This paper analyzes the representation behaviors of a comparison measure between two compared fuzzy sets. Three types of restrictions on two fuzzy sets are considered in this paper: the two disjoint union fuzzy sets, the two disjoint fuzzy sets and the two general fuzzy sets. Differences exist among the numbers of possible representations of a comparison measure for the three types of fuzzy sets restrictions. The value of comparison measure is constant for the two disjoint union fuzzy sets. There are 42 candidate representations of a comparison measure for the two disjoint fuzzy sets. Of which 13 candidate representations with one or two terms can be used to easily calculate and compare a comparison measure.

In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the partition requirement, that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measuring terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy.

The synchronous generator, as the main component of power systems, plays a key role in these system’s stability. Therefore, utilizing the most effective control strategy for modeling and control the synchronous generator results in the best outcomes in power systems’ performances. The advantage of using a powerful controller is to have the synchronous generator modeled and controlled as well as its main task i.e. stabilizing power systems. Since the synchronous generator is known as a complicated nonlinear system, modeling and control of it is a difficult task. This paper presents a sum of squares (SOS) approach to modeling and control the synchronous generator using polynomial fuzzy systems. This method as an efficacious control strategy has numerous superiorities to the well-known T–S fuzzy controller, due to the control framework is a polynomial fuzzy model, which is more general and effectual than the well-known T–S fuzzy model. In this case, a polynomial Lyapunov function is used for analyzing the stability of the polynomial fuzzy system. Then, the number of rules in a polynomial fuzzy model is less than in a T-S fuzzy model. Besides, derived stability conditions are represented in terms of the SOS approach, which can be numerically solved via the recently developed SOSTOOLS. This approach avoids the difficulty of solving LMI (Linear Matrix Inequality). The Effectiveness of the proposed control strategy is verified by using the third-part Matlab toolbox, SOSTOOLS.

The Diophantine equation for which p is prime 2^n = p^2 + 7 and n is integers with p > 0, is examined in this work. It is demonstrated by examining the characteristics of the equation that the only solutions meeting these requirements are p = 3 with n = 5 and p = 5 with n = 7. In order to analyze the above equation, it is necessary to look at the properties of primes and how they relate to powers of two. These results advance our knowledge of prime numbers and how they behave in certain mathematical problems.

Adenoviruses are associated with respiratory tract, gastrointestinal or, less frequently, other involvement. Epidemics of adenovirus infections occur globally, in communities and in closed or crowded settings. In our institution, an outbreak of Adenovirus infection in infants and children was recently observed. Two main patterns of clinical presentation were observed: 68 patients had mainly respiratory symptoms (pharyngitis n=67, cough n=44; tonsillar exudate n=17; other respiratory signs n=4) while 26 patients showed prevalent gastrointestinal involvement (diarrhea n=26, vomiting n=8). Patients with respiratory symptoms had a significantly higher count of WBC, PMN and platelets, while CRP level approached statistical significance (p=0.07) for higher values in the patients with diarrhea. In order to explore the impact of selected presenting features, possible association between level of CRP and presence of pharyngeal exudate, cough, vomiting, diarrhea, duration of fever, number of neutrophils, and administration of antibiotics was analyzed. Patients falling in the tertile with more elevated CRP values had significantly more often tonsillar exudate and diarrhea, while those in the lower tertile had a 4.4 days duration of fever, vs. ≥5.0 days in the remaining patients. Antibiotic therapy was administered more frequently to patients with higher values of CRP (p=0.006). Duration of hospitalization was not associated with the CRP level. The median time from the receipt of positive adenovirus PCR test result to patient discharge was 1 day in 73% of cases. The number of copies of adenovirus detected by PCR ranged between 47 million and 15/L. Falling in the highest terzile of copy number was significantly associated with pharyngitis. The 24 patients with evidence of viral coinfection had no difference in the demographics or presenting features, with the only exception of a significantly higher leukocyte count. Rapid turn-around of results of molecular testing of adenovirus genome on pharyngeal swab allowed us to rapidly diagnose adenovirus infection, allowing stopping antibiotic therapy and immediate discharge, with reduced discomfort for the families and more appropriate use of hospital beds. A high copy number of adenovirus from pharyngeal swab should not be taken as an indicator of worse prognosis, thus allowing preferential use of qualitative rather than quantitaive assay.

The accurate identification of the primary tumor origin in metastatic cancer cases is crucial for guiding treatment decisions and improving patient outcomes. Copy Number Alterations (CNA) have emerged as valuable genomic markers for predicting the origin of metastases. This research article presents a comprehensive analysis of CNA-based prediction models in metastatic cancer. The study utilizes a dataset comprising CNA profiles from twenty different cancer types and employs advanced AI-based techniques for prediction. The research workflow consists of two models. The first is convolution network-based, while the other is a multi-stage model. In the first stage, a RELU model is developed to differentiate between 16 cancer types, considering their CNA, chromosome location, strand, and overall location. The second stage involves building specialized models to detect differences between cancer types within the same location or organs, such as brain lower-grade glioma and glioblastoma multiforme. Both generalized models achieve an overall accuracy of over 90%, while the specialized models achieve an accuracy of approximately 95% with minimal loss values. The results demonstrate the potential of AI-based approaches utilizing CNA data for improved diagnosis and personalized treatment strategies in metastatic cancer. This research establishes a solid foundation for future advancements in the field, paving the way for more effective and targeted approaches in metastatic cancer management.

The Goldbach Conjecture, which is frequently termed as “1 + 1”, has been a fascinating goal for many mathematicians over centuries. A Chinese mathematician, Dr. Jingrun Chen, proved 1 + 2, which is a great success and the best result so far achieved. Although there were several attempts proving the conjecture, these attempts are either tediously long, complicated, or logically imperfect, thus not widely accepted. Taking advantage of the periodicity of primes, here the author provides a straight forward rigorous proof for the Conjecture.

In this paper, we examine the weak abc conjecture and the strong abc conjecture using some functions. we attempt to discuss the possibilty that the negative consequence of the weak abc conjecture. Namely, we derive that the weak abc conjecture is not true. Additionally, we show that the strong abc conjecture is not true.

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. vital chromatic number and n-vital chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using vital edge from connectedness to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

In 2020, the world was plagued with COVID-19 which was first identified in Wuhan, China in November 2019. During the early phase of the pandemic with no known treatment and WHO-approved vaccines, most government and public health officials were pushing for non-pharmaceutical intervention in trying to curb the spread of COVID-19. One such intervention is the restriction on movement to reduce social mixing. However, the economic cost of locking down cities especially in developing countries is unbearable as most of these countries are running economies that were on life support before the COVID-19 pandemic. We analyze the daily COVID-19 cases in Ghana to evaluate whether there was a significant change in transmission of COVID-19 after the partial lockdown of the two main cities (Kumasi and Accra) was lifted. The results showed that there was no increase in the transmissibility of COVID-19 after the partial lockdown was lifted. Contrary to the expectation that transmissibility will increase after lifting the partial lockdown, there was a reduction of the time-dependent reproduction ratio from 3.17 to 1.23.

The paper proves that an odd composite integer $N$ can be factorized in at most $O( 0.125u(log_2N)^2)$ searching steps if $N$ has a divisor of the form $2^a{u} +1$ or $2^a{u}-1$ with $a > 1$ being a positive integer and $u > 1$ being an odd integer. Theorems and corollaries are proved with detail mathematical reasoning. Algorithms to factorize the kind of odd composite integers are designed and tested by factoring certain Fermat numbers. The results in the paper are helpful to factorize the related kind of odd integers as well as some big Fermat numbers

A twin prime numbers are two prime numbers which have the difference of 2 exactly. In other words, twin primes is a pair of prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Up to date there is no any valid proof/disproof for twin prime conjecture. Through this research paper, my attempt is to provide a valid disproof for twin prime conjecture.

A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse modes of perturbation. The study of the analytical dispersion relation leads to the conditions for the onset of convective instability as well as to the determination of the parametric threshold for the transition to absolute instability. The results are generalised to the case of three-dimensional perturbations.

We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The strength of our method is that no additional information is required about the given original identity. The method readily extends to a generalized Fibonacci sequence.

Formal Calculation uses an auxiliary form to calculate various nested sums and provides results in three forms. In addition to computation, it is also a powerful tool for analysis, allowing one to study various numbers in a unified way. This article contains many results of two types of Stirling numbers, associated Stirling numbers, and Eulerian numbers, making a great generalization of Euler polynomials, Wilson's theorem, and Wolstenholme's theorem, showing that they are just special cases. Formal Calculation provides a novel method for obtaining combinatorial identities and analyzing q-binomial.This article has obtained a large number of results in q-analogues, including inversion formulas for q-binomial coefficients. This article also introduces a theorem on symmetry.

New setting is introduced to study co-neighborhood, neutrosophic t-neighborhood, neutrosophic quasi-vertex set, neutrosophic quasi-order, neutrosophic neighborhood, neutrosophic co-t-neighborhood, neutrosophic quasi-edge set, neutrosophic quasi-size, Neutrosophic number, neutrosophic co-neighborhood, co-neutrosophic number, quasi-number and quasi-co-number. Some classes of neutrosophic graphs are investigated.

