Search results for: delay equations

Authors: Sergio Haram Sarmiento, Arcady Ponosov

Abstract:

Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

Procedia PDF Downloads 480

Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

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The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

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Authors: Anna Avramenko, Heikki Haario

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This paper reports the development and application of a 2D depth-averaged model. The main goal of this contribution is to apply the depth averaged equations to a wind park model in which the treatment of the geometry, introduced on the mathematical model by the mass and momentum source terms. The depth-averaged model will be used in future to find the optimal position of wind turbines in the wind park. K-E and 2D LES turbulence models were consider in this article. 2D CFD simulations for one hill was done to check the depth-averaged model in practise.

Keywords: depth-averaged equations, numerical modeling, CFD, wind park model

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Authors: Shubham Jaiswal

Abstract:

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

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

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Authors: DucTho Le, Duy Kien Dao, Quoc Tinh Bui, Haidang Phan

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The article is concerned with the motion of ultrasonic guided waves in a unidirectional fiber-reinforced composite plate under acoustic sources. Such unidirectional composite material has orthotropic elastic properties as it is very stiff along the fibers and rather compliant across the fibers. The dispersion equations of free Lamb waves propagating in an orthotropic layer are derived that results in the dispersion curves. The connection of these equations to the Rayleigh-Lamb frequency relations of isotropic plates is discussed. By the use of reciprocity in elastodynamics, closed-form solutions of elastic wave motions subjected to time-harmonic loads in the layer are computed in a simple manner. We also consider the problem of Lamb waves generated by a set of time-harmonic sources. The obtained computations can be very useful for developing ultrasound-based methods for nondestructive evaluation of composite structures.

Keywords: lamb waves, fiber-reinforced composite plates, dispersion equations, nondestructive evaluation, reciprocity theorems

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Authors: Baziana Peristera

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The idea of the asynchronous transmission in wavelength division multiplexing (WDM) ring MANs is studied in this paper. Especially, we present an efficient access technique to coordinate the collisions-free transmission of the variable sizes of IP traffic in WDM ring core networks. Each node is equipped with a tunable transmitter and a tunable receiver. In this way, all the wavelengths are exploited for both transmission and reception. In order to evaluate the performance measures of average throughput, queuing delay and packet dropping probability at the buffers, a simulation model that assumes symmetric access rights among the nodes is developed based on Poisson statistics. Extensive numerical results show that the proposed protocol achieves apart from high bandwidth exploitation for a wide range of offered load, fairness of queuing delay and dropping events among the different packets size categories.

Keywords: asynchronous transmission, collision avoidance, wavelength division multiplexing, WDM

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Authors: Ahmadu Maidorawa, Kamalrulnizam Abu Bakar

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This paper proposed an Enhanced Connectivity Aware Routing (ECAR) protocol for Vehicular Ad hoc Network (VANET). The protocol uses a control broadcast to reduce the number of overhead packets needed in a route discovery process. It is also equipped with an alternative backup route that is used whenever a primary path to destination failed, which highly reduces the frequent launching and re-launching of the route discovery process that waste useful bandwidth and unnecessarily prolonging the average packet delay. NS2 simulation results show that the performance of ECAR protocol outperformed the original connectivity aware routing (CAR) protocol by reducing the average packet delay by 28%, control overheads by 27% and increased the packet delivery ratio by 22%.

Keywords: alternative path, primary path, protocol, routing, VANET, vehicular ad hoc networks

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari

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In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.

Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load

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Authors: Hani Baek, Gwang Min Sun, Chansun Shin, Sung Ho Ahn

