It is known that the class of p-normed spaces (0 < p ≤ 1) is an important generalization of usual normed spaces with rich topological and geometrical structure, but the most of tools and general principles in nature with nonlinearity have not been developed yet, thus the main goal of this paper is to develop tools for nonlinear analysis under the framework of p-vector spaces. In particular, we first develop the general fixed point theorems which provide solutions to answer Schauder conjecture since 1930’s in the affirmative for p-vector spaces when p = 1 (which is just general topological vector spaces); then the one best approximation result for upper semi-continuous mappings is given, which is used as a powerful tool to establish fixed points for non-self set-valued mappings with either inward or outward set conditions; and finally we establish comprehensive existence results of solutions for Birkhoff-Kellogg Problems, and the general principle of nonlinear alternative by including Leray-Schauder alternative and related results. The results given in this paper not only include the corresponding results in the existing literature as special cases, but also expected to be useful tools for the study of nonlinear problems arising from theory to practice.

As matrix representations of magic labelings of related hypergraphs, magic squares and their various variants have been applied to many domains. Among various subclasses, trimagic squares have been investigated for over a hundred years. The existence problem for trimagic squares with singly even orders and orders 16n has been solved completely. However, very little is known for the existence of trimagic squares with other even orders except for the only three examples and three families. We construct normal trimagic squares by using product constructions, row-square magic rectangles, and trimagic pairs of orthogonal diagonal Latin squares. We give a new product construction: For positive integers p, q, and r having the same parity other than 1, 2, 3, 6, if normal p × q and r × q row-square magic rectangles exist, then a normal trimagic square with order pqr exists. As its application, we construct normal trimagic squares of orders 8q^3 and 8pqr for all odd integers q not less than 7 and p,r ∈ {7, 11, 13, 17, 19, 23, 29, 31, 37}. Our construction can easily be extended to construct multimagic squares.

Iron is an essential nutrient and necessary for biological functions from DNA replication and repair to transcriptional regulation, mitochondrial respiration, electron transfer, oxygen transport, photosynthesis, enzymatic catalysis, and nitrogen fixation. However, due to iron’s propensity to generate toxic radicals which can cause damage to DNA, proteins, and lipids, multiple processes regulate uptake and distribution of iron in living systems. Understanding how intracellular iron metabolism is optimized and how iron is utilized to regulate other intracellular processes is important to our overall understanding of a multitude of biological processes. One of the tools that the cell utilizes to regulate a multitude of functions is ligation of the iron-sulfur (Fe-S) cluster cofactor. Fe-S clusters comprised of iron and inorganic sulfur are ancient components of living matter on earth that are integral for physiological function in all domains of life. Here we will explore the ways in which the cell utilizes Fe-S clusters to sense the intracellular environment and respond to maintain equilibrium.

Astronauts in space are subject to a continuous bombardment of ionizing radiation. The Earth's magnetic field and the ISS shield some biologically damaging particles traveling through. Still, travel beyond low-Earth orbit and extravehicular activities are exceedingly more dangerous and there is a concern for the acute and late-occurring adverse health effects befalling astronauts. So, it is vital to consider the current tools and models used to describe and study the organic consequences of ionizing radiation exposure. It is equally important to see where these models may improve. This article reviews the historical development and current state of knowledge of radiation effects impacting astronauts in orbit. We explain the space radiation environment, cellular microenvironment, and how these may be incorporated in radiobiological models to aid in our understanding of the influence space travel may have on astronaut health. The topics discussed in this paper include a review of DNA damage and repair mechanisms and the numerical models that aim to explain the biological effects resulting from ionizing radiation damage. Historically, radiobiological models focused on how radiation damages nuclear DNA, built upon the hypotheses of Crowther and Lea in the 1940s and 1960s, and neglected other sub-cellular targets outside of nuclear DNA.

This paper addresses a mode-dependent state-feedback H∞ control for descriptor hybrid systems, considering both the absence and presence of actuator saturation. Firstly, the necessary and sufficient conditions for the stochastic admissibility criterion with H∞ performance ? of the closed-loop system is proposed. Given the proposed non-convex condition, the author reformulates it into linear matrix inequalities (LMIs). Then, to extend the result to the systems with actuator saturation, the actuator saturated control input is expressed as a linear combination of given state-feedback control input and a virtual control input that remains under the saturation level. To verify this expression, the set invariant condition is also suggested by using the singular mode-dependent Lyapunov function candidate. Therefore, the LMI conditions for the existence of the mode-dependent state-feedback H∞ control and the ellipsoidal shape of invariant set are successfully derived. Two numerical examples demonstrate the effectiveness of the proposed approach in optimizing H∞ performance $\gamma$ and identifying the largest invariant set.

Multi-Object Tracking (MOT) is a key technology for Unmanned Aerial Vehicles (UAVs). Traditional tracking-by-detection methods firstly employ an object detector to retrieve targets in each image and then track them based on a matching algorithm. Recently, the popular multi-task learning methods has been dominating this area since they can detect targets and extract Re-Identification (Re-ID) features in a computationally efficient way. However, the detection task and the tracking task have conflicting requirements on image features, leading to the poor performance of the joint learning model compared to separate detection and tracking methods. The problem is more severe when it comes to UAV images due to the presence of irregular motion of large number of small targets. In this paper, we propose a balanced Joint Detection and Re-ID learning (JDR) network to address the MOT problem in UAV vision. To better handle the non-uniform motion of objects in UAV videos, the Set-Member Filter is applied which describes object state as a bounded set. An appearance matching cascade is then proposed based on target state set. Furthermore, a Motion-Mutation module is designed to address the challenges posed by the abrupt motion of UAV. Extensive experiments on the VisDrone-MOT2019 dataset demonstrate that our proposed model, termed as SMFMOT, outperforms state-of-the-arts by a large margin and achieves superior performance on the MOT tasks in UAV videos.

Soil quality is related to food security and human survival and development. In recent years, due to the acceleration of urbanization and the increase of abandoned land, land degradation occurs, poor topsoil quality. In this study, the minimum data set (MDS) was constructed through principal component analysis (PCA) to determine the indicator data set for evaluating topsoil quality in Tieling County, China. In addition, the soil quality index (SQI) was calculated to analyze the spatial distribution characteristics and influencing reasons of topsoil quality in Tieling County. The re-sults showed that MDS included total potassium (TK), Clay, zinc (Zn), soil organic matter (SOM), soil water content (SWC), cation exchange capacity (CEC), pH, and copper (Cu). The MDS indicators can well replace all indicators to evaluate the topsoil quality in the study area. The overall soil quality of Tieling County showed a trend of low in the east and high in the west, and gradually increased from the hilly area to the plain area. The evaluation results are consistent with field research, which can provide reference for other topsoil quality evaluation, and it also provide a basis for the formulation of soil quality improvement measures.

In this paper we prove that if the product $X^{n}$ of a space $X$ has some tightness-type properties, then the space of permutation degree ${\sf SP^{n}}X$ also has these properties. It is proved that the set tightness (resp. $T$-tightness) of the space of permutation degree ${\sf SP^{n}}X$ is equal to the set tightness (resp. $T$-tightness) of the product $X^{n}$.

One of matrix equalities composed of multiple products of matrices and their generalized inverses is given by $A_1B_1^{-}A_2B_2^{-} \cdots A_kB_k^{-}A_{k+1}= A$ where $A_1$, $B_1$, $A_2$, $B_2$, $\ldots$, $A_k$, $B_k$, $A_{k+1}$, and $A$ are given matrices of appropriate sizes, and $B_1^{-}$, $B_2^{-}$, $\cdots$, $B_k^{-}$ are generalized inverses of matrices. The cases for $k = 1, 2$ and their special forms were properly approached in the theory of generalized inverses of matrices. In this note, the author presents an algebraic procedure to derive explicit necessary and sufficient conditions for the equality with $k = 3$ to always hold using certain rank equalities for the block matrices constructed by the given matrices, and then mention a key step of extending the previous work to a general situation.