The growing importance of sustainability in organizational success, particularly in the pharma-ceutical industry, underscores the need for leveraging technologies like blockchain to enhance sustainability indicators across environmental, social, and economic pillars. This study aims to identify and understand the challenges hindering the adoption of blockchain in the pharmaceuti-cal sector for improving sustainability performance, addressing two research questions: the spe-cific challenges faced by blockchain adoption in this context and the interdependencies among these challenges. Employing a two-step approach, the study compiles challenges through a litera-ture review, refines them via expert opinions, and establishes their interrelationships using methodologies like Fuzzy Interpretive Structural Modeling (FISM) and Cross-Impact Matrix Multiplication Applied to Classification (MICMAC). The research contributes to unraveling the complex relationships and dependencies within the system, providing a structured framework for improved decision-making and strategic planning. It fills a literature gap by being the first attempt to outline driving and dependent factors related to the challenges of adopting blockchain technology for sustainability enhancement in the pharmaceutical sector, offering insights that can significantly impact brand image, company perception, and consumer value.

This paper will present the torque control design of an AFPMSM, one stator, and one rotor, using an FLC and ANFIS in-wheels fed by a three-level T-type inverter. The Surgeon ambiguous inference file of the FLC controller is built by two input vectors, the stator current error and the derivative of the stator error. These input variables include five membership functions, Negative big (NB), Negative small (NS), Equal zero (ZE), Positive small (PS), and Positive big (PB). The FLC controller is implemented with a 5x5 matrix so that the output stator voltage of the controller is required. The ANFIS controller for the neural network-based feature set and the fuzzy system. The neural network develops the dataset on the stator current error (e) and error integral (∆e). Then, the generated dataset is fed to the fuzzy logic method, and the control rules are developed. This ANFIS controller is caused by the training and testing phases. Finally, the FLC and ANFIS torque controllers are compared with the PI controller. The correctness of the proposed control structured solution is demonstrated by the simulation results of MATLAB/SIMULINK.

Coagulation is the most sensitive step in drinking water treatment. Underdosing may not yield the required water quality, whereas overdosing may result in higher costs and excess sludge. Traditionally, the coagulant dosage is set based on bath experiments performed manually. Therefore, this test does not allow real-time dosing control, and its accuracy is subject to operator experience. Alternatively, solutions based on machine-learning (ML) have been evaluated as a computer-aided alternative. Despite these advances, there is open debate on the most suitable ML method applied to the coagulation process, capable of the most highly accurate prediction. This study addresses this gap, where a comparative analysis between ML methods was performed. As a research hypothesis, a novel data-driven fuzzy inference system (FIS) should provide the best performance due to its ability to deal with uncertainties inherent to complex processes. Although ML methods have been widely investigated, only a few studies report hybrid neuro-fuzzy systems applied to coagulation. Thus, to the best of our knowledge, this is the first study thus far to address the accuracy of this novel data-driven FIS for such application. The novel FIS provided the smallest error (0.86), indicating a promising alternative tool for real-time and highly accurate coagulant dosing in drinking water treatment.

This study aims to elucidate a soft computing approach for quantitative assessment of the scoring grade or rubrics for students in an outcome based education system. The intended approach resorts to a fuzzy membership based assessment of the different parameters of the scoring system, thereby yielding a novel and humanly assessment technique. The selection of the membership functions is based on the human behavior so as to make a realistic representation of the scoring strategy. The novelty of the proposed strategy lies in assigning fuzzy membership based weighted scores instead of simply assigning score bands to rubric categories, as is performed in normal rubrics based assessment. Comparative results demonstrated on a case study of Indian education scenario reveal the effectiveness of the proposed strategy over other fuzzy membership and normal rubrics based assessment procedures.

More than 110 countries including 500 cities worldwide have set the goal of reaching carbon neutrality. Heating contributes to most of the residential energy consumption and carbon emissions. The green energy transition of fossil-based heating systems is needed to reach the emission goals. However, the heating systems vary in energy source, heating technology, equipment location, and these complexities make it challenging for households to compare heating systems and make decisions. Hence, a decision support tool that provides a generalized ranking of individual heating alternatives is proposed for households as decision-makers to identify the optimal choice. This paper presents an analysis of 13 heating alternatives and 19 quantitative criteria in technological, environmental, and financial aspects, combines ideal solution based Multi-Criteria Decision Making with 6 weighting methods and 4 normalization methods, and introduces ensemble learning with a fuzzy membership function derived from Cauchy distribution to finalize the final ranking. The robustness of the proposed method is verified by 3 sensitive analyses from different aspects. Air to water heat pump, solar heating and direct district heating are the top three rankings in the final result under Danish national average data. A framework is designed to guide the decision-makers apply this ranking guideline with their practical feasible situations.

The aim of this paper is the evaluation of the success of graduating with distinction in higher education (SGDHE) using the fuzzy DEMATEL method. The observation has been done using cause and effect criteria. 11 cause and 14 effect clusters have been used in this study. The study result of this work shows that all the effects are connected to the given causes and a cause-effect graph has been generated for each connection. This proposed approach is demonstrated with the empirical case of Dire Dawa University students in Dire Dawa Ethiopia.

Monitoring complex electro-mechanical processes is not straightforward despite the arsenal of techniques nowadays availanle. This paper presents a method based on Adaptive-Network-based Fuzzy Inference System (ANFIS) to estimate eccentricity of its spinning axis. The method is experimentally tested on an ultra-precision rotating device commonly used for micro-scale turning. The developed model has three inputs, two obtained from a frequency domain analysis of a vibration signal and the third, which is the device rotation frequency. A comparative study demonstrates that an adaptive neural-fuzzy inference system model provides better error-based performance indices for detecting imbalance than a non-linear regression model. This simple, fast, and non-intrusive imbalance detection strategy is proposed to counteract eventual deterioration in the performance of ultra-high precision rotating machines due to vibrations.

In modern mathematics, many concepts and ideas are described in terms of category theory. From this viewpoint, it is desirable to analyze what can be determined if, instead of the basic category of sets, we consider a similar category of fuzzy sets. In this paper, we describe a natural fuzzy analog of the category of sets and functions, and we show that, in this category, fuzzy relations (a natural fuzzy analogue of functions) can be determined in category terms -- of course, modulo 1-1 mapping of the corresponding universe of discourse and 1-1 re-scaling of fuzzy degrees.

In this paper, we scrutinize the axiomatic system of effect algebras which is given by D. J. Foulis and M.K. Bennett in the paper Effect Algebras and Unsharp Quantum Logics. We prove that this axiomatic system consists of independent axioms. To do this, we construct some models to indicate the indepence of each axiom. Therefore none of these axioms can be reduced when constructing any effect algebra. As a result, any algebra is an effect algebra if and only if it verifies (E1)-(E4) axioms.

The literature on substance use usually extracts conclusions from data with correlational methods. Our study shows the usefulness of complementing ordered logistic regression (OLR) and fuzzy set qualitative comparative analysis (fsQCA) to assess factors inducing cannabis consumption in a sample of 1,935 teenagers. OLR showed a significant influence of gender (odd ratio (OR) =0.383, p<0.0001), parental monitoring (OR=0.587, p=0.0201); religiousness (OR=0.476, p=0.006); parental tolerance to substance use (OR=42.01, p<0.0001) and having close peers that consume substances (OR=5.60, p<0.0001). FsQCA has allowed fitting linkages between factors from a complementary perspective. (1) Coverage (cov) and consistency (cons) attained by solutions explaining use (cons=0.808, cov=0.357) are clearly lower than by recipes of non-use (cons=0.952, cov=0.869) (2) The interaction of gender, a tolerant family to use and the attitude toward substances by peers is very consistent to explain cannabis use. (3) The most important recipe explaining resistance to cannabis is simply parental disagreement with substance consumption (cons=0.956, cov=0.861) (4) Factors as gender, religiosity, parental monitoring and age show also a relevant impact on attitude toward cannabis use. However, whereas some of them impact symmetrically on use and non-use this does not follow in factors such as parental monitoring or age.

The accurate prediction of the solar Diffuse Fraction (DF), sometimes called the Diffuse Ratio, is an important topic for solar energy research. In the present study, the current state of Diffuse Irradiance research is discussed and then three robust, Machine Learning (ML) models, are examined using a large dataset (almost 8 years) of hourly readings from Almeria, Spain. The ML models used herein, are a hybrid Adaptive Network-based Fuzzy Inference System (ANFIS), a single Multi-Layer Perceptron (MLP) and a hybrid Multi-Layer Perceptron-Grey Wolf Optimizer (MLP-GWO). These models were evaluated for their predictive precision, using various Solar and Diffuse Fraction (DF) irradiance data, from Spain. The results were then evaluated using two frequently used evaluation criteria, the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE). The results showed that the MLP-GWO model, followed by the ANFIS model, provided a higher performance, in both the training and the testing procedures.

This paper presents a method to detect and classify the high impedance fault that occur in the medium voltage distribution network using discrete wavelet transform (DWT) and adaptive neuro-fuzzy inference system (ANFIS). The network is designed using Matlab software and various faults such as high impedance, symmetrical and unsymmetrical fault have been applied to study the effectiveness of the proposed ANFIS classifier method. This is achieved by training the ANFIS classifier using the features (standard deviation values) extracted from the three phase fault current signal by DWT technique for various cases of fault with different values of fault resistance in the system. The success and discrimination rate obtained for identifying and classifying the high impedance fault from the proffered method is 100% whereas the values are 66.7% and 85% respectively for conventional fuzzy based approach. The results indicate that the proposed method is more efficient to identify and discriminate the high impedance fault accurately from other power system faults in the system.

