Search results for: mathematical expectation

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: A. Bari

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Integer programming is a branch of mathematical programming techniques in operations research in which some or all of the variables are required to be integer valued. Various cuts have been used to solve these problems. We have also developed cuts known as NAZ cut & A-T cut to solve the integer programming problems. These cuts are used to reduce the feasible region and then reaching the optimal solution in minimum number of steps.

Keywords: Integer Programming, NAZ cut, A-T cut, Cutting plane method

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Authors: Pablo Oteiza, Ricardo Alvarez, Mehrdad Pirnia, Fuat Can

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To effectively combat climate change, many countries around the world have committed to a decarbonisation of their electricity, along with promoting a large-scale integration of renewable energy sources (RES). While this trend represents a unique opportunity to effectively combat climate change, achieving a sound and cost-efficient energy transition towards low-carbon power systems poses significant challenges for the multi-year Transmission Network Expansion Planning (TNEP) problem. The objective of the multi-year TNEP is to determine the necessary network infrastructure to supply the projected demand in a cost-efficient way, considering the evolution of the new generation mix, including the integration of RES. The rapid integration of large-scale RES increases the variability and uncertainty in the power system operation, which in turn increases short-term flexibility requirements. To meet these requirements, flexible generating technologies such as energy storage systems must be considered within the TNEP as well, along with proper models for capturing the operational challenges of future power systems. As a consequence, TNEP formulations are becoming more complex and difficult to solve, especially for its application in realistic-sized power system models. To meet these challenges, there is an increasing need for developing efficient algorithms capable of solving the TNEP problem with reasonable computational time and resources. In this regard, a promising research area is the use of artificial intelligence (AI) techniques for solving large-scale mixed-integer optimization problems, such as the TNEP. In particular, the use of AI along with mathematical optimization strategies based on decomposition has shown great potential. In this context, this paper presents an efficient algorithm for solving the multi-year TNEP problem. The algorithm combines AI techniques with Column Generation, a traditional decomposition-based mathematical optimization method. One of the challenges of using Column Generation for solving the TNEP problem is that the subproblems are of mixed-integer nature, and therefore solving them requires significant amounts of time and resources. Hence, in this proposal we solve a linearly relaxed version of the subproblems, and trained a binary classifier that determines the value of the binary variables, based on the results obtained from the linearized version. A key feature of the proposal is that we integrate the binary classifier into the optimization algorithm in such a way that the optimality of the solution can be guaranteed. The results of a study case based on the HRP 38-bus test system shows that the binary classifier has an accuracy above 97% for estimating the value of the binary variables. Since the linearly relaxed version of the subproblems can be solved with significantly less time than the integer programming counterpart, the integration of the binary classifier into the Column Generation algorithm allowed us to reduce the computational time required for solving the problem by 50%. The final version of this paper will contain a detailed description of the proposed algorithm, the AI-based binary classifier technique and its integration into the CG algorithm. To demonstrate the capabilities of the proposal, we evaluate the algorithm in case studies with different scenarios, as well as in other power system models.

Keywords: integer optimization, machine learning, mathematical decomposition, transmission planning

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Authors: F. Bellali, M. Kharroubi, Y. Rady, N. Bourhim

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In Morocco, fish processing industry is an important source income for a large amount of by-products including skins, bones, heads, guts, and scales. Those underutilized resources particularly scales contain a large amount of proteins and calcium. Sardina plichardus scales from resulting from the transformation operation have the potential to be used as raw material for the collagen production. Taking into account this strong expectation of the regional fish industry, scales sardine upgrading is well justified. In addition, political and societal demands for sustainability and environment-friendly industrial production systems, coupled with the depletion of fish resources, drive this trend forward. Therefore, fish scale used as a potential source to isolate collagen has a wide large of applications in food, cosmetic, and biomedical industry. The main aim of this study is to isolate and characterize the acid solubilize collagen from sardine fish scale, Sardina pilchardus. Experimental design methodology was adopted in collagen processing for extracting optimization. The first stage of this work is to investigate the optimization conditions of the sardine scale deproteinization on using response surface methodology (RSM). The second part focus on the demineralization with HCl solution or EDTA. And the last one is to establish the optimum condition for the isolation of collagen from fish scale by solvent extraction. The advancement from lab scale to pilot scale is a critical stage in the technological development. In this study, the optimal condition for the deproteinization which was validated at laboratory scale was employed in the pilot scale procedure. The deproteinization of fish scale was then demonstrated on a pilot scale (2Kg scales, 20l NaOH), resulting in protein content (0,2mg/ml) and hydroxyproline content (2,11mg/l). These results indicated that the pilot-scale showed similar performances to those of lab-scale one.

Keywords: deproteinization, pilot scale, scale, sardine pilchardus

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Authors: Aliaa M. S. Salem, Soliman I. El-Hout, Amira Gaber, Hassan Nageh

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Nowadays, the development of poisonous gas detectors is considered to be an urgent matter to secure human health and the environment from poisonous gases, in view of the fact that even a minimal amount of poisonous gas can be fatal. Of these concerns, various inorganic or organic sensing materials have been used. Among these are conducting polymers, have been used as the active material in the gassensorsdue to their low-cost,easy-controllable molding, good electrochemical properties including facile fabrication process, inherent physical properties, biocompatibility, and optical properties. Moreover, conducting polymer-based chemical sensors have an amazing advantage compared to the conventional one as structural diversity, facile functionalization, room temperature operation, and easy fabrication. However, the low selectivity and conductivity of conducting polymers motivated the doping of it with varied materials, especially graphene, to enhance the gas-sensing performance under ambient conditions. There were a number of approaches proposed for producing polymer/ graphene nanocomposites, including template-free self-assembly, hard physical template-guided synthesis, chemical, electrochemical, and electrospinning...etc. In this work, we aim to prepare a novel gas sensordepending on Electrospun nanofibers of conducting polymer/RGO composite that is the effective and efficient expectation of poisonous gases like ammonia, in different application areas such as environmental gas analysis, chemical-,automotive- and medical industries. Moreover, our ultimate objective is to maximize the sensing performance of the prepared sensor and to check its recovery properties.

