Search results for: Hypercomplex Cauchy type integral

Authors: Adel Salem Bahakeem, Ahmad Jamal, Mir Md. Maruf Morshed, Elwaleed Awad Khidir

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Direct Current (DC) servo motors, or simply DC motors, play an important role in many industrial applications such as manufacturing of plastics, precise positioning of the equipment, and operating computer-controlled systems where speed of feed control, maintaining the position, and ensuring to have a constantly desired output is very critical. These parameters can be controlled with the help of control systems such as the Proportional Integral Derivative (PID) controller. The aim of the current work is to investigate the effects of Proportional (P) and Integral (I) controllers on the steady state and transient response of the DC motor. The controller gains are varied to observe their effects on the error, damping, and stability of the steady and transient motor response. The current investigation is conducted experimentally on a servo trainer CE 110 using analog PI controller CE 120 and theoretically using Simulink in MATLAB. Both experimental and theoretical work involves varying integral controller gain to obtain the response to a steady-state input, varying, individually, the proportional and integral controller gains to obtain the response to a step input function at a certain frequency, and theoretically obtaining the proportional and integral controller gains for desired values of damping ratio and response frequency. Results reveal that a proportional controller helps reduce the steady-state and transient error between the input signal and output response and makes the system more stable. In addition, it also speeds up the response of the system. On the other hand, the integral controller eliminates the error but tends to make the system unstable with induced oscillations and slow response to eliminate the error. From the current work, it is desired to achieve a stable response of the servo motor in terms of its angular velocity subjected to steady-state and transient input signals by utilizing the strengths of both P and I controllers.

Keywords: DC servo motor, proportional controller, integral controller, controller gain optimization, Simulink

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Yousfi Abdelkader, Chaker Abdelkader, Bot Youcef

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This article proposes a five-level shunt active power filter for power quality improvement using a interval type-2 fuzzy logic controller (IT2 FLC). The reference compensating current is extracted using the P-Q theory. The majority of works previously reported are based on two-level inverters with a conventional Proportional integral (PI) controller, which requires rigorous mathematical modeling of the system. In this paper, a IT2 FLC controlled five-level active power filter is proposed to overcome the problem associated with PI controller. The IT2 FLC algorithm is applied for controlling the DC-side capacitor voltage as well as the harmonic currents of the five-level active power filter. The active power filter with a IT2 FLC is simulated in MATLAB Simulink environment. The simulated response shows that the proposed shunt active power filter controller has produced a sinusoidal supply current with low harmonic distortion and in phase with the source voltage.

Keywords: power quality, shunt active power filter, interval type-2 fuzzy logic controller (T2FL), multilevel inverter

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Authors: Zyrah Lou R. Samar, Genecarlo Liwanag

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Type 2 Diabetes Mellitus is the more prevalent type, caused by a combination of insulin resistance and inadequate insulin response to hyperglycemia1. Aside from pharmacologic interventions, medical nutrition therapy is an integral part of the management of patients with Type 2 Diabetes Mellitus. Whey protein, which is one of the best protein sources, has been investigated for its applicability in improving glycemic control in patients with Type 2 Diabetes Mellitus. This systematic review and meta-analysis was conducted to measure the magnitude of the effect of whey protein on glycemic control in type 2 diabetes mellitus. The aim of this review is to evaluate the efficacy and safety of whey protein in patients with type 2 diabetes mellitus. Methods: A systematic electronic search for studies in the PubMed and Cochrane Collaboration database was done. Included in this review were randomized controlled trials of whey protein enrolling patients with type 2 diabetes mellitus. Three reviewers independently searched, assessed, and extracted data from the individual studies. Results: A systematic literature search on online databases such as Cochrane Central Registry, PubMed, and Herdin Plus was conducted in April to September 2021 to identify eligible studies. The search yielded 21 randomized controlled trials after removing duplicates. Only 5 articles were included after reviewing the full text, which met the criteria for selection. Conclusion: Whey protein supplementation significantly reduced fasting blood glucose. However, it did not reduce post-prandial blood glucose, HbA1c level, and weight when compared with the placebo. There has been a considerate heterogeneity across all studies, which may have contributed/confounded its effects. A larger sample size and better inclusion, and a more specific study may be included in the future reviews.