In my paper, a divisibility rule named the Queen function is de- scribed, which has been generalized for every integer and encompasses all pre- viously established divisibility rules. Subsequently, the paper discusses other areas where this function is instrumental. These include simplifying ratios, generating prime numbers, and more. Towards the end of the paper, a set of hypotheses is also presented. Among these, the most significant is the novel approach involving the application of the Queen function for prime number generation.

Cardiomyopathies are major causes of heart failure. Chagas disease (CD) is caused by the parasite Trypanosoma cruzi, and it is endemic in Central, South America. Thirty percent of the cases evolve into chronic cardiomyopathy (CCC) with worse prognosis as compared with other cardiomyopathies. In vivo bioenergetic analysis and ex vivo proteomic analysis of myocardial tissues highlighted worse mitochondrial dysfunction in CCC, and previous studies identified nuclear-encoded mitochondrial gene variants segregating with CCC. Here, we assessed the role of the mitochondrial genome through mtDNA copy number variations and mtDNA haplotyping and sequencing from heart or blood tissues of severe, moderate CCC and asymptomatic/indeterminate Chagas disease as well as healthy controls as an attempt to help decipher mitochondrial-intrinsic genetic involvement in Chagas disease development. We have found that mtDNA copy number was significantly lower in CCC than in heart tissue from healthy individuals, while blood mtDNA content was similar among asymptomatic Chagas disease, moderate and severe CCC patients. MtDNA haplogrouping study has indicated that African haplogroups were over represented in the Chagas subject groups in comparison with Brazilian healthy individuals. The European lineage is associated to protection against cardiomyopathy and the macro haplogroup H is associated with increased risk towards CCC. By mitochondria DNA sequencing, 84 mtDNA-encoded protein sequence pathogenic variants were associated with CCC. Among them, two variants were associated to left ventricular non-compaction and two to hypertrophic cardiomyopathy. The finding that mitochondrial protein-coding SNPs and mitochondrial haplogroups associate with risk of evolving to CCC is consistent with a key role of mitochondrial DNA in the development of Chronic Chagas disease Cardiomyopathy.

The following is the Collatz Conjecture: Suppose we begin with a positive number, multiply it by 3 and add 1 if it is odd, and divide it by 2 if it is even. Then continue doing this as long as you can. Will it matter where you start, whether you end up at the number 1? The Collatz conjecture has been studied for around 85 years. We transform the Collatz function from decimal to binary, then use the binary string's character to prove the Collatz conjecture. In addition, we use mathematics to give another interpretation to chaos, which is the ultimately periodic positive integer sequence.

In this paper, we derive Von Koch's inequality without using the Riemann Hypothesis. As well known, Von Koch's inequality is equivalent to the Riemann Hypothesis. Namely, we show that the Riemann Hypothesis is true. Furthermore, we show that the upper limit of its can be lowered.

New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. LetNTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing neutrosophic-number Zn(NTG) for a neutrosophic graphNTG : (V,E,σ,μ) is maximal neutrosophic cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) isn’t turned black afterfinitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Failed zero-forcing number and failed zero-forcing neutrosophic-number are about a set of vertices which are applied into the setting of neutrosophic graphs. The structure of set is studied and general results are obtained. Also, some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, bipartite-neutrosophic graphs, and t-partite-neutrosophic graphs are investigated in the terms of maximal set which forms both of failed zero-forcing number and failed zero-forcing neutrosophic-number. Neutrosophic number is reused in this way. It’s applied to use the type of neutrosophic number in the way that, three values of a vertex are used and they’ve same share to construct this number to compare with other vertices. Summation of three values of vertex makes one number and applying it to a comparison. This approach facilitates identifying vertices which form failed zero-forcing number and failed zero-forcing neutrosophic-number. In path-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set but with slightly differences, in cycle-neutrosophic graphs, the set of vertices such that every given two vertices in the set, have distance at least two, forms maximal set. Other classes have same approaches. In complete-neutrosophic graphs, a set of vertices excluding two vertices leads us to failed zero-forcing number and failed zero-forcing neutrosophic-number. In star-neutrosophic graphs, a set of vertices excluding only two vertices and containing center, makes maximal set. In complete-bipartite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set but with slightly differences, in complete-t-partite-neutrosophic graphs, a set of vertices excluding two vertices from same parts makes intended set. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. Using basic set not to extend this set to set of all vertices has key role to have these notions in the form of failed zero-forcing number and failed zero-forcing neutrosophic-number. The cardinality of a set has eligibility to form failed zero-forcing number but the neutrosophic cardinality of a set has eligibility to call failed zero-forcing neutrosophic-number. Some results get more frameworks and perspective about these definitions. The way in that, two vertices don’t have unique connection together, opens the way to do some approaches. A vertex could affect on other vertex but there’s no usage of edges. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this article.

In the paper it is demonstrated that a valid path to a contradiction in complex number theory exists. In the path use is made of Euler’s identity and simple trigonometry. Each step can be easily verified.

The aim of this paper is to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. As a crucial part, alternative approach for generalized quaternion matrix with elliptic number entries are developed.

While examination malpractice has been a recognized social problem among students, the control of the phenomenon remains a challenge. In this study, we formulate a mathematical model describing the population dynamics of examination malpractice among students. Initial insight into the dynamics of the model is gained by analyzing some important mathematical features of the model such as the basic malpractice number. The malpractice-free equilibrium and endemic equilibrium points of the model are shown to be locally asymptotically stable when the basic malpractice number is less than unity. This result implies that examination malpractice can be totally eradicated among students when the basic malpractice number is less than unity. To understand the impact of controlling this social problem, we extend the model to incorporate awareness campaign and disciplinary measure as control strategies in curtailing the act. Our analysis reveals that incorporating control strategies have some influence in reducing examination malpractice among students. Further analysis indicates that considering both control strategies simultaneously yields a better result in reducing examination malpractice and examination malpractice will grow faster when control strategies are not introduced.

Some cognitive functions, shared by humans and certain animals, were acquired early in the course of phylogeny and, in humans, are operational in their primitive form shortly after birth. This is the case for the quantification of discrete objects. The further phylogenetic evolution of the human brain allows such functions to be reconstructed in a much more sophisticated way during child development. Certain functional characteristics of the brain (plasticity, multiple cognitive processes involved in the same response, interactions and substitution relationships between those processes) provide degrees of freedom that open up the possibility of different pathways of reconstruction. The within- and between-individual variability of these developmental pathways offers an original window on the dynamics of development. Here, I will illustrate this theoretical approach to cognitive development—which can be called “reconstructivist” and “pluralistic”—using children's construction of number as an example.

The sustainability of cities often changes as rapid urban developments and population growth affect the carrying capacity. Understanding the dynamics of carrying capacity then becomes crucial for tourist-oriented cities. This study focused on Baguio City, the "Summer Capital of the Philippines," attracting large crowds on holidays and actively promoting various events on non-holidays, thereby having temporal context variations classified as regular days, days with events, and holidays. Using the enhanced urban carrying capacity load number (EUCCLN) model, load number (LN) changes for different temporal contexts are calculated based on spatial indicators grouped into air, traffic, economy, and waste. The city experiences the worst pressures on air quality during holidays with $99.23\%$ districts under very high to critical levels followed by regular and days with events. However, the total LN is balanced by favorable economic conditions with only $9.23\%$ at critical. EUCCLN effectively pinpoints areas experiencing critical states at any time, advocating targeted government monitoring. We demonstrate that Night Time Light, for places with no economic data available, can be used as a proxy to highlight areas requiring improved urban vibrancy. This work suggests that EUCCLN monitoring urban pressures can easily be expanded to nowcasting with real-time data.

Low-Level Virtual Machine (LLVM) compiler infrastructure is a useful tool for building Just-in-time (JIT) compilers, besides its reliable front-end represented by clang compiler and its elaborated middle-end containing different optimizations that improve the runtime performance. This paper addresses specifically the part of building a JIT compiler using LLVM with the scope of getting the hardware architecture details of the underlying machine such as the number of cores and the number of logical cores per processing unit and providing them to NUMA-BTLP static thread classification algorithm and to NUMA-BTDM static thread mapping algorithm. Afterwards, the hardware-aware algorithms are run by the JIT compiler within an optimization pass. JIT compiler in this paper is designed to run on a parallel C/C++ application (which creates threads using Pthreads), before the first time the application is executed on a machine. To do that, the JIT compiler takes the native code of the application, gets the corresponding LLVM IR (Intermediate Representation) for the native code and executes the hardware-aware thread classification and the thread mapping algorithms on the IR. The NUMA-Balanced Task and Loop Parallelism (NUMA-BTLP) and NUMA-Balanced Thread and Data Mapping (NUMA-BTDM) are expected to optimize the energy consumption up to 15%, on NUMA systems.

In the paper, the authors express the Fuss–Catalan numbers as several forms in terms of the Catalan–Qi function, find some analytic properties, including the monotonicity, logarithmic convexity, complete monotonicity, and minimality, of the Fuss–Catalan numbers, and derive a double inequality for bounding the Fuss–Catalan numbers.