Most of the existing influence maximization algorithms are not suitable for large-scale social networks due to their high time complexity or limited influence propagation range. Therefore, a D-RIS influence maximization algorithm is proposed based on the independent cascade model and combined with the reverse reachable set sampling. Under the premise that the influence propagation function satisfies monotonicity and submodularity, the D-RIS algorithm uses automatic debugging method to determine the critical value of the number of reverse reachable sets, which not only obtains a better influence propagation range, and greatly reduce the time complexity. The experimental results on the two real data sets of Slashdot and Epinions show that D-RIS algorithm is close to the CELF algorithm and higher than RIS algorithm, HighDegree algorithm, LIR algorithm and pBmH algorithm in influence propagation range. At the same time, it is significantly better than the CELF algorithm and RIS algorithm in running time, which indicates that D-RIS algorithm is more suitable for large scale social network.

In this paper, the set-membership affine projection (SM-AP) algorithm is utilized to censor non-informative data in big data applications. To this end, the probability distribution of the additive noise signal and the excess of mean-squared error (EMSE) in steady-state are employed in order to estimate the threshold parameter of the single threshold SM-AP (ST-SM-AP) algorithm aiming at attaining the desired update rate. Furthermore, by defining an acceptable range for the error signal, the double threshold SM-AP (DT-SM-AP) algorithm is proposed to detect very large errors due to the irrelevant data such as outliers. The DT-SM-AP algorithm can censor non-informative and irrelevant data in big data applications, and it can improve misalignment and convergence rate of the learning process with high computational efficiency. The simulation and numerical results corroborate the superiority of the proposed algorithms over traditional algorithms.

A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves wheras when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature.

Using insights from cybernetics and an information-based understanding of biological systems, a precise, scientifically inspired, definition of free-will is offered and the essential requirements for an agent to possess it in principle are set out. These are: a) there must be a self to self-determine; b) there must be a non-zero probability of more than one option being enacted; c) there must be an internal means of choosing among options (which is not merely random, since randomness is not a choice). For (a) to be fulfilled, the agent of self-determination must be organisationally closed (a `Kantian whole'). For (c) to be fulfilled: d) options must be generated from an internal model of the self which can calculate future states contingent on possible responses; e) choosing among these options requires their evaluation using an internally generated goal defined on an objective function representing the overall `master function' of the agent and f) for `deep free-will', at least two nested levels of choice and goal (d-e) must be enacted by the agent. The agent must also be able to enact its choice in physical reality. The only systems known to meet all these criteria are living organisms, not just humans, but a wide range of organisms. The main impediment to free-will in present-day artificial robots, is their lack of being a Kantian whole. Consciousness does not seem to be a requirement and the minimum complexity for a free-will system may be quite low and include relatively simple life-forms that are at least able to learn.

The migration from MATLAB to Python (M-to-PY) has gained significant traction in recent computational research. While MATLAB has long served as a linchpin in myriad scientific endeavors, there's an emerging trend to rejuvenate these projects using Python's extensive AI tools and libraries. This study presents a semi-automated process for M-to-PY conversion, using a detailed case study of an image skeletonization project comprising fifteen MATLAB files and a 1404-image dataset. Skeletonization is foundational for ongoing 3D motion detection research using AI transformers, predominantly developed in Python. The utilization of ChatGPT-4, acting as an AI co-programmer, is pivotal in this conversion. By leveraging the public OpenAI API, we developed an M-to-PY converter prototype, evaluated its efficacy using test cases from the Bard bot, and subsequently employed the converted code in an AI application. The dual contributions encompass a well-tested M-to-PY converter and a Skeleton App capable of sketching and skeletonizing any given image, enriching the AI toolset. This study accentuates how AI resources, like ChatGPT-4, can simplify code transitions, opening doors for innovative AI implementations using primarily MATLAB-coded scientific research.

Scheduling and optimization have a central place in the research area of computing because it is increasingly important to achieve fully automated production processes to adjust manufacturing systems to the requirements of Industry 4.0. In this paper, we demonstrate how an automated wet-etch scheduling problem for a semiconductor industry can be solved by constraint answer set programming (CASP) and, its solver called clingcon. The considered scheduling problem includes a robot for lot transfers between the baths. CASP is a hybrid approach in automated reasoning that combines different research areas such as answer set programming, Constraint Processing and Satisfiability Modulo Theories. For a long time, exact methods such as constraint programming have displayed difficulties in solving real large-scale problem instances. Currently, the performance of state-of-the-art constrains solvers is comparatively better than a decade ago, and some complex combinatorial problems can be optimally solved. These theoretical and technical achievements open new horizons for declarative programming applications such as logistics. A successful solution to this problem is achieved and we found that in most cases tested, CASP is faster and obtains in most cases similar makespan values than solutions based on mixed integer linear programming and constraint paradigms.

The identification of fetal cells in the blood and tissues of healthy mothers raised questions about the potential alloreactive origins of various diseases, such as autoimmunity, diabetes, arteriosclerosis, and cancer. However, the extent to which alloreactivity contributes to these diseases remains unverified. This study presents a basic mathematical disease model based on the genes’ origin and immunological interactions. This model, grounded in set theory, classifies these immunological interactions based on their intrinsic, extrinsic, and allogeneic nature. Therefore, this model offers an unexpected common theoretical foundation for understanding alloreactivity, genetic diseases, and infections. Furthermore, this model provides a valuable framework for scrutinizing the role of alloreactivity in health and disease.

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb-Douglas functions embed the endogenous space factor as new capital to form the space travel firm's production function, which is also transformed into the consumer's utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT presents the equivalence between the spatial geometric tensor and the energy-momentum tensor, which explains the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers' incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and analogy method was applied to infer the space travel pricing by the model of profit maximization, single-minded, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the math models and algorithm. Results show that space travel pricing remains the principle of market equilibrium but needs to be extended to the spacetime tensor of GRT.

The multiobjective optimization problem is a key research direction in the field of optimization. Based on the multivariant optimization algorithm (MOA), this paper puts forward a multiobjective multivariant optimization algorithm (MMOA). A good point set is adopted for population initialization and to ensure the homogeneity of the initial solution set and avoid prematurity; global atoms are acquired by non-dominated sorting and an external archiving strategy; a nonlinear search radius is designed to balance global and local searches and enhance the convergence precision of the algorithm. Levy Flight and Sine chaotic mapping are introduced to redesign the update formula for local atoms, increase the convergence rate of the algorithm, and boost the optimization efficiency. Comparative experiments are conducted between MMOA and NSGA-II, MOEA/D, NSWOA, MOGWO, NSMFO on multiobjective test functions and an engineering example. The simulation results show that MMOA has superior convergence and diversity to the other five algorithms.

In order to study the movement characteristics of fuel in the fuel tank during aircraft maneuvering, this paper conducts numerical simulations of a typical wing fuel tank using the finite point set method based on certain boundary conditions and excitation. The results show that the finite point set method can capture the complex phenomena of fuel free surface fluctuations, surging, rolling and breaking, as well as the change in center of gravity caused by fuel movement. Under aircraft acceleration and pitch angle excitation, fuel will generate sustained impact pressure on the fuel tank wall. The velocity attenuation of fuel flowing through the baffle communication hole is fast, and the flow resistance and energy dissipation of the communication hole buffer the impact of fuel on the fuel tank wall.

Instead of the conventional 0 and 1 values, bipolar reasoning uses -1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., “uncertain” lies between “impossible” and “totally sure”). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e., William of Ockham and Nicholas of Autrecourt, who embodied a bipolar mode of thought that is eminently modern. Starting from the trivial observation that “once a wheat sheaf is sealed and tied up, the packed down straws display the same orientation”, we work up a new theory of the bipolar nature of networks, suggesting that orthodromic (i.e., feedforward, bottom-up) projections might be functionally coupled with antidromic (i.e., feedback, top-down) projections via the mathematical apparatus of presheaves/globular sets. When an entrained oscillation such as a neuronal spike propagates from A to B, changes in B might lead to changes in A, providing unexpected antidromic effects. Our account points towards the methodological feasibility of novel neural networks in which message feedback is guaranteed by backpropagation mechanisms endowed in the same feedforward circuits. Bottom-up/top-down transmission at various coarse-grained network levels provides fresh insights in far-flung scientific fields such as object persistence, memory reinforcement, visual recognition, Bayesian inferential circuits and multidimensional activity of the brain. Implying that axonal stimulation by external sources might backpropagate and modify neuronal electric oscillations, our theory also suggests testable previsions concerning the optimal location of transcranial magnetic stimulation’s coils in patients affected by drug-resistant epilepsy.

