Search results for: second order gradient descent

Authors: Sanja O. Podunavac-Kuzmanović, Lidija R. Jevrić, Strahinja Z. Kovačević

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Benzimidazoles are a group of compounds with significant antibacterial, antifungal and anticancer activity. The studied compounds consist of the main benzimidazole structure with different combinations of substituens. This study is based on the two-dimensional and three-dimensional molecular modeling and calculation of molecular descriptors (physicochemical and lipophilicity descriptors) of structurally diverse benzimidazoles. Molecular modeling was carried out by using ChemBio3D Ultra version 14.0 software. The obtained 3D models were subjected to energy minimization using molecular mechanics force field method (MM2). The cutoff for structure optimization was set at a gradient of 0.1 kcal/Åmol. The obtained set of molecular descriptors was used in principal component analysis (PCA) of possible similarities and dissimilarities among the studied derivatives. After the molecular modeling, the quantitative structure-property relationship (QSPR) analysis was applied in order to get the mathematical models which can be used in prediction of pKb values of structurally similar benzimidazoles. The obtained models are based on statistically valid multiple linear regression (MLR) equations. The calculated cross-validation parameters indicate the high prediction ability of the established QSPR models. This study is financially supported by COST action CM1306 and the project No. 114-451-347/2015-02, financially supported by the Provincial Secretariat for Science and Technological Development of Vojvodina.

Keywords: benzimidazoles, chemometrics, molecular modeling, molecular descriptors, QSPR

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Kaitlyn Deierlein, Janet Lydecker

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Stereotypes surrounding anorexia nervosa are that the illness is commonly perceived as a self-inflicted disorder influenced by controlling parents, vanity, and cultural pressures. According to the authors' best knowledge minimal research has examined interactions with other factors, including gender and racial stereotypes involving this disorder. A common stereotype of this disease is that it mainly only affects Caucasian women and is very rarely seen in any other ethnicity. Previous literature has failed to investigate how visual body image and ethnic stereotypes affect the mental health of different ethnic groups, how various cultures impact the type of anorexia nervosa in the patient, and the different stereotypes associated with their eating disorder. Participants completed a pre-test questionnaire with vignettes, an image exposure portion, and a post-test questionnaire, which will all be evaluated and analyzed by ANOVA t-test and SPSS. Results showed that participants picked Caucasian females as more likely to have anorexia nervosa than those of Asian, Latin American, or African American descent subjects in both picture identification and vignettes. Future research should be conducted to further the results of this study by examining differences between gender stereotypes with anorexia nervosa as well as how sexuality has a role in perception.

Keywords: anorexia nervosa, ethnicity, stereotypes, eating disorders, perception

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Authors: Mohammad Bqoor, Mohammad Hamdan, Isam Janajreh, Sufian Abedrabbo

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This extensive theoretical study on a novel Ionized Gas Thermoelectric Generator (IG-TEG) system has shown the ability of continuous energy extracting from the thermal energy of ambient air around standard room temperature and even below. This system does not need a temperature gradient in order to work, unlike the other TEGs that use the Seebeck effect, and therefore this new system can be utilized in sustainable energy systems, as well as in green cooling solutions, by extracting energy instead of wasting energy in compressing the gas for cooling. This novel system was designed based on Static Ratchet Potential (SRP), which is known as a spatially asymmetric electric potential produced by an array of positive and negative electrodes. The ratchet potential produces an electrical current from the random Brownian Motion of charged particles that are driven by thermal energy. The key parameter of the system is particle transportation, and it was studied under the condition of flashing ratchet potentials utilizing several methods and examined experimentally, ensuring its functionality. In this study, a different approach is pursued to estimate particle transportation by evaluating the charged particle distribution and applying the other conditions of the SRP, and showing continued energy harvesting potency from the particles’ transportation. Ultimately, power levels of 10 Watt proved to be achievable from a 1 m long system tube of 10 cm radius.

Keywords: thermoelectric generator, ratchet potential, Brownian ratchet, energy harvesting, sustainable energy, green technology

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Dheyaa W. Abbood, Rafa H. AL-Suhaili, May S. Saleh

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A model using the artificial neural networks and genetic algorithm technique is developed for obtaining optimum dimensions of the foundation length and protections of small hydraulic structures. The procedure involves optimizing an objective function comprising a weighted summation of the state variables. The decision variables considered in the optimization are the upstream and downstream cutoffs length sand their angles of inclination, the foundation length, and the length of the downstream soil protection. These were obtained for a given maximum difference in head, depth of impervious layer and degree of anisotropy.The optimization carried out subjected to constraints that ensure a safe structure against the uplift pressure force and sufficient protection length at the downstream side of the structure to overcome an excessive exit gradient. The Geo-studios oft ware, was used to analyze 1200 different cases. For each case the length of protection and volume of structure required to satisfy the safety factors mentioned previously were estimated. An ANN model was developed and verified using these cases input-output sets as its data base. A MatLAB code was written to perform a genetic algorithm optimization modeling coupled with this ANN model using a formulated optimization model. A sensitivity analysis was done for selecting the cross-over probability, the mutation probability and level ,the number of population, the position of the crossover and the weights distribution for all the terms of the objective function. Results indicate that the most factor that affects the optimum solution is the number of population required. The minimum value that gives stable global optimum solution of this parameters is (30000) while other variables have little effect on the optimum solution.