In this paper, experimental results about the performance of a Takagi-Sugeno Fuzzy Controller (TSFC) for an EV3 Ballbot Robotic System (EV3BRS) are reported. The physical configuration for the EV3BRS has the form of an inverted pendulum mounted on a ball. The EV3BRS is an underactuated robotic system with four outputs and two control torques. The Takagi-Sugeno Fuzzy Model (TSFM) design comes from linearization of the nonlinear model around two operation points near from the upright position of the EV3BRS's body. The Parallel Distributed Compensation (PDC) approach is used to the design of the TSFC. The Linear Matrix Inequalities (LMIs) approach is used to get the feedback gains for every local linear controller guaranteeing global asymptotically stability, via a more relaxed stability condition, of the overall fuzzy control system. Measurement and control data from and to the EV3BRS are transferred via telecontrol and telemetry.

This study presents a vibration control using actively tunable vibration absorbers (ATVA) to suppress vibration of a thin plate. The ATVA’s is made of a sandwich hollow structure embedded with the electrorheological fluid (ERF). ERF is considered to be one of the most important smart fluids and it is suitable to be embedded in a smart structure due to its controllable viscosity property. ERF’s apparent viscosity can be controlled in response to the electric field and the change is reversible in 10 microseconds. Therefore, the physical properties of the ERF-embedded smart structure, such as the stiffness and damping coefficients, can be changed in response to the applied electric field. A mathematical model is difficult to be obtained to describe the exact characteristics of the ERF embedded ATVA because of the nonlinearity of ERF’s viscosity. Therefore, a fuzzy modeling and experimental validations of ERF-based ATVA from stationary random vibrations of thin plates are presented in this study. Because Type-2 fuzzy sets generalize Type-1 fuzzy sets so that more modelling uncertainties can be handled, a semi-active vibration controller is proposed based on Type-2 fuzzy sets. To investigate the different performances by using different types of fuzzy controllers, the experimental measurements employing type-1 fuzzy and interval type-2 fuzzy controllers are implemented by the Compact RIO embedded system. The fuzzy modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of ATVA from stationary random vibration of thin plates.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

Chromatographic separation is a critical technique in the manufacturing processes of both chemical products and biopharmaceuticals. Its principle relies on exploiting the differences in distribution between the stationary and mobile phases to achieve the separation of mixtures. The precision of substance concentration during separation directly impacts the quality and usability of the final product. Therefore, the development of an effective and precise separation control technique has long been a vital concern in the field of chromatographic separation control. Currently, the employment of Simulated Moving Bed (SMB) technology for chromatographic separation, which allows for continuous feed, has been recognized as a cutting-edge technique. SMB is a continuous process technology that enhances the efficiency of adsorbents within the bed. This sequential multi-column SMB technology not only increases production capacity but also reduces the consumption of solvents and water. It is acknowledged as one of the cleanest manufacturing technologies in the biopharmaceutical industry. However, multi-column SMB involves various variables such as flow rates in multiple sections and valve switching times, rendering its system control highly complex. Unlike traditional control objectives that aim to minimize control output errors, the control objective of SMB is to achieve a specific proportion of substance concentration. Consequently, designing and implementing traditional control theories for SMB is challenging, leading to SMB systems largely being controlled based on simple PLC controls. Moreover, these controls are often applicable only to single or a few-column SMB setups, limiting the effectiveness of high-capacity applications. To achieve effective control of SMB, this study employs an adjustable intelligent fuzzy controller with a structure like an approximate neural network (NN) for SMB control research. Simulation results demonstrate that the intelligent controller effectively achieves desirable control outcomes for the SMB system.

In this paper, we introduce an innovative approach to distinguish Gliosarcoma (GSM) from Glioblastoma (GBM). Our method combines causal fuzzy logic rules with the Big Bird architecture, a Transformer-based Deep Learning algorithm. Unlike prior research, which often relied on statistical models to reduce dataset dimensions before causal analysis, our approach harnesses the complete dataset in tandem with our causal fuzzy Big Bird architecture. Additionally, we benchmark our results not only against previous Gliosarcoma/Glioblastoma studies but also against GPT-2 for a comprehensive evaluation.

For a nonzero normed linear space X‎, ‎we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals‎. ‎Also separate continuity of the elements of each class are investigated‎. ‎The aim of this research is to introduce a source of examples and counterexamples in the field of fuzzy normed spaces‎.

This paper presents a novel approach for individual design perception modeling using the YUKI-trained Fuzzy Inference System. The study focuses on understanding how individuals perceive design based on personality traits, particularly openness to experience. The proposed YUKI algorithm optimizes the FCM clustering algorithm, enhancing its ability to handle uncertain and imprecise data. The YUKI-trained FIS generates several Sugeno-type FIS models to predict design perception, to minimize the Root Mean Squared Error between the model prediction and the actual design perception of participants. The results demonstrate that the YUKI-trained FIS offers more accurate predictions compared to the traditional FCM-trained FIS, and the RMSE values for individual design perceptions fall within a satisfactory range of 0.84 to 1.32. The YUKI-trained FIS proves effective in clustering individuals based on their level of openness, providing insights into how personality traits influence design perception.

Interferon-beta is one of the most widely prescribed disease-modifying therapies for multiple sclerosis patients. However, this treatment is only partially effective, and a significant proportion of patients do not respond to this drug. This paper proposes an alternative fuzzy logic system based on the opinion of a neurology expert to classify relapsing-remitting multiple sclerosis patients: high, medium, and low responder to interferon-beta. Also, a pipeline prediction model trained with biomarkers associated to interferon-beta response is proposed for predicting whether patients are potential candidates to be treated with this drug, in order to avoid ineffective therapies. The classification results shows that the fuzzy system presents a 100% efficiency compared with an unsupervised hierarchical clustering method (52%). So, the performance of the prediction model is evaluated, and a 0.8 testing accuracy is achieved. Hence, a pipeline model including data standardization, data compression, and a learning algorithm, can be a useful tool for getting reliable predictions about the response to interferon-beta.

At present, aeroponic control is mainly regulated according to the environmental factors of aeroponics, such as the temperature, humidity, light intensity, carbon dioxide concentration, pH, and electrical conductivity (EC) of the nutrient solution. There is a lack of knowledge available in the literature for an aeroponic control system for plant growth information as the primary feedback signal. Therefore, a fuzzy logic-controlled aeroponics system was developed for the growth of lettuce as a feedback signal. After designing, the effectiveness test of system was performed with experiment having three treatments T1 (180C), T2 (220C) and without control (CK). The results show an increasing trend in shoot length, root length, and shoot area over time in all treatments. In terms of shoot area, the maximum of 345 cm² was observed in the T1 treatment, while the CK treatment had a minimum of 241.8 cm². Statistical analysis indicated that the T1 and T2 treatments were not significantly different, but both were significantly different from the CK treatment. The study demonstrates the effectiveness of the fuzzy logic control system and an 18°C nutrient solution temperature, resulting in improved lettuce growth and reduced root-to-shoot ratio. The findings suggest the potential of using fuzzy logic control in aeroponics for optimized cultivation outcomes.

Accelerators play a critical role in fostering innovative ecosystems and nurturing startups. The evaluation and selection of startups, particularly technology-based startups, for acceleration programs are essential in accelerator economy and management. Assessment of startups requires consideration of numerical and qualitative criteria such as sales, prior startup experience, demand validation, and product maturity. Startups must be ranked based on the varying importance of criteria, which can be identified as a fuzzy multi-criteria decision-making (MCDM) problem. MCDM methods have proven effective in managing complex problems. However, the use of MCDM techniques in startup selection and evaluation of criteria interrelationships from the accelerator perspective is yet to be researched. This study proposes a hybrid DEMATEL-ANP-based fuzzy PROMETHEE II model to rank startups and examine the interrelationships between factors. The final preference values are fuzzy numbers, making a fuzzy ranking method necessary for decision-making. An extension of ranking fuzzy numbers using a spread area-based relative maximizing and minimizing set is suggested to improve the flexibility of existing ranking MCDM methods. Algorithms and formulas are derived and a comparison demonstrates the merits of the proposed method. Finally, a numerical experiment is designed to address the viability of the hybrid DEMATEL-ANP-based fuzzy PROMETHEE II model.

The estimation of the efficiency of road transport vehicles remains a significant problem for contemporary transport companies, as the technological process is influenced by numerous stochastic impacts, such as demand stochasticity, road conditions uncertainty, transport market fluctuations, etc. To consider the uncertainty related to the estimation of the vehicles’ fleet efficiency, we propose a fuzzy-logic approach, where the efficiency of a given vehicle is described by a membership function. The efficiency of the whole fleet and its rational structure in that case can be evaluated as a fuzzy set. To demonstrate the developed approach, we depict a case study of using cargo vehicles for deliveries of agricultural products in the Republic of Kazakhstan. The numeric results are presented for the selected models of vehicles that a transport company uses to service a set of clients located in Northern Kazakhstan.

We demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogoliubov transformations lead to pairs of spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

The purpose of this research article is to provide a comprehensive method that allows the evaluation of the public transportation in their different transport lines that offer in Ciudad Juárez, Chihuahua. This study presents a description of the public transport system as part of the literature review that describes an appropriate model based on the more outstanding publications about urban mobility and public transportation for passengers’ as well as success cases published which serves as a starting point to check the actual state of the public transportation system based on the Pythagorean Fuzzy CODAS to analyze and evaluate the alternatives through criteria that defines the general performance. The integration of these methods provides an adequate methodology for decision-making concerning urban planning and mobility to detect and improve the performance of criteria not considered within sustainable urban mobility plans.

