Search results for: differential histogram of normal vectors

Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Abhishek Jha, Manoj Kumar

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This paper proposes a new type of two wheels differential type odometry to estimate the next position and orientation of mobile robots. The proposed odometry is composed for two independent wheels with respective encoders. The two wheels rotate independently, and the change is determined by the difference in the velocity of the two wheels. Angular velocities of the two wheels are measured by rotary encoders. A mathematical model is proposed for the mobile robots to precisely move towards the goal. Using measured values of the two encoders, the current displacement vector of a mobile robot is calculated by kinematics of the mathematical model. Using the displacement vector, the next position and orientation of the mobile robot are estimated by proposed odometry. Result of simulator experiment by the developed odometry is shown.

Keywords: mobile robot, odometry, unicycle, differential type, encoders, infrared range sensors, kinematic model

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Authors: Kittipong Tripetch

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This paper proposes studies of input impedance of two types of the CMOS active inductor. It derives two input impedance formulas. The first formula is the input impedance of a grounded active inductor. The second formula is an input impedance of floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of a fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption

Keywords: grounded active inductor, floating active inductor, fully differential bandpass amplifier

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Authors: Srinivasacharya Darbhasayanam, Jagadeeshwar Pashikanti

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This paper analyzes the Soret and Dufour effects on mixed convection flow, heat and mass transfer from an exponentially stretching surface in a viscous fluid with Hall Effect. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. The nonlinear coupled ordinary differential equations are reduced to a system of linear differential equations using the successive linearization method and then solved the resulting linear system using the Chebyshev pseudo spectral method. The numerical results for the velocity components, temperature and concentration are presented graphically. The obtained results are compared with the previously published results, and are found to be in excellent agreement. It is observed from the present analysis that the primary and secondary velocities and concentration are found to be increasing, and temperature is decreasing with the increase in the values of the Soret parameter. An increase in the Dufour parameter increases both the primary and secondary velocities and temperature and decreases the concentration.

Keywords: Exponentially stretching sheet, Hall current, Heat and Mass transfer, Soret and Dufour Effects

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Authors: Monika Rawat, Rahul Kumar

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Input output Buffer Information Specification (IBIS) models are used for describing the analog behavior of the Input Output (I/O) buffers of a digital device. They are widely used to perform signal integrity analysis. Advantages of using IBIS models include simple structure, IP protection and fast simulation time with reasonable accuracy. As design complexity of driver and receiver increases, capturing exact behavior from transistor level model into IBIS model becomes an essential task to achieve better accuracy. In this paper, an improvement in existing methodology of generating IBIS model for complex I/O interfaces such as Inter-Integrated Circuit (I2C) and Low Voltage Differential Signaling (LVDS) is proposed. Furthermore, the accuracy and computational performance of standard method and proposed approach with respect to SPICE are presented. The investigations will be useful to further improve the accuracy of IBIS models and to enhance their wider acceptance.

Keywords: IBIS, signal integrity, open-drain buffer, low voltage differential signaling, behavior modelling, transient simulation

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Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

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The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: Maria C. Proença, Maria T. Rebelo, Maria J. Alves, Sofia Cunha

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Vector-borne diseases are transmitted to humans by mosquitos, sandflies, bugs, ticks, and other vectors. Some are re-transmitted between vectors, if the infected human has a new contact when his levels of infection are high. The vector is infected for lifetime and can transmit infectious diseases not only between humans but also from animals to humans. Some vector borne diseases are very disabling and globally account for more than one million deaths worldwide. The mosquitoes from the complex Culex pipiens sl. are the most abundant in Portugal, and we dispose in this moment of a data set from the surveillance program that has been carried on since 2006 across the country. All mosquitos’ species are included, but the large coverage of Culex pipiens sl. and its importance for public health make this vector an interesting candidate to assess risk of disease amplification. This work focus on ports and airports identified as key areas of high density of vectors. Mosquitoes being ectothermic organisms, the main factor for vector survival and pathogen development is temperature. Minima and maxima local air temperatures for each area of interest are averaged by month from data gathered on a daily basis at the national network of meteorological stations, and interpolated in a geographic information system (GIS). The range of temperatures ideal for several pathogens are known and this work shows how to use it with the meteorological data in each port and airport facility, to focus an efficient implementation of countermeasures and reduce simultaneously risk transmission and mitigation costs. The results show an increased alert with decreasing latitude, which corresponds to higher minimum and maximum temperatures and a lower amplitude range of the daily temperature.

