Related Equations Research Articles

Integral representations in the complex plane and iterated boundary value problems

Fundamental solutions to differential operators lead to integral operators providing integral representation formulas for solutions to related differential equations. Proper modifications of the fundamental solutions result in integral operators which are related to certain boundary value problems. For complex partial differential operators of arbitrary order in the plane, fundamental solutions are achievable by properly integrating the Cauchy kernel. Particular such complex model differential operators are the polyanalytic and the polyharmonic operators. A hierarchy of integral operators is available for these model operators leading to polyanalytic Cauchy–Schwarz and to polyharmonic Green, Neumann, Robin, and hybrid Green integral operators. The theory is supplemented here by constructing a new polyanalytic Pompeiu (Pompeiu–Vekua) integral operator of any order adjusted to (iterated) Neumann boundary conditions.

Cavitating flow investigation in low specific speed axial flow waterjet pumps

Abstract In this paper, the cavitating flow in low specific speed axial flow waterjet pumps are treated at different cavitation conditions. In order to analyze the cavitating turbulent flow comprehensively, three axial flow waterjet pumps with the specific speed less than 650 min-1·m3s-1·m are chosen to compare the internal flow phenomenon. The investigations are conducted by numerical simulation, where RANS method is applied with k-ω SST turbulence model and homogeneous cavitation model. The results show that there are several types of cavitation such as tip leakage vortex cavitation, sheet cavitation attached on blade suction surface, and shedding cavity in the pumps. The vortex structure in the low specific speed waterjet pump contains tip leakage vortex, shedding vortex downstream of the sheet cavitation and perpendicular cavitation vortex. It is noted that the cavity firstly occurs at the leading edge near blade tip, and the sheet cavity covering the blade suction surface extends from leading edge to the middle part, while the tip leakage vortex cavitation develops with the decreasing cavitation number. Further analysis using relative vortex transport equation depicts that the vortex stretching term is the main contributor for the vorticity production in the pump, and the vortex dilation and baroclinic torque occur at the interface between cavity and water.

STEM Education of Kinematics and Dynamics Using Arduino

Ever increasing technological progress opens novel opportunities concerning educational activities, and the ability to use the technology effectively is one of the 21st century’s most demanding skills. The Partnership Forum for 21st-Century Skills (P21) states that no organization can achieve satisfying results without using technology and therefore the use of technology particularly in schools should be at the highest level. Some novel teaching methods have recently emerged based on technological developments, such as STEM education, which is based on the integration of science, technology, engineering, and mathematics. In this study, the motion of a body connected to a pulley system is analyzed by using an Arduino microprocessor and also related mathematical equations. Arduino is a programming platform on which various electronic elements can be connected. There are various Arduino compatible sensors (sound, light, distance, temperature, etc.) that can be coded for their intended use. Due to its cost effectiveness, this technological instrument can be used as a measurement tool in many physics experiments. In this work, the time-varying data of the position of the moving object is determined using the HC-SR04 ultrasonic distance sensor (see Fig. 1). The HC-SR04 distance sensor can determine the distance of the obstacle from the sensor when the transmitted signal is reflected from an obstacle and returned to the sensor, and the Arduino IDE computer program is used to load the corresponding codes into the Arduino and to retrieve the incoming data.

Real-Time Analysis and Research of Vehicle CAN

Abstract The real-time evaluation method of CAN bus is studied. The event-triggered CAN protocol has no limitation on the worst transmission time of information. Based on the study of ratio monotone analysis (RMA), a single step recursive relation equation is deduced. Using LabWindows /CVI design and analysis software, the research method is applied to offline realtime analysis of CAN bus information of a certain vehicle. The results show that this method is of great significance to the real-time evaluation of CAN bus.

Differential and integrodifferential equations for Gould–Hopper–Frobenius–Euler polynomials

The fundamental aim of this paper is to derive the recurrence relation, shift operators, differential, integrodifferential and partial differential equations for Gould–Hopper–Frobenius–Euler polynomials using factorization method, which may be utilised in solving some emerging problems in different branches of science and technology.

Pemodelan Pengeringan Menggunakan Microwave Dengan Model Relative Energy Activation (REA) Untuk Pengeringan Kacang Hijau Berbentuk Sphere

One of the advantages of the REA model is that the relative activation energy equation obtained from the experimental data can be used for other drying conditions with the same initial material and moisture content. Through convective data, an equation of activation energy is obtained which will be used for drying the data using a microwave. The simulation carried out is to compare the model data with experimental data of a microwave with a power of 0.25 W/g and a drying air temperature of 50 0C, then a power of 0.7 W/g and a drying temperature of 70 0C. increasing with microwave, the higher the value of the heat transfer coefficient (h) the simulation results are getting closer to the experimental data for the initial period of development, even making experimental data with increasing time.