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Fast neutron irradiation using nuclear reactors is an effective method to improve switching loss and short circuit durability of power semiconductor (insulated gate bipolar transistors (IGBT) and insulated gate transistors (IGT), etc.). However, not only fast neutrons but also thermal neutrons, epithermal neutrons and gamma exist in the nuclear reactor. And the electrical properties of the IGBT may be deteriorated by the irradiation of gamma. Gamma irradiation damages are known to be caused by Total Ionizing Dose (TID) effect and Single Event Effect (SEE), Displacement Damage. Especially, the TID effect deteriorated the electrical properties such as leakage current and threshold voltage of a power semiconductor. This work can confirm the effect of the gamma irradiation on the electrical properties of 600 V NPT-IGBT. Irradiation of gamma forms lattice defects in the gate oxide and Si-SiO₂ interface of the IGBT. It was confirmed that this lattice defect acts on the center of the trap and affects the threshold voltage, thereby negatively shifted the threshold voltage according to TID. In addition to the change in the carrier mobility, the conductivity modulation decreases in the n-drift region, indicating a negative influence that the forward voltage drop decreases. The turn-off delay time of the device before irradiation was 212 ns. Those of 2.5, 10, 30, 70 and 100 kRad(Si) were 225, 258, 311, 328, and 350 ns, respectively. The gamma irradiation increased the turn-off delay time of the IGBT by approximately 65%, and the switching characteristics deteriorated.

Keywords: NPT-IGBT, gamma irradiation, switching, turn-off delay time, recombination, trap center

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Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

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The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: dispersive wave equations, multiple soliton solution, Hirota Bilinear Method, symbolic computation

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Nidhal Jamia, Sami El-Borgi

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In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: functionally graded piezoelectric material (FGPM), mixed-mode crack, non-local theory, Schmidt method

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Authors: C. Recommandé, J. C. Blind, A. Clavel, R. Gourichon, V. Le Gal

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Simulations are developed in this paper with usual DSGE model equations. The model is based on simplified version of Smets-Wouters equations in use at European Central Bank which implies 10 macro-economic variables: consumption, investment, wages, inflation, capital stock, interest rates, production, capital accumulation, labour and credit rate, and allows take into consideration the banking system. Throughout the simulations, this model will be used to evaluate the impact of rate shocks recounting the actions of the European Central Bank during 2008.

Keywords: CC-LM, Central Bank, DSGE, liquidity shock, non-standard intervention

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Authors: Mohsen Solimani Babarsad, Payam Taheri

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Numerical results of vertical slot fishways with and without cylinders study are presented. The simulated results and the measured data in the fishways are compared to validate the application of the model. This investigation is made using FLUENT V.6.3, a Computational Fluid Dynamics solver. Advantages of using these types of numerical tools are the possibility of avoiding the St.-Venant equations’ limitations, and turbulence can be modeled by means of different models such as the k-ε model. In general, the present study has demonstrated that the CFD model could be useful for analysis and design of vertical slot fishways with cylinders.

Keywords: slot Fish-way, CFD, k-ε model, St.-Venant equations’

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Authors: DRIS Mohammed El-Amine, BOUNIF Abdelhamid

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This paper considers an experimental and numerical investigation of variable density in axisymmetric turbulent free jets. Special attention is paid to the study of the scalar dissipation rate. In this case, dynamic field equations are coupled to scalar field equations by the density which can vary by the thermal effect (jet heating). The numerical investigation is based on the first and second order turbulence models. For the discretization of the equations system characterizing the flow, the finite volume method described by Patankar (1980) was used. The experimental study was conducted in order to evaluate dynamical characteristics of a heated axisymmetric air flow using the Laser Doppler Anemometer (LDA) which is a very accurate optical measurement method. Experimental and numerical results are compared and discussed. This comparison do not show large difference and the results obtained are in general satisfactory.

Keywords: Scalar dissipation rate, thermal effects, turbulent axisymmetric jets, second order modelling, Velocimetry Laser Doppler.

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Authors: Kala Bharathan, R. Seshasayanan

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In this paper, a 1-bit Embedded Logic Full Adder (EFA) circuit in transistor level is proposed, which reduces logic complexity, gives low power and high speed. The design is further extended till 64 bits. To evaluate the performance of EFA, a 16, 32, 64-bit both Linear and Square root Carry Select Adder/Subtractor (CSLAS) Structure is also proposed. Realistic testing of proposed circuits is done on 8 X 8 Modified Booth multiplier and comparison in terms of power and delay is done. The EFA is implemented for different multiplier architectures for performance parameter comparison. Overall delay for CSLAS is reduced to 78% when compared to conventional one. The circuit implementations are done on TSMC 28nm CMOS technology using Cadence Virtuoso tool. The EFA has power savings of up to 14% when compared to the conventional adder. The present implementation was found to offer significant improvement in terms of power and speed in comparison to other full adder circuits.