Keywords: electro spinning process, conducting polymer, polyaniline, polypyrrole, polythiophene, graphene oxide, reduced graphene oxide, functionalized reduced graphene oxide, spin coating technique, gas sensors

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Authors: Stephen M. Magu

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The 9/11 and Christmas bombing attacks in the United States are mostly associated with the inability of intelligence agencies to connect dots based on intelligence that was already available. The 1998, 2002, 2013 and several 2014 terrorist attacks in Kenya, on the other hand, are probably driven by a completely different dynamic: the invisible hand of corruption. The World Bank and Transparency International annually compute the Worldwide Governance Indicators and the Corruption Perception Index respectively. What perhaps is not adequately captured in the corruption metrics is the impact of corruption on terrorism. The World Bank data includes variables such as the control of corruption, (estimates of) government effectiveness, political stability and absence of violence/terrorism, regulatory quality, rule of law and voice and accountability. TI's CPI does not include measures related to terrorism, but it is plausible that there is an expectation of some terrorism impact arising from corruption. This paper, by examining the incidence, frequency and total number of terrorist attacks that have occurred especially since 1990, and further examining the specific cases of Kenya and Nigeria, argues that in addition to having major effects on governance, corruption has an even more frightening impact: that of facilitating and/or violating security mechanisms to the extent that foreign nationals can easily obtain identification that enables them to perpetuate major events, targeting powerful countries' interests in countries with weak corruption-fighting mechanisms. The paper aims to model interactions that demonstrate the cost/benefit analysis and agents' rational calculations as being non-rational calculations, given the ultimate impact. It argues that eradication of corruption is not just a matter of a better business environment, but that it is implicit in national security, and that for anti-corruption crusaders, this is an argument more potent than the economic cost / cost of doing business argument.

Keywords: corruption, global south, identification, passports, terrorism

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Authors: Ridhish Kumar, Sudeep Nadukkandy, Anirban Roy

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The development of reverse osmosis happened in 1960. Along the years this technique has been widely accepted all over the world for varied applications ranging from seawater desalination to municipal water treatment. Forward osmosis (FO) is one of the foremost technologies for low energy consuming solutions for water purification. In this study, we have carried out a detailed analysis on selection, design, and pricing for a prototype of potable water system for purifying water in emergency situations. The portable and light purification system is envisaged to be driven by FO. This pouch will help to serve as an emergency water filtration device. The current effort employs a model to understand the interplay of permeability and area on the rate of purification of water from any impure source/brackish water. The draw solution for the FO pouch is considered to be a combination of salt and sugar such that dilution of the same would result in an oral rehydration solution (ORS) which is a boon for dehydrated patients. However, the effort takes an extra step to actually estimate the cost and pricing of designing such a prototype. While the mathematical model yields the best membrane (compositions are taken from literature) combination in terms of permeability and area, the pricing takes into account the feasibility of such a solution to be made available as a retail item. The product is envisaged to be a market competitor for packaged drinking water and ORS combination (costing around $0.5 combined) and thus, to be feasible has to be priced around the same range with greater margins in order to have a better distribution. Thus a proper business plan and production of the same has been formulated in order to be a feasible solution for unprecedented calamities and emergency situations.

Keywords: forward osmosis, water treatment, oral rehydration solution, prototype

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Authors: Abolghasem Yousefi-Babadi, Ali Bozorgi-Amiri, Aida Kazempour, Reza Tavakkoli-Moghaddam, Maryam Irani

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All over the world, natural disasters (e.g., earthquakes, floods, volcanoes and hurricanes) causes a lot of deaths. Earthquakes are introduced as catastrophic events, which is accident by unusual phenomena leading to much loss around the world. Such could be replaced by disasters or any other synonyms strongly demand great long-term help and relief, which can be hard to be managed. Supplies and facilities are very important challenges after any earthquake which should be prepared for the disaster regions to satisfy the people's demands who are suffering from earthquake. This paper proposed disaster response facility allocation problem for disaster relief operations as a mathematical programming model. Not only damaged people in the earthquake victims, need the consumable commodities (e.g., food and water), but also they need non-consumable commodities (e.g., clothes) to protect themselves. Therefore, it is concluded that paying attention to disaster points and people's demands are very necessary. To deal with this objective, both commodities including consumable and need non-consumable commodities are considered in the presented model. This paper presented the multi-objective multi-period mathematical programming model regarding the minimizing the average of the weighted response times and minimizing the total operational cost and penalty costs of unmet demand and unused commodities simultaneously. Furthermore, a Chebycheff multi-objective solution procedure as a powerful solution algorithm is applied to solve the proposed model. Finally, to illustrate the model applicability, a case study of the Tehran earthquake is studied, also to show model validation a sensitivity analysis is carried out.

Keywords: facility location, multi-objective model, disaster response, commodity

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Authors: Choki, Supatchai Boonpratham, Suwannee Luppanapornlarp

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The objective of this study was to find a correlation between cephalometric measurements and visual perception of facial profile in skeletal type II patients. In this study, 250 lateral cephalograms of female patients from age, 20 to 22 years were analyzed. The profile outlines of all the samples were hand traced and transformed into silhouettes by the principal investigator. Profile ratings were done by 9 orthodontists on Visual Analogue Scale from score one to ten (increasing level of convexity). 37 hard issue and soft tissue cephalometric measurements were analyzed by the principal investigator. All the measurements were repeated after 2 weeks interval for error assessment. At last, the rankings of visual perceptions were correlated with cephalometric measurements using Spearman correlation coefficient (P < 0.05). The results show that the increase in facial convexity was correlated with higher values of ANB (A point, nasion and B point), AF-BF (distance from A point to B point in mm), L1-NB (distance from lower incisor to NB line in mm), anterior maxillary alveolar height, posterior maxillary alveolar height, overjet, H angle hard tissue, H angle soft tissue and lower lip to E plane (absolute correlation values from 0.277 to 0.711). In contrast, the increase in facial convexity was correlated with lower values of Pg. to N perpendicular and Pg. to NB (mm) (absolute correlation value -0.302 and -0.294 respectively). From the soft tissue measurements, H angles had a higher correlation with visual perception than facial contour angle, nasolabial angle, and lower lip to E plane. In conclusion, the findings of this study indicated that the correlation of cephalometric measurements with visual perception was less than expected. Only 29% of cephalometric measurements had a significant correlation with visual perception. Therefore, diagnosis based solely on cephalometric analysis can result in failure to meet the patient’s esthetic expectation.