Knowledge-based approaches are useful alternatives to predict the Failure Probability (FP) coping with the insufficient data, process integrity, and complexity issue in manufacturing systems. This study proposes a Fault Tree Analysis (FTA) approach as proactive knowledge-based technique to estimate the FP based maintenance planning with subjective information from domain experts. However, the classical-FTA still suffers from uncertainty and static structure limitations which poses a substantial dilemma in predicting FP. To deal with the uncertainty issues, a Fuzzy-FTA (FFTA) model was developed by statistical analysing the effective attributes such as experts' trait impacts, scales variation and, assorted membership and defuzzification functions. Besides, a Bayesian Network (BN) theory was conducted to overcome the static limitation of classical-FTA. The results of FFTA model revealed that the changes in decision attributes were not statistically significant on FP variation while BN model considering conditional rules to reflect the dynamic relationship between events had more impact on predicting FP. After all, the integrated FFTA-BN model was used in the optimization model to find the optimal maintenance intervals according to estimated FP and the total expected cost. As a practical example, the proposed model was implemented in a semi-automatic filling system in an automotive production line. The outcomes could be useful for upgrading the availability and safety of complex equipment in manufacturing systems.

The purpose of this paper is to find the time optimal control to a target set for semilinear stochastic functional differential equations involving time delays or memories under general conditions on a target set and nonlinear terms even though the equations contain unbounded principal operators. Our research approach is construct a fundamental solution for corresponding linear systems and establish variations of constant formula of solutions for given stochastic equations. The existence result of time optimal controls for one point target set governed by the given semilinear stochastic equation is also established.

This note reconsiders a matrix equality $A_1A_2^{-}A_3A_4^{-}A_5 = A$ composed by six matrices of appropriate sizes, where $A_2^{-}$ and $A_4^{-}$ are generalized inverses of $A_2$ and $A_4$, respectively, and solves a selection of matrix set inclusion problems associated with various mixed reverse order laws for generalized inverses of products of two, three, and four matrices by means of this equality and its variations.

Once a wheat sheaf has been sealed and tied up, its packed down straws display the same orientation and zero-divergence. This observation brings us to the mathematical notion of presheaf, i.e., a topological structure in which diverging functions are locally superimposed. We show how the concepts of presheaves and the correlated globular sets, borrowed from category theory and algebraic topology, allow a well-founded mathematical approach to otherwise elusive activities of the brain. The mathematical assessment of brain functions in terms of presheaves: a) explains why spontaneous random spikes synchronize; b) leads to the counterintuitive intuition of antidromic effects in neuronal spikes: when an entrained oscillation propagates from A to B, changes in B lead to changes in A. We provide testable previsions: a) we suggest the proper locations of transcranial magnetic stimulation’s coils to improve the clinical outcomes of drug-resistant epilepsy; b) we advocate that axonal stimulation by external sources backpropagates and alters the neuronal electric oscillatory frequency. Further, we describe how the hierarchical information transmission inside globular sets provides fresh insights concerning different issues at various coarse-grained scales, such as object persistence, memory reinforcement in spite of random noise, Bayesian inferential circuits.

In this paper, we first define the concepts of r-fuzzy soft α-open (semi-open and δ-open) sets on fuzzy soft topological spaces based on the article Aygunoglu et al. (Hacet. J. Math. Stat., 43 (2014), 193-208), and the relations of these sets with each other are established. In addition, we introduce the concepts of fuzzy soft δ-closure (δ-interior) operators, and study some properties of them. Also, the concept of r-fuzzy soft δ-connected sets is introduced and studied with help of fuzzy soft δ-closure operators. Thereafter, we define the concepts of fuzzy soft α-continuous (β-continuous, semi-continuous, pre-continuous and δ-continuous) functions, which are weaker forms of fuzzy soft continuity, and some properties of these functions along with their mutual relationships are discussed. Moreover, a decomposition of fuzzy soft α-continuity and a decomposition of fuzzy soft semi-continuity is obtained. Finally, as a weaker form of a fuzzy soft continuity, the concepts of fuzzy soft almost (weakly) continuous functions are defined, and some properties are specified. Additionally, we explore the notion of continuity in a very general setting called, fuzzy soft (L, M, N, O)-continuous functions and a historical justification is introduced.

There were designed and synthesized two new sulfone 2-aminobenzimidazole derivatives. Coordination compounds were obtained with nickel(II), copper(II), zinc(II), cadmium(II) and mercury(II) and these novel ligands. There were fully characterized by spectroscopic and analytical techniques. Single crystal X-ray structural analysis was performed on order to study the relevant intra and inter non-covalent interactions, mainly H...π, lone pair·...π, π...π, highlighting the difference between the ethyl and phenyl groups in such interactions. Dimeric and trimeric supramolecular syntons were found for some of these compounds. Their biological activity was investigated, being the copper(II) compounds with the sulfone phenyl derivative the most active.

In this paper, we propose an efficient numerical method to solve the diffusive logistic model with a free boundary which is often used to simulate the spreading of the new or invasive species. The boundary movement is tracked by the level-set method, where the Hamilton-Jacobi weighted essentially nonoscillatory (HJ-WENO) scheme is utilized to capture the boundary curve embedded by the Cartesian grids via the embedded boundary method. Then the radial basis function-finite difference (RBF-FD) method is adopted to the spatial discretization and the IMEX scheme is considered for time integration. A variety of numerical examples are carried out to demonstrate the evolution of diffusive logistic model in different initial boundaries.

In this article, we introduce the concept of soft intervals, soft ordering and sequences of soft real numbers, and some of their structural properties are studied. The notion of soft Lebesgue measure on the soft real numbers has been introduced. Also, a correspondence relationship has been established between the soft Lebesgue measure and the classical Lebesgue measure. Furthermore, we have studied some exciting results and relations between the soft Lebesgue measure and the Lebesgue measure of soft real sets.

Automated spectrum analysis serves as a troubleshooting tool that helps to diagnose faults in wireless networks like difficult signal propagation conditions and coexisting wireless networks. It provides a higher monitoring coverage while requiring less expertise compared to manual spectrum analysis. In this paper, we introduce a data set that can be used to train and evaluate deep learning models, capable of detecting frames from different wireless standards as well as interference between single frames. Since manually labelling a high variety of frames in different environments is too challenging, an artificial data generation pipeline has been developed. The data set consists of 20 000 augmented signal segments, each containing a random number of different Wi-Fi and Bluetooth frames, their spectral image representations and labels that describe the position and type of frame within the spectrogram. The data set contains results of intermediate processing steps that enables the research or teaching community to create new data sets for specific requirements or to provide new interesting examination examples.

A detection system, modeled in a graph, uses "detectors" on a subset of vertices to uniquely identify an "intruder" at any vertex. We consider two types of detection systems: open-locating-dominating (OLD) sets and identifying codes (ICs). An OLD set gives each vertex a unique, non-empty open neighborhood of detectors, while an IC provides a unique, non-empty closed neighborhood of detectors. We explore their fault-tolerant variants: redundant OLD (RED:OLD) sets and redundant ICs (RED:ICs), which ensure that removing/disabling at most one detector guarantees the properties of OLD sets and ICs, respectively. This paper focuses on constructing optimal RED:OLD sets and RED:ICs on the infinite king's grid, and presents the proof for the bounds on their minimum densities; [3/10, 1/3] for RED:OLD sets and [3/11, 1/3] for RED:ICs.

In this article, we show the existence of fixed point for the derivative of interval-valued functions. Meanwhile, the fixed point inquiry will utilize the common fixed point methods under the condition of compatibility of the hybrid composite mappings in the sense of the Hausdorff metric. Some examples are given to support the usability of the result of this research .