Keywords: whey protein, diabetes, nutrition, fasting blood sugar, postprandial glucose, HbA1c, weight reduction

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Nasser Mohamed Ramli, Nurul Izzati Zulkifli

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Sump can be defined as a reservoir which contains slurry; a mixture of solid and liquid or water, in it. Sump system is an unsteady process owing to the level response. Sump level shall be monitored carefully by using a good controller to avoid overflow. The current conventional controllers would not be able to solve problems with large time delay and nonlinearities, Fuzzy Logic controller is tested to prove its ability in solving the listed problems of slurry sump. Therefore, in order to justify the effectiveness and reliability of these controllers, simulation of the sump system was created by using MATLAB and the results were compared. According to the result obtained, instead of Proportional-Integral (PI) and Proportional-Integral and Derivative (PID), Fuzzy Logic controller showed the best result by offering quick response of 0.32 s for step input and 5 s for pulse generator, by producing small Integral Absolute Error (IAE) values that are 0.66 and 0.36 respectively.

Keywords: fuzzy, sump, level, controller

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Authors: Karthik K. R, Viswanath V, Asraff A. K

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The first stage of a new-generation launch vehicle of ISRO makes use of large pressure vessels made of Aluminium alloy AA2219 to store fuel and oxidizer. These vessels have many weld joints that may contain cracks or crack-like defects during their fabrication. These defects may propagate across the vessel during pressure testing or while in service under the influence of tensile stresses leading to catastrophe. Though ductile materials exhibit significant stable crack growth prior to failure, it is not generally acceptable for an aerospace component. There is a need to predict the initiation of stable crack growth. The structural integrity of the vessel from fracture considerations can be studied by constructing the Failure Assessment Diagram (FAD) that accounts for both brittle fracture and plastic collapse. Critical crack sizes of the pressure vessel may be highly conservative if it is predicted from FAD alone. If the J-R curve for material under consideration is available apriori, the critical crack sizes can be predicted to a certain degree of accuracy. In this paper, a novel approach is proposed to predict the integrity of a weld in a pressure vessel made of AA2219 material. Fracture parameter ‘J-integral’ at the crack front, evaluated through finite element analyses, is used in the new procedure. Based on the simulation of tension tests carried out on SCT specimens by NASA, a cut-off value of J-integral value (J?ᵤₜ_ₒ??) is finalised. For the pressure vessel, J-integral at the crack front is evaluated through FE simulations incorporating different surface cracks at long seam weld in a cylinder and in dome petal welds. The obtained J-integral, at vessel level, is compared with a value of J?ᵤₜ_ₒ??, and the integrity of vessel weld in the presence of the surface crack is firmed up. The advantage of this methodology is that if SCT test data of any metal is available, the critical crack size in hardware fabricated using that material can be predicted to a better level of accuracy.

Keywords: FAD, j-integral, fracture, surface crack

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Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

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In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: 2d Toda equation, Hirota bilinear method, Lump-type solution, multiple-lump-type solution

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Authors: H. M. Al-Qassem, L. Cheng, Y. Pan

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In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, Orlicz spaces, Block spaces, extrapolation, L^{p} boundedness

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Authors: Jason Sheng-Hong Tsai, Faezeh Ebrahimzadeh, Min-Ching Chung, Shu-Mei Guo, Leang-San Shieh, Tzong-Jiy Tsai, Li Wang

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In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.

Keywords: non-minimum phase system, optimal linear quadratic tracker, proportional plus integral observer, state and disturbance estimator

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Authors: Dong Sang Yoo

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We consider nonlinear uncertain systems such that a priori information of the uncertainties is not available. For such systems, we assume that the upper bound of the uncertainties is represented as a Fredholm integral equation of the first kind and we propose an adaptation law that is capable of estimating the upper bound and design a continuous robust control which renders nonlinear uncertain systems ultimately bounded.