Keywords: embedded logic, full adder, pdp, xor gate

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Authors: Khenfer-Koummich Fatima, Mesbahi Larbi, Hendel Fatiha

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This paper presents a recognition system for isolated words like robot commands. It’s carried out by Time Delay Neural Networks; TDNN. To teleoperate a robot for specific tasks as turn, close, etc… In industrial environment and taking into account the noise coming from the machine. The choice of TDNN is based on its generalization in terms of accuracy, in more it acts as a filter that allows the passage of certain desirable frequency characteristics of speech; the goal is to determine the parameters of this filter for making an adaptable system to the variability of speech signal and to noise especially, for this the back propagation technique was used in learning phase. The approach was applied on commands pronounced in two languages separately: The French and Arabic. The results for two test bases of 300 spoken words for each one are 87%, 97.6% in neutral environment and 77.67%, 92.67% when the white Gaussian noisy was added with a SNR of 35 dB.

Keywords: TDNN, neural networks, noise, speech recognition

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Authors: Anu Malhotra

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An Ad-hoc network is one that is an autonomous, self configuring network made up of mobile nodes connected via wireless links. Ad-hoc networks often consist of nodes, mobile hosts (MH) or mobile stations (MS, also serving as routers) connected by wireless links. Different routing protocols are used for data transmission in between the nodes in an adhoc network. In this paper two protocols (OLSR and AODV) are analyzed on the basis of two parameters i.e. time delay and throughput with different data rates. On the basis of these analysis, we observed that with same data rate, AODV protocol is having more time delay than the OLSR protocol whereas throughput for the OLSR protocol is less compared to the AODV protocol.

Keywords: routing adhoc, mobile hosts, mobile stations, OLSR protocol, AODV protocol

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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Authors: Kyungsuk Cho, Seungun Chae, Jihun Choi

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Elevators are examined as one of evacuation methods in super-tall buildings. However, data on the use of elevators for evacuation at a fire are extremely scarce. Therefore, a test to measure delay time in using an evacuation elevator was conducted. In the test, time taken to get on and get off an elevator was measured and the case in which people gave up boarding when the capacity of the elevator was exceeded was also taken into consideration. 170 men and women participated in the test, 130 of whom were young people (20 ~ 50 years old) and 40 were senior citizens (over 60 years old). The capacity of the elevator was 25 people and it travelled between the 2nd and 4th floors. A video recording device was used to analyze the test. An elevator at an ordinary building, not a super-tall building, was used in the test to measure delay time in getting on and getting off an elevator. In order to minimize interference from other elements, elevator platforms on the 2nd and 4th floors were partitioned off. The elevator travelled between the 2nd and 4th floors where people got on and off. If less than 20 people got on the elevator which was empty, the data were excluded. If the elevator carrying 10 passengers stopped and less than 10 new passengers got on the elevator, the data were excluded. Getting-on an empty elevator was observed 49 times. The average number of passengers was 23.7, it took 14.98 seconds for the passengers to get on the empty elevator and the load factor was 1.67 N/s. It took the passengers, whose average number was 23.7, 10.84 seconds to get off the elevator and the unload factor was 2.33 N/s. When an elevator’s capacity is exceeded, the excessive number of people should get off. Time taken for it and the probability of the case were measure in the test. 37% of the times of boarding experienced excessive number of people. As the number of people who gave up boarding increased, the load factor of the ride decreased. When 1 person gave up boarding, the load factor was 1.55 N/s. The case was observed 10 times, which was 12.7% of the total. When 2 people gave up boarding, the load factor was 1.15 N/s. The case was observed 7 times, which was 8.9% of the total. When 3 people gave up boarding, the load factor was 1.26 N/s. The case was observed 4 times, which was 5.1% of the total. When 4 people gave up boarding, the load factor was 1.03 N/s. The case was observed 5 times, which was 6.3% of the total. Getting-on and getting-off time data for people who can walk freely were obtained from the test. In addition, quantitative results were obtained from the relation between the number of people giving up boarding and time taken for getting on. This work was supported by the National Research Council of Science & Technology (NST) grant by the Korea government (MSIP) (No. CRC-16-02-KICT).