Keywords: human health, risk assessment, risk management, vector-borne diseases

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Faith-Michael E. Uzoka, Boluwaji A. Akinnuwesi, Taiwo Amoo, Flora Aladi, Stephen Fashoto, Moses Olaniyan, Joseph Osuji

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The overarching aim of this study is to develop a soft-computing system for the differential diagnosis of tropical diseases. These conditions are of concern to health bodies, physicians, and the community at large because of their mortality rates, and difficulties in early diagnosis due to the fact that they present with symptoms that overlap, and thus become ‘confusable’. We report on the first phase of our study, which focuses on the development of a fuzzy cognitive map model for early differential diagnosis of tropical diseases. We used malaria as a case disease to show the effectiveness of the FCM technology as an aid to the medical practitioner in the diagnosis of tropical diseases. Our model takes cognizance of manifested symptoms and other non-clinical factors that could contribute to symptoms manifestations. Our model showed 85% accuracy in diagnosis, as against the physicians’ initial hypothesis, which stood at 55% accuracy. It is expected that the next stage of our study will provide a multi-disease, multi-symptom model that also improves efficiency by utilizing a decision support filter that works on an algorithm, which mimics the physician’s diagnosis process.

Keywords: medical diagnosis, tropical diseases, fuzzy cognitive map, decision support filters, malaria differential diagnosis

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Authors: Yusef Karimi, Masoomeh Esmaeily, Razgar Mohammadi

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Following the events of September 11th, one of the most important concerns of governments, politicians and, researchers has been to answer the question that why does an ordinary person become fundamentalism? One of the major controversies in past researches was about as to whether a fundamentalist person is normal or abnormal. In this regard, the purpose of this research is to investigate whether a Salafi-jihadi individual is normal or abnormal. The participants included 6 Jihadi Salafism individuals who were living in the Middle East and had been purposefully selected. This research is a qualitative study which examines these people′s retrospective experience of their lives. The data were collected through collaborative observation and interview. This continued till data saturation. Unlike the introduced concepts of fundamentalist personality in the previous studies such as self-fascination, aggression, paranoid personality and psychopathic, participants in this study had no abnormal symptoms of mental disorders. Hence, in the context of recognizing the fundamentalist personality, we must seek other personality and positional variables.

Keywords: abnormal, fundamentalism, normal, personality, Salafi

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Authors: Ashish Dhamaniya, Satish Chandra

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Speed and traffic volume data are collected on different sections of four lane and six lane roads in three metropolitan cities in India. Speed data are analyzed to fit the statistical distribution to individual vehicle speed data and all vehicles speed data. It is noted that speed data of individual vehicle generally follows a normal distribution but speed data of all vehicle combined at a section of urban road may or may not follow the normal distribution depending upon the composition of traffic stream. A new term Speed Spread Ratio (SSR) is introduced in this paper which is the ratio of difference in 85^th and 50^th percentile speed to the difference in 50^th and 15^th percentile speed. If SSR is unity then speed data are truly normally distributed. It is noted that on six lane urban roads, speed data follow a normal distribution only when SSR is in the range of 0.86 – 1.11. The range of SSR is validated on four lane roads also.