Keywords: adaptive control, estimation, Fredholm integral, uncertain system

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Authors: R. Z. Wang, B. C. Lin, C. H. Huang

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This study proposes a new method to simulate the crack propagation under mode-I loading using Vector Form Intrinsic Finite Element (VFIFE) method. A new idea which is expected to combine both VFIFE and J-integral is proposed to calculate the stress density factor as the crack critical in elastic crack. The procedure of implement the cohesive crack propagation in VFIFE based on the fictitious crack model is also proposed. In VFIFIE, the structure deformation is described by numbers of particles instead of elements. The strain energy density and the derivatives of the displacement vector of every particle is introduced to calculate the J-integral as the integral path is discrete by particles. The particle on the crack tip separated into two particles once the stress on the crack tip satisfied with the crack critical and then the crack tip propagates to the next particle. The internal force and the cohesive force is applied to the particles.

Keywords: VFIFE, crack propagation, fictitious crack model, crack critical

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Authors: Bojan Radisic, Katarina Stavlic

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The paper describes two economics terms consumer surplus and producer surplus using the definite integrals (the Riemann integral). The consumer surplus is the difference between what consumers are willing to pay and actual price. The producer surplus is the difference between what producers selling at the current price, rather than at the price they would have been are willing to accept. Using the definite integrals describe terms and mathematical formulas of the consumer surplus and the producer surplus and will be applied to the numerical examples.

Keywords: consumer surplus, producer surplus, definite integral, integration

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Jafar Razmi

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Integral abutment bridges are bridges that do not have joints. If these bridges are subject to large seasonal and daily temperature variations, the expansion and contraction of the bridge slab is transferred to the piles. Since the piles are deep into the soil, displacement induced by slab can cause bending and stresses in piles. These stresses cause fatigue and failure of piles. A complex mechanical interaction exists between the slab, pile, soil and abutment. This complex interaction needs to be understood in order to calculate the stresses in piles. This paper uses a mechanical approach in developing analytical equations for the complex structure to determine the stresses in piles. The solution to these analytical solutions is developed and compared with finite element analysis results and experimental data. Our comparison shows that using analytical approach can accurately predict the displacement in piles. This approach offers a simplified technique that can be utilized without the need for computationally extensive finite element model.

Keywords: integral abutment bridges, piles, thermo-mechanical stress, stress and strains

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Authors: N. Chayaopas, W. Assawinchaichote

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In order to maximize energy capturing from wind energy, controlling the doubly fed induction generator to have optimal power from the wind, generator speed and output electrical power control in wind energy system have a great importance due to the nonlinear behavior of wind velocities. In this paper purposes the design of a control scheme is developed for power control of wind energy system via H∞ fuzzy integral controller. Firstly, the nonlinear system is represented in term of a TS fuzzy control design via linear matrix inequality approach to find the optimal controller to have an H∞ performance are derived. The proposed control method extract the maximum energy from the wind and overcome the nonlinearity and disturbances problems of wind energy system which give good tracking performance and high efficiency power output of the DFIG.

Keywords: doubly fed induction generator, H-infinity fuzzy integral control, linear matrix inequality, wind energy system

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Authors: H. Al-Qassem, L. Cheng, Y. Pan

Abstract:

In this paper, we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log (deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Our results substantially improve many previously known results. Among key ingredients of our methods are an L¹→L² sharp estimate and using extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, orlicz spaces, block spaces, extrapolation, L^{p} boundedness

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Authors: Luis F. Bianchessi, Gustavo G. Shimamoto, Matthieu Tubino

