Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

From their discovery in 2002, BRAF mutations have been identified as clear drivers of oncogenesis in several cancer types. Currently, their incidence rate is nearly 7% of all solid tumors with BRAF V600E constituting approximately 90% of these diagnoses [1]. In melanoma, thyroid cancer, and histiocytic neoplasms, BRAF hotspot mutations are found at a rate of about 50%, while in lung and colorectal cancers they range from 3 to 10% of reported cases [2-5]. Though present in other malignancies such as breast and ovarian cancers, they constitute a small portion of diagnoses (<1%). Given their frequency along with advancements in screening technologies, various methods are used for the detection of BRAF-mutant cancers. Among these are targeted next-generation sequencing (NGS) on tumor tissue or circulating tumor DNA (ctDNA) and immunohistochemistry (IHC)-based assays. With advancements in detection technologies, several approaches have been taken for the treatment of BRAF mutant cancers. In this review we retrace the milestones that led to the clinical development of targeted therapies currently available for these tumors.

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

This article puts forward the bi-matrix games with crisp parametric payoffs based on interval value function approach. We conclude that the equilibrium solution of the game model can converted into optimal solutions of the pair of the non-linear optimization problem. Finally, experiment results show the efficiency of the model.

In this paper, improved matrix Reduction Method is proposed for the solution of fuzzy transportation problem in which all inputs are taken as fuzzy numbers. Since ranking fuzzy number is important tool in decision making, Fuzzy trapezoidal number is converting in to crisp set by using Mean techniques and solved by proposed method for fuzzy transportation problem. We give suitable numerical example for unbalanced and compare the optimal value with other techniques. The Result shows that the optimum profit of transportation problem using proposed technique under robust ranking method is better than the other method. Novelty: The numerical illustration demonstrates that the new projected method for managing the transportation problems on fuzzy algorithms.

Atomic structure of N-electron atoms is often determined using the Hartree-Fock method, which is an integro-differential equation. The exchange term of the Hartree-Fock equations is usually treated as an inhomogeneous term of a differential equation, or with a local density approximation. This work uses matrix methods to solve for the Hartree-Fock equations, rather than the more commonly-used shooting method to integrate an inhomogeneous differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using computer linear-algebra packages. We extend the same technique to integro-differential equations, where a discretized integral can be written as a sum in matrix form. This method is compared against experiment and standard atomic structure calculations. We also can use this method for free-electron wavefunctions. This technique is important for spectral line broadening in two ways: improving the atomic structure calculations, and improving the motion of the plasma electrons that collide with the atom.

The shallow water equations are widely applied for the simulation of flow routing in rivers and floodplains, as well as for flood inundation mapping. From a mathematical point of view, they are a hyperbolic system of nonlinear partial differential equations, whose numerical integration is sometimes computationally burdensome. For this reason, the interest of many researchers has been focused on the study of simplified forms of the original set of equations, which requires less computational effort. One of the most commonly applied simplifications consists in neglecting the inertial terms, which changes the hyperbolic model to a parabolic one. The effects of such a choice on the outputs of the simulations of flooding events are controversial and an important topic of debate. In the present paper, two numerical models, recently proposed for the solution of the complete and zero-inertia forms of the shallow waters equations, are applied to several unsteady flow routing scenarios. We simulate synthetic and laboratory studies, starting from very simple geometries and moving towards complex topographies. Analyzing the role of the terms in the momentum equations, we try to understand the effect, on the computed results, of neglecting the inertial terms in the zero-inertia formulation. We analyze the computational costs.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

Growing agricultural demands for the global population are unlocking the path to developing innovative solutions for efficient water management. Herein, an intelligent variable rate irrigation system (fuzzy-VRI) is proposed for rapid decision-making to achieve optimized irrigation in various delimited zones. The proposed system automatically creates irrigation maps for a center pivot irrigation system for a variable-rate application of water. Primary inputs are spatial imagery on remotely sensed soil moisture (SSM), soil adjusted vegetation index (SAVI), canopy temperature (CT), and nitrogen content (NI). To eliminate localized issues with soil characteristics, we used the crop nitrogen content map to provide a focused insight on issues related to water shortage. The system relates these inputs to set reference values for the rotation speed controllers and individual openings of each central pivot sprinkler valve. The results showed that the system can detect and characterize the spatial variability of the crop and further, the fuzzy logic solved the uncertainties of an irrigation system and defined a control model for high-precision irrigation. The proposed approach is validated through the comparison between the recommended irrigation and actual irrigation at two field sites, and the results showed that the developed approach gives an accurate estimation of irrigation with a reduction in the volume of irrigated water of up to 27% in some cases. Future research should implement the fuzzy-VRI real-time during field trials in order to quantify its effect on irrigation use, yield, and water use efficiency.