Keywords: cephalometric measurements, facial profile, skeletal type II, visual perception

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Authors: Rojan Afrouz

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Introduction: The immigration is a complex process of transitioning and transformation. Immigrants are more likely to come from the patriarchal and hierarchical society with traditional gender roles and women’s stereotypes. Changing the perception of women’s gender roles may result in challenges between women and their family and community. In this article, Afghan women’s perspectives on gender roles and stereotypes have been investigated as well as their experience of changes in the new context of Australia. Australian initiatives of challenging gender roles have provided the opportunities for Afghan women to emancipate from the traditional gender roles and pursue the value of gender equality. In this process, they may face many challenges in intersectional levels within their family, community and wider society which is a complex conflate of oppressive factors that may not be addressed easily and straightforward. Methods: This qualitative study has been conducted among Afghan women who have lived in Australia less than ten years. Semi-structured interviews either face to face or by phone have been used to collect data for this study. The interviews have been audio-recorded and transcribed verbatim. Nvivo software has been used for data analysis. Findings: Many participants mentioned that they had been taught that a good Afghan woman is devoted, obedient and loyal to their family and community. They believed that for many Afghan families, Afghan women's natural place was inside the home as a housewife, mother, daughter involving so many responsibilities and expectation of making sacrifices. Many women stated that their attitudes toward gender roles and their feeling of being a woman had been changed since they came to Australia although the process of change for women was complex and diverse. Some had to deal with conflicts with their stereotypes, traditional gender roles as well as strong disagreement with their family and community. Conclusion: Moving to a different country with more gender equality is an opportunity for Afghan women to change their perceptions of gender roles and stereotypes. However, challenging traditional stereotypes and gender roles in the new context is a complex process comprising intersectional levels.

Keywords: stereotypes, gender role, immigration, Afghan women

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Authors: Syed Muhammad Basit Ali, Usama Saleem, Irtiza Ali

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Internal combustion engines have been pioneers in the aviation industry, use of piston engines for aircraft propulsion, from propeller-driven bi-planes to turbo-prop, commercial, and cargo airliners. To provide an adequate amount of thrust piston engine rotates the propeller at a specific rpm, allowing enough mass airflow. Thrust is the only forward-acting force of an aircraft that helps heavier than air bodies to fly, depending on the mathematical model and variables included in that with the correct measurement. Test-benches have been a bench-mark in the aerospace industry to analyse the results before a flight, having paramount significance in reliability and safety engineering, depending on the mathematical model and variables included in that with the correct measurement. Calculation of thrust from a piston engine also depends on environmental changes, the diameter of the propeller, and the density of air. The project would be centered on piston engines used in the aviation industry for light aircraft and UAVs. A static thrust test bench involves various units, each performing a designed purpose to monitor and display. Static thrust tests are performed on the ground, and safety concerns hold paramount importance. The execution of this study involves research, design, manufacturing, and results based on reverse engineering initiating from virtual design, analytical analysis, and simulations. The final evaluation of results gathered from various methods such as co-relation between conventional mass-spring and digital loadcell. On average, we received 17.5kg of thrust (25+ engine run-ups – around 40 hours of engine run), only 10% deviation from analytically calculated thrust –providing 90% accuracy.

Keywords: aviation, aeronautics, static thrust, test bench, aircraft maintenance

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Authors: Donatella Giuliani

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In this research, we propose an unsupervised grayscale image segmentation method based on a combination of the Firefly Algorithm and the Gaussian Mixture Model. Firstly, the Firefly Algorithm has been applied in a histogram-based research of cluster means. The Firefly Algorithm is a stochastic global optimization technique, centered on the flashing characteristics of fireflies. In this context it has been performed to determine the number of clusters and the related cluster means in a histogram-based segmentation approach. Successively these means are used in the initialization step for the parameter estimation of a Gaussian Mixture Model. The parametric probability density function of a Gaussian Mixture Model is represented as a weighted sum of Gaussian component densities, whose parameters are evaluated applying the iterative Expectation-Maximization technique. The coefficients of the linear super-position of Gaussians can be thought as prior probabilities of each component. Applying the Bayes rule, the posterior probabilities of the grayscale intensities have been evaluated, therefore their maxima are used to assign each pixel to the clusters, according to their gray-level values. The proposed approach appears fairly solid and reliable when applied even to complex grayscale images. The validation has been performed by using different standard measures, more precisely: the Root Mean Square Error (RMSE), the Structural Content (SC), the Normalized Correlation Coefficient (NK) and the Davies-Bouldin (DB) index. The achieved results have strongly confirmed the robustness of this gray scale segmentation method based on a metaheuristic algorithm. Another noteworthy advantage of this methodology is due to the use of maxima of responsibilities for the pixel assignment that implies a consistent reduction of the computational costs.

Keywords: clustering images, firefly algorithm, Gaussian mixture model, meta heuristic algorithm, image segmentation

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Authors: Mona Shojaei

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The Sub-Atmospheric Vapor Pipeline (SAVP) introduces a distinct approach to seawater desalination with promising applications in both land and industrial sectors. SAVP systems exploit the temperature difference between a hot source and a cold environment to facilitate efficient vapor transfer, offering substantial benefits in diverse industrial and field applications. This approach incorporates dynamic boundary conditions, where the temperatures of hot and cold sources vary over time, particularly in natural and industrial environments. Such variations critically influence convection and diffusion processes, introducing challenges that require the refinement of the convection-diffusion equation and the derivation of temperature profiles along the pipeline through advanced engineering mathematics. This study formulates vapor temperature as a function of time and length using two mathematical approaches: Eigen functions and Green’s equation. Combining detailed theoretical modeling, mathematical simulations, and extensive field and industrial tests, this research underscores the SAVP system’s scalability for real-world applications. Results reveal a high degree of accuracy, highlighting SAVP’s significant potential for energy conservation and environmental sustainability. Furthermore, the integration of SAVP technology within smart and green building systems creates new opportunities for sustainable urban water management. By capturing and repurposing vapor for non-potable uses such as irrigation, greywater recycling, and ecosystem support in green spaces, SAVP aligns with the principles of smart and green buildings. Smart buildings emphasize efficient resource management, enhanced system control, and automation for optimal energy and water use, while green buildings prioritize environmental impact reduction and resource conservation. SAVP technology bridges both paradigms, enhancing water self-sufficiency and reducing reliance on external water supplies. The sustainable and energy-efficient properties of SAVP make it a vital component in resilient infrastructure development, addressing urban water scarcity while promoting eco-friendly living. This dual alignment with smart and green building goals positions SAVP as a transformative solution in the pursuit of sustainable urban resource management.

