International Journal of Mathematical Sciences and Computing @ijmsc
Journal articles - International Journal of Mathematical Sciences and Computing
All articles: 294
Stochastic Rules in Nucleotide Sequences in Genomes of Higher and Lower Organisms
Scientific article
The article presents new stochastic rules of nucleotide sequences in single-stranded DNA of eukaryotic and prokaryotic genomes. These discovered rules are candidates for the role of universal genomic rules. To reveal such rules, the authors represent any of genomic sequences in single-stranded DNA as a set of n parallel texts (or layers), each of which is written based on one of the different n-plets alphabets (n = 1, 2, 3, ...). Then comparison analysis of percentages of the 4n kinds of n-plets in the n parallel texts in such sequence is fulfield. In the result, unexpected stochastic rules of invariance of total sums of percentages for certain tetra-groupings of n-plets in different parallel texts of genomic DNA sequences are revealed.The presented rules significantly expand modern knowledge about stochastic regularities in long single-stranded DNA sequences, and they can be considered as generalizations of the second Chargaff's rule. A tensor family of matrix representations of interrelated DNA-alphabets of 4 nucleotides, 16 doublets, 64 triplets, and 256 tetraplets is used in the study. Some analogies of the discovered genetic phenomena with phenomena of Gestalt psychology are noted. The authors connect the received results about the genomic percentages rules with a supposition of P. Jordan, who is one of the creators of quantum mechanics and quantum biology, that life's missing laws are the rules of chance and probability of the quantum world.
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Study of memory effect in an inventory model with linear demand and shortage
Scientific article
For real market studies of any business, inclusion of memory or past experience in inventory model has great impact. Memory means it depends on the past state of the process not only current state of the process. Indeed, the inventory system is an appropriate example as a memory affected system. Presence of long past experiences or short past experiences of any company or shop has different importance on increasing or decreasing profit. The description of the memory dependent inventory model is more appropriate process compared to the memory less inventory model. Depending on demand rate, a comparison between the minimized total average costs of different numerical example has been presented. Fractional order derivative and integration have been used to establish the model. Our considered numerical example establishes that if linear type demand rate is only time proportional, profit of the business is high compared to the linear type demand rate.
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Study on Influencing Factors of Regional Economy Based on Multilevel Model
Scientific article
Based on the relevant data of economic development of 31 provinces in China from 2016 to 2021, this paper selects the level of economic development as the response variable. The explanatory variables are selected from the aspects of location, human capital, industrial structure, foreign trade, system, science and technology and employment level. Aiming at the data with hierarchical structure, a multilevel model is proposed for analysis. It is concluded that human capital, industrial structure, foreign trade and system have a significant impact on the level of economic development. The impact of technology and employment level on the level of economic development is not significant. At the same time, this paper also makes a comparative analysis of the linear regression model, random intercept model and random intercept-slope growth model, which shows the advantages of random intercept-slope growth model.
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The Application of Meta-Heuristic Algorithms in Automatic Software Test Case Generation
Scientific article
Nowadays, software test is one of the most important activities that software's quality will be certified by it. Test operation includes program's implement on test case set and comparison of results with expected one. Manual test case for operation test program and error detect is time consuming with insufficient precision and complicated coverage of program, so, the use of algorithms in automatic test case generation has been considered. Meta-heuristic algorithms are known tools which are optimized and used in test case generation. Most of complicated matters need a lot of possible states assessment in order to reach the valid answer. With the proper answer, test case optimization and meta-heuristic algorithms play a constructive role. In this paper we would compare methods and their traits, and the software test case generation methods based on meta-heuristic algorithms with their description.