In this paper, we propose the set-membership quaternion normalized least-mean-square (SM-QNLMS) algorithm. For this purpose, first, we review the quaternion least-mean-square (QLMS) algorithm, then go into the quaternion normalized least-mean-square (QNLMS) algorithm. By having the QNLMS algorithm, we propose the SM-QNLMS algorithm in order to reduce the update rate of the QNLMS algorithm and avoid updating the system parameters when there is not enough innovation in upcoming data. Moreover, the SM-QNLMS algorithm, thanks to the time-varying step-size, has higher convergence rate as compared to the QNLMS algorithm. Finally, the proposed algorithm is utilized in wind profile prediction and quaternionic adaptive beamforming. The simulation results demonstrate that the SM-QNLMS algorithm outperforms the QNLMS algorithm and it has higher convergence speed and lower update rate.

Compound databases of natural products have a major impact on drug discovery projects and other areas of research. The number of databases in the public domain with compounds from natural origin is increasing. Several countries have initiatives in place to construct and maintain compound databases that are representative of their diversity. Examples are Brazil, France, Panama and recently Vietnam. Herein, we discuss the first version of BIOFACQUIM, a novel compound database with natural products isolated and characterized in Mexico. We discuss its construction, curation, and a complete chemoinformatic characterization of the content and coverage in chemical space. It is reported the profile of physicochemical properties, scaffold content, and diversity, as well as structural diversity based on molecular fingerprints. BIOFACQUIM is freely available.

We present a new unsupervised method aimed to obtain a partition of a complex urban system in homogenous urban areas, called urban contexts. The area of study is initially partitioned in microzones, homogeneous portion of the urban system, that are the atomic reference elements for the census data. With the contribution of domain experts, we identify the physical, morphological, environmental and socio-economic indicators need to identify synthetic characteristics of urban contexts and create the fuzzy rule set necessary to determine the type of urban context. We implement the set of spatial analysis processes necessary to calculate the indicators for microzone and apply a Mamdani fuzzy rule system to classify the microzones. Finally, the partition of the area of study in urban contexts is obtained by dissolving continuous microzones belonging to the same type of urban context. Tests are performed on the Municipality of Pozzuoli (Naples - Italy); the reliability of out model is measured by comparing the results with the ones obtained by detailed analysis.

Inherent in every Active Magnetic Bearing (AMB) are differences between the expected geometric axes and the actual magnetic axes due to a combination of discrepancies, including physical variation from manufacturing tolerances and misalignment from mechanical assembly, fringing and leakage effects, as well as variations in magnetic material properties within a single AMB. A method is presented here for locating the magnetic axes of an AMB that will facilitate the accurate characterization of the bearing air gaps for potential improvement in field tuning, performance analyses and certain shaft force measurement techniques. This paper presents an extension of the application of the bias current perturbation method for the determination of the magnetic center [4] to the determination of magnetic axes for the further development of accurate current-based force measurement techniques [1].

Properties of the Voronoi tessellations arising from the random 2D distribution points are reported. We applied the procedure of dividing the sides of Voronoi cells into equal or random parts to Voronoi diagrams generated by a set of randomly placed on the plane points. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude, that by applying even a simple set of rules to a random set of seeds we introduce order into an initially disordered system. At the same time, the Voronoi entropy showed a tendency to values typical for completely random patterns and did not distinguish the short-range ordering. The Voronoi entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase of the number of the iteration steps. Voronoi entropy grew, with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Voronoi entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Voronoi entropy.

The General Theory of Information (GTI) tells us that information is represented, processed and communicated using physical structures. The physical universe is made up of structures combining matter and energy. According to GTI, “Information is related to knowledge as energy is related to matter.” GTI also provides tools to deal with transformation of information and knowledge. We present here, the application of these tools for the design of digital autopoietic machines with higher efficiency, resiliency and scalability than the information processing systems based on the Turing machines. We discuss the utilization of these machines for building autopoietic and cognitive applications in a multi-cloud infrastructure.

Gas Path Analysis and matching turbine engine models to experimental data are inverse problems of mathematical modelling which are characterized by parametric uncertainty. This results from the fact that the number of measured parameters is significantly lower than the number of components’ performance parameters needed to describe the real engine. In these conditions, even small measurement errors can result in a high variation of results, and obtained efficiency, loss factors etc. can appear out of the physical range. The current methods of engine model identification have developed considerably to provide stable, precise and physically adequate solutions. Presented in this work is an estimation method of engine components’ parameters based on multi-criteria identification which provides stable estimations of parameters and their confidence intervals with the known measurement errors. A priori information about the engine, its parameters and performance is used directly in the regularised identification procedure. The mathematical basis for this approach is the fuzzy sets theory. Forming objective functions and scalar convolutions synthesis of these functions is used to estimate gas-path components’ parameters. A comparison of the proposed approach with traditional methods showed that its main advantage is high stability of estimation in the parametric uncertainty conditions. Regularization reduces scattering, excludes incorrect solutions which do not correspond to a priori assumptions, and also helps to implement the Gas Path Analysis at the limited number of measured parameters. The method can be used for matching thermodynamic models to experimental data, Gas Path Analysis and also adapting dynamic models for the needs of the engine control system.

In this manuscript, we first introduce some properties of r-fuzzy soft α-open sets in fuzzy soft topological spaces based on the manuscript Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). In addition, we define the concepts of fuzzy soft α-closure (α-interior) operators, and investigate some properties of them. Furthermore, the concept of r-fuzzy soft α-connected sets is defined and characterized with help of fuzzy soft α-closure operators. Thereafter, we introduce and study the concepts of fuzzy soft almost (weakly) α-continuous mappings, which are weaker forms of fuzzy soft α-continuous mappings, and we discuss some properties of fuzzy soft α-continuity. Moreover, we establish that fuzzy soft α-continuity → fuzzy soft almost α-continuity → fuzzy soft weakly α-continuity, but the converse may not be true. It is also we show that the composition is fuzzy soft almost α-continuous mapping if, is fuzzy soft α-continuous mapping and is fuzzy soft almost continuous mapping. Finally, some new types of compactness via r-fuzzy soft α-open sets are defined, and the relationships between them are examined.

This study describes all the properties of high T_c cuprates by introducing rotating holes that are created by angular momentum conservations on a 2D CuO₂ surface, and which have a different mass from that of a normal hole because of the magnetic field energy induced by the rotation. This new particle called a macroscopic Boson describes the doping dependences of pseudo-gap temperature and the transition temperature at which an anomaly metal phase appears and describes the origin of the pseudo-gap. Furthermore, this study introduces a new model to handle many-body interactions, which results in a new statistic equation. This statistic equation describing many-body interactions accurately explains why high T_c cuprates have significantly high critical temperatures. Moreover a partition function of macroscopic Bosons describes all the properties of anomaly metal phase, which sufficiently agree with experiments, using the result from our previous study [1] that analytically describes the doping dependence of T_c. By introducing a macroscopic Boson and the new statistical model for many-body interactions, this study uncovered the mystery of high T_c cuprates, which have been a challenge for many researchers. An important point is that, in this study, pure analytical calculations are consistently conducted, which agree with experimental data well (i.e., they do not use numerical calculations or fitting methods but use many actual physical constants).

Scanning underwater areas, using magnetometers, in search of unexploded ordnance is a difficult challenge, where machine learning methods can find a significant application. However, this requires the creation of a set enabling the training of prediction models. Such a task is difficult and costly due to the limited availability of relevant data. To meet this challenge in the article, we propose the use of numerical modeling to solve this task. The conducted experiments allow us to conclude that it is possible to obtain high compliance of the numerical model with the results of physical tests. In addition, the paper discusses the methodology of simplifying the computational model, allowing for almost three times reduction of the calculation time. In addition, in the work we present the methodology of creating an appropriate data set, enabling the generation of any number of training samples.