Keywords: sub-atmospheric vapor pipeline, seawater desalination, energy efficiency, vapor transfer dynamics, mathematical modeling, sustainable water solutions, smart buildings

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Authors: Ann Dashwood

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Using Standard Australian English with confidence is a cultural expectation of parents of primary school aged children who want to engage effectively with their children’s teachers and school administration. That confidence in support of their children’s learning at school is seldom experienced by parents whose first language is not English. Sharing language with competence in an intercultural environment is the common denominator for meaningful communication and engagement to occur in a school community. Experience in relevant, interactive sessions is known to enhance engagement and participation. The purpose of this paper is to identify a pedagogy for parents otherwise isolated from daily use of functional Australian cultural language learned to engage effectively in their children’s learning at school. The outcomes measure parents’ intercultural engagement with classroom teachers and attention to the school’s administrative procedures using quantitative and qualitative methods. A principled communicative task-based language learning approach, combined with intercultural communication strategies provide the theoretical base for intensive English inquiry-based learning and engagement. The quantitative analysis examines data samples collected by classroom teachers and administrators and parents’ writing samples. Interviews and observations qualitatively inform the study. Currently, significant numbers of projects are active in community centers and schools to enhance English language knowledge of parents from Language Backgrounds Other Than English (LBOTE). The study is significant to explore the effects of an intensive English pedagogy with parents of varied English language backgrounds, by targeting inquiry-based language use for social interactions in the school and wider community, specific engagement and cultural interaction with teachers and school activities and procedures.

Keywords: engagement, intercultural communication, language teaching pedagogy, LBOTE, school community

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Authors: Deepshikha Shukla, C. H. Solanki, Mayank Desai

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In the last few years, it has been observed that earthquake is proving a threat to the scientist across the world. With a large number of earthquakes occurring in day to day life, the threat to life and property has increased manifolds which call for an urgent attention of all the researchers globally to carry out the research in the field of Earthquake Engineering. Any hazard related to the earthquake and seismicity is considered to be seismic hazards. The common forms of seismic hazards are Ground Shaking, Structure Damage, Structural Hazards, Liquefaction, Landslides, Tsunami to name a few. Among all the natural hazards, the most devastating and damaging is the earthquake as all other hazards are triggered only after the occurrence of an earthquake. In order to quantify and estimate the seismicity and seismic hazards, many methods and approaches have been proposed in the past few years. Such approaches are Mathematical, Conventional and Computational. Convex Set Theory, Empirical Green’s Function are some of the Mathematical Approaches whereas the Deterministic and Probabilistic Approaches are the Conventional Approach for the estimation of the seismic Hazards. Ground response and Ground Shaking of a particular area or region plays an important role in the damage caused due to the earthquake. In this paper, seismic study using Deterministic Approach and 1 D Ground Response Analysis has been carried out for Madhya Pradesh Tourism Office in Indore Region in Madhya Pradesh in Central India. Indore lies in the seismic zone III (IS: 1893, 2002) in the Seismic Zoning map of India. There are various faults and lineament in this area and Narmada Some Fault and Gavilgadh fault are the active sources of earthquake in the study area. Deepsoil v6.1.7 has been used to perform the 1 D Linear Ground Response Analysis for the study area. The Peak Ground Acceleration (PGA) of the city ranges from 0.1g to 0.56g.

Keywords: seismicity, seismic hazards, deterministic, probabilistic methods, ground response analysis

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Authors: Tadeusz Nowicki, Radosław Pytlak, Robert Waszkowski, Jerzy Bertrandt, Anna Kłos

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This paper presents methods for formal modeling of activities in the area of sanitary inspectors outbreak of food-borne diseases. The models allow you to measure the characteristics of the activities of sanitary inspection and as a result allow improving the performance of sanitary services and thus food security.

Keywords: food-borne disease, epidemic, sanitary inspection, mathematical models

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Authors: Ebru Dural, M. Zulfu Asık

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Laminated glass is a kind of safety glass, which is made by 'sandwiching' two glass sheets and a polyvinyl butyral (PVB) interlayer in between them. When the glass is broken, the interlayer in between the glass sheets can stick them together. Because of this property, the hazards of sharp projectiles during natural and man-made disasters reduces. They can be widely applied in building, architecture, automotive, transport industries. Laminated glass can easily undergo large displacements even under their own weight. In order to explain their true behavior, they should be analyzed by using large deflection theory to represent nonlinear behavior. In this study, a nonlinear mathematical model is developed for the analysis of laminated glass cylindrical shell which is free in radial directions and restrained in axial directions. The results will be verified by using the results of the experiment, carried out on laminated glass cylindrical shells. The behavior of laminated composite cylindrical shell can be represented by five partial differential equations. Four of the five equations are used to represent axial displacements and radial displacements and the fifth one for the transverse deflection of the unit. Governing partial differential equations are derived by employing variational principles and minimum potential energy concept. Finite difference method is employed to solve the coupled differential equations. First, they are converted into a system of matrix equations and then iterative procedure is employed. Iterative procedure is necessary since equations are coupled. Problems occurred in getting convergent sequence generated by the employed procedure are overcome by employing variable underrelaxation factor. The procedure developed to solve the differential equations provides not only less storage but also less calculation time, which is a substantial advantage in computational mechanics problems.