Reinforcement learning (RL) is an extensively applied control method for the purpose of designing intelligent control systems to achieve high accuracy as well as better performance. In the present article, the PID controller is considered as the main control strategy for brushless DC (BLDC) motor speed control. For better performance, the fuzzy Q-learning (FQL) method as a reinforcement learning approach is proposed to adjust the PID coefficients. A comparison with the adaptive PID (APID) controller is also performed for the superiority of the proposed method, and the findings demonstrate the reduction of the error of the proposed method and elimination of the overshoot for controlling the motor speed. MATLAB/SIMULINK has been used for modeling, simulation, and control design of the BLDC motor.

model checking techniques are often used for the verification of software systems. Such techniques are accompanied with several advantages. However, state space explosion is one of the drawbacks to model checking. During recent years, several methods have been proposed based on evolutionary and meta-heuristic algorithms to solve this problem. In this paper, a hybrid approach is presented to cope with the SSE problem in model checking of systems modeled by GTS with an ample state space. Most of existence proposed methods that aim to verify systems are applied to detect deadlocks by graph transformations. The proposed approach is based on the fuzzy genetic algorithm and is designed to decline the safety property by verifying the reachability property and detecting deadlocks. In this solution, the state space of the system is searched by a fuzzy genetic algorithm to find the state in which the specified property is refuted/verified. To implement and evaluate the suggested approach, GROOVE is used as a powerful designing and model checking toolset in GTS. The experimental results indicate that the presented hybrid fuzzy method improves speed and performance by comparing other techniques

The most important issue in integrated next generation wireless systems (NGWS) by fourth generation networks which consists of various wireless architectures extending from cellular networks to satellite networks is to allow everyone around the world to connect seamlessly to applications anywhere at any time through the best network. Heterogeneous networks have created many challenges such as mobility management, handoff, resource management. For always best connectivity the selection of parameters plays an important role in the decision of vertical handoff, some of parameters are depend upon MT and some are depend upon the network conditions . In this paper we designed Intelligent Vertical Handoff based on Fuzzy Logic Decision model ( IVH-FL), IVH-FL model which has five parameters for vertical handoff decision : Received Signal Strength (RSS), Available bandwidth (B), Users Preference (UP), Mobile Speed (SM) and Power Consumption (PC), with the help of Fuzzy Logic tool box and concept of fuzzy linguistic variables. The results confirmed improvement performance , and reduced the number of unnecessary handover .

Recently, various relations and criteria have been presented to establish a proper relationship between control systems and control Global Positioning System (GPS)-intelligent buoy system. Given the importance of controlling the position of buoys and the construction of intelligent systems, in this paper, dynamic system modeling is applied to position marine buoys through the improved neural network with a backstepping technique. This study aims at developing a novel controller based on adaptive fuzzy neural network to optimally track the dynamically positioned vehicle on water with unavailable velocities and unidentified control parameters. In order to model the network with the proposed technique, uncertainties and the unwanted disturbances are studied in the neural network. The presented study aims at developing a neural controlling which applies the vectorial back-stepping technique to the surface ships, which have been dynamically positioned with undetermined disturbances and ambivalences. Moreover, the objective function is to minimize the output error for the neural network (NN) based on closed-loop system. The most important feature of the proposed model for the positioning buoys is its independence from comparative knowledge or information on the dynamics and the unwanted disturbances of ships. The numerical and obtained consequences demonstrate that the controller system can adjust the routes and the position of the buoys to the desired objective with relatively few position errors.

The paper presents design methodology for the production process of a new product from the point of view of the assembly operations technology criterion (Design for Assembly - DFA) in the conditions of high-volume production. Mentioned are DFA methods and techniques used in the implementation of a new product. Author presents a new method to assess design for manufacturability based on fuzzy variables based on fuzzy variables. An example was given to illustrate the proposed course of action

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

Satellites are subject to various severe vibration during different phases of flight. The concept of satellite smart adapter is proposed in this study to achieve active vibration control of launch vehicle on satellite. The satellite smart adapter has 18 active struts in which the middle section of each strut is made of piezoelectric stack actuator. Comprehensive conceptual design of the satellite smart adapter is presented to indicate the design parameters, requirements and philosophy applied which are based on the reliability and durability criterions to ensure successful functionality of the proposed system. The coupled electromechanical virtual work equation for the piezoelectric stack actuator in each active strut is drived by applying D'Alembert's principle. Modal analysis is performed to characterize the inherent properties of the smart adapter and extraction of a mathematical model of the system. Active vibration control analysis was conducted using fuzzy logic control with triangular membership functions and acceleration feedback. The control results conclude that the proposed satellite smart adapter configuration which benefits from piezoelectric stack actuator as elements of its 18 active struts has high strength and shows excellent robustness and effectiveness in vibration suppression of launch vehicle on satellite.

Objective: This paper aims to build an Effort Estimation Model for design, coding and testing Web Applications Based Fuzzy and Practical Models, which will help in optimizing the efforts in software development. Methods/Analysis: Soft computing approach is adopted and applied in the effort estimation and then compared with practical efforts in the development process with interpreting the historical data available for the existing functionalities. Findings: The effort estimation model presented in this paper focuses on the first level estimates published by Project Managers and the second level estimates presented by Project Leaders or Developers for any new requirement or enhancement for a web application built on 3-tier architecture using Microsoft technologies. The model considers the classification of each task as either Low or Medium or High complexity. These tasks pertain to the lowest level parts in bottom-up estimation. Efforts are estimated for designing, coding and unit testing of these tasks and the efforts are summed up to get the effort estimation for the higher level which is a feature to be implemented. Novelty/Improvement: The paper also discusses about the application of the effort estimation model by taking a new requirement as a case study. The first level estimates calculated using the effort estimation model has a variance of about 25% when compared with the actual effort. This variance is very much acceptable considering the fact that the first level estimates can be tolerable up to 35%. The proposed effort estimation tool would help the project managers to efficiently control the project, manage the resources effectively, and improve the software development process and also trade off analyses among schedule, performance, quality and functionality. Fuzzy logic is used to verify the claims made in efforts estimation. It is proposed a new relation between the number of data and efforts value membership for actual data. And converts it into crisp value in the range [0…1] which helps to classify the complexity of the task and subtask in the design, coding and testing phases.

In the manufacturing industry, cutting tool failure is a probable fault which causes damage to the cutting tools, workpiece quality and unscheduled downtime. It is very important to develop a reliable and inexpensive intelligent tool wear monitoring system for use in cutting processes. A successful monitoring system can effectively maintain machine tools, cutting tool and workpiece. In the present study, the tool condition monitoring system has been developed for Die steel (H13) milling process. Effective design of experiment and robust data acquisition system ensured the machining forces impact in the milling operation. Also, ANFIS based model has been developed based on cutting force-tool wear relationship in this research which has been implemented in the tool wear monitoring system. Prediction model shows that the developed system is accurate enough to perform an online tool wear monitoring system in the milling process.

Human non-conscious reasoning is one of the most successful procedures developed to solve everyday problems in an efficient way. This is why the field of artificial intelligence should analyze, formalize and emulate the multiple ways of non-conscious reasoning with the purpose of applying them in knowledge based systems, neurocomputers and similar devices for aiding people in the problem-solving process. In this paper, a framework for those non-conscious ways of reasoning is presented based on object-oriented representations, fuzzy sets and multivalued logic.

Natural events such as floods, fires, tsunamis, earthquakes and others have nowadays caused serious damage to human beings and nature. The precise detection of these natural events and especially the earthquake has nowadays become the focus of many computer and geoscientific researchers. Computer science and machine learning algorithms have revolutionized early detection and prediction of these events. Hence, a fuzzy method has been initially used in this article to enhance the authenticity of data based on application of effective variables and then combination of neural network algorithms of the MLP perceptron and radial network of RBF in form of a collective learning system in order to more accurately identify seismic events on a small scale. It was observed after simulating the proposed method that the proposed method has significantly improved based on actual error and root-mean-square error (RMSE) criteria compared to basic methods.

This paper presents a) the novel hybrid learning method to train the type-1 non-singleton interval type-3 (IT3) fuzzy logic systems (IT3 NSFLS-1) and b) the novel method named enhanced Wagner-Hagras (EWH) IT3 NSFLS-1 fuzzy systems which includes the level alpha 0 output to calculate the output y alpha using the average of the outputs y alpha k instead of their weighted average. The development of the proposed methodology uses the orthogonal least square (OLS) method to train the consequent parameters and the back propagation (BP) method to train the antecedent parameters. This proposal dynamically changes the parameters of only the level alpha 0 minimizing some criterion function as new information becomes available to each level alpha k. The antecedent sets are type-2 fuzzy sets, the consequent sets are fuzzy centroids, the inputs are type-1 non-singleton fuzzy numbers with uncertain standard deviations, and the secondary membership functions are modeled as two Gaussians with uncertain standard deviation and the same mean. Based on the firing set of the level alpha 0, the proposed methodology calculates each firing set of each level alpha k to dynamically construct and update the EWH IT3 NSFLS-1 (OLS-BP) system. The algorithm was tested in a hot strip mill facility to predict the transfer bar surface temperature showing its superior capability to obtain the industrial pyrometer’s knowledge uncertainty for tuning and its better performance when compared with IT2 SFLS, IT2 NSFLS-1, GT2 SFLS, GT2 NSFLS-1, IT3 SFLS, and IT3 NSFLS-1 trained with the BP-BP algorithm.

