Search results for: Feynman formulas

Authors: Wu Sa, Zhang Qian, Li Qi, Wang Ye

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Currently in humidity tests having not put the Dew point temperature as a control parameter, this paper selects wet and dry bulb thermometer to measure the vapor pressure, and introduces several the saturation vapor pressure formulas easily calculated on the controller. Then establish the Dew point temperature calculation model to obtain the relationship between the Dew point temperature and vapor pressure. Finally check through the 100 groups of sample in the range of 0-100 ℃ from "Psychrometric handbook", find that the average error is small. This formula can be applied to calculate the Dew point temperature in the humidity test.

Keywords: dew point temperature, psychrometric handbook, saturation vapor pressure, wet and dry bulb thermometer

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Authors: K. Krizova, R. Hela

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The paper a summary of the results of concretes with partial substitution of natural aggregates with recycled concrete is solved. Design formulas of the concretes were characterised with 20, 40 and 60% substitution of natural 8-16 mm fraction aggregates with a selected recycled concrete of analogous coarse fractions. With the product samples an evaluation of coarse fraction aggregates influence on fresh concrete consistency and concrete strength in time was carried out. The results of concretes with aggregates substitution will be compared to reference formula containing only the fractions of natural aggregates.

Keywords: recycled concrete, natural aggregates, fresh concrete, properties of concrete

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Authors: Lele Zhang, Hui Leng Choo, Alexander Konyukhov, Shuguang Li

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Finite Element (FE) model of simplified e-bike structure was generated by main frame with two tiers, which consisted of pipe, mass, beam, and shell elements (pipe 289, beam188, shell 181, shell 281, combin14, link11, mass21). These elements would be introduced and demonstrated using mathematical formulas. Based on coupling theory, constrain equations was proposed. Exporting all the parameters obtained from theory part, the connection stiffness matrix of the whole e-bike structure between each of these elements was detected.

Keywords: coupling theory, stiffness matrix, e-bike, finite element model

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Authors: Tomáš Melichar, Jiří Bydžovský, Vít Černý

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In this article our research focused on study of basic physical and mechanical parameters of polymer-cement repair materials is presented. Namely the influence of applied aggregates in combination with active admixture is specially considered. New formulas which were exposed in ambient with temperature even to 1000°C were suggested. Subsequently densities and strength characteristics including their changes were evaluated. Selected samples were analyzed using electron microscope. The positive influence of porous aggregates based on sintered ash was definitely demonstrated. Further it was found than in terms of thermal resistance the effective micro silica amount represents 5% to 7.5% of cement weight.

Keywords: aggregate, ash, high, lightweight, microsilica, mortar, polymer-cement, repair, temperature

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Authors: Akram Khaleghei, Ghosheh Balagh, Viliam Makis

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In this paper, we investigate the residual life prediction problem for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model with unknown parameters. The parameter estimation procedure based on an EM algorithm is developed and the formulas for the conditional reliability function and the mean residual life are derived, illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, residual life prediction

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Authors: Iman Mohseni

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Current studies indicate that neglecting the effect of intermediate diaphragms might lead to highly conservative values for bending moment distribution factors and result in non-economic designs for skew bridges. This paper reports on a parametric study performed on 160 prototypes of straight and skew concrete multicell box-girder bridges. The obtained results were used to develop practical expressions to account for the diaphragm effects on American Association of State Highway and Transportation Officials formulas for live load distribution factors. It was observed that decks with internal transverse diaphragms perpendicular to the longitudinal webs are the best arrangement for load distribution in skew bridges.

Keywords: box bridges, truck, distribution factor, diaphragm

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Authors: Melike Tascioglu

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This paper aims to combine film editing principles to basic design principles to explore what graphic designers do in terms of storytelling. The sequential aspect of film is designed and examined through the art of editing. Examining the rules, principles and formulas of film editing can be a method for graphic designers to further practice the art of storytelling. Although there are many research and publications on design basics, time, pace, dramatic structure and choreography are not very well defined in the area of graphic design. In this era of creative storytelling and interdisciplinary collaboration, not only film editors but also graphic designers and students in the arts and design should understand the theory and practice of editing to be able to create a strong mise-en-scène and not only a mise-en-page.

Keywords: design principles, editing principles, editorial design, film editing, graphic design, storytelling

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Authors: S. Mehrab Amiri, Nasser Talebbeydokhti

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Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: artificial neural network, morphodynamic model, sediment continuity equation, shallow water equations

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Authors: Sanju Vaidya, Aihua Li

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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry Wiener introduced a topological index related to molecular branching. Now there are more than 100 topological indices for graphs. For example, Hosoya polynomials (also called Wiener polynomials) were introduced to derive formulas for certain vulnerability measures and topological indices for various graphs. In this paper, we will find a relation between the Hosoya polynomials of any graph and its Mycielskian graph. Additionally, using this we will compute vulnerability measures, closeness and betweenness centrality, and extended Wiener indices. It is fascinating to see how Hosoya polynomials are useful in the two diverse fields, cybersecurity and chemistry.