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The Construction of two classes of 4-valent tri- Cayley Graphs over Cyclic Group
Scientific article
The symmetry of the graph has always been a hot topic in graph theory and the vertex-transitive graphs are a class of graphs with high symmetry. Cayley graphs which are the highly symmetrical graphs play an important role and much work has been done in the study. The tri-Cayley graph is a natural generalization of the Cayley graph. A graph is said to be a tri-Cayley graph if it admits a semiregular subgroup of automorphisms having three orbits of equal length. Koács et al. classified the cubic symmetric tricirculants in 2012 and Potočnik et al. classified the cubic vertex-transitive tricirculants in 2018. Currently, there is no research on the classification of 4-valent tri-Cayley graphs over cyclic group. In this paper, we will construct two classes of 4-valent tri-Cayley graphs over cyclic group and discuss their automorphism groups. In addition, the vertex transitivity, edge transitivity and arc transitivity are proved.
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The Forecast of Jute Export in Bangladesh for Optimal Smoothing Constants
Scientific article
Forecasting is estimating the magnitude of uncertain future events and provides different results with different supposition. In order to identify the core data pattern of jute bale requirements for yarn production, we examined 10 years' worth of data from Jute Yarn/Twin that were shipped by their member mills Limited. Exponential smoothing and Holt’s methods are commonly used to forecast this output because it provides an adequate result. Selecting the right smoothing constant value is essential for reducing predicting errors. In this work, we created a method for choosing the smoothing constant's ideal value to reduce study errors measured by the mean square error (MSE), mean absolute deviation (MAD), and mean square percent error (MAPE). At the contrary, we discuss research finding result and future possibility so that Jute Mills Limited and similar companies may execute forecasting smoothly and develop the expertise level of the procurement system to stay competitive in the worldwide market.
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Scientific article
We study the prime spectrum of idealistic S-algebras, defined via an algebraic structure with a complete lattice of ideals and a suitable notion of prime ideals. The spectrum is equipped with a natural topology and is shown to form a spectral space, possessing key properties such as compactness, separation, and sobriety. We further establish that the spectrum construction is functorial and provides a correspondence between minimal prime ideals and irreducible components under appropriate conditions. Examples are included to illustrate the role of the underlying structure, showing that the existence of minimal primes depends critically on the ideal-theoretic properties.
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The Study of Slow Manifolds in the Lorenz-Haken Model Using Differential Geometry
Scientific article
In order to explore the Lorenz-Haken model, we will concentrate on the flow curvature technique, a recently created method based on differential geometry. This approach treats a dynamical system's trajectory curve or flow as a curve in Euclidean space. Analytical calculations may be used to determine the flow curvature, which is the trajectory curve's curvature. The flow curvature manifold, which is related to the dynamical system of any dimension, is defined by the locations where the flow curvature is null. For the slow invariant manifold of the same dynamical system, the flow curvature manifold offers an analytical equation. The slow invariant manifold equation may be discovered using the flow curvature technique without the need of any asymptotic expansions. In this study, we compute the analytical equation of the slow invariant manifold for the three-dimensional Lorenz-Haken model using the flow curvature approach for the first time. This analytical equation, together with its visual representation in phase space, makes it possible to distinguish between the slow development of trajectory curves and the rapid one, which advances our knowledge of this slow-fast domain. This study also advances the field relative to earlier similar work. Aside from that, we utilize the Darboux theorem to demonstrate the slow manifold's invariance characteristic.
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The better pseudo-random number generator derived from the library function rand() in C/C++
Scientific article
We choose a better pseudo-random number generator from a list of eight pseudo-random number generators derived from the library function rand() in C/C++, including rand(); i.e. a random number generator which is more random than all the others in the list. rand() is a repeatable pseudo-random number generator. It is called pseudo because it uses a specific formulae to generate random numbers, i.e. to speak the numbers generated are not truly random in strict literal sense. There are available several tests of randomness, some are easy to pass and others are difficult to pass. However we do not subject the eight set of pseudo random numbers we generate in this work to any known tests of randomness available in literature. We use statistical technique to compare these eight set of random numbers. The statistical technique used is correlation coefficient.