In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

By the study of the pattern book Ying Zao Fa Shi (building regulations of Song Dynasty, 1103 AD), while analyzing the combining and dimensioning rule of timber framework and tile work, a model self-generating program has been compiled for the first time. The operating framework has been firstly defined, while solving the issues of clustering principle, connecting method, output classification, etc. with the detailed description of algorithm theory. Taking the corner bracket set and nine-ridge roof for example, after the compilation and debug by Grasshopper, according to various input parameters, various models have been generated automatically by the plugin, proving the velocity and the veracity of the algorithm.

The complete-lattice approach to optimization problems with a vector- or even set-valued objective already produced a variety of new concepts and results and was successfully applied in finance, statistics and game theory. For example, the duality issue for multi-criteria and vector optimization problems could be solved using the complete-lattice approach, compare [11]. So far, it has been applied to set-valued dynamic risk measures (in the stochastic case), as discussed in Feinstein, Rudloff etc. (see [11], for example), but it has not been applied to deterministic calculus of variations and optimal control problems. In this paper, the following problem of set-valued optimization is considered: minimize the functional $$ \overline J_t[y]=\int_0^t \overline L(s,y(s),\dot y(s))\ ds + U_0(y(0)) $$ over all admissible arcs $y$, where $\overline L$ is the associated multifunction to a vector-valued Lagrangian $L$, the integral is in the Aumann sense and $U_0$ is the initial cost. A new concept of \emph{value function}, for which a Bellman's optimality principle holds, is introduced. Also the classical result of the Hopf-Lax formula holds for the generalized value function. Finally, a derivative with respect to the time $t$ and a directional derivative with respect to $x$ of the value function are defined, based on ideas close to the concepts in [12]. The value function is proved to be solution of a suitable Hamilton-Jacobi equation.

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

In this paper, we observe that if X is a set and (Bin(X), □) is the semigroup of binary systems on X, then its center ZBin(X) consists of the locally-zero-semigroups and that these can be modeled as (simple) graphs and conversely. Using this device we show that we may obtain many results of interest concerning groupoids by reinterpreting graph theoretical properties and at the same time results on graphs G may be obtained by considering them as elements of centers of the semigroups of binary systems (Bin(X), □) where X = V(G), the vertex set of G.

Software fault prediction is the very consequent research topic for software quality assurance. Data driven approaches provide robust mechanisms to deal with software fault prediction. However, the prediction performance of the model highly depends on the quality of dataset. Many software datasets suffers from the problem of class imbalance. In this regard, under-sampling is a popular data pre-processing method in dealing with class imbalance problem, Easy Ensemble (EE) present a robust approach to achieve a high classification rate and address the biasness towards majority class samples. However, imbalance class is not the only issue that harms performance of classifiers. Some noisy examples and irrelevant features may additionally reduce the rate of predictive accuracy of the classifier. In this paper, we proposed two-stage data pre-processing which incorporates feature selection and a new Rough set Easy Ensemble scheme. In feature selection stage, we eliminate the irrelevant features by feature ranking algorithm. In the second stage of a new Rough set Easy Ensemble by incorporating Rough K nearest neighbor rule filter (RK) afore executing Easy Ensemble (EE), named RKEE for short. RK can remove noisy examples from both minority and majority class. Experimental evaluation on real-world software projects, such as NASA and Eclipse dataset, is performed in order to demonstrate the effectiveness of our proposed approach. Furthermore, this paper comprehensively investigates the influencing factor in our approach. Such as, the impact of Rough set theory on noise-filter, the relationship between model performance and imbalance ratio etc. comprehensive experiments indicate that the proposed approach shows outstanding performance with significance in terms of area-under-the-curve (AUC).

Contact with nature is suggested to be as an important resource for human health and well-being. Stress alleviation and reduction of mental fatigue are main instances of improvement of human health and well-being in contact with nature. Although the term restoration experience in contact with nature has been used repeatedly for concepts of stress alleviation and reduction of mental fatigue, these refer to different sets of theories and research studies. In this paper, by reviewing the nature-health related theories of Biophilia, Stress Recovery Theory, Attention Restoration Theory and Supportive Environment Theory (SET), the similarities and differences between these two concepts have been discussed. Moreover, the measurement approach instruments based on different study methodologies and aims are provided. This paper could provide information for future studies with focus on factors to be of benefit for restoration experience in design and planning of natural landscape environments with the aim of health and well-being development.

In this paper, firstly, some questionable formulas and conceptual oversights of previous reduced sigma set unscented transformation (UT) methods are revised through theoretical analysis. Then the revised UT methods based Kalman filters are used in a GPS/INS tightly-coupled system. The Kalman filter flows are the kind of square-root, since the square-root unscented Kalman filters (SRUKFs) can guarantee the stability of the system. By using the reduced sigma set SRUKFs (which contain simplex sigma set square-root unscented Kalman filter (S-SRUKF), spherical simplex sigma set square-root unscented Kalman filter (SS-SRUKF) and minimum sigma set square-root unscented Kalman filter (M-SRUKF)), the computation cost is greatly saved compared with the standard SRUKF, while the accuracy of the GPS/INS tightly-coupled system still maintained. The structure of the GPS/INS tightly-coupled system is in the form of error state, and the time updates of the state and the state covariance of SRUKFs are directly estimated without using UT, thus the computational time is also greatly saved. The pseudo-satellite is introduced to aid the system when the observation information is deficient, for example, when the GPS signal is deficient in the maneuver environment. By using the pseudo-satellite, the optimal performance of the system is guaranteed. Experiment of unmanned aerial vehicle (UAV) showed that the pseudo-satellite aided mechanism worked well.

Let  β= (((24!)!)!)!, and let {${\mathcal P}_{n^2+1}$} denote the set of all primes of the form {$n^2+1$}. Let ${\mathcal M}$ denote the set of all positive multiples of elements of the set {${\mathcal P}_{n^2+1} \cap (\beta,\infty)$}. The set {${\mathcal X}=\{0,\ldots,\beta\} \cup {\mathcal M}$} satisfies the following conditions: (1) ${\rm card}({\mathcal X})$ is greater than a huge positive integer and it is conjectured that ${\mathcal X}$ is infinite, (2)} we do not know any algorithm deciding the finiteness of ${\mathcal X}$, (3)~a~known and short algorithm for every {$n \in N$} decides whether or not {$n \in {\mathcal X}$}, (4) a known and short algorithm returns an integer~$n$ such that ${\mathcal X}$ is infinite if and only if ${\mathcal X}$ contains an element greater than $n$. The following problem is open: {\em simply define a set {${\mathcal X} \subseteq N$} such that ${\mathcal X}$ satisfies conditions (1)-(4), and \underline{we do not know any representation of~~${\mathcal X}$~~as a finite union of sets whose definitions are simpler than} \underline{the definition of ${\mathcal X}$}} {\tt (5)}. Let {$f(1)=2$}, {$f(2)=4$}, and let {$f(n+1)=f(n)!$} for every integer {$n \geqslant 2$}. For a positive integer $n$, let {$\Psi_n$} denote the following statement: {\em if a system of equations ${\mathcal S} \subseteq \Bigl\{x_i!=x_k: i,k \in \{1,\ldots,n\}\Bigr\} \cup \Bigl\{x_i \cdot x_j=x_k: i,j,k \in \{1,\ldots,n\}\Bigr\}$ has only finitely many solutions in positive integers \mbox{$x_1,\ldots,x_n$}, then each such solution \mbox{$(x_1,\ldots,x_n)$} satisfies {$x_1,\ldots,x_n \leqslant f(n)$}.} We prove that for every statement $\Psi_n$ the bound {$f(n)$} cannot be decreased. The author's guess is that the statements {$\Psi_1,\ldots,\Psi_9$} are true. We prove that the statement $\Psi_9$ implies that the set ${\mathcal X}$ of all {non-negative} integers $k$ whose number of digits belongs to {${\mathcal P}_{n^2+1}$} satisfies conditions {\tt (1)-(5)}.

