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Pressure Control Design of High-Pressure Fuel Pipe
Shi Wei,
Chunyong Wang,
Tailin Cen,
Yuhua Su
Issue:
Volume 9, Issue 4, August 2021
Pages:
92-103
Received:
7 June 2021
Accepted:
28 June 2021
Published:
5 July 2021
Abstract: In order to ensure the normal operation of the engine, the stability of the fuel supply system must be ensured. The fuel supply system needs to obtain fuel from the outside, and then pressurized into the high-pressure oil pipe, and then input into the engine cylinder. Therefore, the fuel parameters in the components of the fuel supply system affect each other. In this paper, a mathematical model is established to describe the relationship between the fuel parameters of each part of the fuel supply system, and then the stability of the fuel supply system can be controlled by controlling some parameters under given conditions. We intercept a very short time, analyze the mutual transfer of fuel in the fuel supply system through the micro element method, and establish the differential equations. Because some differential equations are more complex, it is difficult to find the formula solution, so we discretize the differential equations and get a group of recurrence relations. After calculating the initial state and related parameters, the fuel pressure parameters and fuel density parameters of each part of the fuel supply system at each time can be obtained recursively. Because the pressure and density of the fuel can express each other, we focus on the density parameter of the fuel, and do the conversion when the pressure is needed. On the basis of this group of recursive relations, we established an optimization model of fuel pressure control in high-pressure oil pipe: Taking the fuel supply time of one-way valve as decision variables, minimizing the difference between fuel pressure and standard value at each time as optimization objective, taking the practical significance of each physical quantity as constraint condition, and gave a discrete algorithm.
Abstract: In order to ensure the normal operation of the engine, the stability of the fuel supply system must be ensured. The fuel supply system needs to obtain fuel from the outside, and then pressurized into the high-pressure oil pipe, and then input into the engine cylinder. Therefore, the fuel parameters in the components of the fuel supply system affect...
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On the Unique Solvability of the Generalized Absolute Value Matrix Equation
Issue:
Volume 9, Issue 4, August 2021
Pages:
104-107
Received:
13 July 2021
Accepted:
26 July 2021
Published:
2 August 2021
Abstract: The generalized absolute value matrix equation has application in a variety of optimization problems, its unique solvability is still on the way. In this note, the unique solvability of the generalized absolute value matrix equation is considered. A new unique solvability of generalized absolute value matrix equation is given. The obtained result can be regarded as an extension of the absolute value equation to the generalized absolute value matrix equation. As an application, new convergence of matrix multisplitting Picard-iterative method is presented.
Abstract: The generalized absolute value matrix equation has application in a variety of optimization problems, its unique solvability is still on the way. In this note, the unique solvability of the generalized absolute value matrix equation is considered. A new unique solvability of generalized absolute value matrix equation is given. The obtained result c...
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Modelling Forest Growth Indices on Vegetation Pattern Formation
Peter Kwesi Nyarko,
Christiana Cynthia Nyarko
Issue:
Volume 9, Issue 4, August 2021
Pages:
108-122
Received:
16 July 2021
Accepted:
24 July 2021
Published:
2 August 2021
Abstract: Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.
Abstract: Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indice...
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An Axiomatic Approach to Gröbner Basis Theory by Examining Several Reduction Principles
Günter Landsmann,
Christoph Fürst
Issue:
Volume 9, Issue 4, August 2021
Pages:
123-140
Received:
28 May 2021
Accepted:
26 June 2021
Published:
2 August 2021
Abstract: Several variants of the classical theory of Gröbner bases can be found in the literature. They come, depending on the structure they operate on, with their own specific peculiarity. Setting up an expedient reduction concept depends on the arithmetic equipment that is provided by the structure in question. Often it is necessary to introduce a term order that can be used for determining the orientation of the reduction, the choice of which might be a delicate task. But there are other situations where a different type of structure might give the appropriate basis for formulating adequate rewrite rules. In this paper we have tried to find a unified concept for dealing with such situations. We develop a global theory of Gröbner bases for modules over a large class of rings. The method is axiomatic in that we demand properties that should be satisfied by a reduction process. Reduction concepts obeying the principles formulated in the axioms are then guaranteed to terminate. The class of rings we consider is large enough to subsume interesting candidates. Among others this class contains rings of differential operators, Ore-algebras and rings of difference-differential operators. The theory is general enough to embrace the well-known classical Gröbner basis concepts of commutative algebra as well as several modern approaches for modules over relevant noncommutative rings. We start with introducing the appropriate axioms step by step, derive consequences from them and end up with the Buchberger Algorithm, that makes it possible to compute a Gröbner basis. At the end of the paper we provide a few examples to illustrate the abstract concepts in concrete situations.
Abstract: Several variants of the classical theory of Gröbner bases can be found in the literature. They come, depending on the structure they operate on, with their own specific peculiarity. Setting up an expedient reduction concept depends on the arithmetic equipment that is provided by the structure in question. Often it is necessary to introduce a term o...
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The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet
Jing Zhang,
Gang Wang,
Chuanyan Hou,
Xiaoying Yang
Issue:
Volume 9, Issue 4, August 2021
Pages:
141-155
Received:
14 August 2021
Accepted:
26 August 2021
Published:
31 August 2021
Abstract: The construction of wavelets is a key problem in wavelet analysis. In the background of the one-dimensional double wavelet theory and the one dimensional biorthogonal bidirectional wavelet construction theory, this paper extends the one-dimensional bidirectional wavelet to the two-scale three-dimensional eight-direction biorthogonal wavelet. By using the method of tensor products to construct higher dimensional wavelets, the two-scale three-dimensional eight-direction multi-resolution analysis, two-scale three-dimensional eight-direction scale function and wavelet function are obtained. In addition, the conditions satisfied of the orthogonal and biorthogonal properties of the two-scale three-dimensional eight-direction wavelet are studied.
Abstract: The construction of wavelets is a key problem in wavelet analysis. In the background of the one-dimensional double wavelet theory and the one dimensional biorthogonal bidirectional wavelet construction theory, this paper extends the one-dimensional bidirectional wavelet to the two-scale three-dimensional eight-direction biorthogonal wavelet. By usi...
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