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Transmission Dynamics of Malware in Networks Using Caputo Fractional Order Derivative
Scientific article
Fractional calculus plays a crucial role in the representation of various natural and physical phenomena by incorporating the inherent non-locality and long-term memory effect of fractional operators. These models offer a more precise and systematic depiction of the underlying phenomena. The focus of this research paper is on the utilization of fractional calculus in the context of the epidemic model. Specifically, the model considers a fractional order ρ, where 0<ρ≤1, and employs the Caputo fractional order derivative to describe the transmission of malware in both wireless and wired networks. The basic reproduction number, along with the fractional order ρ, is identified as the threshold parameter in this model. The stability of the system is analysed at different stages of the reproduction number, considering both local and global asymptotic stability. Additionally, sensitivity analysis is conducted on the model parameters to determine the direction of change in the reproduction number. This analysis aids in understanding whether the reproduction number will increase or decrease under different scenarios. To obtain numerical results, the Fractional Forward Euler Method is utilized for simulation purposes. This method enables the computation of the model's dynamics and offers insights into the behaviour of the system. While the Caputo fractional order derivative offers a promising framework for modelling epidemic dynamics, they often entail significant computational overhead, limiting the scalability and practical utility of fractional calculus-based epidemic models, especially in real-time simulation and forecasting scenarios.
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Trend Analysis and Forecasting of Water Level in Mtera Dam Using Exponential Smoothing
Scientific article
This study presents trend analysis and forecasting of water level in Mtera dam. Data for water level were obtained from Rufiji Basin Development Authority (RUBADA). The study analyzed trend of water level using time series regression while forecasting of water level in Mtera dam was done using Exponential smoothing. Results revealed that both maximum and minimum water level trends were decreasing. Forecasted values show that daily water level will be below 690 (m.a.s.l) which is the minimum level required for electricity generation on 2023. It was recommended that proper strategies should be taken by responsible authorities to reduce effects that may arise. Strategies my include constructing small dams on upper side of Mtera dam to harvest rain water during rainy season as reserves to be used on dry season. In long run Tanzania Electric Supply Company (TANESCO) should invest into alternative sources of energy.
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Use of the Ontological Model for Personification of the Semantic Search
Scientific article
Semantic search is an important component of modern intelligent applications oriented on work in open information environment. The intelligence level of application depends of it's capabilities in knowledge processing and defines it's facilities. Now applications widely use ontologies for knowledge representation. Therefore criteria of intelligence level estimation (that can analyze ontologies) of applications and retrieval systems as their particular case are proposed. In this paper, an ontological model of the intelligent interaction of the main objects and subjects of the semantic search (the Web information resources, information objects and information consumers etc.) is developed. Software realization of semantic search on base of this ontological model and integration of this search instrument with applied systems are describes.
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Using Deep Learning Towards Biomedical Knowledge Discovery
Scientific article
A vast amount of knowledge exists within biomedical literature, publications, clinical notes and online content. Identifying hidden, interesting or previously unknown biomedical knowledge from free text resources using an automated approach remains an important challenge. Towards this problem, we investigate the use of deep learning methods that have shown significant promise in identifying hidden patterns from large corpus of text in an unsupervised manner. For example, it can deduce that 'husband' - 'man' + 'woman' = 'wife'. We use the text corpus from MRDEF file in the Unified Medical Language System (UMLS) dataset as training set to discover potential relationships. To evaluate our approach, we cross-verify new relationships against the UMLS MRREL dataset and conduct a manual evaluation from a sample of the non-overlapping set. The algorithm found 32% of new relationships not originally represented in the UMLS. The deep learning methods provide a promising approach in discovering potential new biomedical knowledge from free text.
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Vertex Connected Domination Polynomial of some Coalescence of Complete and Wheel Graphs
Scientific article
In this paper, we introduce new results of vertex connected dominating set and vertex connected domination polynomial of vertex identification, edge introduced and t-tuple of complete graph, also we determine new results of vertex connected dominating set and vertex connected domination polynomial of vertex identification, edge introduced and t-tuple of wheel graph.
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