The airport ground handling service (AGHS) equipment vendor selection (AGHSEVS) problem is critical for ramp work safety management, because AGHS equipment malfunctions affect airport ramp work safety. Appropriate vendor selection can prevent aircraft damage and delays in airlines schedules, and ensure reliable and high-quality ground handling service. The AGHSEVS problem is a time-consuming and complex process that requires professional knowledge and experience to make judgments. Specifically, AGHSEVS is a multi-criteria decision-making (MCDM) problem. Previous research has seldom integrated MCDM methods with linear and goal programming to solve the AGHSEVS problem. The objective of this study was to develop a new system evaluation model for AGHSEVS by considering both qualitative and quantitative methods. We test the proposed approach on an AGHS company in Taiwan.

When discussing the Diophantine quintic equation $p(a^5 + b^5) = q(c^5 + d^5)$ where p is a prime and q is an integer, there is a clear gap between the mathematical literature and online forums. Because of the intrinsic complexity of parameterizing fifth-degree equations, this equation re- mains largely unexplored. In this work, we approach this quintic problem through algebraic methods with the goal of providing numerical solutions that illuminate its properties and behaviors.Our research uncovers in- triguing patterns and connections that shed light on the enigmatic nature of Diophantine quintic equations in this particular form.

The Collatz conjecture is a well-known number theory puzzle that states that every positive integer would eventually converge to the trivial cycle of 1, 2, 1, 2,... when repeatedly exposed to a particular transformation. In this transformation, even numbers are divided in half, odd numbers are tripled, and one is added. In this study, we present a new method for creating a directed graph and using it to display and analyze Collatz sequences. Our technique creates what we call a Collatz directed graph by joining an endless number of simple directed graphs, each of which corresponds to a natural number. We show by careful mathematical analysis that all positive integers are included in this Collatz directed graph. Moreover, we give an evidence that verifies the Collatz conjecture by showing that the sole cycle in this graph is the trivial cycle of 1, 2, 1, 2,... We also prove that there is no sequence that diverges to infinity in this graph. Our results provide insights into the fundamental structure of Collatz sequences and further our knowledge of the Collatz conjecture .

In this study, I examined the Beals conjecture on the basis of formulas that produce composite numbers, and I developed some other conjectures that, if answered, would be an answer to the Beals conjecture. Apart from this, I have examined the Beals conjecture from another perspective and posed The Germany Problem.

In this paper, we examine a modified Friedmann model designed to explain cosmic structures and late-time accelerated expansion of the universe, grounded in the spatial distribution of luminous matter. Through comprehensive simulations of our universe, we observe a notable surge in the formation rate of galaxies at redshift z≈1, characterized by a peak expansion rate in cosmic structures formed at z ≈0.9, reaching its zenith at z ≈2. Subsequently, a transition occurs before the onset of dark matter-induced accelerated expansion. The acceleration of the universe stands as an entrenched and virtually model-independent theoretical tenet, resilient to the ongoing debate surrounding the enigma of dark energy. A distinctive redshift transition zone marks the shift from cosmic deceleration to accelerated expansion. The transition is proportional to matter density and contingent upon the geometry of the universe. The influence of the cosmological constant on the evolution of cosmic structures in the CDM paradigm appears insufficient in curtailing the efficiency of late-time structure formation compared to the observed values in the modified model

The Harmonic Graphs Conjecture states that there exists an asymptotic relation involving the Harmonic Index and the natural logarithm as the order of the graph increases. This conjecture, grounded in the novel context of Prime Graphs, draws upon the Prime Number Theorem and the sum of divisors function to unveil a compelling asymptotic connection. By carefully expanding the definitions of the harmonic index and the sum of divisors function, and leveraging the prime number theorem's approximations, we establish a formula that captures this intricate relationship. This work is an effort to contribute to the advancement of graph theory, introducing a fresh lens through which graph connectivity can be explored. The synthesis of prime numbers and graph properties not only deepens our understanding of structural complexity but also paves the way for innovative research directions.

The efficient generation of high-quality random numbers is essential in the operation of cryptographic modules. The quality of a random number generator is evaluated by the min-entropy of its entropy source. Typical method used to achieve high min-entropy of the output sequence is an entropy accumulation based on a hash function. This is grounded in the famous Leftover Hash Lemma which guarantees a lower bound on the min-entropy of the output sequence. However, the hash function based entropy accumulation has slow speed in general. For a practical perspective we need a new efficient entropy accumulation with the theoretical background for the min-entropy of the output sequence. In this work, we obtain the theoretical bound for the min-entropy of the output random sequence through the very efficient entropy accumulation using only bitwise XOR operations, where the input sequences from the entropy source are independent. Moreover we examine our theoretical results by applying to the quantum random number generator that uses dark noise arising from image sensor pixels as its entropy source.

Counting in terms of cycles allows modeling many processes of Nature. We make use of a slight numerical incongruence within the numbering system to find a translational mechanism which connects sequential ↔ commutative properties of assemblies. The algorithms allow picturing the logical syntax Nature uses when reading the DNA. Ordering a collection on two different properties of its members will impose two differing sequences on the members. The coordinates of a point on a plane of which the axes are the two sorting orders sidestep the logical contradiction arising from the different linear assignments. During a reorder, elements aggregate into cycles. Using an etalon collection of simple logical symbols (which are pairs of natural numbers), which we reorder, we see typical movement patterns along the path of the string of elements that are members of the same cycle. We split the {value, position} descriptions of a natural number and observe the places the unit occupies at specific instances of time among its peers, while being a member of a cycle, under different orders prevailing. Which places elements occupy among their peers, under specific order conditions, is determined by numeric properties of the natural numbers that make up the element. The model presented is therefore tautologic, and can be compared to a hybrid of sudokus with the ultimate form of Rubik‘s cube. It is necessary for the reader to do some self-education on the matter of cycles as a prerequisite to understanding the working principle of the model. The contraption being a new development, it can’t have references in literature.One cannot lose a bet on the idea that sorting and ordering a collection of elementary logical elements will turn up typical patterns and that these archetypes of patterns will be of interest to Theoretical Physics, Chemistry, Biology, Information Theory, and some other fields, too.

Nowadays the practice of developing algorithms to maintain the confidentiality of data shows that there is a lack of some features, such as velocity, predictability, etc. Generating pseudorandom numbers is one such problem that lies in the basement of many algorithms, even in hardware microprograms. An unreliable generator can cause cyberattacks on it, despite the security in the upper layers. At the same time, the algorithm should be fast enough to provide uninterrupted circuit work for the entire system. The paper presents a new algorithm generating pseudorandom numbers on cellular automata, which is not only fast and easy-repeating, but unpredictable enough and can be used in cryptographic systems. Using the NIST statistical test suite for random and pseudorandom number generators (PRNG), it is shown that the presented algorithm is more than three times superior to the state-of-the-art methods and algorithms in terms of ? − ?????. A high level of the presented algorithm’s parallelization allows for implementation it effectively on calculators with parallel structure. CPU-based architecture, FPGA-based architecture, CUDA- based architecture of PRNG and different PRNG implementations are presented to confirm high performance of the proposed solution.

Pollination is the process by which pollen grains are exchanged in plant flowers to allow for fertilisation and production to take place. However, challenges occur when crops are grown under protected structures where there are minimal activities of natural pollination agents such as wind and animals which are responsible for transferring pollen grains from the anther to the stigma. Therefore, the study objective was to determine the effect on hand pollination on the yield of African horned cucumber grown under greenhouse and shade net environment. A factorial experiment with two factors (hand pollinated and non-hand pollinated/control) was conducted under two different growing environments (greenhouse and shade net). African horned cucumber plants were hand self-pollinated in the morning. Pollen were manually transferred with a hand using the new earbud from the male to the female flowers on the same plant (selfing). Results showed that hand pollinated African horned cucumber plants increased total biomass from 0.93 to 2.23 kg under greenhouse environment. Hand pollinated plants increased harvest index from 0.07 to 0.35 under shade net environment. It can thus, be deduced that hand pollination increases African horned cucumber yield in the greenhouse and shade net environments.

In this article, some kinds of triple belongs to metric dimensions are defined. Some classes of graphs in the matter of these kinds, are studied and the relation amid these kinds are considered. The kind of having equivalency amid these notions and some classes of graphs, is obtained. The kind of locating some vertices by some vertices when the number of locating vertices is increased, has the key role to analyze the classes of graphs, general graphs, and graph's parameters.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

In this article, some notions about set, weight of set, number, number's position, special vertex are introduced. Some classes of graph under these new notions have been opted as if the study on the special attributes of these new notion when they've acted amid each other is considered. Internal and external relations amid these new notions have been obtained as if some classes of graphs in the matter of these notions are been pointed out.

