational concept in mathematics, not only for understanding congruence and similarity but for proofs, algebraic functions, and calculus etc. Geometric transformations also underpin the secondary mathematics curriculum, as features of transformations transfer to other areas of mathematics. Teachers’ instructional decisions in terms of goals, orientations, and resources that support these instructional decisions were analyzed using open-coding. Open-coding is recognized as an initial first step in qualitative analysis, where comparisons are made, and preliminary categories are considered. Initial codes and categories from current research on teachers’ thinking processes that are related to the decisions they make while planning and reflecting on the lessons were also noted. Surfacing ideas and additional themes common across teachers while seeking patterns, were compared and analyzed. Finally, attributes of teachers’ goals, orientations and resources were identified in order to begin to build a picture of the reasoning behind their instructional decisions. These categories became the basis for the organization and conceptualization of the data. Preliminary results suggest that teachers often rely on their own orientations about teaching geometric transformations. These beliefs are underpinned by the teachers’ own mathematical knowledge related to teaching transformations. When a teacher does not have a robust understanding of transformations, they are limited by this lack of knowledge. These shortcomings impact students’ opportunities to learn, and thus disadvantage their own understanding of transformations. Teachers’ goals are also limited by their paucity of knowledge regarding transformations, as these goals do not fully represent the range of comprehension a teacher needs to teach this topic well.

Keywords: coordinate plane, geometric transformations, instructional decisions, middle school mathematics

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Authors: Marina Nechayeva, Malgorzata Marciniak, Vladimir Przhebelskiy, A. Dragutan, S. Lamichhane, S. Oikawa

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This presentation is a progress report on a faculty-student research collaboration at CUNY LaGuardia Community College (LaGCC) aimed at designing a small horizontal axis wind turbine optimized for the wind patterns on the roof of our campus. Our project combines statistical and engineering research. Our wind modeling protocol is based upon a recent wind study by a faculty-student research group at MIT, and some of our blade design methods are adopted from a senior engineering project at CUNY City College. Our use of genetic algorithms has been inspired by the work on small wind turbines’ design by David Wood. We combine these diverse approaches in our interdisciplinary project in a way that has not been done before and improve upon certain techniques used by our predecessors. We employ several estimation methods to determine the best fitting parametric probability distribution model for the local wind speed data obtained through correlating short-term on-site measurements with a long-term time series at the nearby airport. The model serves as a foundation for engineering research that focuses on adapting and implementing genetic algorithms (GAs) to engineering optimization of the wind turbine design using Blade Element Momentum Theory. GAs are used to create new airfoils with desirable aerodynamic specifications. Small scale models of best performing designs are 3D printed and tested in the wind tunnel to verify the accuracy of relevant calculations. Genetic algorithms are applied to selected airfoils to determine the blade design (radial cord and pitch distribution) that would optimize the coefficient of power profile of the turbine. Our approach improves upon the traditional blade design methods in that it lets us dispense with assumptions necessary to simplify the system of Blade Element Momentum Theory equations, thus resulting in more accurate aerodynamic performance calculations. Furthermore, it enables us to design blades optimized for a whole range of wind speeds rather than a single value. Lastly, we improve upon known GA-based methods in that our algorithms are constructed to work with XFoil generated airfoils data which enables us to optimize blades using our own high glide ratio airfoil designs, without having to rely upon available empirical data from existing airfoils, such as NACA series. Beyond its immediate goal, this ongoing project serves as a training and selection platform for CUNY Research Scholars Program (CRSP) through its annual Aerodynamics and Wind Energy Research Seminar (AWERS), an undergraduate summer research boot camp, designed to introduce prospective researchers to the relevant theoretical background and methodology, get them up to speed with the current state of our research, and test their abilities and commitment to the program. Furthermore, several aspects of the research (e.g., writing code for 3D printing of airfoils) are adapted in the form of classroom research activities to enhance Calculus sequence instruction at LaGCC.

Keywords: engineering design optimization, genetic algorithms, horizontal axis wind turbine, wind modeling

Procedia PDF Downloads 185