Keywords: laminated glass, mathematical model, nonlinear behavior, PVB

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Authors: Hugo Daneluzzo, Christelle Rabbat, Alan Jean-Marie

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Water electrolysis is one of the most advanced technologies for producing hydrogen and can be easily combined with electricity from different sources. Under the influence of electric current, water molecules can be split into oxygen and hydrogen. The production of hydrogen by water electrolysis favors the integration of renewable energy sources into the energy mix by compensating for their intermittence through the storage of the energy produced when production exceeds demand and its release during off-peak production periods. Among the various electrolysis technologies, anion exchange membrane (AEM) electrolyser cells are emerging as a reliable technology for water electrolysis. Modeling and simulation are effective tools to save time, money, and effort during the optimization of operating conditions and the investigation of the design. The modeling and simulation become even more important when dealing with multiphysics dynamic systems. One of those systems is the AEM electrolysis cell involving complex physico-chemical reactions. Once developed, models may be utilized to comprehend the mechanisms to control and detect flaws in the systems. Several modeling methods have been initiated by scientists. These methods can be separated into two main approaches, namely equation-based modeling and graph-based modeling. The former approach is less user-friendly and difficult to update as it is based on ordinary or partial differential equations to represent the systems. However, the latter approach is more user-friendly and allows a clear representation of physical phenomena. In this case, the system is depicted by connecting subsystems, so-called blocks, through ports based on their physical interactions, hence being suitable for multiphysics systems. Among the graphical modelling methods, the bond graph is receiving increasing attention as being domain-independent and relying on the energy exchange between the components of the system. At present, few studies have investigated the modelling of AEM systems. A mathematical model and a bond graph model were used in previous studies to model the electrolysis cell performance. In this study, experimental data from literature were simulated using OpenModelica using bond graphs and mathematical approaches. The polarization curves at different operating conditions obtained by both approaches were compared with experimental ones. It was stated that both models predicted satisfactorily the polarization curves with error margins lower than 2% for equation-based models and lower than 5% for the bond graph model. The activation polarization of hydrogen evolution reactions (HER) and oxygen evolution reactions (OER) were behind the voltage loss in the AEM electrolyzer, whereas ion conduction through the membrane resulted in the ohmic loss. Therefore, highly active electro-catalysts are required for both HER and OER while high-conductivity AEMs are needed for effectively lowering the ohmic losses. The bond graph simulation of the polarisation curve for operating conditions at various temperatures has illustrated that voltage increases with temperature owing to the technology of the membrane. Simulation of the polarisation curve can be tested virtually, hence resulting in reduced cost and time involved due to experimental testing and improved design optimization. Further improvements can be made by implementing the bond graph model in a real power-to-gas-to-power scenario.

Keywords: hydrogen production, anion-exchange membrane, electrolyzer, mathematical modeling, multiphysics modeling

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Authors: Karun K. Karki

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Globalization has intensified the transnational movement of people, mainly from the Global South to the Global North. In this context of transnationalism, migration is framed within the national interests required for economic prosperity. More specifically, the competition for the ‘best and the brightest of highly educated immigrants from around the world can be perceived as evidence that countries in the North are competing in the knowledge-based global economy. Canada is not an exception. Since the early 1970s, Canada has successfully admitted, on average, 200,000 to 280,000 immigrants annually for permanent residency, primarily for economic development, family reunification and humanitarian affairs. Among these three components, economic class immigrants are the highest priority in its immigration policy. Although Canada admits highly qualified immigrant professionals with the expectation of easily integrating them, many highly skilled immigrants are marginalized in the labour market due to a myriad of layered structural and institutional barriers that prevent them from working in the professions for which they were trained in their country of origin. More than 67% of highly skilled immigrants are more likely to be in jobs for which they are formally overqualified. The deteriorating employment situation of highly educated immigrants, particularly the immigrants of racialized groups, needs analytical scrutiny of the immigration policy of Canada. In this paper, author examine how the historical legacy of colonialism still continues in Canada’s immigration policymaking and how this legacy has impacted developing countries in the global South. Author argue that the Canadian immigration policy is based on the notion of exploiting/dominating smaller countries and immigrants from these countries. Such colonial policies have systematically ‘Othered’ immigrants based on their race, ethnicity, gender, culture, and linguistic characteristics. Recommendations are made to revisit contemporary immigration and settlement policies to effectively integrate immigrants into Canadian society.

Keywords: colonialism, Canadian immigration policy, racialized immigrants, skilled immigrants

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Authors: John Adebayo Oloyhede

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This paper examines effect of financial liberalization on the stability of the demand for money function and its implication for exchange rate behaviour of three African countries. As the demand for money function is regarded as one of the two main building blocks of most exchange rate determination models, the other being purchasing power parity, its stability is required for the monetary models of exchange rate determination to hold. To what extent has the liberalisation policy of these countries, for instance liberalised interest rate, affected the demand for money function and what has been the consequence on the validity and relevance of floating exchange rate models? The study adopts the Autoregressive Instrumental Package (AIV) of multiple regression technique and followed the Almon Polynomial procedure with zero-end constraint. Data for the period 1986 to 2011 were drawn from three developing countries of Africa, namely: Gambia, Ghana and Nigeria, which did not only start the liberalization and floating system almost at the same period but share similar and diverse economic and financial structures. Its findings show that the demand for money was a stable function of income and interest rate at home and abroad. Other factors such as exchange rate and foreign interest rate exerted some significant effect on domestic money demand. The short-run and long-run elasticity with respect to income, interest rates, expected inflation rate and exchange rate expectation are not greater than zero. This evidence conforms to some extent to the expected behaviour of the domestic money function and underscores its ability to serve as good building block or assumption of the monetary model of exchange rate determination. This will, therefore, assist appropriate monetary authorities in the design and implementation of further financial liberalization policy packages in developing countries.