A novel method for lung nodule detection in computed tomography scans based on Boolean equations and vector of filters techniques

This work presents a novel method that uses a Vector of Pre-processing Filters combined with simple relational and Boolean equations for pulmonary nodule detection. To isolate nodules from other lung structures, we propose a 16 filter scheme endowed with multiscale median masks, statistical-based thresholds, and 3-D morphological operations. In the Boolean False Positive Reduction stage, relational and Boolean equations select nodule candidates from pre-processing filters using our descriptor with 20 attributes. Finally, a Convolutional Neural Network (CNN) classifies the remaining structures into nodule or no nodule. The method reached 92.75% sensitivity for an average of 8 false positives per exam using all exams in the public Lung Image Database Consortium (LIDC) with a slice thickness of less than 2 mm that contains lesions larger than 3 mm marked “nodule” by at least 3 radiologists. For a less consensual gold standard, our method reaches the highest sensitivity levels among listed results.

Numerical solution of anH(curl)-elliptic hemivariational inequality

AbstractThis paper is concerned with the analysis and numerical solution of an $\boldsymbol {H}({\textbf {curl}})$-elliptic hemivariational inequality (HVI). One source of the HVI is through a temporal semidiscretization of a related hyperbolic Maxwell equation problem. An equivalent minimization principle is introduced, and the solution existence and uniqueness of the $\boldsymbol {H}({\textbf {curl}})$-elliptic HVI are proved. Numerical analysis of the HVI is provided with a general Galerkin approximation, including a Céa’s inequality for convergence and error estimation. When the linear edge finite element method is employed, an optimal-order error estimate is derived under a suitable solution regularity assumption. A fully discrete scheme based on the backward Euler difference in time and a mixed finite element method in space is also analyzed, and stability estimates are derived for first-order terms of the fully discrete solution. Numerical results are reported on linear edge finite element solutions of the $\boldsymbol {H}({\textbf {curl}})$-elliptic HVI for numerical evidence of the theoretically predicted convergence order.

Thermophysical Properties of Nanofluid in Two-Phase Fluid Flow through a Porous Rectangular Medium for Enhanced Oil Recovery.

It is necessary to sustain energy from an external reservoir or employ advanced technologies to enhance oil recovery. A greater volume of oil may be recovered by employing nanofluid flooding. In this study, we investigated oil extraction in a two-phase incompressible fluid in a two-dimensional rectangular porous homogenous area filled with oil and having no capillary pressure. The governing equations that were derived from Darcy’s law and the mass conservation law were solved using the finite element method. Compared to earlier research, a more efficient numerical model is proposed here. The proposed model allows for the cost-effective study of heating-based inlet fluid in enhanced oil recovery (EOR) and uses the empirical correlations of the nanofluid thermophysical properties on the relative permeability equations of the nanofluid and oil, so it is more accurate than other models to determine the higher recovery factor of one nanoparticle compared to other nanoparticles. Next, the effect of nanoparticle volume fraction on flooding was evaluated. EOR via nanofluid flooding processes and the effect of the intake temperatures (300 and 350 K) were also simulated by comparing three nanoparticles: , , and . The results show that adding nanoparticles (<5 v%) to a base fluid enhanced the oil recovery by more than 20%. Increasing the inlet temperature enhanced the oil recovery due to changes in viscosity and density of oil. Increasing the relative permeability of nanofluid while simultaneously reducing the relative permeability of oil due to the presence of nanoparticles was the primary reason for EOR.

Multidimensional transonic shock waves and free boundary problems

We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for the Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments in the analysis of multidimensional transonic shock waves and corresponding free boundary problems for the compressible Euler equations and related nonlinear partial differential equations (PDEs) of mixed type. The nonlinear PDEs under our analysis include the steady Euler equations for potential flow, the steady full Euler equations, the unsteady Euler equations for potential flow, and related nonlinear PDEs of mixed elliptic–hyperbolic type. The transonic shock problems include the problem of steady transonic flow past solid wedges, the von Neumann problem for shock reflection–diffraction, and the Prandtl–Meyer problem for unsteady supersonic flow onto solid wedges. We first show how these longstanding multidimensional transonic shock problems can be formulated as free boundary problems for the compressible Euler equations and related nonlinear PDEs of mixed type. Then we present an effective nonlinear method and related ideas and techniques to solve these free boundary problems. The method, ideas, and techniques should be useful to analyze other longstanding and newly emerging free boundary problems for nonlinear PDEs.