Keywords: hosoya polynomial, mycielskian graph, graph vulnerability measure, topological index

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Authors: Mari Chaikovskaia, Jean-Philippe Gayon, Alain Quilliot

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We consider a fleet of elementary robots that can be connected in different ways to transport loads of different types. For instance, a single robot can transport a small load, and the association of two robots can either transport a large load or two small loads. We seek to determine the optimal number of robots to transport a set of loads in a given time interval, with or without reconfiguration. We show that the problem with reconfiguration is strongly NP-hard by a reduction to the bin-packing problem. Then, we study a special case with unit capacities and derive simple formulas for the minimum number of robots, up to 3 types of loads. For this special case, we compare the minimum number of robots with or without reconfiguration and show that the gain is limited in absolute value but may be significant for small fleets.

Keywords: fleet sizing, reconfigurability, robots, transportation

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Aigul Manapova

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We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

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Authors: Haitham A. Hussein, Rozi Abdullah, Issa Saket, Md. Azlin

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The gravitational effect has been extensively applied to separate oil from water in water and wastewater treatment systems. The maximum oil globules removal efficiency is improved by obtaining the best flow uniformity in separator tanks. This study used 2D computational fluid dynamics (CFD) to investigate the effect of different inlet baffle positions inside the separator tank. Laboratory experiment has been conducted, and the measured velocity fields which were by Nortek Acoustic Doppler Velocimeter (ADV) are used to verify the CFD model. Computational investigation results indicated that the construction of an inlet baffle in a suitable location provides the minimum recirculation zone volume, creates the best flow uniformity, and dissipates kinetic energy in the oil and water separator tank. Useful formulas were predicted to design the oil and water separator tanks geometry based on an experimental model.

Keywords: oil/water separator tanks, inlet baffles, CFD, VOF

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Authors: Xiaoping Qiu, Binci You, Yue Hu

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The executive time of the workflow network has an important effect on the efficiency of the business process. In this paper, the activity executive time is divided into the service time and the waiting time, then the lead time can be extracted from the waiting time. The executive time formulas of the three basic structures in the workflow network are deduced based on the activity lead time. Taken the process of e-commerce logistics as an example, insert appropriate lead time for key activities by using Petri net, and the executive time optimization model is built to minimize the waiting time with the time-cost constraints. Then the solution program-using VC++6.0 is compiled to get the optimal solution, which reduces the waiting time of key activities in the workflow, and verifies the role of lead time in the timeliness of e-commerce logistics.

Keywords: electronic business, execution time, lead time, optimization model, petri net, time workflow network

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Authors: O. Benaziz, A. Dorbane, S. Djeraba

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The objective of this work is to formulate a dry dispersible form of furosemide in the context of pediatric dose adjustment. To achieve this, we have produced a set of formulas that will be tested in process and after compression. The formula with the best results will be improved to optimize the final shape of the product. Furosemide is the most widely used pediatric diuretic because of its low toxicity. The manufacturing process was chosen taking into account all the data relating to the active ingredient and the excipients used and complying with the specifications and requirements of dispersible tablets. The process used to prepare these tablets was wet granulation. Different excipients were used: lactose, maize starch, magnesium stearate and two superdisintegrants. The mode of incorporation of super-disintegrant changes with each formula. The use of super-disintegrant in the formula allowed optimization of the disintegration time. Prepared tablets were evaluated for weight, content uniformity, hardness, disintegration time, friability and in vitro dissolution test. 

Keywords: formulation, dispersible tablets, wet granulation, superdisintegrants, disintegration

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Authors: Malika Yaici, Anis Oussayah, Mohamed Ahmed Takerrabet

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Security of context-aware ubiquitous systems is paramount, and authentication plays an important aspect in cloud computing and ubiquitous computing. Trust management has been identified as vital component for establishing and maintaining successful relational exchanges between trading partners in cloud and ubiquitous systems. Establishing trust is the way to build good relationship with both client and provider which positive activates will increase trust level, otherwise destroy trust immediately. We propose a new context-aware authentication system using a trust management system between client and server, and between servers, a trust which induces partnership, thus to a close cooperation between these servers. We defined the rules (algorithms), as well as the formulas to manage and calculate the trusting degrees depending on context, in order to uniquely authenticate a user, thus a single sign-on, and to provide him better services.