Traditional gene set enrichment analysis falters when applied to large genomic domains, where neighboring genes often share functions. This spatial dependency creates misleading enrichments, mistaking mere physical proximity for genuine biological connections. Here we present Spatial Adjusted Gene Ontology (SAGO), a novel cyclic permutation-based approach, to tackle this challenge. SAGO separates enrichments due to spatial proximity from genuine biological links by incorporating the genes' spatial arrangement into the analysis. We applied SAGO to various datasets in which the identified genomic intervals are large, including replication timing domains, H3K9me3 and H3K27me3 large domains, HiC compartments and lamina associated domains (LADs). Intriguingly, applying SAGO to prostate cancer samples with large copy number alteration (CNAs) domains eliminated most of the enriched GO terms, thus helping to accurately identify biologically relevant gene sets linked to oncogenic processes, free from spatial bias.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

The objective of the paper is to introduce new similarity measure for single valued neutrosophic sets based on logarithm function. We define logarithm similarity measure and their weighted similarity measure for single valued neutrosophic sets. Then we define hybrid logarithm similarity measure and weighted hybrid logarithm similarity measure for single valued neutrosophic sets. We prove the basic properties of the proposed measures. We then define an entropy function using logarithm function to determine unknown attribute weights. We develop a novel multi attribute group decision making strategy for single valued neutrosophic sets based on the weighted hybrid logarithm similarity measure. We address an illustrative example to demonstrate the effectiveness and aptness of the proposed strategies. We conduct a sensitivity analysis of the developed strategy. We also make a comparison between the obtained results from proposed strategies and different existing strategies in the literature.

In general, a superconductor has zero resistance, although it requires significant refrigeration or high pressures with high manufacturing costs, which prevents it into practical applications. In other words, solving these issues implies main superconducting researches. To solve these problems, this paper describes a new type of superconductivity, which is independent for temperatures and which operates without pressures. The principles of the presented system are as follows:First a voltage source, a current source and a load are connected in series. Then, the voltage of the voltage source is adjusted to balance the voltage of the load. Under this condition, the balance of the two voltages provides a zero voltage between the taps of the current source and the generated current from the voltage source becomes zero because of the internal infinite resistance of the current source. As a result, the electric powers generated by the two sources are zero, and therefore, the load cannot generate Joule heating because of energy conservation. However, the current from the current source (not the voltage source) is not zero; therefore, we can predict that the resistance of the load must be zero. As a theory, we derived a new electric field and transient attractive force, which result in a very short coherence of an electron pair because there is not the Coulomb repulsive force due to the existence of the above transient attractive force. Note that both the forces are derived by the Poisson equation, which implies that they cannot be compatible. Therefore, the pair combination energy from spins becomes extremely strong, which is not destroyed by the normal heat energy. Moreover, every center-of-mass motion of electron pair results in the Bose-Einstein condensation and the macroscopic wave function, which produces the London equation (i.e., the Meissner effect). Moreover, by introducing the equivalent circuit, this paper conducted numerical calculations. As a result, we could derive numerically zero resistance and responses for additional static magnetic fields as a discharged current, which implies the Meissner effect. Note that this paper has prepared Appendix section, which provides a guide to reproduce actual experiments and preliminary experimental results. These results in the Appendix indicate the zero resistances and Meissner effects.

The current work reports the upper bound of the state variable of the of the Pointwise Steady Fluid Flow Approximation (PSFFA) model of non-stationary M/Ek/1 queueing system.

There are many applications of anomaly detection in IoT domain. IoT technology consists of large number of interconnecting digital devices not only generating huge data continuously but also making real-time computations. Since IoT devices are highly exposed due to Internet, they frequently meet with the challenges of illegitimate accesses in the form of intrusions, anomaly, fraud, etc. Identifying these illegitimate accesses in IoT domain can be an exciting research problem. In numerous applications fuzzy clustering and rough set theory have been successfully employed. As the data generated in IoT domains are high-dimensional, the clustering methods used for lower dimensional data cannot be applied efficiently. In this article, mixed approaches consisting of nano topology and fuzzy clustering techniques are proposed for anomaly detection. First of all, the nano topology is generated to find lower dimensional apace and then a couple of well-known fuzzy clustering techniques are employed on it for the efficient anomaly detection. The effectiveness of the proposed approaches is evaluated using time-complexity analysis, experimental studies with a synthetic dataset and a real-life dataset along with comparative studies with traditional fuzzy clustering approaches namely fuzzy c-means clustering (FCM) algorithm, Gustafson-Kessel (GK) Algorithm, Gath-Geva (GG) Algorithm, Mahalanobis Distance based Fuzzy C-Means algorithm (M-FCM), and Common Mahalanobis Distance based Fuzzy C-Means algorithm (CM-FCM). Experimentally, it has been found that the proposed approaches outperform the aforesaid algorithms in terms of detection rates, accuracy rates, false alarm rates and computational times.

Finding anomalies in the real-time system is recognized as one of most challenging study in information security. It has so many applications like IoT, and Stock-Market. In any IoT system the data generated are real-time, and temporal in nature. Since due to the extreme exposure to Internet and interconnectivity of devices, the IoT systems often face issues like fraud, anomalies, intrusions etc. Discovering anomaly in such domain can be interesting. Clustering and rough set theory have been tried in many cases. Considering the time-stamp associated with IoT data, time-dependent patterns like periodic clusters can be generated which could be helpful for the efficient detection of anomalies by providing more in-depth analysis of the system. In this paper, a mixed method comprising of nano topology, a modified k-means clustering and an interval superimposition technique is used for finding fuzzy periodic clusters in the subspace generated by the nano topology. For every clusters there will be an associated sequence of time-intervals where it exists. The sequence time-intervals accompanying with each clusters may exhibit some remarkable patterns. For example, there may exist different types of periodicity namely yearly, monthly, daily, and hourly etc. For finding such fuzzy periodicity, an operation called interval-superimposition has been used. The time-intervals associated with each cluster are superimposed if they have reasonable overlapping. Each superimposed time-interval generates a fuzzy time-interval. The data instances are thought to be anomalous if they either belong to sparse clusters or don't belong to any clusters. The efficacy of the method can be assessed by means of both time-complexity analysis and comparative studies with existing clustering-based anomaly detection algorithms with a real-life and a synthetic dataset. It can been found experimentally that our method can extract anomaly with 98% of accuracy and it runs cubic time approximately.

In this paper, we introduce a new class of open sets that is called is*-open set . Also, we present the notion of is*-continuous, is*-open, is*-irresolute, is*-totally continuous, and is-contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some is*-separation axioms, and is*-mappings are related with is*-separation axioms. . .

Myocardial infarction, more commonly known as heart attack, is a huge health problem around the world. It is a result of inadequate blood supply to certain parts of the heart and death of heart muscle cells in that region. Although it has been around for a long time, newer and newer ways of probing myocardial infarction is being followed. Bioinformatics and Systems Biology are relatively recent fields to try to give new insights into myocardial infarction. Following the footsteps of others, this in silico study has tried to chime in on the investigation into myocardial infarction. The study began with the gene expression omnibus dataset uploaded to the NCBI from a whole-genome gene expression analysis carried out at Mayo Clinic in Rochester, Minnesota. From the dataset, differentially expressed genes following first-time myocardial infarction were identified and classified into up-regulated and down-regulated ones. Gene Set Enrichment Analysis (GSEA) was carried out on the up-regulated genes which were statistically significant and corresponded with the NCBI generated annotations. Protein-Protein Interaction Network for these genes was constructed. GSEA revealed 5 transcription factors, 5 microRNAs and 3 pathways significantly associated with them. From the Protein-Protein Interaction Network, 6 key proteins (hub nodes) have been identified. These 6 proteins may open a new window of opportunity for the discovery/design of new drugs for mitigating the damage caused by myocardial infarction.

The aim of this article is introduced the concept of double framed T-soft fuzzy set (DFT-soft fuzzy set) which is the combination of soft set and fuzzy set. We also defined the notions and apply this concept in BCK/BCI-algebras. By using example, we also discussed the concept of double framed T-soft fuzzy algebra (DFT-soft fuzzy algebra) and double framed B-soft fuzzy algebra (DFB-soft fuzzy algebra) and also investigated their properties. Each double framed T-soft fuzzy algebra is double framed B-soft fuzzy algebra but by using example, we proved that converse may or may not be possible.