The broad global distribution of freshwater clams belonging to the genus Corbicula is driven by multiple hermaphroditic lineages. These lineages, characterized by shared morphological traits and phenotypic plasticity, pose challenges to morphological identification. Genetic markers, such as the mitochondrial COI gene, play a crucial role in delineating these lineages and their ranges. Morphotypes represent observed phenotypic variations, while lineages are defined based on genetic markers. Here, we comprehensively review Corbicula's distribution in Argentina, dis-criminate extant lineages based on both morphological and genetic (COI) data, and describe variation in internal and external morphology using 15 Argentine populations. Haplotype net-works identified two mitochondrial lineages: A/R morphotype (FW5 haplotype) and C/S mor-photype (FW17 haplotype). Strikingly, despite having similar vectors, origins, and invasive stages, Corbicula lineages exhibit virtually segregated distributions. However, intermediate morphotypes and both mitochondrial haplotypes are found in sympatry in northeastern Argen-tina, suggesting the presence of hybrids due to maternal genome retention. These findings con-tribute to the clarification of the identity and distribution of Corbicula lineages in Argentina, where the genus has been found for over half a century. Similar studies are needed in other areas to better understand the invasion patterns of a successful and plastic group.

The multiphase motors due to their reliability find new areas of application in the industry and transportation. Developing of any system with multiphase motors at first requires elaborate model of the system, define control mode and controllers. The model of control system for the six-phase drive is based on its conventional d-q mathematical model and indirect field-oriented control. Simulink model of six-phase drive with indirect field-oriented control and simulated with two types PID and PID fuzzy controllers. The simulation results, reflecting step response and provided speed reference law as well as load application at constant speed, are presented and analyzed. Fuzzy controller with 49 rules is considered and applied. Six-phase electric drive with field-oriented control at well-tuned PID controller has good step response specifications: settling time 0.13 s at starting without load, step response has no overshoot, small about 1 % short time decrease of speed at load of 5 Nm application. The system employing PID fuzzy controller shows slightly better results in response to torque application: the decrease in speed 1 % is eliminated in shorter time. Simulation results indicate the robustness of both systems with six-phase drive to disturbance and provide high quality transient specifications at determined reference speed.

In this paper, we introduce as a pedagogical strategy an internal division-free, straightforward, and symmetrically progressing algorithm in manually computing matrix inverse and solving systems of linear equations by revisiting the application of elementary row operations in the Gauss-Jordan reduction method and connecting it to the determinant method. The proposed cross-multiplication-flip (CMF) algorithm employs cross-multiplication similar to the butterfly movement in computing determinants as a strategic application of elementary row operations to efficiently reduce the rows and then applies flipping of rows and entries to put an upper triangular matrix into lower triangular form to continue the reduction process.

Parkinson’s disease (PD) is a neurodegenerative disease that progresses with increasing age and some of its major symptoms include tremor, postural and movement related difficulties. Till date, the treatment of PD remains a challenge because available drugs only treat the symptoms of the disease or possess serious side effects. In light of this, new treatment options are needed, hence this study investigates the neuroprotective effects of an organic Boophone haemanthoides extract (BHE) and its bioactive compounds using an in vitro model of PD involving the toxin 1-methyl-4-phenylpyridinium (MPP+) and SH-SY5Y neuroblastoma cells. A total of seven compounds were isolated from BHE viz: distichamine (1), 1α,3α-diacetylnerbowdine (2), hippadine (3), stigmast-4-ene-3, 6-dione (4), cholest-4-en-3-one (5), tyrosol (6), and 3-hydroxy-1-(4`-hydroxyphenyl)-1-propanone (7). Six compounds (1, 2, 4, 5, 6, 7) were investigated and five showed neuroprotection alongside the BHE. This study gives insight into the bioactivity of the non-alkaloidal constituents of Amaryllidaceae since the isolated compounds and the BHE showed improved cell viability, increased ATP generation in the cells as well as inhibition of MPP+-induced apoptosis. Together, these findings support the claim that the Amaryllidaceae plant family could be a potential reserve of bioactive compounds for the discovery of neuroprotective agents.