Keywords: ubiquitous computing, authentication, context-awareness, trust management

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Authors: S. Kongtun-Janphuk, S. Niwitpong Jr., J. Saengsai

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Low-sugar snack bars were formulated with 3 main formulas depending on the main ingredient, which were peanut-green bean-sesame, apple, and prune. The most acceptable formula of each group was obtained by sensory evaluation using a nine-point hedonic scale. The moisture content, total ash, protein, fat and fiber were analyzed by the standard methods of AOAC. The peanut-mung bean-sesame snack bar showed the highest protein content (88.32%) and total fat (0.48%) with the lowest of fiber content (0.01%) while the prune formula showed the lowest protein content (71.91%) and total fat (0.21%) with the highest of fiber content (0.03%). This result indicated that the prune formula could be used as diet food to assist in weight loss program.

Keywords: low-sugar snack bar, diet food, nutrition analysis, food formulation

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Authors: Safia Hocine, Djamil Aïssani

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Risk models, recently studied in the literature, are becoming increasingly complex. It is rare to find explicit analytical relations to calculate the ruin probability. Indeed, the stability issue occurs naturally in ruin theory, when parameters in risk cannot be estimated than with uncertainty. However, in most cases, there are no explicit formulas for the ruin probability. Hence, the interest to obtain explicit stability bounds for these probabilities in different risk models. In this paper, we interest to the stability bounds of the univariate classical risk model established using the regenerative processes approach. By adopting an algorithmic approach, we implement this approximation and determine numerically the bounds of ruin probability in the case of large claims (heavy-tailed distribution).

Keywords: heavy-tailed distribution, large claims, regenerative process, risk model, ruin probability, stability

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Authors: Shih-Kuei Lin

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The characterization of the arbitrage-free dynamics of interest rates is developed in this study under the presence of Markov jump risks, when the term structure of the interest rates is modeled through simple forward rates. We consider Markov jump risks by allowing randomness in jump sizes, independence between jump sizes and jump times. The Markov jump diffusion model is used to capture empirical phenomena and to accurately describe interest jump risks in a financial market. We derive the arbitrage-free model of simple forward rates under the spot measure. Moreover, the analytical pricing formulas for a cap and a floor are derived under the forward measure when the jump size follows a lognormal distribution. In our empirical analysis, we find that the LIBOR market model with Markov jump risk better accounts for changes from/to different states and different rates.

Keywords: arbitrage-free, cap and floor, Markov jump diffusion model, simple forward rate model, volatility smile, EM algorithm

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Authors: Nurhayati Abdullah, Fauziah Sulaiman, Muhamad Azman Miskam, Rahmad Mohd Taib

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Banana pseudo-stem and fruit-bunch-stem are agricultural residues that can be used for conversion to bio-char, bio-oil, and gases by using thermochemical process. The aim of this work is to characterize banana pseudo-stem and banana fruit-bunch-stem through proximate analysis, elemental analysis, chemical analysis, thermo-gravimetric analysis, and heating calorific value. The ash contents of the banana pseudo-stem and banana fruit-bunch-stem are 11.0 mf wt.% and 20.6 mf wt.%; while the carbon content of banana pseudo-stem and fruit-bunch-stem are 37.9 mf wt.% and 35.58 mf wt.% respectively. The molecular formulas for banana stem and banana fruit-bunch-stem are C24H33NO26 and C19H29NO33 respectively. The measured higher heating values of banana pseudo-stem and banana fruit-bunch-stem are 15.5MJ/kg and 12.7 MJ/kg respectively. By chemical analysis, the lignin, cellulose, and hemicellulose contents in the samples will also be presented. The feasibility of the banana wastes to be a feedstock for thermochemical process in comparison with other biomass will be discussed in this paper.

Keywords: banana waste, biomass, renewable energy, thermo-chemical characteristics

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Authors: Marwan Jarrah, Nadia Nugrush, Sukainah Ali, Areej Allawzi

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This research article investigates how illnesses (different types and severity) are expressed in Arabic discourse with a particular focus on input coming from Colloquial Jordanian Arabic (CJA). Drawing on a corpus of naturally occurring conversations, this article offers evidence that illnesses are predominantly expressed through two different sets of expressive strategies, namely direct expressive strategies (DES) and indirect expressive strategies (IES). The latter are exclusively used when cancer and mental health disorders are targeted. IES include the substitution of the name of the illness with some religious expressions (e.g., ʔallah ʔijdʒi:rna ‘May Allah keeps us safe’) or certain terms especially when cancer is meant (e.g., haðˤa:k ʔil-maraðˤ ‘that disease’). On the other hand, DES are used in conjunction with other illnesses (e.g., heart, kidneys, diabetes, etc.), regardless of their severity. DES include specific formulas that remarkably mention the name of the inflicted organ (e.g., [with-SOMEONE the ORGAN] as in ʕinduh ʔil-qalb ‘lit. with-him the heart’ meaning ‘He has a heart disease). We discuss the effects of religious beliefs and local norms and values in determining the use of these strategies.