Keywords: normal distribution, percentile speed, speed spread ratio, traffic volume

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Authors: Bowen Ding, Yihao Kuang

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In recent years, with the development of large-scale pre-trained lan-guage models, building vector representations of text through deep neural network models has become a standard practice for natural language processing tasks. From the performance on downstream tasks, we can know that the text representation constructed by these models contains linguistic information, but its encoding mode and extent are unclear. In this work, a structural probe is proposed to detect whether the vector representation produced by a deep neural network is embedded with a syntax tree. The probe is trained with the deep metric learning method, so that the distance between word vectors in the metric space it defines encodes the distance of words on the syntax tree, and the norm of word vectors encodes the depth of words on the syntax tree. The experiment results on ELMo and BERT show that the syntax tree is encoded in their parameters and the word representations they produce.

Keywords: deep metric learning, syntax tree probing, natural language processing, word representations

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Authors: Malika El Kyal, Ahmed Machmoum

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We prove the superlinear convergence of asynchronous multi-splitting methods applied to differential equations. This study is based on the technique of nested sets. It permits to specify kind of the convergence in the asynchronous mode.The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, ODE

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Authors: Ammara Mehmood, Aneela Zameer, Muhammad Asif Zahoor Raja, Muhammad Faisal Fateh

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In this work, the strength of bio-inspired computational intelligence based technique is exploited for parameter estimation for the periodic signals using Continuous Differential Evolution (CDE) by defining an error function in the mean square sense. Multidimensional and nonlinear nature of the problem emerging in sinusoidal signal models along with noise makes it a challenging optimization task, which is dealt with robustness and effectiveness of CDE to ensure convergence and avoid trapping in local minima. In the proposed scheme of Continuous Differential Evolution based Signal Parameter Estimation (CDESPE), unknown adjustable weights of the signal system identification model are optimized utilizing CDE algorithm. The performance of CDESPE model is validated through statistics based various performance indices on a sufficiently large number of runs in terms of estimation error, mean squared error and Thiel’s inequality coefficient. Efficacy of CDESPE is examined by comparison with the actual parameters of the system, Genetic Algorithm based outcomes and from various deterministic approaches at different signal-to-noise ratio (SNR) levels.

Keywords: parameter estimation, bio-inspired computing, continuous differential evolution (CDE), periodic signals

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Authors: M. Nili, S. Tavasoli, A. R. Yazdandoost

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In this paper, an experimental investigation on the effect of Isfahan Ground Granulate Blast Furnace Slag (GGBS) on the compressive strength development of self-consolidating concrete (SCC) and normal concrete (NC) was performed. For this purpose, Portland cement type I was replaced with GGBS in various Portions. For NC and SCC Mixes, 10*10*10 cubic cm specimens were tested in 7, 28 and 91 days. It must be stated that in this research water to cement ratio was 0.44, cement used in cubic meter was 418 Kg/m³ and Superplasticizer (SP) Type III used in SCC based on Poly-Carboxylic acid. The results of experiments have shown that increasing GGBS Percentages in both types of concrete reduce Compressive strength in early ages.

Keywords: compressive strength, GGBS, normal concrete, self-consolidating concrete

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Authors: Parminder K. Laroiya, Sukhdeep S. Kang

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The Present cross-sectional study was conducted on 610 boys (ranging in age bracket of 11 to 17 years) to assess their developmental age to check percentage of early, normal and late maturity among them, and to check whether there is any significant difference in their calendar age and developmental age. Developmental age of these subjects has been accessed by TW2 method (using hand wrist X-rays) and their chronological age was checked from their date of birth certificate. Developmental status of subjects i.e. early, normal or late mature was considered with +2 years or -2 years from their calendar age. Results of this study shows that 50% boys were normal in their maturity status in all age brackets and rest of subjects were either early maturers 24.92% or late maturers 25.08%. When pattern of maturity was studied in each age group it has been found that till the age of 15 years, percentage of normal maturity was less than 50 % whereas in 16 and 17 years age groups, this percentage of normal maturity increased to 60% - 65 % ( this may be because at this age mostly boys attain adolescence) Further investigation of each age group showed that till the age of 14 years percentage of late maturity among these boys were approximately 35% to 40% whereas early maturity lies between 15% to 20%. It has been found from the present study that at the age of 15 years, there is a twist among percentage of late and early maturity among boys-early maturers are 38.61% and late maturers are 16.84%. At the age of 16 and 17 years percentage of late maturity has been decreased to 3% to 6%, whereas percentage of early maturity increased to 35.64 % and 30.69 % respectively.

