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Research Article
Pompeiu-Hausdorff Fuzzy b-metric Spaces Are Associated with a Common Fixed Point and Multivalued Mappings
Noreddine Makran*
Issue:
Volume 13, Issue 5, October 2024
Pages:
118-129
Received:
14 July 2024
Accepted:
14 August 2024
Published:
29 August 2024
DOI:
10.11648/j.acm.20241305.11
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Abstract: The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an element either belongs to the set or does not, in fuzzy logic, the affiliation of the element to the set is expressed as a number from the interval [0, 1]. The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential part of real-world problems, leading Zadeh to address the problem of indeterminacy. The theory of a fixed point in fuzzy metric spaces can be viewed in different ways, one of which involves the use of fuzzy logic. Fuzzy metric spaces, which are specific types of topological spaces with pleasing ”geometric” characteristics, possess a number of appealing properties and are commonly used in both pure and applied sciences. Metric spaces and their various generalizations frequently occur in computer science applications. For this reason, a new space called a Pompeiu-Hausdorff fuzzy b-metric space is constructed in this paper. In this space, some new fixed point results are also formulated and proven. Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy b-metric spaces is investigated. The findings obtained in fuzzy metric spaces, such as those discussed in Remark 3.1, are generalized by the results in this paper, and additional specific findings are produced and supported by examples. The study of denotational semantics and their applications in control theory using fuzzy b-metric spaces and Pompeiu-Hausdorff fuzzy b-metric spaces will be an important next step.
Abstract: The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an element either belongs to the set or does not, in fuzzy logic, the affiliation of the element to the set is expressed as a number from the interval [0, 1]. The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential par...
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Review Article
Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction
Paul Wachira Githaiga,
Mathew Ngugi Kinyanjui,
Roy Phineas Kiogora*
Issue:
Volume 13, Issue 5, October 2024
Pages:
130-139
Received:
17 July 2024
Accepted:
24 August 2024
Published:
5 September 2024
Abstract: This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is θ. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.
Abstract: This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed no...
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Research Article
The Modeling and Optimization of a Multi-dam System
Pengcheng Xie*
Issue:
Volume 13, Issue 5, October 2024
Pages:
140-152
Received:
1 August 2024
Accepted:
24 August 2024
Published:
5 September 2024
Abstract: In this paper, we present a maintenance plan for the Kariba Dam in Africa. The Kariba Dam, a double curvature concrete arch dam in Zambia's capital, is crucial for regional energy and water management. Ensuring its safety and functionality is essential. This study provides a comprehensive analysis and maintenance plan to safeguard the dam's long-term viability. Our mathematical analysis begins with a threshold evaluation of three proposed options, considering costs such as relocation, dam removal, construction of new dams, repairs, and ecological damage, as well as benefits like energy generation, flood prevention, employment, tourism, and ecological protection. The data-driven analysis indicates that our option is the most economically viable. We assess water management capabilities, using them as a safety coefficient for the dams. We selected 30 seed points along the riverbank to establish dams. Our recommendation is to increase the number of dams and ensure their strategic distribution. An assessment model based on the analytic hierarchy process was then developed, focusing on three factors: safety, economy, and population. We determined the weights of each factor. The optimal scheme was identified through this model, and the sensitivity of the results was also evaluated. The greatest impact under extreme conditions was found. This paper provides the details of the theoretical analysis and the numerical experiments, which include the use of modeling, optimization, mathematical programming, and so on.
Abstract: In this paper, we present a maintenance plan for the Kariba Dam in Africa. The Kariba Dam, a double curvature concrete arch dam in Zambia's capital, is crucial for regional energy and water management. Ensuring its safety and functionality is essential. This study provides a comprehensive analysis and maintenance plan to safeguard the dam's long-te...
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Research Article
Powell-Eyring Nanofluid Flow over a Stretching Sheet
Nictor Mwamba*
Issue:
Volume 13, Issue 5, October 2024
Pages:
153-164
Received:
6 July 2024
Accepted:
26 August 2024
Published:
6 September 2024
Abstract: This research investigates the flow of a Powell-Eyring Nanofluid flowing over an exponentially stretching sheet. Thermal radiation, Soret, dissipation, and Dufour effects have been put into consideration. The obtained partial differential equations(PDE) have been transformed into ordinary differential equations (ODE) using similarity transformation. Numerical solutions are obtained in MATLAB using bvp4c frame work of fourth order accuracy integration scheme. It has been observed that the boundary layer for momentum increases with the velocity ratio while the boundary layers for thermal and concentration decrease. The velocity diminishes with increasing magnetic parameter while the temperature and concentration increased. The temperature increases with an increase in thermophoresis and Brownian motion. Increasing the fluid parameter resulted in decreased Nusselt number, skin friction, and Sherwood number. Increasing Powell-Eyring fluid parameter decreases the Nusselt number and Sherwood number but increases skin friction. This research may find use in the development of microelectronics, chemical processes, human targeted drug delivery, and heating and cooling system.
Abstract: This research investigates the flow of a Powell-Eyring Nanofluid flowing over an exponentially stretching sheet. Thermal radiation, Soret, dissipation, and Dufour effects have been put into consideration. The obtained partial differential equations(PDE) have been transformed into ordinary differential equations (ODE) using similarity transformation...
