Search results for: differential invariant signature curves

Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Josef Slapal

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Digital images are approximations of real ones and, therefore, to be able to study them, we need the digital plane Z2 to be equipped with a convenient structure that behaves analogously to the Euclidean topology on the real plane. In particular, it is required that such a structure allows for a digital analogue of the Jordan curve theorem. We introduce certain adjacency graphs on the digital plane and prove digital Jordan curves for them thus showing that the graphs provide convenient structures on Z2 for the study and processing of digital images. Further convenient structures including the wellknown Khalimsky and Marcus-Wyse adjacency graphs may be obtained as quotients of the graphs introduced. Since digital Jordan curves represent borders of objects in digital images, the adjacency graphs discussed may be used as background structures on the digital plane for solving the problems of digital image processing that are closely related to borders like border detection, contour filling, pattern recognition, thinning, etc.

Keywords: digital plane, adjacency graph, Jordan curve, quotient adjacency

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Authors: Mohamad Amin Amini, Mehdi Poursha

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Nonlinear response history analysis (NL-RHA) is a robust analytical tool for estimating the seismic demands of structures responding in the inelastic range. However, because of its conceptual and numerical complications, the nonlinear static procedure (NSP) is being increasingly used as a suitable tool for seismic performance evaluation of structures. The conventional pushover analysis methods presented in various codes (FEMA 356; Eurocode-8; ATC-40), are limited to the first-mode-dominated structures, and cannot take higher modes effect into consideration. Therefore, since more than a decade ago, researchers developed enhanced pushover analysis procedures to take higher modes effect into account. The main objective of this study is to propose an enhanced invariant lateral displacement distribution to take higher modes effect into consideration in performing a displacement-based pushover analysis, whereby a set of laterally applied displacements, rather than forces, is monotonically applied to the structure. For this purpose, the effect of different parameters such as the spectral displacement of ground motion, the modal participation factor, and the effective modal participating mass ratio on the lateral displacement distribution is investigated to find the best distribution. The major simplification of this procedure is that the effect of higher modes is concentrated into a single invariant lateral load distribution. Therefore, only one pushover analysis is sufficient without any need to utilize a modal combination rule for combining the responses. The invariant lateral displacement distribution for pushover analysis is then calculated by combining the modal story displacements using the modal combination rules. The seismic demands resulting from the different procedures are compared to those from the more accurate nonlinear response history analysis (NL-RHA) as a benchmark solution. Two structures of different heights including 10 and 20-story special steel moment resisting frames (MRFs) were selected and evaluated. Twenty ground motion records were used to conduct the NL-RHA. The results show that more accurate responses can be obtained in comparison with the conventional lateral loads when the enhanced modal lateral displacement distributions are used.

Keywords: displacement-based pushover, enhanced lateral load distribution, higher modes effect, nonlinear response history analysis (NL-RHA)

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Authors: M. Samadzadeh Mahabadi, J. Shanbehzadeh

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This paper presents a hybrid digital image-watermarking scheme, which is robust against varieties of attacks and geometric distortions. The image content is represented by important feature points obtained by an image-texture-based adaptive Harris corner detector. These feature points are extracted from LL2 of 2-D discrete wavelet transform which are obtained by using the Harris-Laplacian detector. We calculate the Fourier transform of circular regions around these points. The amplitude of this transform is rotation invariant. The experimental results demonstrate the robustness of the proposed method against the geometric distortions and various common image processing operations such as JPEG compression, colour reduction, Gaussian filtering, median filtering, and rotation.

Keywords: digital watermarking, geometric distortions, geometrical attack, Harris Laplace, important feature points, rotation, scale invariant feature

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Authors: Ibrahim Can, Fatih Tosunoğlu

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The flow duration curve (FDC) is an informative method that represents the flow regime’s properties for a river basin. Therefore, the FDC is widely used for water resource projects such as hydropower, water supply, irrigation and water quality management. The primary purpose of this study is to obtain synthetic daily flow duration curves for Çoruh Basin, Turkey. For this aim, we firstly developed univariate auto-regressive moving average (ARMA) models for daily flows of 9 stations located in Çoruh basin and then these models were used to generate 100 synthetic flow series each having same size as historical series. Secondly, flow duration curves of each synthetic series were drawn and the flow values exceeded 10, 50 and 95 % of the time and 95% confidence limit of these flows were calculated. As a result, flood, mean and low flows potential of Çoruh basin will comprehensively be represented.