Keywords: evacuation elevator, super tall buildings, evacuees, delay time

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Authors: Muhammad A. Alsubaie, Mubarak K. H. Alhajri, Tarek S. Altowaim

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A repetitive controller designed to accommodate periodic disturbances via state feedback is discussed. Periodic disturbances can be represented by a time delay model in a positive feedback loop acting on system output. A direct use of the small gain theorem solves the periodic disturbances problem via 1) isolating the delay model, 2) finding the overall system representation around the delay model and 3) designing a feedback controller that assures overall system stability and tracking error convergence. This paper addresses uncertainty conditions for the repetitive controller designed in state feedback in either past error feedforward or current error feedback using singular values. The uncertainty investigation is based on the overall system found and the stability condition associated with it; depending on the scheme used, to set an upper/lower limit weighting parameter. This creates a region that should not be exceeded in selecting the weighting parameter which in turns assures performance improvement against system uncertainty. Repetitive control problem can be described in lifted form. This allows the usage of singular values principle in setting the range for the weighting parameter selection. The Simulation results obtained show a tracking error convergence against dynamic system perturbation if the weighting parameter chosen is within the range obtained. Simulation results also show the advantage of weighting parameter usage compared to the case where it is omitted.

Keywords: model mismatch, repetitive control, singular values, state feedback

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Authors: Hamdy Elgohary, Majid Assas

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Estimation of lateral displacement and interstory drifts represent a major step in multistory frames design. In the preliminary design stage, it is essential to perform a fast check for the expected values of lateral deformations. This step will help to ensure the compliance of the expected values with the design code requirements. Also, in some cases during or after the detailed design stage, it may be required to carry fast check of lateral deformations by design reviewer. In the present paper, a parametric study is carried out on the factors affecting in the lateral displacements of multistory frame buildings. Based on the results of the parametric study, simplified empirical equations are recommended for the direct determination of the lateral deflection of multistory frames. The results obtained using the recommended equations have been compared with the results obtained by finite element analysis. The comparison shows that the proposed equations lead to good approximation for the estimation of lateral deflection of multistory RC frame buildings.

Keywords: lateral deflection, interstory drift, approximate analysis, multistory frames

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Authors: Bhuvnesh Narayanan, Bernhard Weiss, Tvrtko Mandic, Adrijan Baric

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This paper discusses a method to reconstruct internal high-frequency signals through subsampling techniques in an IC using an on-chip sensor. Though there are existing methods to internally probe and reconstruct high frequency signals through subsampling techniques; these methods have been applicable mainly for synchronized systems. This paper demonstrates a method for making such non-intrusive on-chip reconstructions possible also in non-synchronized systems. The TLP pulse is used to demonstrate the experimental validation of the concept. The on-chip sensor measures the voltage in an internal node. The jitter in the input pulse causes a varying pulse delay with respect to the on-chip sampling command. By measuring this pulse delay and by correlating it with the measured on-chip voltage, time domain waveforms can be reconstructed, and the influence of the pulse on the internal nodes can be better understood.

Keywords: on-chip sensor, jitter, transmission line pulse, subsampling

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Authors: Eugene Stepanov, Arkadi Ponossov

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Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities.

Keywords: hybrid feedback control, ill-posed problems, singular perturbation analysis, step-like nonlinearities

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Authors: Mohmd Sarireh

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The geotechnical study can be employed successfully to assess and follow the expected development or delay in the project construction. The development project of city center or downtown was taken as a case study for the investigation of the project conditions that might support progress or cause delay. The project was proposed to build 7447 m2 by reinforced concrete mainly to serve and support the services provided to people in Tafila. The project construction had faced challenges and obstacles such as soil collapse because of excavation of the weak soil that found in the project site. In addition, the topography of the project area showed a high slope from South-West to North. The slope through the project footprint reached to 83.3% which is considered very high slope. One year and a half proposed to finish the project construction since the 1st of March 2013 and it was planned to be finished by the 31th of August 2014, but the project needs more than one year and a half as extension according to the consultant engineer. The collecting of data was conducted through the interviews with the engineers and officials, and by analyzing the soil reports and samples taken during design and excavation. The major findings came out to weak and fractured soil and construction waste that were found at project site. Also, soil was considered very fine according to the plasticity index (PI) values, in addition to the high depths required for foundation that contribute to the collapse of soil and the increase of project cost. The current project aims to present how the unseen conditions can delay the project construction and increase the cost of the project that rises to JD8.305 Million.