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The use of biodiesel has been diffused in Brazil and all over the world by the trading of biodiesel (B100). In Brazil, the diesel oil currently being sold is a blend, containing 7% biodiesel (B7). In this context, it is necessary to develop methods capable of identifying this blend composition, especially regarding the biodiesel quality used for making these blends. In this study, hydrogen nuclear magnetic resonance spectra (1H-NMR) are proposed as a form of identifying and confirming the quality of type B10 blends (10% of biodiesel and 90% of diesel). Furthermore, the presence of vegetable oils, which may be from fuel adulteration or as an evidence of low degree of transesterification conversion during the synthesis of B100, may also be identified. Mixtures of diesel, vegetable oils and their respective biodiesel were prepared. Soybean oil and macauba kernel oil were used as raw material. The diesel proportion remained fixed at 90%. The other proportion (10%) was varied in terms of vegetable oil and biodiesel. The 1H-NMR spectra were obtained for each one of the mixtures, in order to find a correlation between the spectra and the amount of biodiesel, as well as the amount of residual vegetable oil. The ratio of the integral of the methylenic hydrogen H-2 of glycerol (exclusive of vegetable oil) with respect to the integral of the olefinic hydrogens (present in vegetable oil and biodiesel) was obtained. These ratios were correlated with the percentage of vegetable oil in each mixture, from 0% to 10%. The obtained correlation could be described by linear relationships with R2 of 0.9929 for soybean biodiesel and 0.9982 for macauba kernel biodiesel. Preliminary results show that the technique can be used to monitor the biodiesel quality in commercial diesel-biodiesel blends, besides indicating possible adulteration.

Keywords: biodiesel, diesel, biodiesel quality, adulteration

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Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar

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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem

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Authors: Reham Algheshairy

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The purpose of this research study is to identify the beneficial effects of Nigella sativa seeds, cherries and Ajwah dates on blood glucose levels among people with type 2 diabetes in the KSA population and healthy people in the UK. My hypothesis questions whether or not people with type 2 diabetes can lead a healthier life using these dietary supplements.

Keywords: diabetes type 2, cherry, nigella seeds, Ajwa date

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: Payel Das, Gnaneshwar Nelakanti

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In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equations with smooth kernel. Using sufficiently accurate numerical quadrature rule, we obtain superconvergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and $L^2$-norm. Numerical examples are given to illustrate the theoretical results.

Keywords: hammerstein integral equations, spectral method, discrete galerkin, numerical quadrature, superconvergence

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Authors: Sanjay Kumar, Lillie Dewan

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The study of complex dynamic systems has advanced through various scientific approaches with the help of computer modeling. The common design trends in aerospace system design can be applied to quadcopter design. A quadcopter is a nonlinear, under-actuated system with complex aerodynamics parameters and creates challenges that demand new, robust, and effective control approaches. The flight control stability can be improved by planning and tracking the trajectory and reducing the effect of sensors and the operational environment. This paper presents a modern design Simmechanics visual modeling approach for a mechanical model of a quadcopter with three degrees of freedom. The Simmechanics model, considering inertia, mass, and geometric properties of a dynamic system, produces multiple translation and rotation maneuvers. The proportional, integral, and derivative (PID) controller is integrated with the Simmechanics model to follow a predefined quadcopter rotational trajectory for a fixed time interval. The results presented are satisfying. The simulation of the quadcopter control performed operations successfully.

Keywords: nonlinear system, quadcopter model, simscape modelling, proportional-integral-derivative controller

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Authors: Cui Fu, Yi-Zhou Zhuang, Sheng-Zhi Wang

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Full scale tests of six micropiles with different predrilled-hole parameters under low frequency cyclic lateral loading in-sand were carried out using the MTS hydraulic loading system to analyze the seismic performance of micropiles. Hysteresis curves, skeleton curves, energy dissipation capacity and ductility of micropiles were investigated. The experimental results show the hysteresis curves appear like plump bows in the elastic–plastic stage and failure stage which exhibit good hysteretic characteristics without pinching phenomena and good energy dissipating capacities. The ductility coefficient varies from 2.51 to 3.54 and the depth and loose backfill of oversized holes can improve ductility, but the diameter of predrilled-hole has a limited effect on enhancing its ductility. These findings and conclusions could make contribution to the practical application of the semi-integral abutment bridges and provide a reference for the predrilled oversized hole technology in integral abutment bridges.