Keywords: ARMA models, Çoruh basin, flow duration curve, Turkey

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Authors: K. Sanjayani, C. Saraswathy, S. Sreenivasan, S. Sudhahar, D. Suganya, K. S. Neelukumari, N. Vijayarangan

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Double Base Number System (DBNS) is an imminent system of representing a number using two bases namely 2 and 3, which has its application in Elliptic Curve Cryptography (ECC) and Digital Signature Algorithm (DSA).The previous binary method representation included only base 2. DBNS uses an approximation algorithm namely, Greedy Algorithm. By using this algorithm, the number of digits required to represent a larger number is less when compared to the standard binary method that uses base 2 algorithms. Hence, the computational speed is increased and time being reduced. The standard binary method uses binary digits 0 and 1 to represent a number whereas the DBNS method uses binary digit 1 alone to represent any number (canonical form). The greedy algorithm uses two ways to represent the number, one is by using only the positive summands and the other is by using both positive and negative summands. In this paper, arithmetic operations are used for elliptic curve cryptography. Elliptic curve discrete logarithm problem is the foundation for most of the day to day elliptic curve cryptography. This appears to be a momentous hard slog compared to digital logarithm problem. In elliptic curve digital signature algorithm, the key generation requires 160 bit of data by usage of standard binary representation. Whereas, the number of bits required generating the key can be reduced with the help of double base number representation. In this paper, a new technique is proposed to generate key during encryption and extraction of key in decryption.

Keywords: cryptography, double base number system, elliptic curve cryptography, elliptic curve digital signature algorithm

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Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: Malika Elkyal

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We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does 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. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

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Authors: Krish Jhurani

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The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

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Authors: Milad Alizadeh Galdiani, Jabbar Ali Zakeri

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Lateral movement of CWR ballasted track occurs in sharp curves because of the lack of adequate lateral resistance. Several strategies have been proposed and used for increase the lateral resistance of ballasted tracks, but still there are some problems in tracks with small radius curves. In this paper, a new method has been presented for increase the lateral resistance. This method is using the lateral supports as numerical and field studies. In this paper, the field and laboratory tests have been conducted by using the single tie pressure test (STPT) and track panel loading test (LTPT). Then, their results were compared with the numerical results. The results of numerical and field tests showed that the lateral stiffness of ballasted tracks significantly increased when there were lateral supports in ballasted tracks. Also, the track structure had a bilinear behavior.

Keywords: ballasted railway, Lateral resistance, railway buckling, field and numerical studies

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Authors: T. Vamsee Kiran, A. Gopi

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The undesired torque and flux ripple may occur in conventional direct torque control (DTC) induction motor drive. DTC can improve the system performance at low speeds by continuously tuning the regulator by adjusting the Kp, Ki values. In this differential evolution (DE) is proposed to adjust the parameters (Kp, Ki) of the speed controller in order to minimize torque ripple, flux ripple, and stator current distortion.The DE based PI controller has resulted is maintaining a constant speed of the motor irrespective of the load torque fluctuations.

Keywords: differential evolution, direct torque control, PI controller

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Authors: Praveen Huded, Suresh Dash

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Pile foundations are one of the most preferred deep foundation system for high rise or heavily loaded structures. In many instances, the failure of the pile founded structures in liquefiable soils had been observed even in many recent earthquakes. Recent centrifuge and shake table experiments on two layered soil system have credibly shown that failure of pile foundation can occur because of buckling, as the pile behaves as an unsupported slender structural element once the surrounding soil liquefies. However the buckling capacity depends on largely on the depth of soil liquefied and its residual strength. Hence it is essential to check the pile against the possible buckling failure. Beam on non-linear Winkler Foundation is one of the efficient method to model the pile-soil behavior in liquefiable soil. The pile-soil interaction is modelled through p-y springs, different author have proposed different types of p-y curves for the liquefiable soil. In the present paper the influence two such p-y curves on the buckling capacity of pile foundation is studied considering initial geometric and non-linear behavior of pile foundation. The proposed method is validated against experimental results. Significant difference in the buckling capacity is observed for the two p-y curves used in the analysis. A parametric study is conducted to understand the influence of pile diameter, pile flexural rigidity, different initial geometric imperfections, and different soil relative densities on buckling capacity of pile foundation.