In various countries of the global south, school feeding programs are implemented in order to alleviate short-time hunger in children, improved their nutrition and provide employment for food vendors. The impact of these programs is important not only in terms of pupils’ nutrition but also in improving farmers’ livelihoods. This study analyzes the impact of the school feeding program on smallholders' food security based on data collected in 2021 from 240 farmers surveyed in northeast Nigeria. Differently from other studies, several econometric methods are used to analyze the data, namely, binary probit regression, propensity score matching, inverse probability weighted adjusted regression and endogenous switching regression. The results show that about 40% of the beneficial smallholder farmers are food secure compared to 20% of the non-beneficiary households. Findings revealed that the Homegrown school feeding program (HGSF) positively improved smallholder farmers improve household food security status. Results provide evidence for the need to expand school feeding programs vis-a-vis interventions in facilitating farmers’ access to capital and capacity building for better integration in the supply chain.

In this paper, we study the semilinear pseudo-parabolic equations $\displaystyle u_{t} - \triangle_{\mathbb{B}}u - \triangle_{\mathbb{B}}u_{t} = \left|u\right|^{p-1}u$ on a manifold with conical singularity, where $\triangle _{\mathbb{B}}$ is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary $x_{1} = 0$. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence and nonexistence of global weak solution: for the low initial energy $J(u_{0})<d$, the solution is global in time with $I(u_{0}) >0$ or $\displaystyle\Vert \nabla_{\mathbb{B}}u_{0}\Vert_{L_{2}^{\frac{n}{2}}(\mathbb{B})} = 0$ and blows up in finite time with $I(u_{0}) < 0$; for the critical initial energy $J(u_{0}) = d$, the solution is global in time with $I(u_{0}) \geq0$ and blows up in finite time with $I(u_{0}) < 0$. The decay estimate of the energy functional for the global solution and the estimates of the lifespan of local solution are also given.

The release of the active substance from the matrix modified-release tablets based on Kollidon®SR and chitosan depends on its solubility in the dissolution medium and on the composition of the matrix-forming polymers. The study is based on new oral matrix tablets based on Kollidon®SR and chitosan, formulated to optimize the low oral bioavailability of chlorzoxazone, a non-steroidal anti-inflammatory drug, a class II Biopharmaceutical Classification System. Nine types of chlorzoxazone matrix tablets were obtained using the direct compression method, and their combination at 1:1, 1:2, 1:3 chlorzoxazone/ excipients, 20%-40% (w/w) Kollidon®SR, 3-7% (w/w) chitosan and the auxiliary substances were formulated in constant concentrations. Pharmaco-technical characterization included the analysis of flowability and compressibility properties (flow time, friction coefficient, angle of repose, Hausner ratio, Carr Index), and of pharmaco-chemical characteristics (mass and dose uniformity, thickness, diameter, mechanical strength, Friability, degree of softening, in vitro release profile) of the tablets. Based on the initial evaluation of the pharmaco-technical analysis, pharmaco-chemical characteristics, and in vitro release profile, only three matrix tablet formulations (F1b, F2b, and F3b) were further tested. They were evaluated through Fourier-transform infrared spectrometry, X-ray Diffraction, thermogravimetry, differential scanning calorimetry, and in vitro dissolution tests. The three formulations were comparatively studied regarding the release kinetics of active substances using in vitro release testing. The results were analyzed by fitting into four representative mathematical models for the modified release oral formulations. In vitro kinetic study reveals a complex mechanism of release occurring in the first (0 - 2 hours) and second (2.0 hours – 36 hours) steps of drug release. Two factors have been calculated to assess the release profile of chlorzoxazone: f1 - the similarity factor and f2 - the factor difference. The results have shown that both Kollidon®SR and chitosan may be used as matrix-forming agents when combined with chlorzoxazone. In vitro dissolution tests revealed the F2b sample, data suggesting a faster drug release. The three formulations showed optimum pharmaco-technical properties and in vitro kinetic study, and they had tremendous potential to be used in oral pharmaceutical products for the controlled delivery of chlorzoxazone.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

This investigation mainly focused on the microstructural analysis of Al based hybrid metal matrix composites. Aluminium as base metal and reinforced with 2% B4 C, ZrO2 (2%,4%,6%), SiC (4%,8%,12%). Specimens were manufactured by using conventional stir casting technique. Hybrid metal matrix composites were examined by using Scanning electron microscope. This research explained XRD, EDS and Fractography analysis. This investigation shows the reinforced material has given better results in all aspects than pure Al6061 alloy and homogeneous dispersion of particles inside the matrix. Porosity, delamination, cracks, particle distributions were observed through microstructural analysis. Additionally determined the crystal size of pure Aluminium 6061 alloy and hybrid composites.