Keywords: maturity status, developmental age, chronological age, X-rays

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Authors: S. Zith Dey Babu, S. Kour, S. Verma, C. Verma, V. Pathania, A. Agrawal, V. Chaudhary, A. Manoj Puthur, R. Goyal, A. Pal, T. Danti Dey, A. Kumar, K. Wadhwa, O. Ved

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Background: Skin cancer is now is the buzzing button in the field of medical science. The cyst's pandemic is drastically calibrating the body and well-being of the global village. Methods: The extracted image of the skin tumor cannot be used in one way for diagnosis. The stored image contains anarchies like the center. This approach will locate the forepart of an extracted appearance of skin. Partitioning image models has been presented to sort out the disturbance in the picture. Results: After completing partitioning, feature extraction has been formed by using genetic algorithm and finally, classification can be performed between the trained and test data to evaluate a large scale of an image that helps the doctors for the right prediction. To bring the improvisation of the existing system, we have set our objectives with an analysis. The efficiency of the natural selection process and the enriching histogram is essential in that respect. To reduce the false-positive rate or output, GA is performed with its accuracy. Conclusions: The objective of this task is to bring improvisation of effectiveness. GA is accomplishing its task with perfection to bring down the invalid-positive rate or outcome. The paper's mergeable portion conflicts with the composition of deep learning and medical image processing, which provides superior accuracy. Proportional types of handling create the reusability without any errors.

Keywords: computer-aided system, detection, image segmentation, morphology

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: Yongyu Duo, Xiaogang Liu, Qingrui Yue

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The anchor plays a critical role in the utilization of the tensile strength of carbon fiber-reinforced polymer (CFRP) plate when it is applied for the prestressed retrofitted and cable structures. In this paper, the anchor behavior of planar clamping anchor (PCA) under different interface treatment forms and normal pressures was investigated by the uniaxial static tensile test. Two interface treatment forms were adopted, including pure friction and the coupling action of friction and bonding. The results indicated that the load-bearing capacity of PCA could be obviously improved by the coupling action of friction and bonding compared with the action of pure friction. Under the normal pressure of 11 MPa, 22 MPa, and 33 MPa, the load-bearing capacity of PCA was enhanced by 164.61%, 68.40%, and 52.78%, respectively, and the tensile strength of the CFRP plate was fully exploited when the normal pressure reached 44 MPa. In addition, the experimental coefficient of static friction between the galling CFRP plate and a sandblasted steel plate was in the range of 0.28-0.30, corresponding to various normal pressure. Moreover, the failure mode was determined by the interface treatment form and normal pressure. The research in this paper has important guiding significance to optimize the design of the mechanical clamping anchor, contributing to promoting the application of CFRP plate in reinforcement and cable structure.

Keywords: PCA, CFRP plate, interface treatment form, normal pressure, friction, coupling action

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Authors: Appasaheb Raul

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Numerical analysis of a plate fin heat exchanger accounting for the effect of fluid flow maldistribution on the inlet header configuration of the heat exchanger is investigated. It is found that the flow maldistribution is very significant in normal to the flow direction. Various inlet configuration has been studied for various Reynolds Number. By the study, a modified header configuration is proposed and simulated. The two-dimensional parameters are used to evaluate the flow non-uniformity in the header, global flow maldistribution parameter (Sg), and Velocity Ratio (θ). A series of velocity vectors and streamline graphs at different cross-section are achieved and studied qualitatively with experimental results in the literature. The numerical result indicates that the flow maldistribution is serious in the conventional header while in the improved configuration less maldistribution occurs. The flow maldistribution parameter (Sg) and velocity ratio (θ) is reduced in improved configuration. The vortex decreases compared to that of the conventional configuration so the energy and pressure loss is reduced. The improved header can effectively enhance the efficiency of plate fin heat exchanger and uniformity of flow distribution.