Keywords: Pile foundation , Liquefaction, Buckling load, non-linear py curve, Opensees

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Authors: Jiya Mohammed, Ibrahim Ismail Giwa

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Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Daniel O'Shea, Mario M. Attard, David C. Kellermann

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In this paper, we propose a hyperelastic strain energy function that maps isotopic hyperelastic constitutive laws for the use of orthotropic materials without the use of structural tensors or any kind of fiber vector, or the use of standard invariants. In particular, we focus on neo-Hookean class of models and represent them using an invariant-free formulation. To achieve this, we revise the invariant-free formulation of isotropic hyperelasticity. The formulation uses quadruple contractions between fourth-order tensors, rather than scalar products of scalar invariants. We also propose a new decomposition of the orthotropic Hookean stiffness tensor into two fourth-order Lamé tensors that collapse down to the classic Lamé parameters for isotropic continua. The resulting orthotropic hyperelastic model naturally maintains all of the advanced properties of the isotropic counterparts, and similarly collapse back down to their isotropic form by nothing more than equality of parameters in all directions (isotropy). Comparisons are made with large strain experimental results for transversely isotropic rubber type materials under tension.

Keywords: finite strain, hyperelastic, invariants, orthotropic

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Authors: Muhammad Younis

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A ternary 4-point approximating non-stationary subdivision scheme has been introduced that generates the family of $C^2$ limiting curves. The theory of asymptotic equivalence is being used to analyze the convergence and smoothness of the scheme. The comparison of the proposed scheme has been demonstrated using different examples with the existing 4-point ternary approximating schemes, which shows that the limit curves of the proposed scheme behave more pleasantly and can generate conic sections as well.

Keywords: ternary, non-stationary, approximation subdivision scheme, convergence and smoothness

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Authors: S. Altmeyer, B. Hof, F. Marques, J. M. Lopez

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We present numerical simulations concerning the reversal of spiraling vortices in short highly counter-rotating cylinders. Increasing the differential cylinder rotation results in global flow-inversion is which develops various different and complex flow dynamics of several quasi-periodic solutions that differ in their number of vortex cells in the bulk. The dynamics change from being dominated of the inner cylinder boundary layer with ’passive’ only responding outer one to be dominated by the outer cylinder boundary layer with only responding inner one. Solutions exist on either two or three tori invariant manifolds whereby they appear as symmetric or asymmetric states. We find for either moderate and high inner cylinder rotation speed the quasiperiodic flow to consist of only two vortex cells but differ as the vortices has opposite spiraling direction. These both flows live on 2-tori but differ in number of symmetries. While for the quasi-periodic flow (q^a_2) at lower rotation speed a pair of symmetrically related 2-tori T2 exists the quasi-periodic flow (q^s_2) at higher rotation speeds is symmetric living on a single 2-torus T2. In addition these both flows differ due to their dominant azimuthal m modes. The first is dominated by m=1 whereas for the latter m=3 contribution is largest. The 2-tori states are separated by a further quasi-periodic flow (q^a_3) living on pair of symmetrically related 3-tori T3. This flow offers a ’periodical’ competition between a two and three vortex cell states in the bulk. This flow is also an m=1 solution as for the quasiperiodic flows living on the pair of symmetrically-related 2-tori states. Moreover we find hysteresis resulting in coexisting regions of different quasiperiodic flows q^s_2 and q^a_3 with increasing and decreasing the differential rotation.