Keywords: geotechnical, management, progress, risk, soil unseen conditions management

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Authors: Mahendrapal Singh Pachlaniya, Laxmi Kumre

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The AOI (AND – OR- INVERTER) based design of XOR gate is proposed in this paper with less number of gates. This new XOR gate required four basic gates and basic gate include only AND, OR, Inverter (AOI). Conventional XOR gate required five basic gates. Ripple Carry Adder (RCA) used in parallel addition but propagation delay time is large. RCA replaced with Carry Select Adder (CSLA) to reduce propagation delay time. CSLA design with dual RCA considering carry = ‘0’ and carry = ‘1’, so it is not an area efficient adder. To make area efficient, modified CSLA is designed with single RCA considering carry = ‘0’ and another RCA considering carry = ‘1’ replaced with Binary to Excess 1 Converter (BEC). Now replacement of conventional XOR gate by new design of XOR gate in modified CSLA reduces much area compared to regular CSLA and modified CSLA.

Keywords: CSLA, BEC, XOR gate, area efficient

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Authors: Shreeyam, Ranjan Kumar Sah, Shivangi

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Recognizing and solving handwritten mathematical expressions can be a challenging task, particularly when certain characters are segmented and classified. This project proposes a solution that uses Convolutional Neural Network (CNN) and image processing techniques to accurately solve various types of equations, including arithmetic, quadratic, and trigonometric equations, as well as logical operations like logical AND, OR, NOT, NAND, XOR, and NOR. The proposed solution also provides a graphical solution, allowing users to visualize equations and their solutions. In addition to equation solving, the platform, called CNNCalc, offers a comprehensive learning experience for students. It provides educational content, a quiz platform, and a coding platform for practicing programming skills in different languages like C, Python, and Java. This all-in-one solution makes the learning process engaging and enjoyable for students. The proposed methodology includes horizontal compact projection analysis and survey for segmentation and binarization, as well as connected component analysis and integrated connected component analysis for character classification. The compact projection algorithm compresses the horizontal projections to remove noise and obtain a clearer image, contributing to the accuracy of character segmentation. Experimental results demonstrate the effectiveness of the proposed solution in solving a wide range of mathematical equations. CNNCalc provides a powerful and user-friendly platform for solving equations, learning, and practicing programming skills. With its comprehensive features and accurate results, CNNCalc is poised to revolutionize the way students learn and solve mathematical equations. The platform utilizes a custom-designed Convolutional Neural Network (CNN) with image processing techniques to accurately recognize and classify symbols within handwritten equations. The compact projection algorithm effectively removes noise from horizontal projections, leading to clearer images and improved character segmentation. Experimental results demonstrate the accuracy and effectiveness of the proposed solution in solving a wide range of equations, including arithmetic, quadratic, trigonometric, and logical operations. CNNCalc features a user-friendly interface with a graphical representation of equations being solved, making it an interactive and engaging learning experience for users. The platform also includes tutorials, testing capabilities, and programming features in languages such as C, Python, and Java. Users can track their progress and work towards improving their skills. CNNCalc is poised to revolutionize the way students learn and solve mathematical equations with its comprehensive features and accurate results.

Keywords: AL, ML, hand written equation solver, maths, computer, CNNCalc, convolutional neural networks

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Authors: Rajendra Kumar Dubey

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Einstein’s field equations with variable cosmological term Λ are considered in the presence of viscous fluid for Bianchi type I space time. Exact solutions of Einstein’s field equations are obtained by assuming cosmological term Λ Proportional to (R is a scale factor and m is constant). We observed that the shear viscosity is found to be responsible for faster removal of initial anisotropy in the universe. The physical significance of the cosmological models has also been discussed.

Keywords: bianchi type, I cosmological model, viscous fluid, cosmological constant Λ

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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