Keywords: inclined cutoff, optimization, genetic algorithm, artificial neural networks, geo-studio, uplift pressure, exit gradient, factor of safety

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Authors: A. Ritcey, J. R. Mcdermid, S. Ziada

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Wall shear stress was experimentally measured under a planar impinging air jet as a function of jet Reynolds number (Rejet = 5000, 8000, 11000) and different normalized impingement distances (H/D = 4, 6, 8, 10, 12) using the razor blade technique to complete a parametric study. The wall pressure, wall pressure gradient, and wall shear stress information were obtained.

Keywords: experimental fluid mechanics, impinging planar jets, skin friction factor, wall shear stress

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Authors: Benjamin K. Ghansah, Richard K. Appoh, Iliya Nababa, Eric K. Forkuo

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The Nasia River is an important source of water for domestic and agricultural purposes to the inhabitants of its catchment. Major farming activities takes place within the floodplain of the river and its network of tributaries. The actual inundation extent of the river system is; however, unknown. Reasons for this lack of information include financial constraints and inadequate human resources as flood modelling is becoming increasingly complex by the day. Knowledge of the inundation extent will help in the assessment of risk posed by the annual flooding of the river, and help in the planning of flood recession agricultural activities. This study used a simple terrain based algorithm, Height Above Nearest Drainage (HAND), to delineate the floodplain of the Nasia River and its tributaries. The HAND model is a drainage normalized digital elevation model, which has its height reference based on the local drainage systems rather than the average mean sea level (AMSL). The underlying principle guiding the development of the HAND model is that hillslope flow paths behave differently when the reference gradient is to the local drainage network as compared to the seaward gradient. The new terrain model of the catchment was created using the NASA’s SRTM Digital Elevation Model (DEM) 30m as the only data input. Contours (HAND Contour) were then generated from the normalized DEM. Based on field flood inundation survey, historical information of flooding of the area as well as satellite images, a HAND Contour of 2m was found to best correlates with the flood inundation extent of the river and its tributaries. A percentage accuracy of 75% was obtained when the surface area created by the 2m contour was compared with surface area of the floodplain computed from a satellite image captured during the peak flooding season in September 2016. It was estimated that the flooding of the Nasia River and its tributaries created a floodplain area of 1011 km².

Keywords: digital elevation model, floodplain, HAND contour, inundation extent, Nasia River

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

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Authors: Ying Yi Wu

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The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Reema Tiwari, U. C. Kulshrestha

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As a key regulator of atmospheric oxidative capacity and secondary aerosol formations, the signatures of reactive nitrogen (Nr) emissions are becoming increasingly evident in the cascade of air pollution, acidification, and eutrophication of the ecosystem. However, their accurate estimates in N budget remains limited by the photochemical conversion processes where occurrence of differential atmospheric residence time of gaseous (NOₓ, HNO₃, NH₃) and particulate (NO₃⁻, NH₄⁺) Nr species becomes imperative to their spatio temporal evolution on a synoptic scale. The present study attempts to quantify such interactions under tropical conditions when low anticyclonic winds become favorable to the advections from west during winters. For this purpose, a diurnal sampling was conducted using low volume sampler assembly where ambient concentrations of Nr trace gases along with their ionic fractions in the aerosol samples were determined with UV-spectrophotometer and ion chromatography respectively. The results showed a spatial gradient of the gaseous precursors with a much pronounced inter site variability (p < 0.05) than their particulate fractions. Such observations were confirmed for their limited photochemical conversions where less than 1 ratios of day and night measurements (D/N) for the different Nr fractions suggested an influence of boundary layer dynamics at the background site. These phase conversion processes were further corroborated with the molar ratios of NOₓ/NOᵧ and NH₃/NHₓ where incomplete titrations of NOₓ and NH₃ emissions were observed irrespective of their diurnal phases along the sampling transect. Their calculations with equilibrium based approaches for an NH₃-HNO₃-NH₄NO₃ system, on the other hand, were characterized by delays in equilibrium attainment where plots of their below deliquescence Kₘ and Kₚ values with 1000/T confirmed the role of lower temperature ranges in NH₄NO₃ aerosol formation. These results would help us in not only resolving the changing atmospheric inputs of reduced (NH₃, NH₄⁺) and oxidized (NOₓ, HNO₃, NO₃⁻) Nr estimates but also in understanding the dependence of Nr mixing ratios on their local meteorological conditions.