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.

Two well-known drawbacks in fuzzy clustering are the requirement of assign in advance the number of clusters and random initialization of cluster centers.; the quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of FCM using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.

Agricultural greenhouse is largely answered in the agricultural sphere, despite the shortcomings it has, including overheating during the day and night cooling which sometimes results in the thermal inversion mainly due to its low inertia. The glasshouse dressed chapel is relatively more efficient than the conventional tunnel greenhouse. Its proliferation on the ground is more or less timid because of its relatively high cost[14-22]. Agricultural greenhouse aims to create a favorable microclimate to the requirements of growth and development of culture, from the surrounding weather conditions, produce according to the cropping calendars fruits, vegetables and flower species out of season and widely available along the year. It is defined by its structural and functional architecture, the quality thermal, mechanical and optical of its wall, with its sealing level and the technical and technological accompanying[12-13]. The greenhouse is a very confined environment, where multiple components are exchanged between key stakeholders and them factors are light, temperature and relative humidity[8]. This state of thermal evolution is the level sealing of the cover of its physical characteristics to be transparent to solar, absorbent and reflective of infrared radiation emitted by the enclosure where the solar radiation trapping effect otherwise called "greenhouse effect" and its technical and technological means of air that accompany. The socio-economic analysis of populations in the world leaves appear especially the last two decades of rapid and profound transformations These changes are accompanied by changes in eating habits, mainly characterized by rising consumption spread along the year[14]. To effectively meet this demand, greenhouse-systems have evolved, particularly towards greater control of production conditions (climate, irrigation, ventilation techniques, CO2 supply, etc ...). Technological progress has allowed the development of greenhouses so that they become increasingly sophisticated and of an industrial nature (heating, air conditioning, control, computer, regulation, etc ...). New climate driving techniques have emerged, including the use of control devices from the classic to the use of artificial intelligence[10-11] such as neural networks and / or fuzzy logic, etc... As a result, the greenhouse growers prefer these new technologies while optimizing the investment in the field to effectively meet the supply and demand of these fresh products cheaply and widely available throughout the year.

Thin people who undergo implant insertion into the chest wall face a high risk of implant exposure to the external environment. Five months after an 8-year-old boy underwent implantable cardioverter-defibrillator (ICD) implantation in a subcutaneous pocket in the left anterolateral chest wall to manage long QT syndrome, ICD replacement became necessary owing to exposure risk from distal and lateral thinning of the ICD pocket. Pocket rupture and exposure would increase the risk of infection; therefore, we performed ICD removal and primary pocket closure. Two weeks later, a new suprafascial pocket was created, acellular dermal matrix (ADM) was attached to the inner wall to prevent ICD protrusion, and a new ICD was inserted. One year postoperatively, the ADM was engrafted, and no complications were observed. A thin subcutaneous layer increases the risk of ICD implantation complications. Inner wall strengthening with ADM can help prevent pocket rupture.

The reviews usefulness has been the aim of several research studies. However, results regarding the significance of usefulness determinants are often contradicting, thus decreasing the accuracy of reviews’ helpfulness estimation. Also, bias in user reviews attributed to differences e.g. in gender, nationality, etc., may result into misleading judgments thus diminishing reviews’ usefulness. Research is needed for sentiment analysis algorithms that incorporate bias embedded in reviews, thus improving their usefulness, readability, credibility, etc. This study utilizes fuzzy relations and fuzzy synthetic evaluation (FSE) in order to calculate reviews’ usefulness by incorporating users’ biases as expressed in terms of reviews’ articulacy and sentiment polarity. It selected and analysed 95.678 hotel user reviews from Tripadvisor, for five nationalities. The findings indicate that there are differences among nationalities. The British are most consistent in their judgments expressed in titles and review documents. The British and the Greek review titles suffice to convey any negative sentiments. The Dutch use fewer words in their reviews than the other nationalities. This study suggests that fuzzy logic captures subjectivity which is often found in reviews, and it can be used to quantify users’ behavioral differences, calculate reviews usefulness, and provide the means for developing more accurate voting systems.