Keywords: global flow maldistribution parameter, Sg, velocity ratio, plate fin heat exchanger, fluent 14.5

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Authors: Gleda Kutrolli, Maksi Kutrolli, Etjon Meco

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SARS-CoV-2 virus is currently one of the most infectious pathogens for humans. It started in China at the end of 2019 and now it is spread in all over the world. The origin and diffusion of the SARS-CoV-2 epidemic, is analysed based on the discussion of viral phylogeny theory. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the spread of the virus and simulate its activity. In this paper, the prediction of coronavirus outbreak is done by using SIR model without vital dynamics, applying different numerical technique solving ordinary differential equations (ODEs). We find out that ABM and MRT methods perform better than other techniques and that the activity of the virus will decrease in April but it never cease (for some time the activity will remain low) and the next cycle will start in the middle July 2020 for Norway and Denmark, and October 2020 for Sweden, and September for Finland.

Keywords: forecasting, ordinary differential equations, SARS-COV-2 epidemic, SIR model

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Authors: M. Osibemhe, I. O. Onoagbe

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Diabetes mellitus is a common disease that has no known cure. The available orthodox drugs used for its management have one or more disadvantages. This study investigated the potency of aqueous and ethanol extracts of Strophanthus hispidus (SH) stem bark in the management of diabetes mellitus. Glucose concentration and lipid profile parameters of normal and streptozotocin-induced diabetic rats were monitored for 12weeks. Diabetes mellitus was induced by intraperitoneal injection of streptozotocin (55 mg/kg). Male rats (wistar strain) numbering 30 were randomly selected into six groups of five rats each. Groups 1 and 6 served as normal and diabetic control respectively and received distilled water for 12weeks. Groups 2 and 3 were normal rats treated orally with the aid of a gavage, 250 mg/kg of aqueous and ethanol extracts respectively for 12weeks. Groups 4 and 5 were diabetic rats and were treated with the respective dose of aqueous and ethanol extracts for the same period. A significant (P˂0.05) progressive decrease in blood glucose concentrations of both normal and diabetic rats treated with the extracts were observed from the 2nd to 12th weeks when compared with the respective controls. No significant (P˃0.05) effects were observed in the basal values of both normal and diabetic rats. Administration of both extracts of SH to diabetic rats significantly (P˂0.05) lowered the concentrations of Total cholesterol, TG, and LDL, whereas it increases the concentration of HDL when compared with diabetic control. The concentrations of total cholesterol and LDL in normal rats treated with SH were also reduced when compared with normal control whereas SH had no significant (P˃0.05) effect on HDL. However, TG level of normal control was significantly (P˂0.05) lower than normal rats treated with both extracts. A progressive increase in weight of normal and diabetic rats treated with the extracts was observed on the 2nd – 12th weeks of administration, whereas diabetic control showed a progressive decrease in weight. The findings from this study indicated that SH has hypoglycemic and anti-lipidemic properties as well as anti-diabetic potentials. It also showed that ethanol extract had greater glucose lowering effect. Hence, SH may be considered as a potent anti-diabetic plant and could be used as alternative drug for the management of diabetes mellitus.

Keywords: concentration, ethanol extract, hypoglycemic, total cholesterol

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Authors: D. Mehdizadeh, M. Rahimian, M. Eskandari-Ghadi

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This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.