A novel Bethe ansatz scheme for the one-dimensional Hubbard model

We propose a novel characterization of the exact solution of the one-dimensional Hubbard model with unparallel boundary magnetic fields. The non-diagonal boundary terms break the U(1) symmetry of the system and the number of electrons with fixed spin is not conserved. Thus it is difficult to study the physical quantities in the thermodynamic limit based on the previously obtained inhomogeneous T−Q relation and Bethe ansatz equations. In order to solve this problem, we propose the t−W scheme. The basic idea is that the eigenvalues of the transfer matrix can be expressed by its zero-roots instead of the usual Bethe roots. This method allows us to study thermodynamic properties of the system such as the ground state, surface energy, charge and spin excitations. The t−W scheme is universal and can be applied to the systems either with or without U(1) symmetry.

Mechanical and Maxwell’s equations relative to an observer and principle of general relativity

The principle of general relativity states that every observer has the right to analyze the physical world from his point of view. However, a transcription code is necessary to compare different descriptions. It is just this code that allows to obtain a physics that is universal in the class of observers. First of all, an observer, identified with a frame of reference R, must have procedures not only to attribute coordinates to each event but also to measure any physical quantity. In the literature, formal procedures are proposed to derive physical quantities and equations relative to an observer starting from the absolute ones. In this paper, these formal approaches are shown to be equivalent to entrust the proper inertial frame [Formula: see text] at an event [Formula: see text] to carry out the measure of physical quantities. Then the observer R adopts the results obtained by [Formula: see text] without introducing his own measures. Since these adopted measures are carried out in the absence of gravitation, the obtained relative equations describe how the evolution with respect to R of proper quantities is modified by gravitation. Finally, after determining the transformation of proper quantities in going from R to another frame R’, a principle of general relativity is formulated in an appropriate class of observers.

A GIS-based framework using fuzzy relation equation system solutions in urban planning

Several fuzzy decision models are proposed in literature to solve urban planning problems. In this research we present a novel GIS-based framework to solve decision problems in urban planning based on a System of Fuzzy Relation Equations in which the unknowns represent characteristics affecting observable facts constituting the input variables. Aim of this research is to partition the urban study area into subzones, each of which identifies a sub-area of the study area within which the set of analyzed characteristics are homogeneous. The study area is initially decomposed in atomic urban areas called microzones; for each microzone are calculated the greatest and lowest solutions of a System of Fuzzy Relation Equations by using the Universal solution Algorithm and are calculated and fuzzified the values of the output variables. Spatially adjoining microzones with same output variables are dissolved forming homogeneous urban areas with reference to the problem analyzed, called Urban Contexts. For each output variable a thematic map is constructed; in addition, a thematic map of its reliability is created. This framework is tested on a study area given by the district of Ponticelli in the municipality of Naples (Italy); comparison tests performed with respect to a previous GIS-based framework based on a System of Fuzzy Relation Equations show that our method provides a more detailed knowledge of the characteristics of the urban study area with reference to the problem dealt with.

Energy performance and flow characteristics of a slanted axial-flow pump under cavitation conditions

Cavitation is a complex flow phenomenon that hinders the efficient, safe, and stable operation of hydraulic machinery. To investigate the effect of cavitation on energy performance and flow characteristics of hydraulic machinery, cavitating flow in a slanted axial-flow pump based on entropy production theory and vortex dynamics is studied. The results show that the impeller chamber is a primary region of cavitation and energy loss generation under different cavitation conditions, including the incipient, growing, and wedge-shaped cavitation stages. In the incipient cavitation stage, as degree of cavitation strengthens, the flow at the impeller blade is smooth with little cavitation, and the variation in entropy production is constant, resulting in a stable energy performance. As it evolves into the wedge-shaped stage, the cavitation grows from the tip region near the impeller blade to the hub. At this time, the entropy production increases in the impeller chamber, resulting in a drop in energy performance. Meanwhile, flow separation appears at the impeller blade, and a secondary tip leakage vortex is promoted. The region with high vorticity basically matches the region with the high local entropy production rate. According to the relative vorticity transport equation, compressibility of cavitation strongly affects the relative vorticity in the impeller chamber, indicating that cavitation indirectly increases entropy production and energy loss by affecting the vorticity distribution, resulting in the drop in energy performance.