Minerals are the chief constituents of rocks and they have varied properties such as surface area, surface charge, site densities etc. Hence, numerous interactions are bound to occur in the reservoir during rock-fluids (i.e., rock, crude oil and brine) interactions. This study seeks to assess the role of mineralogical composition on the wettability of Sandstone Rocks (SR) and Mineral Mixture (MM) using both Surface Complexation Modelling (SCM) and flotation test. From the considered sandstone rocks, both the experimental results and its simulated counterpart revealed that, the SR were preferentially hydrophilic. For the MM, when the mass fraction of the hydrophobic mineral was increased, the affinity of the MM became slightly hydrophobic and vice-versa. For the dominant sandstone reservoir rock minerals with predominantly negatively charged surfaces, negligible oil adsorption took place due the interfacial repulsive forces at the oil-brine and mineral-brine interfaces. For the MM with low calcite content, the wetting preference was influenced by the mineral with prominent surface area. Our developed model portrayed that the main mechanism for oil adhesion onto sandstone minerals was divalent cations bridging. Nonetheless, adhesion of carboxylate (&gt;COO-) onto the illite, montmorillonite and calcite sites also took place with the latter being more pronounced.

Genomic selection (GS) can accelerate variety improvement when training set (TS) size, and its relationship with the breeding set (BS) are optimized for prediction accuracies (PA) of genomic prediction (GP) models. Sixteen GP algorithms were run on phenotypic best linear unbiased predictors (BLUPs) and estimators (BLUEs) of resistance to both fall armyworm (FAW) and maize weevil (MW) in a tropical maize panel. For MW resistance, 37% of the panel was the TS, and BS was the remainder whilst for FAW, random-based training sets (RBTS) and pedigree-based training sets (PBTS) were designed. PAs achieved with BLUPs varied from 0.66 to 0.82 for MW resistance traits, and, for FAW resistance, 0.694 to 0.714 for RBTS of 37%, and 0.843 to 0.844 for RBTS of 85%, and, these were at least two-fold those from BLUEs. For PBTS, FAW resistance PAs were generally higher than those for RBTS, except for one dataset. GP models generally showed similar PAs across individual traits whilst the TS designation was determinant since a positive correlation (R=0.92***) between TS size and PAs was observed for RBTS and, for the PBTS, it was negative (R=0.44**). This study pioneers the use of GS for maize resistance to insect pests in sub-Saharan Africa.

In the present study. At first, some properties of r-fuzzy soft β-closed sets are introduced on fuzzy soft topological spaces based on the paper Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). Also, we define the closure and interior operators with respect to the classes of r-fuzzy soft β-closed and r-fuzzy soft β-open sets, and investigate some of their properties. In addition, the concept of r-fuzzy soft β-connected sets is introduced and characterized with help of fuzzy soft β-closure operators. Thereafter, some properties of a fuzzy soft β-continuity are studied. Furthermore, we introduce and study the concepts of fuzzy soft almost (weakly) β-continuous functions, which are weaker forms of a fuzzy soft β-continuity. Also, the relationships between these classes of functions are specified with the help of some illustrative examples. Finally, we explore new types of fuzzy soft functions called, fuzzy soft β-irresolute (strongly β-irresolute, β-irresolute open, β-irresolute closed and β-irresolute homeomorphism) functions, and discuss some properties of them. Also, we show that fuzzy soft strongly β-irresolute → fuzzy soft β-irresolute → fuzzy soft β-continuity, but the converse may not be true.

The purpose of this paper is to demonstrate the existence of an artificial magnetic monopole and to introduce new electromagnetic equations by altering an electric field and a magnetic field vectors.As a principle device, a cylindrical condenser is prepared, and a superconducting loop is inserted into it. By this conduction, radial electric fields take a role as the centripetal force and both counterclockwise and clockwise motions are induced. As a result, a stationery wave is formed in which the nodes take a part in creating a monopole as follows.First, employing the Lorentz conservations and because node of the stationary wave has no phases, the momentum k and the vector potential A vanish and instead a magnetic potential appears in order to maintain the Lorentz conservation. This magnetic potential has relationship with an electric potential, and thus consequently, a dependent relationship is obtained between an electric field and a magnetic field vectors. Using this conclusive dependent relationship, we can derive new Maxwell equation assembly which are created by altering the electric field and the magnetic field vectors. In this process, we derive a divergent equation of magnetic fields which is not zero, i.e., the existence of a magnetic monopole. Employing these newly derived Maxwell equation, an electromagnetic wave is derived whose speed is the same as one the existing Maxwell equations provide. As a monopole configuration, this paper discusses the energy gap of the vacuum, which is a result of the Dirac equation and describes a monopole as pairs between two Cooper pairs (i.e. four electrons) whose interaction is a photon. As mentioned, because the total momenta and phases are zero, this paper defines the wave function as the Dirac function and demonstrate the condensation, employing the Bloch’s theorem. Moreover, using the macroscopic basic equations, we retrace the creation of the divergent magnetic field in view of macroscopic phenomenon., which provides results in this paper.In Result section in this paper, we succeeded in demonstrating the distribution of the divergent magnetic field of monopole in terms of both microscopic and macroscopic scales. Furthermore, Discussion section describes properties a magnetic monopole should follow.

This paper presents a two-dimensional mathematical model of compound eye vision. Such a model is useful for solving navigation issues for autonomous mobile robots on the ground plane. The model is inspired by the insect compound eye that consists of ommatidia, which are tiny independent photoreception units, each of which combines a cornea, lens, and rhabdom. The model describes the planar binocular compound eye vision, focusing on measuring distance and azimuth to a circular feature with an arbitrary size. The model provides a necessary and sufficient condition for the visibility of a circular feature by each ommatidium. On this basis, an algorithm is built for generating a training data set to create two deep neural networks (DNN): the first detects the distance, and the second detects the azimuth to a circular feature. The hyperparameter tuning and the configurations of both networks are described. Experimental results showed that the proposed method could effectively and accurately detect the distance and azimuth to objects.

Germplasm is a long-term resource management mission and investment for civilization. For both food and nutritional health, the present changing environmental scenario has become an urgent universal concern. Multiple excellent studies have been previously performed, although the advancement and innovation of practices will require the exploration of the potentiality of crop germplasm. In this study, we emphasized (i) germplasm activates, current challenges and ongoing trends of the crop germplasm, and (ii) how the system biology will be helpful to understand the complex traits such as water use efficiency (WUE), and nitrogen use efficiency (NUE) to mitigate challenges for sustainable development under growing food requirement and climate change conditions. We focused on a vision for transforming PGR into a bio-digital resource system, for the development of climate-smart crops for sustainable food production. Moreover, this review attempted to address current challenges, research gaps and describe the advanced integrated strategies that could provide a platform for future crop improvement research.

Intuitionistic fuzzy set, which can be represented using the triangular intuitionistic fuzzy number (TIFN), is a more generalized platform for expressing imprecise, incomplete and inconsistent information when solving multi-criteria decision-making problems, as well as for reflecting the evaluation information exactly in different dimensions. In this paper, the TIFN has been applied for solving some multi-criteria decision-making problems by developing a new triangular intuitionistic fuzzy geometric aggregation operator, that is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator, and defining some triangular intuitionistic fuzzy geometric aggregation operators including the triangular intuitionistic fuzzy weighted geometric averaging (TIFWGA) operator, the ordered weighted geometric averaging (TIFOWGA) operator and the hybrid geometric averaging (TIFHWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed has been proposed. Finally, the proposed method has been compared with some similar existing computational approaches by virtue of a numerical example to verify its feasibility and rationality.