Keywords: financial liberalisation, exchange rates, demand for money, developing economies

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Authors: Nwadioha Samuel Iheanacho, Abah Paul, Odimayo Simidele Michael

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Background: The World Health Assembly through the Global Health Sector Strategy on viral hepatitis calls for the elimination of viral hepatitis as a public health threat by 2030. All hands are on deck to actualize this goal through an effective and active vaccination and monitoring tool. Aim: To combine the Epidemiologic with Laboratory Hepatitis B Virus vaccination monitoring tools. Method: Laboratory results analysis of subjects recruited during the World Hepatitis week from July 2020 to July 2021 was done after obtaining their epidemiologic data on Hepatitis B virus risk factors, in the Medical Microbiology Laboratory of Benue State University Teaching Hospital, Nigeria. Result: A total of 500 subjects comprising males 60.0%(n=300/500) and females 40.0%(n=200/500) were recruited. A fifty-three percent majority was of the age range of 26 to 36 years. Serologic profiles were as follows, 15.0%(n=75/500) HBsAg; 7.0% (n=35/500) HBeAg; 8.0% (n=40/500) Anti-Hbe; 20.0% (n=100/500) Anti-HBc and 38.0% (n=190/500) Anti-HBs. Immune responses to vaccination were as follows, 47.0%(n=235/500) Immune naïve {no serologic marker + normal ALT}; 33%(n=165/500) Immunity by vaccination {Anti-HBs + normal ALT}; 5%(n=25/500) Immunity to previous infection {Anti-HBs, Anti-HBc, +/- Anti-HBe + normal ALT}; 8%(n=40/500) Carriers {HBsAg, Anti-HBc, Anti-HBe +normal ALT} and 7% (35/500) Anti-HBe serum- negative infections {HBsAg, HBeAg, Anti-HBc +elevated ALT}. Conclusion: The present 33.0% immunity by vaccination coverage in Central Nigeria was much lower than the 41.0% national peak in 2013, and a far cry from the global expectation of attainment of a Global Health Sector Strategy on the elimination of viral hepatitis as a public health threat by 2030. Therefore, more creative ideas and collective effort are needed to attain this goal of the World Health Assembly.

Keywords: Hepatitis B, vaccination status, laboratory tools, resource-limited settings

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Authors: Ann Dashwood

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Using standard Australian English with confidence is a cultural expectation of parents of primary school aged children who want to engage effectively with their children’s teachers and school administration. That confidence in support of their children’s learning at school is seldom experienced by parents whose first language is not English. Sharing language with competence in an intercultural environment is the common denominator for meaningful communication and engagement to occur in a school community. Experience in relevant interactive sessions is known to enhance engagement and participation. The purpose of this paper is to identify interactional settings for which parents who are isolated from the daily use of functional Australian cultural language learned to engage more effectively in their children’s learning at school. The outcomes measured parents’ intercultural engagement with classroom teachers and attention to the school’s administrative procedures. The study used quantitative and qualitative methods. The principles of communicative task-based language learning combined with intercultural communication principles provided the theoretical base for intensive English task-based learning and engagement. The quantitative analysis examined data samples collected by classroom teachers and administrators and parents’ writing samples. Interviews and observations qualitatively informed the study. Currently significant numbers of projects are active in community centres and schools to enhance English language knowledge of parents from Language Backgrounds Other Than English (LBOTE). The study was significant to explore the effects of conducting intensive English with parents of varied English language backgrounds by targeting language use for social interactions in the community, specific engagement in school activities, cultural interaction with teachers and responsiveness to complying with school procedures.

Keywords: engagement, intercultural communication, LBOTE, school community

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Authors: Jingcheng Ma, Patricia B. Weisensee, Young H. Shin, Yujin Chang, Junjiao Tian, William P. King, Nenad Miljkovic

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Water droplet impact on surfaces is a ubiquitous phenomenon in both nature and industry. The transfer of mass, momentum and energy can be influenced by the time of contact between droplet and surface. In order to reduce the contact time, we study the influence of substrate motion prior to impact on the dynamics of droplet recoil. Using optical high speed imaging, we investigated the impact dynamics of macroscopic water droplets (~ 2mm) on rigid nanostructured superhydrophobic surfaces vibrating at 60 – 300 Hz and amplitudes of 0 – 3 mm. In addition, we studied the influence of the phase of the substrate at the moment of impact on total contact time. We demonstrate that substrate vibration can alter droplet dynamics, and decrease total contact time by as much as 50% compared to impact on stationary rigid superhydrophobic surfaces. Impact analysis revealed that the vibration frequency mainly affected the maximum contact time, while the amplitude of vibration had little direct effect on the contact time. Through mathematical modeling, we show that the oscillation amplitude influences the possibility density function of droplet impact at a given phase, and thus indirectly influences the average contact time. We also observed more vigorous droplet splashing and breakup during impact at larger amplitudes. Through semi-empirical mathematical modeling, we describe the relationship between contact time and vibration frequency, phase, and amplitude of the substrate. We also show that the maximum acceleration during the impact process is better suited as a threshold parameter for the onset of splashing than a Weber-number criterion. This study not only provides new insights into droplet impact physics on vibrating surfaces, but develops guidelines for the rational design of surfaces to achieve controllable droplet wetting in applications utilizing vibration.

Keywords: contact time, impact dynamics, oscillation, pear-shape droplet

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Authors: Nhi Ngoc Thien

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Franchising is a popular trend in Vietnam retail industry, especially in fast food industry. Several famous foreign fast food brands such as KFC, Lotteria, Jollibee or Pizza Hut invested on this potential market since the 1990s. Following this trend, in 2011, Burger King - the second largest fast food hamburger chain all over the world - entered Vietnam with its first store located in Tan Son Nhat International Airport, with the expectation to become the leading brand in the country. However, the business performance of Burger King was not going well in the first few years making it questioned about its strategy. The given assumption was that its business performance was affected negatively by its store location selection strategy. This research aims to investigate the current performance of Burger King Vietnam in terms of the controllable variables like store location as well as to explore the key factors influencing customer decision to choose Burger King. Therefore, a case study research method was conducted to approach deeply on the opinions and evaluations of 10 Burger King’s customers, Burger King's staffs and other fast food experts on Burger King’s performance through in-depth interview, direct observation and documentary analysis. Findings show that there are 8 determinants affecting the decision-making of Burger King’s customers, which are store location, quality of food, service quality, store atmosphere, price, promotion, menu and brand reputation. Moreover, findings present that Burger King’s staffs and fast food experts also mentioned the main problems of Burger King, which are about store location and food quality. As a result, there are some recommendations for Burger King Vietnam to improve its performance in the market and attract more Vietnamese target customers by giving suitable promotional activities among its customers and being differentiated itself from other fast food brands.