Keywords: transversely isotropic, rigid disc, elasticity, dual integral equations, tri-material full-space

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Authors: Lina Wu, Ye Li, Jia Liu

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

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

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Authors: Gilbert Makanda

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The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: F. Waffo Tchuimmo, G. S. Kwandio Dongoua, C. U. Yves Mbono Samba, O. Dafounansou, L. Nana

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The strength criterion is an important condition of great interest to guarantee the stability of the structural elements. The present work is based on the study of the free vibration of Euler’s Bernoulli column of equal strength in compression while considering its own weight and the axial load in compression and tension subjected to symmetrical boundary conditions. We use the differential quadrature method to investigate the first fifth naturals frequencies parameters of the column according to the different forms of geometrical sections. The results of this work give help in making a judicious choice of type of cross-section and a better boundary condition to guarantee good stability of this type of column in civil constructions.

Keywords: free vibration, equal strength, self-weight, tip force, differential quadrature method

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Authors: S. S. Abas, Y. M. Yatim

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In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

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Authors: Surendra Kumar Patel

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Disability is not just a health problem; it is a complex phenomenon, reflecting the interaction between features of a person’s age and physiology. Population ageing is a major demographic issue for India in the 21st century. Older population of India constituted 8% of total population, while 5.19% has affected by disability of older age group. Objective of the present research paper is to examine the state wise differential in disability among 60+ population and to access the health care of disabled population especially the 60+ disabled persons. The data sources of the present paper are census 2001 and 2011. For analyzing the state wise differentials by disability types and comparative advantage of data, rate, ratio, and percentage have been used. The Standardized Index of Diversity of Disability (SIDD) studies differential and diversity in disability. The results show that there are 5.19% persons have disability among 60+ population and sex differential not very significant, as it is 5.3 % of male and 5.05% in female in India but place of residence shows significant variation from 2001 to 2011 census. There is huge diversity in disability prevalence among 60+ in India, highest in Sikkim followed by Rajasthan, approximately, they comprise 11%, and the lowest found in Tamil Nadu as 2.53%. This huge gap in prevalence percentage shows the health care needs of highly prevailing states.

Keywords: disability, Standardized Index of Diversity of Disability (SIDD), differential and diversity in disability, 60+ population

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Authors: Mohammad Taghi Karimi, Maryam Hasan Zahraee

Abstract:

Background: Low back pain (LBP) is a common health and socioeconomic problem, especially the chronic one. The joint contact force is an important parameter during walking which increases the incidence of injury and degenerative joint disease. To our best knowledge, there are not enough evidences in literature on the muscular forces and joint contact forces in subjects with low back pain. Purpose: The main hypothesis associated with this research was that joint contact force of L4/L5 of non-specific chronic low back pain subjects was the same as that of normal. Therefore, the aim of this study was to determine the joint contact force difference between non-specific chronic low back pain and normal subjects. Method: This was an experimental-comparative study. 20 normal subjects and 20 non-specific chronic low back pain patients were recruited in this study. Qualysis motion analysis system and a Kistler force plate were used to collect the motions and the force applied on the leg, respectively. OpenSimm software used to determine joint contact force and muscle forces in this study. Some parameters such as force applied on the legs (pelvis), kinematic of hip and pelvic, peaks of muscles, force of trunk musculature and joint contact force of L5/S1 were used for further analysis. Differences between mean values of all data were measured using two-sample t-test among the subjects. Results: The force produced by Semitendinosus, Biceps Femoris, and Adductor muscles were significantly different between low back pain and normal subjects. Moreover, the mean value of breaking component of the force of the knee joint increased significantly in low back pain subjects, besides a significant decrease in mean value of the vertical component of joint reaction force compared to the normal ones. Conclusions: The forces produced by the trunk and pelvic muscles, and joint contact forces differ significantly between low back pain and normal subjects. It seems that those with non-specific chronic low back pain use trunk muscles more than normal subjects to stabilize the pelvic during walking.

Keywords: low back pain, joint contact force, kinetic, muscle force

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