Accurate prediction of the membrane potential by membrane theory is possible on the basis that the plasma membrane is selectively permeable to ions and that permeability determines the characteristics of the membrane potential. However, an experimental and artificial cell system with an impermeable membrane serving as a model plasma membrane has a non-zero membrane potential, and this potential generated across the membrane is somehow consistent with the potential characteristics predicted by the membrane theory, despite the impermeability of the membrane to ions. A long-forgotten theory, called the association-induction hypothesis (AIH), has emerged as a more plausible mechanism for generating the membrane potential than the membrane theory to explain this unexpected behavior. The AIH asserts that ion-selective membrane permeability is not necessary for the generation of the membrane potential, which is contrary to the membrane theory. Although such an idea is not easy to accept, the experimental results clearly suggest the correctness of the AIH.

In Indonesia, types of meat are still identified manually due to increasing prices for beef and buf-falo ahead of Idul Fitri. Traders mix beef with pork to thwart the beef scam. Haar wavelet and GLCM, GLCM with angles of 0°, 45°, 90°, and 135°, as well as matrices using contrast, correlation, energy, homogeneity, and entropy, are used in feature extraction. The following are the results of meat image classification testing using k-NN, Haar wavelet, and GLCM: The k-NN algorithm shows superiority in identifying fresh (99%), frozen (99%), and rotten (96%) meat texture images with the most fantastic accuracy results in every situation. Meanwhile, GLCM routinely provides good results, especially regarding the texture image of fresh meat (183.21) and rotten meat (115.79). However, despite delivering less throughput than k-NN and GLCM, Haar wavelets are still helpful, especially when dealing with fresh meat texture images (89,96).

Several series of new polymers were synthesized: binary copolyesters of vanillic (VA) and hydroxybiphenylcarboxylic (HBCA) acids, as well as ternary copolyesters additionally containing hydroxybenzoic acid (HBA) and obtained via three different ways (in solution, in melt and in solid state). The high values of logarithmic intrinsic viscosities and insolubility of several samples proved its high molecular weights. It has been shown that the use of vanillic acid leads to the production of copolyesters with a relatively high glass transition temperature (about 130°C). Thermogravimetric analysis revealed onset of weight loss temperatures of ternary copolyesters occurred at 330-350 °C, the temperature of 5% mass loss is in the range of 390-410 °C. Two-stage thermal destruction is observed for all aromatic copolyester of vanillic acid: decomposition begins with VA units at 420-480 °C, and then decomposition of more heat-resistant units demonstrated above 520 °C. The copolyesters are thermotropic and exhibit a typical nematic type of liquid crystalline order. Mechanical characteristics of copolyesters are close to those for semi-aromatic copolyesters, but are much lower than typical values for fully aromatic thermotropic polymers. Thus, vanillic acid is a mesogenic monomer suitable for the synthesis of thermotropic fully aromatic and semi-aromatic copolyester, but resulting processing temperature must not exceed 280°C.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. Among which, the fuzzy preference relation is the reasonable one to represent preference relation by a fuzzy membership function. This paper studies the Nakamura’s and Kołodziejczyk’s preference relations. Eight cases of representing different level of overlapping between two triangular fuzzy numbers are considered. We analyze the ranking behaviors of all possible combinations of decomposition and intersection of two fuzzy numbers for the Nakamura’s and Kołodziejczyk’s preference relations of these test cases. The results indicate that the decomposition and intersection can affect the fuzzy preference relations, thereby the final total order relation of fuzzy numbers.

Trans fatty acids (TFA) are a concern for public health due to their negative impact on cardiovascular health. This study aimed to assess the levels of TFA and other fatty acids in popular edible oils and fried foods commonly consumed in Tanzania. A total of 57 samples from 38 brands of edible oils and 20 samples of fried street foods and fast foods were collected in Dar es Salaam, Tanzania. Capillary gas chromatography was used to determine TFA levels, while nutritional labeling and other fatty acid classes were also evaluated. Among the analyzed edible oils, 21% exceeded the recommended TFA levels, primarily found in popular brands of margarine, industrially refined sunflower oils, animal butter, and peanut butter. Only two food items surpassed the 2% TFA limit, but a majority of the foods had high levels of saturated fatty acids and a fatty acid profile similar to palm oil. Additionally, only 22% of the edible oils provided TFA content information. These findings indicate the persistence of TFA levels beyond recommended limits and inadequate TFA nutritional labeling in Tanzanian food products. Urgent interventions are necessary to reduce TFA levels and improve nutritional labeling practices to safeguard public health.