Keywords: transition, bifurcation, torus, symmetries

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Authors: Lungile Maliba, O. I. Nkwonta, E Onyari

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Water resources development and management are regarded as crucial for poverty reduction in many developing countries and sustainable economic growth such as South Africa. The contribution of large hydraulic infrastructure and management of it, particularly reservoirs, to development remains controversial. This controversy stems from the fact that from a historical point of view construction of reservoirs has brought fewer benefits than envisaged and has resulted in significant environmental and social costs. A further complexity in reservoir management is the variety of stakeholders involved, all with different objectives, including domestic and industrial water use, flood control, irrigation and hydropower generation. The objective was to evaluate technical adaptation options for kleinfontein Dam’s current operating rule curves. To achieve this objective, the current operating rules curves being used in the sub-basin were analysed. An objective methodology was implemented in other to get the operating rules with regards to the target storage curves. These were derived using the Water Resources Yield/Planning Model (WRY/PM), with the aim of maximising of releases to demand zones. The result showed that the system is over allocated and in addition the demands exceed the long-term yield that is available for the system. It was concluded that the current operating rules in the system do not produce the optimum operation such as target storage curves to avoid supply failures in the system.

Keywords: infrastructure, Kleinfontein dam, operating rule curve, water resources yield and planning model

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Authors: Mayada Al Meghari

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Recently, grid middlewares have provided large integrated use of network resources as the shared data and the CPU to become a virtual supercomputer. In this work, we present the design and implementation of the middleware for Data Warehouse Signature, DWS Framework. The aim of using the middleware in our DWS framework is to achieve the high performance by the parallel computing. This middleware is developed on Alchemi.Net framework to increase the security among the network nodes through the authentication and group-key distribution model. This model achieves the key security and prevents any intermediate attacks in the middleware. This paper presents the flow process structures of the middleware design. In addition, the paper ensures the implementation of security for DWS middleware enhancement with the authentication and group-key distribution model. Finally, from the analysis of other middleware approaches, the developed middleware of DWS framework is the optimal solution of a complete covering of security issues.

Keywords: middleware, parallel computing, data warehouse, security, group-key, high performance

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Authors: M. Azarbarmas, J. M. Cabrera, J. Calvo, M. Aghaie-Khafri

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The modeling of hot deformation behavior for unseen conditions is important in metal-forming. In this study, the hot deformation of IN718 has been characterized in the temperature range 950-1100 and strain rate range 0.001-0.1 s-1 using hot compression tests. All stress-strain curves showed the occurrence of dynamic recrystallization. These curves were implemented quantitatively in mathematics, and then constitutive equation indicating the relationship between the flow stress and hot deformation parameters was obtained successfully.

Keywords: compression test, constitutive equation, dynamic recrystallization, hot working

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Authors: Reza Abbasi, Ahmad Hamidi Benam

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Shell structures have many geometrical variables that modify some of these parameters to improve the mechanical behavior of the shell. On the other hand, the behavior of such structures depends on their geometry rather than on mass. Optimization techniques are useful in finding the geometrical shape of shell structures to improve mechanical behavior, especially to prevent or reduce bending anchors. The overall objective of this research is to optimize the shape of concrete shells using the thickness and height parameters along the reference curve and the overall shape of this curve. To implement the proposed scheme, the geometry of the structure was formulated using nonlinear curves. Shell optimization was performed under equivalent static loading conditions using the modified bird community algorithm. The results of this optimization show that without disrupting the initial design and with slight changes in the shell geometry, the structural behavior is significantly improved.

Keywords: concrete shells, shape optimization, spinless curves, modified particle community algorithm

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Xiaoli Zhang, Xiongfei Li, Yuncong Feng

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ROC curves, as a widely used evaluating tool in machine learning field, are the tradeoff of true positive rate and negative rate. However, they are blamed for ignoring some vital information in the evaluation process, such as the amount of information about the target that each instance carries, predicted score given by each classification model to each instance. Hence, in this paper, a new classification performance method is proposed by extending the Receiver Operator Characteristic (ROC) curves to 3D space, which is denoted as 3D ROC Histogram. In the histogram, the

Keywords: classification, performance evaluation, receiver operating characteristic histogram, hardness prediction