Keywords: diurnal ratios, gas-aerosol interactions, spatial gradient, thermodynamic equilibrium

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Authors: Hsin Lee, Hsuan Lee

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Legal artificial intelligence (LegalAI) has been increasing applications within legal systems, propelled by advancements in natural language processing (NLP). Compared with general documents, legal case documents are typically long text sequences with intrinsic logical structures. Most existing language models have difficulty understanding the long-distance dependencies between different structures. Another unique challenge is that while the Judiciary of Taiwan has released legal judgments from various levels of courts over the years, there remains a significant obstacle in the lack of labeled datasets. This deficiency makes it difficult to train models with strong generalization capabilities, as well as accurately evaluate model performance. To date, models in Taiwan have yet to be specifically trained on judgment data. Given these challenges, this research proposes a Longformer-based pre-trained language model explicitly devised for retrieving similar judgments in Taiwanese legal documents. This model is trained on a self-constructed dataset, which this research has independently labeled to measure judgment similarities, thereby addressing a void left by the lack of an existing labeled dataset for Taiwanese judgments. This research adopts strategies such as early stopping and gradient clipping to prevent overfitting and manage gradient explosion, respectively, thereby enhancing the model's performance. The model in this research is evaluated using both the dataset and the Average Entropy of Offense-charged Clustering (AEOC) metric, which utilizes the notion of similar case scenarios within the same type of legal cases. Our experimental results illustrate our model's significant advancements in handling similarity comparisons within extensive legal judgments. By enabling more efficient retrieval and analysis of legal case documents, our model holds the potential to facilitate legal research, aid legal decision-making, and contribute to the further development of LegalAI in Taiwan.

Keywords: legal artificial intelligence, computation and language, language model, Taiwanese legal cases

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Authors: Moh'd Alodat

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In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators.

Keywords: fisher information, maximum likelihood estimator, power function distribution, ranked set sampling, selective order statistics sampling

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Authors: Sukru Merey, Caglar Sinayuc

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Gas hydrate deposits which are found in deep ocean sediments and in permafrost regions are supposed to be a fossil fuel reserve for the future. The Black Sea is also considered rich in terms of gas hydrates. It abundantly contains gas hydrates as methane (CH₄~80 to 99.9%) source. In this study, by using the literature, seismic and other data of the Black Sea such as salinity, porosity of the sediments, common gas type, temperature distribution and pressure gradient, the optimum gas production method for the Black Sea gas hydrates was selected as mainly depressurization method. Numerical simulations were run to analyze gas production from gas hydrate deposited in turbidites in the Black Sea by depressurization.

Keywords: CH4 hydrate, Black Sea hydrates, gas hydrate experiments, HydrateResSim

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Authors: Balasooriya B. M. C. M., Sujeeva N., Thowfeek Z., Siddiqa Omo, Liyanagunawardana J. E., Jayawardana Saiu, Manathunga S. S., Katulanda G. W.

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Introduction and objectives: Adrenal venous sampling (AVS) is the gold standard to discriminate unilateral primary aldosteronism (UPA) from bilateral disease (BPA). AVS is technically demanding and only performed in a limited number of centers worldwide. To the best of our knowledge, Except for one study conducted in India, no other research studies on this area have been conducted in South Asia. This study aimed to evaluate the effectiveness of AVS in the management of primary aldosteronism. Methods: A total of 32 patients who underwent AVS at the National Hospital of Sri Lanka from April 2021 to April 2023 were enrolled. Demographic, clinical and laboratory data were obtained retrospectively. A procedure was considered successful when adequate cannulation of both adrenal veins was demonstrated. Cortisol gradient across the adrenal vein (AV) and the peripheral vein was used to establish the success of venous cannulation. Lateralization was determined by the aldosterone gradient between the two sides. Continuous and categorical variables were summarized with mean, SD, and proportions, respectively. The mean and standard deviation of the contralateral suppression index (CSI) were estimated with an intercept-only Bayesian inference model. Results: Of the 32 patients, the average age was 52.47 +26.14 and 19 (59.4%) were males. Both AVs were successfully cannulated in 12 (37.5%). Among them, lateralization was demonstrated in 11(91.7%), and one was diagnosed as a bilateral disease. There were no total failures. Right AV cannulation was unsuccessful in 18 (56.25%), of which lateralization was demonstrated in 9 (50%), and others were inconclusive. Left AV cannulation was unsuccessful only in 2 (6.25%); one was lateralized, and the other remained inconclusive. The estimated mean of the CSI was 0.33 (89% credible interval 0.11-0.86). Seven patients underwent unilateral adrenalectomy and demonstrated significant improvement in blood pressure during follow-up. Two patients await surgery. Others were treated medically. Conclusions: Despite failure due to procedural difficulties, AVS remained useful in the management of patients with PA. Moreover, the success of the procedure needs experienced hands and advanced equipment to achieve optimal outcomes in PA.