Finite Time Convergent Cooperative Guidance Law for Multiple Flight Vehicles Considering Detection Efficiency

Aiming at the problem of cooperative interception of maneuvering target, a cooperative guidance of multiple flight vehicles considering detection efficiency was designed based on the multi-agent finite time consensus theory. Considering the first-order dynamic of the flight vehicle, the guidance law was designed according to the relative motion equations and the model of cooperative detection, which can improve the estimation accuracy of the relative distance using the terminal LOS (Line-of-sight) angle and guarantee simultaneously strike the target in a finite time. Numerical simulation results show that in the case of different maneuvers of an evader, each flight vehicle can hit the target at the same time with a designed terminal LOS angle, and the detection accuracy of the relative distance was continuously improved during the terminal guidance.

Caputo-Fabrizio Fractional Model of Electro-Osmotic Flow of Walters??™-B Fluid in the Presence of Diffusion-Thermo: Exact Solution via Integral Transform

Electrically conducted viscoelastic fluids have recently caught the attention of scientists and engineers due to their extensive applications in various sectors of research and engineering. They're utilized in cancer therapy (hyperthermia), MRI, medication administration, and magnetic refrigeration, to name a few applications (MR). The core objective of the present analysis is to develop the exact solution of the fractional convective flow of Walters B liquid. The effects of thermal radiations, magnetic field, electro-osmosis, and diffusion thermo have been considered in the present phenomenon. With the help of relative constitutive equations, the governing equations of the present phenomenon have been modeled in terms of second-order partial differential equations. To established the closed-form solution for velocity, temperature, and concentration equation, the Caputo-Fabrizio, and the Laplace transform technique have been implemented. To check the influences of various inserted parameters on fluid, graphs have been plotted. It is very important to mention that electro-osmotic and Walters??™-B fluid parameters decline the profile of velocity.?

Optimal control for multistage uncertain random dynamic systems with multiple time delays

A complex system exhibiting uncertainty as well as randomness is an uncertain random dynamic system. A novel idea of an uncertain random matrix is introduced as an interaction between uncertainty and randomness. Thereby a time-delayed uncertain random dynamic system is formulated. And then the corresponding time-delayed optimal control problem is first presented in this paper. To tackle a problem like that, a method is proposed to translate it into an equivalent optimization problem without time delay. The relevant recursion equations are developed with the dynamic programming technique to solve the converted optimization problem. Solving the related recursion equations yields the answer to such an optimization problem. The presented approach offers a unified framework for tackling the discrete-time uncertain random optimal control problem involving time delays. In this framework, three algorithms are successfully devised in doing with time-delayed optimal control problems for dynamic systems regarding linear, quadratic, and cubic controls. Meanwhile, the optimal solutions for numerical examples are found by the raised algorithms. Finally, a problem of optimal control for a two-spool turbofan engine is investigated as an application of our results.

Presented a transformer‐less buck‐boost DC–DC structure with vast voltage range

Here, a transformer-less buck-boost topology is presented which can provide an appropriate voltage conversion ratio in both boost and buck mode. The voltage range of the proposed topology can be increased and decreased for the low content of the duty cycle. Thus, the maximum voltage throughout the semiconductor of the suggested converter is less against the load voltage. On the other hand, the system cost is reduced using the low rating elements in the presented converter. Moreover, only one power switch has been applied in the suggested converter that facilitates its control. In addition, there is zero voltage switching condition through the diodes that is caused to improve the efficiency of the recommended topology. To validate the impressibility of the presented topology, the operation modes analysis with related equations has been carried out. The comparison survey of the recommended structure and other equivalent structures has been investigated. Conclusively, a laboratory scheme via basic experimental waveforms for 150 W load power level in 50 kHz operation frequency is prepared that suggested to be utilized in various applications for instant green energy systems, LED drivers etc.

Some properties of solutions of Itô equations with drift in [formula omitted

This paper is a natural continuation of Krylov (2020), where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in Ld+1(Rd+1). Here we study some properties of these processes such as higher summability of Green’s functions, a maximum principle for related transport equations with irregular coefficients, boundedness of resolvent operators in Lebesgue spaces, establish Itô’s formula, and so on.

Bipolar equations on complete distributive symmetric residuated lattices: The case of a join-irreducible right-hand side

Bipolar max-⁎ equations, with ⁎ a triangular norm, have recently become a popular research topic embedded in the broad field of fuzzy relational equations. In this paper, we lift the work from the restrictive setting of the real unit interval — obfuscating the underlying lattice-theoretical essence — to the general setting of complete distributive symmetric residuated lattices, allowing to build upon the vast body of knowledge on unipolar sup-⁎ equations on complete distributive residuated lattices. We determine the full solution set, with particular emphasis on the extremal solutions, of a bipolar sup-⁎ equation in case the right-hand side is a join-irreducible element. The results are illustrated by means of ample examples.