Keywords: Illnesses, pragmatics, expressive strategies, religion

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Authors: Xiaofei Hu, Zhiyu Cai, Weian Yao

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V-notch problem under dynamic loading condition is considered in this paper. In the time domain, the precise time domain expanding algorithm is employed, in which a self-adaptive technique is carried out to improve computing accuracy. By expanding variables in each time interval, the recursive finite element formulas are derived. In the space domain, a Symplectic Analytical Singular Element (SASE) for V-notch problem is constructed addressing the stress singularity of the notch tip. Combining with the conventional finite elements, the proposed SASE can be used to solve the dynamic stress intensity factors (DSIFs) in a simple way. Numerical results show that the proposed SASE for V-notch problem subjected to dynamic loading condition is effective and efficient.

Keywords: V-notch, dynamic stress intensity factor, finite element method, precise time domain expanding algorithm

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Authors: Marwane Ben Hcine, Ridha Bouallegue

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The aim of this work is to provide an original analytical framework for downlink effective SINR evaluation in LTE networks. The classical single carrier SINR performance evaluation is extended to multi-carrier systems operating over frequency selective channels. Extension is achieved by expressing the link outage probability in terms of the statistics of the effective SINR. For effective SINR computation, the exponential effective SINR mapping (EESM) method is used on this work. Closed-form expression for the link outage probability is achieved assuming a log skew normal approximation for single carrier case. Then we rely on the lognormal approximation to express the exponential effective SINR distribution as a function of the mean and standard deviation of the SINR of a generic subcarrier. Achieved formulas is easily computable and can be obtained for a user equipment (UE) located at any distance from its serving eNodeB. Simulations show that the proposed framework provides results with accuracy within 0.5 dB.

Keywords: LTE, OFDMA, effective SINR, log skew normal approximation

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Authors: Yoftahe Nigussie Worku

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This research focuses on advancing fire tube boiler technology by systematically optimizing design parameters to achieve efficient saturated steam production. The main objective is to design a high-performance boiler with a production capacity of 2000kg/h at a 12-bar design pressure while minimizing costs. The methodology employs iterative analysis, utilizing relevant formulas, and considers material selection and production methods. The study successfully results in a boiler operating at 85.25% efficiency, with a fuel consumption rate of 140.37kg/hr and a heat output of 1610kW. Theoretical importance lies in balancing efficiency, safety considerations, and cost minimization. The research addresses key questions on parameter optimization, material choices, and safety-efficiency balance, contributing valuable insights to fire tube boiler design.

Keywords: safety consideration, efficiency, production methods, material selection

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Authors: David Glassmeyer

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Quantitative reasoning is necessary to robustly understand mathematical concepts ranging from elementary to university levels. Quantitative reasoning involves identifying and representing quantities and the relationships between these quantities. Without reasoning quantitatively, students often resort to memorizing formulas and procedures, which have negative impacts when they encounter mathematical topics in the future. This study investigated how high school students’ quantitative reasoning could be fostered within a unit on arc measure and angle relationships. Arc measure, or the measure of a central angle that cuts off a portion of a circle’s circumference, is often confused with arclength. In this study, the researcher redesigned an activity to clearly distinguish arc measure and arc length by using a quantitative reasoning framework. Data were collected from high school students to determine if this approach impacted their understanding of these concepts. Initial data indicates the approach was successful in supporting students’ quantitative reasoning of these topics. Implications for the work are that teachers themselves may also benefit from considering mathematical definitions from a quantitative reasoning framework and can use this activity in their own classrooms.