Keywords: adrenal venous sampling, lateralization, contralateral suppression index, primary aldosteronism

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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Authors: Huei Chu Weng

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This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: microfluidics, forced convection, thermal creep, second-order boundary conditions

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Adrian Sebastian, Chris Gillespie

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We describe a case of diffuse rectal involvement with cap polyposis, manifesting with a protein-losing colopathy and occurring in the setting of advanced mechanical pelvic floor dysfunction. A 59-year-old male with a 5-year history of persistent excessive flatulence, defecatory difficulties, and diarrhea. He had extensive cap polyposis of the entire rectum endoscopically. His symptoms progressed to severe fecal incontinence with mucus leakage, pelvic pain, weight loss, and hypoalbuminemia. Clinical examination exhibited severe perineal descent, a large rectocele, poor anal squeeze, and a poor defecatory technique. After a trial of nonoperative therapies addressing his defecatory dysfunction, and Helicobacter pylori eradication, surgical resection was offered due to severe symptoms with ongoing incontinence and protein loss with no other reasonable options. A robotic abdominoperineal resection with a permanent colostomy was performed, followed by an uncomplicated recovery. Our observation of coexisting mechanical pelvic floor changes in this patient lends weight to the concept of a prolapse-related phenomenon in the pathophysiology of this rare condition.

Keywords: cap polyposis, pelvic dysfunction, fecal incontinence, case report

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Authors: Migena Mana, Ahmed Khalid Syed, Abdul Malik, Nikhil Cherian

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In recent years, advancements in deep learning enabled researchers to tackle the problem of self-driving cars. Car companies use huge datasets to train their deep learning models to make autonomous cars a reality. However, this approach has certain drawbacks in that the state space of possible actions for a car is so huge that there cannot be a dataset for every possible road scenario. To overcome this problem, the concept of reinforcement learning (RL) is being investigated in this research. Since the problem of autonomous driving can be modeled in a simulation, it lends itself naturally to the domain of reinforcement learning. The advantage of this approach is that we can model different and complex road scenarios in a simulation without having to deploy in the real world. The autonomous agent can learn to drive by finding the optimal policy. This learned model can then be easily deployed in a real-world setting. In this project, we focus on three RL algorithms: Q-learning, Deep Deterministic Policy Gradient (DDPG), and Proximal Policy Optimization (PPO). To model the environment, we have used TORCS (The Open Racing Car Simulator), which provides us with a strong foundation to test our model. The inputs to the algorithms are the sensor data provided by the simulator such as velocity, distance from side pavement, etc. The outcome of this research project is a comparative analysis of these algorithms. Based on the comparison, the PPO algorithm gives the best results. When using PPO algorithm, the reward is greater, and the acceleration, steering angle and braking are more stable compared to the other algorithms, which means that the agent learns to drive in a better and more efficient way in this case. Additionally, we have come up with a dataset taken from the training of the agent with DDPG and PPO algorithms. It contains all the steps of the agent during one full training in the form: (all input values, acceleration, steering angle, break, loss, reward). This study can serve as a base for further complex road scenarios. Furthermore, it can be enlarged in the field of computer vision, using the images to find the best policy.

Keywords: autonomous driving, DDPG (deep deterministic policy gradient), PPO (proximal policy optimization), reinforcement learning

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Authors: Remzi Yildirim, Fatih. V. Çelebi, H. Haldun Göktaş, A. Behzat Şahin

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This study is about a single component cylindrical structured lens with gradient curve which we used for bending laser beams. It operates under atmospheric conditions and bends the laser beam independent of temperature, pressure, polarity, polarization, magnetic field, electric field, radioactivity, and gravity. A single piece cylindrical lens that can bend laser beams is invented. Lenses are made of transparent, tinted or colored glasses and used for undermining or absorbing the energy of the laser beams.

Keywords: laser, bending, lens, light, nonlinear optics

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Authors: Remzi Yildirim, Fatih V. Çelebi, H. Haldun Göktaş, A. Behzat Şahin

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This study is about a single component cylindrical structured lens with gradient curve which we used for bending laser beams. It operates under atmospheric conditions and bends the laser beam independent of temperature, pressure, polarity, polarization, magnetic field, electric field, radioactivity, and gravity. A single piece cylindrical lens that can bend laser beams is invented. Lenses are made of transparent, tinted or colored glasses and used for undermining or absorbing the energy of the laser beams.

Keywords: laser, bending, lens, light, nonlinear optics

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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