Identifying or authenticating a computer user are necessary steps to keep systems secure on the network and to prevent fraudulent users from accessing accounts. Keystroke dynamics authentication can be used as an additional authentication method. Keystroke dynamics involves in-depth analysis of how you type on the keyboard, analysis of how long a key is pressed or the time between two consecutive keys. This field has seen a continuous growth in scientific research. In the last five years alone, about 10,000 scientific researches in this field have been published. One of the main problems facing researchers is the small number of public data sets that include how users type on the keyboard. This paper aims to provide researchers with a data set that includes how to type free text on the keyboard by 80 users. The data were collected in a single session via a web platform. The dataset contains 410,633 key-events collected in a total time interval of almost 24 hours. In similar research, most datasets are with texts written by users in English. The language in which the users wrote for this research is Romanian. This paper also provides an extensive analysis of the data set collected and presents relevant information for the analysis of the data set in future research.

A numerical study for the effect of crest width, breaking parameter and trunk permeability on hydrodynamics and flow behavior in the vicinity of rubble-mound, permeable, zero-freeboard breakwaters (ZFBs) is presented. The modified two dimensional Navier-Stokes equations for two-phase flows in porous media with a Smagorinsky model for the subgrid scale stresses were solved numerically. An immersed-boundary/level-set method was used. The numerical model was validated for the cases of wave propagation over a submerged impermeable trapezoidal bar and over a low-crested permeable breakwater. Five cases of breakwaters were examined, and the main results are: (a) The size of the crest width, B, does not notably affect the wave reflection, vorticity and currents in the seaward region of ZFBs, while wave transmission, currents in the leeward side, and mean overtopping discharge, all decrease with increasing B. A non-monotonic behavior of the wave setup is also observed. (b) As the breaking parameter decreases, wave reflection, transmission, currents, mean overtopping discharge, and wave setup decrease. This observation is also verified by relevant empirical formulas. (c) As the ZFB trunk permeability decreases, an increase of the wave reflection, currents, wave setup, and a decrease of wave transmission and mean overtopping discharge is observed.

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.

The usage of Quantum Similarity through the equation Z = {∀θ ∈ Z → ∃s ∈ S ∧ ∃t ∈ T : θ = (s, t)}, represents a way to analyze the way communication works in our DNA. Being able to create the object set reference for z being (s, t) in our DNA strands, we are able to set logical tags and representations of our DNA in a completely computational form. This will allow us to have a better understanding of the sequences that happen in our DNA. With this approach, we can also utilize mathematical formulas such as the Euler–Mascheroni constant, regression analysis, and computational proofs to answer important questions on Quantum biology, Quantum similarity, and Theoretical Physics.

This paper examines the correlation between numbers of computer cores in parallel genetic algorithms. The objective to determine the linear polynomial complementary equation in order represent the relation between number of parallel processing and optimum solutions. Model this relation as optimization function (f(x)) which able to produce many simulation results. F(x) performance is outperform genetic algorithms. Compression results between genetic algorithm and optimization function is done. Also the optimization function give model to speed up genetic algorithm. Optimization function is a complementary transformation which maps a TSP given to linear without changing the roots of the polynomials.

A time interval only description necessarily needs its own independent definitions, without one moment time coordinates to it. In this paper derived are time interval only set properties, including commutation relations, addition, multiplication and derivatives. Time interval only set commutation relations, consistent with one moment time set properties, are introduced by defining correspondence relations for these sets. Time development and equilibrium within the time interval description depend on the well-known ‘mean velocity theorem’ and the time interval version of the Legendre transform. In contrast, usually applied is only the traditional vector and one moment time coordinate kinematic approach from Newton’s laws. The main results of this paper are correspondences and time interval only set commutation relations. All other properties are derived from these results, while for the time interval only set, different from the one moment time set the canonical property is not valid. The time interval only description can be applied assuming spherical symmetric star-source radiation propagation, with finite time intervals for realistic measurement events. From time development with (a-)symmetry of time intervals, and from Curie’s principle, change can be described with a set theoretic approach. Time interval only set properties include the time interval only version of Noether charges and structure constants. A time interval only description for wave propagation, including group-velocity, for zero and non-zero mass wave particles, relates to the properties of the time interval only set. A second result in terms of the time interval only description is propagation wave energy equivalence with gravitation energy, derived from time interval only set commutation relations. A time interval approach, however including one moment time description dependence, was introduced in earlier publications of this author. In part 1 investigated are the time interval only set and its properties, a forthcoming part 2 to application of the time interval only description to specific groups of stars as emission sources.

In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

While the importance of corporate governance has been broadly acknowledged in global financial markets and academic research, how to devise a practical evaluation system is relatively unexplored. This paper attempts to refine the Corporate Governance Evaluation System (CGES), constructed by the Taiwan Stock Exchange (TWSE) since 2014. The current CGES has several debatable issues in its complicated design (e.g., it comprises over 80 indicators in different types). To resolve those issues, this study invited ten senior domain experts (including several CEOs of financial holding companies) to retrieve 13 essential criteria from the CGES in four dimensions. And this study integrates several multiple criteria decision-making (MCDM) methods (i.e., Decision-making trial and evaluation laboratory (DEMATEL), modified VIKOR, DEMATEL-based analytical network process (DANP)) and the fuzzy evaluation technique to rank the exemplary companies. The obtained ranking is consistent with the one released from the CGES in 2017. This study conducted additional experiments to ensure the robustness of the findings. The newly devised model not only supports the ranking decisions but also provides a managerial guidance for companies to pursue systematic improvements. These findings enrich the understanding of corporate governance and contribute to gaining business sustainability for financial holding companies.

The central promise of personalized medicine is individualized treatments that target molecular mechanisms underlying the physiological changes and symptoms arising from disease. We demonstrate a bioinformatics analysis pipeline as a proof-of-principle to test the feasibility and practicality of comparative transcriptomics to classify two of the most popular in vivo diet-induced models of coronary atherosclerosis, apolipoprotein E null mice and New Zealand White rabbits. Transcriptomics analyses indicate the two models extensively share dysregulated genes albeit with some unique pathways. For instance, while both models have alterations in the mitochondrion, the biochemical pathway analysis revealed, Complex IV in the electron transfer chain is higher in mice, whereas the rest of the electron transfer chain components are higher in the rabbits. Several fatty acids anabolic pathways are expressed higher in mice, whereas fatty acids and lipids degradation pathways are higher in rabbits. This reflects the differences between two translational models of atherosclerosis. This study validates transcriptome analysis as a potential method to precisely identify altered cellular and molecular pathways in atherosclerotic disease, which can be used to individualize treatment even in the absence of genetic data.

In this study, we present the concept of interval-valued fuzzy soft point and then introduce the notions of neighborhood and quasi-neighbourhood of it in interval-valued fuzzy soft topological spaces. Separation axioms in interval-valued fuzzy soft topology, so-called $q$-$T_{i}$ for $ i=0,1,2,3,4 ,$ is introduced and some of its basic properties are also studied.

The influence and importance of research and development (R&D) for business sustainability have gained increasing interests, especially in the high-tech sector. However, the efforts of R&D might cause complex and mixed impacts on the financial results considering the associated expenses. Thus, this study aims to examine how R&D efforts may influence business to improve its financial performance considering the dual objectives: the gross and the net profitability. This research integrated a rough-set-based soft computing technique and multiple criteria decision-making (MCDM) methods to explore this complex and yet valuable issue. A group of public listed companies from Taiwan, all in the semiconductor sector, was analyzed as a case study. Initially, more than 30 variables were considered, and the adopted soft computing technique retrieved 14 core attributes—for the dual profitability objectives—to form the evaluation model. The importance of R&D for pursuing superior financial prospects is confirmed, and the empirical case demonstrates how to guide an individual company to plan for improvements to achieve its long-term sustainability by this hybrid approach.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

We prove: (1) the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable, (2) the set of all Diophantine equations which have at most finitely many solutions in positive integers is not recursively enumerable, (3) the set of all Diophantine equations which have at most finitely many integer solutions is not recursively enumerable, (4) analogous theorems hold for Diophantine equations D(x₁, …, x_p) = 0, where p ∈ N\{0} and for every i ∈ {1, …, p} the polynomial D(x₁, …, x_p) involves a monomial M with a non-zero coefficient such that x_i divides M, (5) the set of all Diophantine equations which have at most k variables (where k ≥ 9) and at most finitely many solutions in non-negative integers is not recursively enumerable.