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Research Article
Approximate Multiplication and Division Calculation for DSP Applications
Dina Mohamed Ellaithy*
Issue:
Volume 13, Issue 5, October 2024
Pages:
179-186
Received:
12 August 2024
Accepted:
2 September 2024
Published:
20 September 2024
DOI:
10.11648/j.acm.20241305.16
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Abstract: Digital signal processing (DSP) is a promising alternative to accomplish a wide variety of signal processing operations. Multiplications and divisions have been urgently proposed to perform different DSP operations in real-time applications. However, the design and implementation of multiplication and division calculations have some limitations such as strict timing, bounded power consumption, and higher accuracy. The exact execution of these complex operations consumes great hardware resources and power consumption. Approximate computation for the main and complex arithmetic functions is a demand solution to decrease power, area, and delay. In this paper, low-power and high-accuracy approximate multiplication and division processes have been implemented using a 90 nm CMOS process, 1.0 V supply voltage standard cell library. The approximate multiplication and division algorithm depends on enhanced logarithmic converters. The logarithm-based arithmetic exhibits a good performance with decreasing the used hardware resources and runs at a higher speed. The proposed scheme achieves less hardware with minimal power consumption. The proposed approximate structure demonstrates up to a 62% saving in power with a rise in the accuracy level as compared with the prior approximate works. At the same time, the proposed multiplier and divider can carry out the multiplication and division processes in 1.8 ns, respectively.
Abstract: Digital signal processing (DSP) is a promising alternative to accomplish a wide variety of signal processing operations. Multiplications and divisions have been urgently proposed to perform different DSP operations in real-time applications. However, the design and implementation of multiplication and division calculations have some limitations suc...
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Research Article
General Definitions of Information, Intelligence, and Consciousness from the Perspective of Generalized Natural Computing
Linsen Zhang*
Issue:
Volume 13, Issue 5, October 2024
Pages:
187-193
Received:
7 September 2024
Accepted:
25 September 2024
Published:
10 October 2024
DOI:
10.11648/j.acm.20241305.17
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Abstract: Atoms themselves have no thoughts and cannot be thinking. Why does the human body, which is composed of atoms, have consciousness? The widely used concepts of information and intelligence in today’s science, which are related to this, do not yet have appropriate general definitions. Answering these interesting questions is a crucial issue for technological development in the historical context of human society entering the era of intelligence. The key lies in how to fully utilize the existing fundamental theories subtly related to information science. Here we attempt to give the definition of general information and general intelligence from the perspective of generalized natural computing, based on the least action principle, Hamilton-Jacobi equation, dynamic programming, reinforcement learning, and point out the relationship between the two. The least action principle for describing conservative systems can be seen as an intelligent manifestation of natural matter, and its equivalent form, the Hamilton-Jacobi equation, can be extended to describe quantum phenomena and is a special case of continuous dynamic programming equations. Dynamic programming is an efficient optimization method under deterministic models, while reinforcement learning, as a manifestation of biological intelligence, is its model-free version. The statement that reinforcement learning is the most promising machine learning method has a profound physical foundation. General information is defined as the degree to which a certain environmental element determines the behavior of the subject. General intelligence is defined as the automatic optimization ability of the action or value function of a system with a certain degree of conservatism. Intelligence is a basic property of material systems, rather than an emergent property that only complex systems possess. Consciousness is an advanced intelligent phenomenon, a reconstruction of quasi conservative systems based on complex systems.
Abstract: Atoms themselves have no thoughts and cannot be thinking. Why does the human body, which is composed of atoms, have consciousness? The widely used concepts of information and intelligence in today’s science, which are related to this, do not yet have appropriate general definitions. Answering these interesting questions is a crucial issue for techn...
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Research Article
Principle and Application for Rumination Computing Algorithms
Issue:
Volume 13, Issue 5, October 2024
Pages:
194-210
Received:
6 September 2024
Accepted:
25 October 2024
Published:
29 October 2024
DOI:
10.11648/j.acm.20241305.18
Downloads:
Views:
Abstract: To fully analyze, mine, and utilize the information and knowledge implied in problem resolving use cases, this paper proposed the autonomous learning method based on machine inducting, hypothesis formulating, and result verifying, which was similar to the biological process of cows ruminating, called rumination computing. Firstly, after inducting and summarizing over 1080 mathematic application problem, the system architecture and general algorithm for humanoid automatic resolving mathematic application problems were represented, which typically included functional modules such as commonsense knowledge base, domain knowledge base, and local knowledge base, preprocessing, word segmentation and part of speech tagging, semantic framework matching, global semantic analyzing, thinking mechanism implementing, etc. Secondly, after the use case solutions were approved, three typical rumination computing modes, including vocabulary sequence, semantic relationship, and computing action, were introduced based on the correct results, resolving steps, and basic rumination actions. The rumination computing step plan was formulated, new knowledge was obtained from the commonsense and results verification, so the continuous autonomous learning loop for machine thinking was formed. Detailed explanations were provided for the three core algorithms implemented (rumination framework algorithm, rumination semantic algorithm, rumination action algorithm). Then, by specific mathematic application problem humanoid resolving user cases, the above three types of rumination computing modes were illumined.
Abstract: To fully analyze, mine, and utilize the information and knowledge implied in problem resolving use cases, this paper proposed the autonomous learning method based on machine inducting, hypothesis formulating, and result verifying, which was similar to the biological process of cows ruminating, called rumination computing. Firstly, after inducting a...
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