Keywords: arc length, arc measure, quantitative reasoning, student content knowledge

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Authors: E. Marei, A. Hammad, S. Ismail, A. El-Gindy

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This study aims to investigate the ability of different formula of mixed bacteria as a biological treatments of wastewater after primary treatment as a bio-treatment and bio-removal and bio-adsorbent of different heavy metals in natural circumstances. The wastewater was collected from Sarpium forest site-Ismailia Governorate, Egypt. These treatments were mixture of free cells and mixture of immobilized cells of different bacteria. These different formulas of mixed bacteria were prepared under Lab. condition. The obtained data indicated that, as a result of wastewater bio-treatment, the removal rate was found to be 76.92 and 76.70% for biological oxygen demand, 79.78 and 71.07% for chemical oxygen demand, 32.45 and 36.84 % for ammonia nitrogen as well as 91.67 and 50.0% for phosphate after 24 and 28 hrs with mixed free cells and mixed immobilized cells, respectively. Moreover, the bio-removals of different heavy metals were found to reach 90.0 and 50. 0% for Cu ion, 98.0 and 98.5% for Fe ion, 97.0 and 99.3% for Mn ion, 90.0 and 90.0% Pb, 80.0% and 75.0% for Zn ion after 24 and 28 hrs with mixed free cells and mixed immobilized cells, respectively. The results indicated that 13.86 and 17.43% of removal efficiency and reduction of total dissolved solids were achieved after 24 and 28 hrs with mixed free cells and mixed immobilized cells, respectively.

Keywords: wastewater bio-treatment , bio-sorption heavy metals, biological desalination, immobilized bacteria, free cell bacteria

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Authors: Revoti Prasad Bora, Nikita Katyal, Saurabh Yadav

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Pre-processing plays an important role in various image processing applications. Most of the time due to the similar nature of images, a particular pre-processing or a set of pre-processing steps are sufficient to produce the desired results. However, in the education domain, there is a wide variety of images in various aspects like images with line-based diagrams, chemical formulas, mathematical equations, etc. Hence a single pre-processing or a set of pre-processing steps may not yield good results. Therefore, a Deep Learning based approach for dynamically selecting a relevant pre-processing technique for each image is proposed. The proposed method works as a classifier to detect hidden patterns in the images and predicts the relevant pre-processing technique needed for the image. This approach experimented for an image similarity matching problem but it can be adapted to other use cases too. Experimental results showed significant improvement in average similarity ranking with the proposed method as opposed to static pre-processing techniques.

Keywords: deep-learning, classification, pre-processing, computer vision, image processing, educational data mining

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Authors: Michaela Chovancova, Jakub Elcner

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Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculating the pressure losses in the real lungs is due to its complexity and diversity lengthy and inefficient process. For these calculations is necessary the lungs to slightly simplify (same cross-section over the length of individual generation) or use one of the models of lungs. The simplification could cause deviations from real values. The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli equation and continuity equation. Then, evaluate the desirability of using this formula to determine the pressure loss across the bronchial tree.

Keywords: pressure gradient, airways resistance, real geometry of bronchial tree, breathing

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Authors: Slobodan B. Tričković

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We present the results concerned with trigonometric series that include sine and cosine functions with a parameter appearing in the denominator. We derive two types of closed-form formulas for trigonometric series. At first, for some integer values, as we know that Riemann’s ζ function and Dirichlet η, λ equal zero at negative even integers, whereas Dirichlet’s β function equals zero at negative odd integers, after a certain number of members, the rest of the series vanishes. Thus, a trigonometric series becomes a polynomial with coefficients involving Riemann’s ζ function and Dirichlet η, λ, β functions. On the other hand, in some cases, one cannot immediately replace the parameter with any positive integer because we shall encounter singularities. So it is necessary to take a limit, so in the process, we apply L’Hospital’s rule and, after a series of rearrangements, we bring a trigonometric series to a form suitable for the application of Choi-Srivastava’s theorem dealing with Hurwitz’s zeta function and Harmonic numbers. In this way, we express a trigonometric series as a polynomial over Hurwitz’s zeta function derivative.

Keywords: Dirichlet eta lambda beta functions, Riemann's zeta function, Hurwitz zeta function, Harmonic numbers

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Authors: M. H. Aissa, Amar Bouzid Dj

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As known, many countries are now planning to build new wind farms with high capacity up to 5MW. Consequently, the size of the foundation increase. These kinds of structures are subject to fatigue damage from environmental loading mainly due to wind and waves as well as from cyclic loading imposed through the rotational frequency (1P) through mass and aerodynamic imbalances and from the blade passing frequency (3P) of the wind turbine which make them behavior dynamically very sensitive. That is why natural frequency must be determined with accuracy from the existing data of the soil and the foundation stiffness sources of uncertainties, to avoid the resonance of the system. This paper presents analytical expressions of stiffness foundation with large diameter in linear soil behavior in different soil stiffness profile. To check the accuracy of the proposed formulas, a mathematical model approach based on non-dimensional parameters is used to calculate the natural frequency taking into account the soil structure interaction (SSI) compared with the p-y method and measured frequency in the North Sea Wind farms.

Keywords: offshore wind turbines, semi analytical FE analysis, p-y curves, piles foundations

Procedia PDF Downloads 445