Background: Our knowledge of prostate cancer (PCa) genomics mainly reflects European (EUR) and Asian (ASN) populations. Our understanding of the influence of Middle Eastern (ME) and African (AFR) ancestry on the mutational profiles of prostate cancer is limited. Design, setting and participants: To characterize genomic differences between ME, EUR, ASN and AFR ancestry, fluorescent in situ hybridization (FISH) studies for NKX3-1 deletions and MYC amplification was carried out on 42 tumors arising in individuals of ME ancestry. These were supplemented by analysis of copy number profiles of 401 tumors of all ancestries. Outcome measurement and statistical analysis: FISH results of NKX3-1 and MYC were assessed in the ME cohort and compared to other ancestries. Gene level copy number aberrations (CNAs) for each sample were statistically compared between ancestry groups. Results and Limitation: NKX3-1 deletions by FISH were observed in 17/42 (17.5%) prostate tumors arising in men of ME ancestry, while MYC amplifications were only observed in 1/42 (0.23%). Using CNAs called from arrays, the incidence of NKX3-1 deletions was significantly lower in ME vs. other ancestries (20% vs. 52%; p = 2.3 x 10-3). No differences in MYC amplifications was noted between the two cohorts using array-based CNAs. Across the genome, tumors arising in men of ME ancestry had fewer CNAs than those of other ancestries (p = 0.014). Additionally, the somatic amplification of 21 specific genes was more frequent in tumors arising in men of ME vs. EUR ancestry (Proportions test; Q < 0.05). Those included amplifications in the glutathione S-transferase family on chromosome 1 (GSTM1, GSTM2, GSTM5) and the IQ Motif Containing family on chromosome 3 (IQCF1, IQCF2, IQCF13, IQCF4, IQCF5, IQCF6). Conclusion: Significant differences in genetic background exists between different ancestries. The lower number of somatic CNAs observed in prostate cancer arising in men of ME ancestry may explain the relatively good prognosis in this population. Larger studies are warranted.

The outburst of the CoVid-19 pandemic has raised several questions leading to a complex system in terms of modeling. Indeed, the modeling of the epidemic, at the level of a country, needs considering each of the different sources of contamination as well as the public health authorities' strategy, in a specific way. With this in mind, in the present paper, we develop a mathematical model of the CoVid-19 epidemic in Senegal. In the model, the population is subdivided into five compartments: susceptible, infected but asymptomatic, symptomatic, quarantined, and recovered immune people. In addition, due to its important impact on the propagation of the disease, we add one more variable: the number of infected objects. %\vspace{1mm} Therefore, the model corresponds to a system of six non-linear ordinary differential equations we submit to an analytical study to prove the relevancy of the model, simulate the evolution of the epidemic, and retrieve epidemiological parameters, namely the infection rate and the basic reproduction number, ${\cal R}_0$. Based on the senegalese territory CoVid-19 data, we simulate various scenarios as for the evolution of the epidemic in the country, in order to predict the peak and its magnitude with regard to the application of barrier measures. We also explore the option of collective immunity with special protection for vulnerable people. In doing so, non-available parameters are identified using some mathematical identification technics.

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. We prove the Riemann hypothesis using the Complexity Theory. Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. The Goldbach's conjecture is one of the most important and unsolved problems in number theory. Nowadays, it is one of the open problems of Hilbert and Landau. We show the Goldbach's conjecture is true using the Complexity Theory as well. An important complexity class is 1NSPACE(S(n)) for some S(n). These mathematical proofs are based on if some unary language belongs to 1NSPACE(S(log n)), then the binary version of that language belongs to 1NSPACE(S(n)) and vice versa.

A framework of similarity laws, termed oriented-density-length-velocity (ODLV) framework, is suggested for the geometric distorted structures subjected to impact loading. The distinct feature of this framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for physical quantity are explicitly expressed by the characteristic lengths of three spatial directions, which overcome the inherent defects that traditional scalar dimensional analysis could not express the effects of structural geometric characteristics and spatial directions for similarity. The non-scalabilities of geometrical distortion as well as other distortions such as different materials and gravity could be compensated by the reasonable correction for the impact velocity, the geometrical thickness and the density, when the proposed dimensionless number of equivalent stress is used between scaled model and prototype. Three analytical models of beam, plate and shell subjected to impact mass or impulsive velocity are verified by equation analysis. And a numerical model of circular plate subjected to dynamic pressure pulse is verified in more detail, form the view of point of space deformation, deformation history and the components of displacement, strain and stress. The results show that the proposed dimensionless numbers have attractively perfect ability to express the dimensionless response equations of displacement, angle, time, strain and strain rate. When the proposed dimensionless numbers are used to regularize impact models, the structural responses of the geometrically distorted scaled models can behave the completely identical behaviors with those of the prototype on space and time —not only for the direction-independent equivalent stress, strain and strain rate but also for the direction-dependent displacement, stress and strain components.

For a positive integer k, a radio k-coloring of a simple connected graph G = (V (G), E(G)) is a mapping | f(u) - f(v)| ≥ k +1-d (u , v ) such that f :V (G)→{0,1, 2,...} for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f, rck(f), is the maximum integer it assigns to some vertex of G. The radio k-chromatic number, rck(G) of G is min{rck(f)}, where the minimum is taken over all radio k-colorings f of G. If k is the diameter of G, then rck(G) is known as the radio number of G. In this work, we propose four algorithms (two serial algorithms and their parallel versions) which related to the radio k-coloring problem. One of them is an approximate algorithm that determines an upper bound of the radio number of a given graph. The other is an exact algorithm which finds the radio number of a graph G. The approximate algorithm is a polynomial time algorithm while the exact algorithm is an exponential time algorithm. The parallel algorithms are parallelized using the Message Passing Interface (MPI) standard. The experimental results prove the ability of the proposed algorithms to achieve a speedup 7 for 8 processors.

In standard construction of hyperrational numbers using ultra-power we assume that the ultralter is selective. It makes possible toassign real value to any nite hyperrational number. So, we can consider hyperrational numbers with selective ultralter as extension of traditional real numbers. Also proved the existence of strictly monotonic or stationary representing sequence for any hyperrational number.

The airline sector is critical in today's globalized society, supporting the efficient movement of people and products worldwide. Airlines are continuously looking for methods to enhance their operational performance to remain competitive in the face of increased competition. This study focuses on the application of Multi-Criteria Decision Making (MCDM) techniques to improve low-cost carrier (LCC) also known or low-cost (budget) airlines' ground operational performance. MCDM techniques have gained considerable attention in recent years to address complex decision problems with multiple conflicting goals. This research aims to bridge this gap by proposing a comprehensive framework that combines MCDM techniques to enhance airline operational strategies to increase performance. The study utilizes qualitative and quantitative data, drawing on previously published materials on MCDM techniques in the aviation sector. It utilizes fuzzy Analytic Hierarchy Process (AHP) and fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methodologies. A case study is conducted to evaluate the ground operational performance of three airline companies based in Türkiye, considering five main criteria and 18 sub-criteria. The findings of this research will contribute to a comprehensive understanding of operational performance in the airline sector. It also highlights the implications and limitations of the research and suggests future research directions.

Air pollution is a situation that negatively affects the health of humans and all living things in nature and causes financial damage to the environment. In the case of air pollution, harmful and foreign substances in the air reach an amount and density above normal values. Air pollution also causes climate change, which affects global warming. Particulate matter is a harmful substance that harms the health of humans and other living things, causes air pollution, increases radiation, and negatively affects cloud formation. Particulate matter is extremely small solid particles and liquid droplets suspended in the air. PM10, which is less than 10 microns in diameter, is defined as small particles that can remain in the air for a long time and settle in the respiratory tract, damaging the lungs. Many criteria affect PM10 density and changes in density. The main criteria are vehicle traffic and fuel consumption, industrialization, coal, fuel oil and wood-burning heaters, greenhouse gas impact, and unregulated urbanization. It is important to identify the underlying causes of air pollution caused by PM10. In this context, these criteria need to be evaluated to minimize the negative effects of PM10. In the study, monthly average PM10 data between 2019 and 2023 obtained from the Air Monitoring Station in Kocaeli, Türkiye are used. After determining the criteria affecting PM10, the criteria are prioritized with the Intuitionistic Fuzzy AHP (IF-AHP) method by taking expert decision-maker opinions. The proposed decision-making model aims to guide obtaining the important causes of PM10 emission in terms of danger and focusing on these causes. Additionally, PM10 data is analyzed in the context of Covid-19 and a statistical analysis is made. One-way ANOVA is used to evaluate whether there is a significant difference in the average monthly data over the years. Games-Howell test, one of the post-hoc tests, is used for differences between groups (years). The study is important in that it provides a focus on the criteria affecting PM10 with an intuitive fuzzy perspective, along with statistical analysis.

This paper provides a comprehensive analysis of food security in Sudan by adopting a unique approach of Hesitant Fuzzy Entropy (HFE) analysis to discern the key determinants influencing food security levels and aligning the findings with the Integrated Food Security Phase Classification (IPC) framework. The research utilized a dataset comprising 32 crucial variables related to food security assessment. Employing entropy values, weight coefficients, heatmaps, and scatterplots, the analysis aimed to unravel the intricate distribution of food security levels among Sudanese individuals in our study area. The study reveals that approximately 26% of the Sudanese population in our study region is poised to experience food security, with an additional 24% categorized as marginally food secure. Moreover, an estimated 35% are expected to confront moderate food insecurity, while 15% are projected to face severe food insecurity between January and June 2024. Anticipations for the period from January 2024 to June 2024 project more than 15 million individuals to encounter IPC Phase 3 and fall under moderately or severely food insecure levels. These findings emphasize the urgent need for both short-term humanitarian aid and long-term strategies to address Sudan's deepening food insecurity crisis.