Keywords: overall retail strategy, controllable variables, store location, quality of food

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Authors: Carol Okigbo

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Mathematical problem solving has long been accorded an important place in mathematics curricula at every education level in both advanced and emerging economies. Its classroom approaches have varied, such as teaching for problem-solving, teaching about problem-solving, and teaching mathematics through problem-solving. It requires engaging in tasks for which the solution methods are not eminent, making sense of problems and persevering in solving them by exhibiting processes, strategies, appropriate attitude, and adequate exposure. Teachers play important roles in helping students acquire competency in problem-solving; thus, they are expected to be good problem-solvers and have proper conceptions of problem-solving. Studies show that teachers’ conceptions influence their decisions about what to teach and how to teach. Therefore, how teachers view their roles in teaching problem-solving will depend on their pedagogical conceptions of problem-solving. If teaching problem-solving is a major component of secondary school mathematics instruction, as recommended by researchers and mathematics educators, then it is necessary to establish teachers’ conceptions, what they do, and how they approach problem-solving. This study is designed to determine secondary school teachers’ conceptions regarding mathematical problem solving, its current situation, how teachers’ conceptions relate to their demographics, as well as the interaction patterns in the mathematics classroom. There have been many studies of mathematics problem solving, some of which addressed teachers’ conceptions using single-method approaches, thereby presenting only limited views of this important phenomenon. To address the problem more holistically, this study adopted an integrated mixed methods approach which involved a quantitative survey, qualitative analysis of open-ended responses, and ethnographic observations of teachers in class. Data for the analysis came from a random sample of 327 secondary school mathematics teachers in two Nigerian states - Anambra State and Enugu State who completed a 45-item questionnaire. Ten of the items elicited demographic information, 11 items were open-ended questions, and 25 items were Likert-type questions. Of the 327 teachers who responded to the questionnaires, 37 were randomly selected and observed in their classes. Data analysis using ANOVA, t-tests, chi-square tests, and open coding showed that the teachers had different conceptions about problem-solving, which fall into three main themes: practice on exercises and word application problems, a process of solving mathematical problems, and a way of teaching mathematics. Teachers reported that no period is set aside for problem-solving; typically, teachers solve problems on the board, teach problem-solving strategies, and allow students time to struggle with problems on their own. The result shows a significant difference between male and female teachers’ conception of problems solving, a significant relationship among teachers’ conceptions and academic qualifications, and teachers who have spent ten years or more teaching mathematics were significantly different from the group with seven to nine years of experience in terms of their conceptions of problem-solving.

Keywords: conceptions, education, mathematics, problem solving, teacher

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Authors: Alexandru-Ion Marinescu

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There exist a plethora of methods in the scientific literature which tackle the well-established task of credit score evaluation. In its most abstract form, a credit scoring algorithm takes as input several credit applicant properties, such as age, marital status, employment status, loan duration, etc. and must output a binary response variable (i.e. “GOOD” or “BAD”) stating whether the client is susceptible to payment return delays. Data imbalance is a common occurrence among financial institution databases, with the majority being classified as “GOOD” clients (clients that respect the loan return calendar) alongside a small percentage of “BAD” clients. But it is the “BAD” clients we are interested in since accurately predicting their behavior is crucial in preventing unwanted loss for loan providers. We add to this whole context the constraint that the algorithm must yield an actual, tractable mathematical formula, which is friendlier towards financial analysts. To this end, we have turned to genetic algorithms and genetic programming, aiming to evolve actual mathematical expressions using specially tailored mutation and crossover operators. As far as data representation is concerned, we employ a very flexible mechanism – LINQ expression trees, readily available in the C# programming language, enabling us to construct executable pieces of code at runtime. As the title implies, they model trees, with intermediate nodes being operators (addition, subtraction, multiplication, division) or mathematical functions (sin, cos, abs, round, etc.) and leaf nodes storing either constants or variables. There is a one-to-one correspondence between the client properties and the formula variables. The mutation and crossover operators work on a flattened version of the tree, obtained via a pre-order traversal. A consequence of our chosen technique is that we can identify and discard client properties which do not take part in the final score evaluation, effectively acting as a dimensionality reduction scheme. We compare ourselves with state of the art approaches, such as support vector machines, Bayesian networks, and extreme learning machines, to name a few. The data sets we benchmark against amount to a total of 8, of which we mention the well-known Australian credit and German credit data sets, and the performance indicators are the following: percentage correctly classified, area under curve, partial Gini index, H-measure, Brier score and Kolmogorov-Smirnov statistic, respectively. Finally, we obtain encouraging results, which, although placing us in the lower half of the hierarchy, drive us to further refine the algorithm.

Keywords: expression trees, financial credit scoring, genetic algorithm, genetic programming, symbolic evolution

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Authors: Ika Jorum

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The aim of this collaborative project was to develop library support that contributes in a long-term way to a technical university’s work on increased equality in education. The background was an assessment made by the Higher Education Authority that showed the need for improvement regarding equality in several programs at the university. The university’s Vice President for equality and Vice President for sustainability announced funds for projects that supported the improvement of equality in education. The library was granted funding for a one-year project that aimed both to support teachers in order to embed equality in education and to support the library staff and improve the organization’s own work. The part of the project that was directed to teachers was performed as activities in different areas and forms, such as acquisition and collections, teaching, exhibitions and book discussions. Besides the activities and support that was offered to teachers, the education team had journal clubs in order to develop and embed equality in their own teaching. The part that was directed to library staff and management was performed as workshops in collaboration with Equality Office in order to identify areas where the library could make improvements on work with equality and inclusion. The expectation was that the activities would be well attended since the project team had got indications that the content would be relevant. The outcome of this project was that some activities turned out to be more attended than others and what is expected to be found relevant, for example, a workshop on information searching from a gender and equality perspective for teachers, might still not attract participants. On the other hand, Ph.D. students and students participated in the book discussions and wanted them to continue after the project had ended. Results will be shared both on what was successful and what was challenging. Some reflections will be given on what can be done to attract participants to activities in the area of gender equality that is most likely relevant for the expected attendants and how results from a project on gender equality can be integrated into an organization’s daily work.