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.

We generalize the concept of a fuzzy metric by introducing its approximating counterpart in order to make it more appropriate for the study of some problems related to words combinatorics. We establish close relations between fuzzy approximating metrics in case of special $t$-norms and approximating parametrized metrics, discuss some relations between fuzzy approximating metrics and fuzzy partial metrics as well as show some possible applications of approximating parametrized metrics in the problems of words combinatorics.

Production of electricity using hydro-kinetic tidal turbines has many challenges that must to be overcome to ensure reliable, economic and practical solutions. Energy from flowing water is converted by a system comprising: the turbine rotor blades, a gearbox, an electrical generator, control systems, power electronics, export cables, and a connection to the electricity grid. To date these have often been modelled using simulations of independent systems, lacking bi-directional, real-time, coupling. This approach leads to critical effects being missed. Turbulence in the flow, results in large velocity fluctuations around the blades, causing rapid variation in the shaft torque and generator speed, and consequently in the voltage seen by the power electronics and consequently the export power quality. The resulting poor quality power may be unacceptable to the grid. Conversely, grid frequency and voltage changes can also cause the generator speed to change, resulting in changes to the shaft speed and torque and consequently changes to the lift and drag forces acting on the blades. Clearly, fully integrated, bi-directional, models are needed. Here we present two fully coupled models which use different approaches to model the hydrodynamics of rotor blades. The first model uses Blade Element Momentum Theory (BEMT), resulting in an efficient tool for turbine designers. The second model also uses BEMT combines this with an actuator line model of the blades coupled to an unsteady computational fluid dynamics (CFD) simulation. This simulation, implemented in OpenFOAM, uses an energy balance to compute the shaft speed. Both the BEMT and CFD models are coupled to an Open Modellica model of the electro-mechanical system. Both models have been used to simulate the performance of a 1.2m diameter, scale model, of a three bladed horizontal axis tidal turbine tested in the University of Edinburgh FloWave Ocean Energy Research Facility. The turbulent flow around the blades and the mechanical-electrical variables during the stable period of operation are analysed. Time series and tabulated average values of mechanical thrust, power, torque, and rotational speed as well as electrical variables of generator power, electromagnetic torque, voltage and current are presented for the coupled system simulation. The relationship between the mechanical and electrical variables and the results from both tidal turbine approaches are discussed. Our comparison shows that while the BEMT model provides an effective design tool (leading to slightly more conservative designs), the CFD/BEMT simulations provide more accurate predictions of the blade loads which can be especially important in assessing fatigue on the blades (though at an increased computational cost).

We studied short- and long-term effects of intravitreal injection of N-methyl-D-aspartate (NMDA) on melanopsin-containing (m⁺) and non-melanopsin-containing (Brn3a⁺) retinal ganglion cells (RGCs). In adult SD-rats, the left eye received a single intravitreal injection of 5µL of 100nM NMDA. At 3 and 15 months, retinal thickness was measured in vivo using SD-OCT. Ex vivo analyses were done at 3, 7, 14 days or 15 months after damage. Whole-mounted retinas were immunolabelled for Brn3a and melanopsin, the total number of Brn3a⁺RGCs and m⁺RGCs were quantified and their topography represented. In control retinas, the mean total numbers of Brn3a⁺RGCs and m⁺RGCs were 78,903±3,572 and 2,358±144 (mean ± SD; n=10), respectively. In the NMDA injected retinas, Brn3a⁺RGCs numbers diminished to 50% and 25%, at 3 and 14 days, respectively, but there was no further loss up to 15 months. The number of immunoidentified m⁺RGCs decreased significantly at 3 days, recovered between 3-7 days and was back to normal thereafter. OCT measurements revealed a significant thinning of the left retinas at 3 and 15 months. Intravitreal injections of NMDA induce a rapid loss of 75% of Brn3a⁺RGCs, a transient downregulation of melanopsin expression but not m⁺RGC death, and a thinning of the inner retinal layers.