The effectiveness of Fuzzy Inference Systems (FISs) in manipulating uncertainty and nonlinearity makes them a subject of significant interest for decision-making in embedded systems. Accordingly, optimizing FIS hardware improves its performance, efficiency, and capabilities, leading to a better user experience, increased productivity, and cost savings. To be compatible with the limited power budget in most embedded systems, this paper presents a framework to realize ultra-low power FIS hardware. It supports optimizations for both conventional arithmetic as well as MSDF-computing to be highly consistent with MSDF-based sensors. In MSDF-computing FIS all the processes of fuzzification, inference, and defuzzification are done on serially coming data bits. To demonstrate the efficiency of the proposed framework, we utilized Matlab, Chisel3, and Vivado to implement it from high-level descriptions of FIS to hardware synthesis. We also developed a Scala library in Chisel3 to establish a connection between these tools, bridging the gap, and facilitating design space exploration at the arithmetic level. Furthermore, we realized an FIS for the navigation of autonomous mobile robots in unknown environments. Synthesis results show the superiority of the output of our suggested design framework in terms of resource usage as well as power and energy consumption compared to the Matlab HDL code generator output.

Landslides around the main roads in the mountains not only cause fatal events but also cause ecosystem damage, including land degradation. This study aims to map the susceptibility of the landslides around the Saqqez-Marivan main rod of Kurdistan province, Iran, using ensemble Fuzzy logic with Analytic Network Process (Fuzzy Logic-ANP; FLANP), and with TOPSIS (Fuzzy Logic-TOPSIS; FLTOPSIS). A total of 100 landslides were first recognized by field surveys and then they were randomly divided into a 70% dataset (70 locations) and a 30% dataset (30 locations), respectively, for training and validating the methods. Eleven landslide conditioning factors, including slope, aspect, elevation, lithology, land use, distance to fault, distance to a river, distance to road, soil type, curvature, and precipitation were used. The performance of the methods was checked by the areas under the receiver operating curve (AUCROC). Results concluded that the prediction accuracy based on validating datasets were, respectively, 0.882 and 0.918 for FLANP and FLTOPSIS methods. Our findings demonstrated that although both models were known as promising techniques, the FLTOPSIS method had a better capacity for predicting the susceptibility of landslides in the studied area. Therefore, the susceptibility map developed by the FLTOPSIS method can be used for the proper management of areas with high landslide potential and also for managers and planners during the implementation of land allocation and development projects, especially in mountainous areas.

During the smelting process of AOD furnace, the unbalanced reaction of material will lead to the occurrence of splashing. It will not only damage the smelting equipment, but also seriously injure the personnel. In this study, first, the information of liquid level, audio information, and vibration information are detected by multiple sensors respectively. Then, the fused information is used to forecast the splashing. Finally, the multitasking fuzzy controller is used to suppress splashing. The results show that the method of forecasting and suppressing splashing can accurately forecast and achieve rapid suppression. Thus, the efficiency of smelting can be improved.

In this article, the evolution in space and in time of the coronavirus pandemic is studied by utilizing a neural network with a self-organizing nature for the spatial analysis of data, and a fuzzy fractal method for capturing the temporal trends of the time series of the countries. Self-organizing neural networks possess the capability for clustering countries in the space domain based on their similar characteristics with respect to their coronavirus cases. In this form enabling finding the countries that are having similar behavior and thus can benefit from utilizing the same methods in fighting the virus propagation. To validate the approach, publicly available datasets of coronavirus cases worldwide have been used. In addition, a fuzzy fractal approach is utilized for the temporal analysis of time series of the countries. Then, a hybrid combination of both the self-organizing maps and the fuzzy fractal approach is proposed for efficient COVID-19 forecasting of the countries. Relevant conclusions have emerged from this study, that may be of great help in putting forward the best possible strategies in fighting the virus pandemic. A lot of the existing works concerned with the Coronavirus have look at the problem mostly from the temporal viewpoint that is of course relevant, but we strongly believe that the combination of both aspects of the problem is relevant to improve the forecasting ability. The most relevant contribution of this article is the proposal of combining neural networks with a self-organizing nature for clustering countries with high similarity and the fuzzy fractal approach for being able to forecast the times series and help in planning control actions for the Coronavirus pandemic.

The success of a software product depends on several factors. Given that different organizations and institutions use software products, the need to have a quality and desirable software according to the goals and needs of the organization makes measuring the quality of software products an important issue for most organizations and institutions. To be sure of having the right software. It is necessary to use a standard quality model to examine the features and sub-features for a detailed and principled study in the quality discussion. In this study, the quality of Word software was measured. Considering the importance of software quality and to have a good and usable software in terms of quality and measuring the quality of software during the study, experts and skilled in this field were used and the impact of each factor and quality characteristics. It was applied at different levels according to their opinion to make the result of measuring the quality of Word software more accurate and closer to reality. In this research, the quality of the software product is measured based on the fuzzy inference system in ISO standard. According to the results obtained in this study, it is understood that quality is a continuous and hierarchical concept and the quality of each part of the software at any stage of production can lead to high quality products.

In this paper we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions.

Metaheuristic algorithms are widely used as optimization methods, due to their global exploration and exploitation characteristics, which obtain better results than a simple heuristic. The Stochastic Fractal Search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic-stochastic diffusion property, an improved Dynamic Stochastic Fractal Search (DSFS) optimization algorithm is presented. The DSFS algorithm was tested with benchmark functions, such as the multimodal, hybrid and composite functions, to evaluate the performance of the algorithm with dynamic parameter adaptation with type-1 and type-2 fuzzy inference models. The main contribution of the article is the utilization of fuzzy logic in the adaptation of the diffusion parameter in a dynamic fashion. This parameter is in charge of creating new fractal particles, and the diversity and iteration are the input information used in the fuzzy system to control the values of diffusion.

A Mamdani-type fuzzy-logic model has been developed to link Mediterranean seagrass abundance to the prevailing environmental conditions. Big Databases, as UNEP-WCMC (seagrass abundance), CMEMS and EMODnet (oceanographic/environmental) and human-impact parameters were utilized for this expert system. Model structure and input parameters were tested according to their capacity to accurately predict seagrass families at specific locations. The optimum FIS comprised of four input variables: water depth, sea surface temperature and nitrates and bottom chlorophyll-a concentration, exhibiting fair accuracy (76%). Results illustrated that Posidoniaceae prefers cool (16-18oC) and low chlorophyll-a presence (&lt; 0.2 mg/m3); Zosteraceae favors cool (16-18oC) and mesotrophic waters (Chl-a &gt; 0.2 mg/m3), but also slightly warmer (18-19.5 oC) with lower Chl-a levels (&lt; 0.2 mg/m3); Cymodoceaceae lives from warm, oligotrophic (19.5-21.0oC and Chl-a &lt; 0.3 mg/m3) to moderately warm mesotrophic sites (18-21.3oC and 0.3 – 0.4 mg/m3 Chl-a). Finally, Hydrocharitaceae thrives in warm Mediterranaean waters (21-23oC) of low chlorophyll-a content (&lt; 0.25 mg/m3). Climate change scenarios showed that Posidoniaceae and Zosteraceae tolerate bathymetric changes, Posidoniaceae and Zosteraceae are mostly affected by sea temperature rise, while Hydrocharitaceae exhibits tolerance in higher sea temperature rise. This FIS could be used by national and regional policy-makers and public authorities.

unlike the volume, the expression for the surface area of a regular conoid has not yet been obtained by means of direct integration or a differential geometry procedure. As this non-developable form is relatively used in engineering, the difficulty to determine its surface, represents a serious shortcoming for several problems which arise in radiative transfer, lighting and construction, to cite just a few. In order to solve the problem, I conceived the surface as a set of linearly dwindling ellipses which remain parallel to a circular directrix, a typical problem appears when searching the length of such ellipses. I employed a new procedure which, in principle, consists in dividing the surface into infinitesimal elliptic strips to which we have successively applied Ramanujan’s second approximation for the longitude of the ellipse. In this manner, we can obtain the perimeter of any transversal curve pertaining to the said form as a function of the radius of the directrix and the position of the ellipse’s center on the X-axis. Integrating the so-found perimeters of the differential strips for the whole span of the conoid, an unexpected solution emerges through the newly found number psi (ψ) which seems like a refined approximation to the third decimal of Pi but derived from a definite integral equation. As the strips are in truth slanted in the symmetry axis, their width is not uniform and we need to perform some adjustments in order to complete the problem with sufficient precision, but this is discussed separately in the annexes. Relevant implications for mathematical symmetry applied to multifarious architectural and engineering forms can be derived from this finding

It is proved that there exist two odd prime numbers, p_i and p_j , such that p_i + p_j = 2r + 2(r ⩾ 2), where p_n denote the n-th odd prime number, 1 ⩽ i, j ⩽ n. By the theory of generating functions, we prove that there exist two positive integers, h_i and h_j , such that h_i + h_j = r(r ⩾ 2), where h_n = (p_n − 1)/2，(p_n ⩾ 3).Then we complete the proof.

We introduce a model of a passive optical cavity based on the two-dimensional Lugiato-Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic-quintic nonlinearity. Up to S = 5, stable vortex-ring states (vortex pixels) are produced by a variational approximation and in a numerical form. Surprisingly, vast stability areas of the vortex states are found, for both the self-focusing and defocusing signs of the nonlinearity, in the plane of the pump-strength and loss parameters. When the vortex-rings are unstable, they are destroyed by azimuthal perturbations which break the axial symmetry. The results suggest new possibilities for mode manipulations in nonlinear optical media.