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Authors: Ayaz Ahmad

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TOPIC: A study of the formation ,existness and stability of localised pulses in pde Ayaz Ahmad ,NITP, Abstract:In this paper we try to govern the evolution deterministic variable over space and time .We analysis the behaviour of the model which allows us to predict and understand the possible behaviour of the physical system .Bifurcation theory provides a basis to systematically investigate the models for invariant sets .Exploring the behaviour of PDE using bifurcation theory which provides many challenges both numerically and analytically. We use the derivation of a non linear partial differential equation which may be written in this form ∂u/∂t+c ∂u/∂x+∈(∂^3 u)/(∂x^3 )+¥u ∂u/∂x=0 We show that the temperature increased convection cells forms. Through our work we look for localised solution which are characterised by sudden burst of aeroidic spatio-temporal evolution. Key word: Gaussian pulses, Aeriodic ,spatio-temporal evolution ,convection cells, nonlinearoptics, Dr Ayaz ahmad Assistant Professor Department of Mathematics National institute of technology Patna ,Bihar,,India 800005 [email protected] +91994907553

Keywords: Gaussian pulses, aeriodic, spatio-temporal evolution, convection cells, nonlinear optics

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Yalda Zarnegarnia, Shari Messinger

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Receiver operating characteristic (ROC) curves have been widely used in medical research to illustrate the performance of the biomarker in correctly distinguishing the diseased and non-diseased groups. Correlated biomarker data arises in study designs that include subjects that contain same genetic or environmental factors. The information about correlation might help to identify family members at increased risk of disease development, and may lead to initiating treatment to slow or stop the progression to disease. Approaches appropriate to a case-control design matched by family identification, must be able to accommodate both the correlation inherent in the design in correctly estimating the biomarker’s ability to differentiate between cases and controls, as well as to handle estimation from a matched case control design. This talk will review some developed methods for ROC curve estimation in settings with correlated data from case control design and will discuss the limitations of current methods for analyzing correlated familial paired data. An alternative approach using Conditional ROC curves will be demonstrated, to provide appropriate ROC curves for correlated paired data. The proposed approach will use the information about the correlation among biomarker values, producing conditional ROC curves that evaluate the ability of a biomarker to discriminate between diseased and non-diseased subjects in a familial paired design.

Keywords: biomarker, correlation, familial paired design, ROC curve

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: L. Guevara, Glória L. S., Corea E. E, A. Ramírez-Zamora M., Salinas-Martinez J. A., Angeles-Hernandez J. C.

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Mathematical models are useful for identifying the characteristics of sheep lactation curves to develop and implement improved strategies. However, the accuracy of these models is influenced by factors such as the recording regime, mainly the intervals between test day records (TDR). The current study aimed to evaluate the effect of different TDR intervals on the goodness of fit of the Wood model (WM) applied to dairy sheep lactations. A total of 4,494 weekly TDRs from 156 lactations of dairy crossbred sheep were analyzed. Three new databases were generated from the original weekly TDR data (7D), comprising intervals of 14(14D), 21(21D), and 28(28D) days. The parameters of WM were estimated using the “minpack.lm” package in the R software. The shape of the lactation curve (typical and atypical) was defined based on the WM parameters. The goodness of fit was evaluated using the mean square of prediction error (MSPE), Root of MSPE (RMSPE), Akaike´s Information Criterion (AIC), Bayesian´s Information Criterion (BIC), and the coefficient of correlation (r) between the actual and estimated total milk yield (TMY). WM showed an adequate estimate of TMY regardless of the TDR interval (P=0.21) and shape of the lactation curve (P=0.42). However, we found higher values of r for typical curves compared to atypical curves (0.9vs.0.74), with the highest values for the 28D interval (r=0.95). In the same way, we observed an overestimated peak yield (0.92vs.6.6 l) and underestimated time of peak yield (21.5vs.1.46) in atypical curves. The best values of RMSPE were observed for the 28D interval in both lactation curve shapes. The significant lowest values of AIC (P=0.001) and BIC (P=0.001) were shown by the 7D interval for typical and atypical curves. These results represent the first approach to define the adequate interval to record the regime of dairy sheep in Latin America and showed a better fitting for the Wood model using a 7D interval. However, it is possible to obtain good estimates of TMY using a 28D interval, which reduces the sampling frequency and would save additional costs to dairy sheep producers.

Keywords: gamma incomplete, ewes, shape curves, modeling

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Authors: H. Loumi-Fergane, A. Belaidi

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The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used.  In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qⁱ, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

Keywords: conservation laws, field theories, multisymplectic geometry, relativistic mechanics

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