Keywords: equality, higher education, critical information literacy, collaboration

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Authors: In-Hwan Baek

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Valsartan is a potent and highly selective antagonist of the angiotensin II type 1 receptor, and is widely used for the treatment of hypertension. The aim of this study was to investigate the pharmacokinetic properties of the valsartan in dogs following oral administration of a single dose using quantitative modeling approaches. Forty beagle dogs were randomly divided into two group. Group A (n=20) was administered a single oral dose of valsartan 80 mg (Diovan® 80 mg), and group B (n=20) was administered a single oral dose of valsartan 160 mg (Diovan® 160 mg) in the morning after an overnight fast. Blood samples were collected into heparinized tubes before and at 0.5, 1, 1.5, 2, 2.5, 3, 4, 6, 8, 12 and 24 h following oral administration. The plasma concentrations of the valsartan were determined using LC-MS/MS. Non-compartmental pharmacokinetic analyses were performed using WinNonlin Standard Edition software, and modeling approaches were performed using maximum-likelihood estimation via the expectation maximization (MLEM) algorithm with sampling using ADAPT 5 software. After a single dose of valsartan 80 mg, the mean value of maximum concentration (Cmax) was 2.68 ± 1.17 μg/mL at 1.83 ± 1.27 h. The area under the plasma concentration-versus-time curve from time zero to the last measurable concentration (AUC24h) value was 13.21 ± 6.88 μg·h/mL. After dosing with valsartan 160 mg, the mean Cmax was 4.13 ± 1.49 μg/mL at 1.80 ± 1.53 h, the AUC24h was 26.02 ± 12.07 μg·h/mL. The Cmax and AUC values increased in proportion to the increment in valsartan dose, while the pharmacokinetic parameters of elimination rate constant, half-life, apparent of total clearance, and apparent of volume of distribution were not significantly different between the doses. Valsartan pharmacokinetic analysis fits a one-compartment model with first-order absorption and elimination following a single dose of valsartan 80 mg and 160 mg. In addition, high inter-individual variability was identified in the absorption rate constant. In conclusion, valsartan displays the dose-dependent pharmacokinetics in dogs, and Subsequent quantitative modeling approaches provided detailed pharmacokinetic information of valsartan. The current findings provide useful information in dogs that will aid future development of improved formulations or fixed-dose combinations.

Keywords: dose-dependent, modeling, pharmacokinetics, valsartan

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Authors: Hui-Chieh Li

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Circular economy promotes greater resource productivity and avoids pollution through greater recycling and re-use which bring benefits for both the environment and the economy. The concept is contrast to a linear economy which is ‘take, make, dispose’ model of production. A well-design reverse logistics service strategy could enhance the willingness of recycling of the users and reduce the related logistics cost as well as carbon emissions. Moreover, the recycle brings the manufacturers most advantages as it targets components for closed-loop reuse, essentially converting materials and components from worn-out product into inputs for new ones at right time and right place. This study considers demand-supply interaction, time-dependent recycle demand, time-dependent surplus value of recycled product and constructs models on recycle service strategy for the recyclable waste collector. A crucial factor in optimizing a recycle service strategy is consumer demand. The study considers the relationships between consumer demand towards recycle and product characteristics, surplus value and user behavior. The study proposes a recycle service strategy which differs significantly from the conventional and typical uniform service strategy. Periods with considerable demand and large surplus product value suggest frequent and short service cycle. The study explores how to determine a recycle service strategy for recyclable waste collector in terms of service cycle frequency and duration and vehicle type for all service cycles by considering surplus value of recycled product, time-dependent demand, transportation economies and demand-supply interaction. The recyclable waste collector is responsible for the collection of waste product for the manufacturer. The study also examines the impacts of utilization rate on the cost and profit in the context of different sizes of vehicles. The model applies mathematical programming methods and attempts to maximize the total profit of the distributor during the study period. This study applies the binary logit model, analytical model and mathematical programming methods to the problem. The model specifically explores how to determine a recycle service strategy for the recycler by considering product surplus value, time-dependent recycle demand, transportation economies and demand-supply interaction. The model applies mathematical programming methods and attempts to minimize the total logistics cost of the recycler and maximize the recycle benefits of the manufacturer during the study period. The study relaxes the constant demand assumption and examines how service strategy affects consumer demand towards waste recycling. Results of the study not only help understanding how the user demand for recycle service and product surplus value affects the logistics cost and manufacturer’s benefits, but also provide guidance such as award bonus and carbon emission regulations for the government.

Keywords: circular economy, consumer demand, product surplus value, recycle service strategy

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Authors: Sudhir Kumar Tewatia, Kanishck Tewatia, Anttriksh Tewatia

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Advancements in soil consolidation are discussed, and further improvements are proposed with particular reference to Tewatia’s Y-Y’ Approach, which is called the Settlement versus Rate of Settlement Approach in consolidation. A branch of calculus named Y-Y' (or y versus dy/dx) is suggested (as compared to the common X-Y', x versus dy/dx, dy/dx versus x or Newton-Leibniz branch) that solves some complicated/unsolved theoretical and practical problems in physical sciences (Physics, Chemistry, Mathematics, Biology, and allied sciences) and engineering in an amazingly simple and short manner, particularly when independent variable X is unknown and X-Y' Approach can’t be used. Complicated theoretical and practical problems in 1D, 2D, 3D Primary and Secondary consolidations with non-uniform gradual loading and irregularly shaped clays are solved with elementary school level Y-Y' Approach, and it is interesting to note that in X-Y' Approach, equations become more difficult while we move from one to three dimensions, but in Y-Y' Approach even 2D/3D equations are very simple to derive, solve, and use; rather easier sometimes. This branch of calculus will have a far-reaching impact on understanding and solving the problems in different fields of physical sciences and engineering that were hitherto unsolved or difficult to be solved by normal calculus/numerical/computer methods. Some particular cases from soil consolidation that basically creeps and diffusion equations in isolation and in combination with each other are taken for comparison with heat transfer. The Y-Y’ Approach can similarly be applied in wave equations and other fields wherever normal calculus works or fails. Soil mechanics uses mathematical analogies from other fields of physical sciences and engineering to solve theoretical and practical problems; for example, consolidation theory is a replica of the heat equation from thermodynamics with the addition of the effective stress principle. An attempt is made to give them mathematical analogies.

Keywords: calculus, clay, consolidation, creep, diffusion, heat, settlement

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