Keywords: ductility, energy dissipation capacity, micropile with predrilled oversized hole, seismic performance, semi-integral abutment bridge

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Authors: K. Manmi, Q. X. Wang

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This paper investigates microbubble dynamics subject to ultrasound in a weakly viscous fluid near a rigid boundary. The phenomenon is simulated using a boundary integral method. The weak viscous effects are incorporated into the model through the normal stress balance across the bubble surface. The model agrees well with the Rayleigh-Plesset equation for a spherical bubble for several cycles. The effects of the fluid viscosity in the bubble dynamics are analyzed, including jet development, centroid movement and bubble volume.

Keywords: microbubble dynamics, bubble jetting, viscous effect, boundary integral method

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Authors: Yang Zhong, Mei-Jie Xu

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To study the dynamic mechanics response of asphalt pavement under the temperature load and vehicle loading, asphalt pavement was regarded as multilayered elastic half-space system, and theory analysis was conducted by regarding dynamic modulus of asphalt mixture as the parameter. Firstly, based on the dynamic modulus test of asphalt mixture, function relationship between the dynamic modulus of representative asphalt mixture and temperature was obtained. In addition, the analytical solution for thermal stress in the single layer was derived by using Laplace integral transformation and Hankel integral transformation respectively by using thermal equations of equilibrium. The analytical solution of calculation model of thermal stress in asphalt pavement was derived by transfer matrix of thermal stress in multilayer elastic system. Finally, the variation of thermal stress in pavement structure was analyzed. The result shows that there is an obvious difference between the thermal stress based on dynamic modulus and the solution based on static modulus. Therefore, the dynamic change of parameter in asphalt mixture should be taken into consideration when the theoretical analysis is taken out.

Keywords: asphalt pavement, dynamic modulus, integral transformation, transfer matrix, thermal stress

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Authors: J. Fernandez de Canete, S. Fernandez-Calvo, I. García-Moral

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This paper presents and discusses the application of the object-oriented modelling software SIMSCAPE to hydraulic systems, with particular reference to multivariable proportional-integral-derivative (PID) control. As a result, a particular modelling approach of a double cylinder-piston coupled system is proposed and motivated, and the SIMULINK based PID tuning tool has also been used to select the proper controller parameters. The paper demonstrates the usefulness of the object-oriented approach when both physical modelling and control are tackled.

Keywords: object-oriented modeling, multivariable hydraulic system, multivariable PID control, computer simulation

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Authors: Chitsanzo Isaac

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Across the world, the ongoing Covid-19 pandemic has challenged urban systems and policy frameworks, highlighting societal vulnerabilities and systemic inequities among many communities. Measures of confinement and social distancing to contain the Covid-19 virus have fragmented the physical and social fabric of cities. This has caused urban dwellers to reassess how they engage with their urban surroundings and maintain social ties. Urbanists have presented strategies that would allow communities to survive and even thrive, in extraordinary times of crisis like the pandemic. Tactical Urbanism, particularly the 15-Minute City, has gained popularity. It is considered a resilient approach in the global north, however, it’s transferability to the global south has been called into question. To this end, this paper poses the question: to what extent is the 15-Minute City framework integral sustainable design, and are there processes that make it adoptable by cities in the global south? This paper explores four issues using secondary quantitative data analysis and convergence analysis in the Paris and Blantyre urban regions. First, it questions how the 15-Minute City has been defined and measured, and how it impacts urban dwellers. Second, it examines the extent to which the 15-minute city performs under the lens of frameworks such as Wilber’s integral theory and Fleming’s integral sustainable design theory. Thirdly this work examines the processes that can be transferred to developing cities which foster community resilience through the perspectives of experience, behaviors, cultures, and systems. Finally, it reviews the principal ways in which a multi-perspective reality can be the basis for resilient community design and sustainable urban development. This work will shed a light on the importance of a multi-perspective reality as a means of achieving sustainable urban design goals in developing urban areas.

Keywords: 15-minute city, developing cities, global south, community resilience, integral sustainable design, systems thinking, complexity, tactical urbanism

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Authors: Saeed Otarod

Abstract:

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

Keywords: explicit, linear, differential, closed form

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