In this paper, we investigate the new degenerate Daehee polynomials and numbers which are called the degenerate Daehee polynomials of the second kind, and derive some new and interesting identities and properties of those polynomials.

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

The second article in the series presents the application of the Smoothed Particle Hydrodynamics (SPH) method to modelling of batch crystallisation in stirred tanks. A methodology to integrate the population balance equations (PBE) in parallel and independently from the Navier-Stokes equations is demonstrated. The benefits of the proposed methodology in terms of computational requirements, accuracy and availability of the crystal size distribution are discussed. The specific formulation of the SPH equations where the resulting system of ordinary differential equations is solved using the weighted contributions rather than numerically by solving a linear system of equations allows for massive parallelisation and a very loose coupling of the population balance and the fluid dynamics. It has been demonstrated, that the population balance equations can be solved on a Shared Memory Architecture (SMA) system using the OpenMP interface while the fluid dynamics equations being computed independently on a General Purpose Graphics Processing Unit (GPGPU) using the NVidia CUDA technology. This way, a significant portion of the computational overhead due to the large number of additional transport equations resulting from the discretisation of the population balance was removed: the SPH simulation coupled with 200 population balance equations was only 40% slower compared to SPH-only simulation. Two methods for the solution of population balance equations that preserve full crystal size distribution were implemented: discretised population balance (DPB) and method of characteristics (MOCH). The DPB equations are solved using the high-resolution finite-volume method with flux limiter and the effect of a large number of different flux limiters have been investigated. Both methods were validated using the case studies from the literature where an analytical solution can be derived. The developed models were applied to a numerical solution of coupled computational fluid dynamics and population balance equations to model a batch crystallization process. The effect of the hydrodynamics on the local temperature/supersaturation and the resulting crystal size distribution was captured and compared to the ideal mixing case. The simulation results from the DPB and MOCH methods were compared in terms of computational requirements and accuracy and MOCH selected as computationally more efficient and accurate.

The study aims to explain the different effects between the multiplication, addition, division and subtraction equations. In this sense, multiplication and addition equations develop a new element or fact, meanwhile, division equations express information within the element or fact, subtraction is the selection of element or fact. Furthermore, for a multiplication and addition equation results in the new element or fact, it is necessary to depend on specific physical concepts, without extreme alteration, as it would result in the alteration of the element or fact. It is worth highlighting the importance of fixed values ​​in the equation to describe the specific nature of the element or fact. The study makes it possible to understand open equations (without solutions) in mathematics and physics, in addition to understanding existing equations. The study makes reference to the theory of obligatory necessity and the theory of differences between elements.

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

This paper discusses a passive control issue for Nonlinear Time-Varying (NTV) systems subject to stability and attenuation performance. Based on the modeling approaches of Takagi-Sugeno (T-S) fuzzy model and the Linear Parameter-Varying (LPV) model, a Parameter-Dependent Polynomial Fuzzy (PDPF) model is constructed to represent the NTV systems. According to Parallel Distributed Compensation (PDC) concept, a parameter-dependent polynomial fuzzy controller is built to achieve robust stability and passivity of PDPF model. Furthermore, the passive theory is applied to achieve the performance constraining the disturbance effect on the PDPF systems. To develop the stability criteria, by introducing a parameter-dependent polynomial Lyapunov function, one can derive some stability conditions which belong to the term of Sum-Of-Squares (SOS) form. Based on the Lyapunov function, two stability criteria are proposed to design the corresponding PDPF controller such that the NTV system is robustly stable and passive. Finally, a numerical example is applied to demonstrate the effectiveness of the proposed stability criterion.

One of the most reliable methods of authentication used today is biometric matching. This authentication process, which is done by using biometrics information such as fingerprint, iris, face, etc. is used in many application areas. Authentication at border gates is one of these areas. However, some restrictions have been introduced to storing and using such data, especially with the General Data Protection Regulation (GDPR). The main goal of this work is to find the practical implementation of fully homomorphic encryption-based biometric matching in border controls. In this paper, we propose a biometric authentication system based on hash expansion and fully homomorphic encryption features, considering these restrictions. One of the most significant drawbacks of the homomorphic encryption method is the long execution time. We solved this problem by executing the matching algorithm in parallel manner. The proposed scheme is implemented as proof-of-concept in the SMILE, and its advantages in privacy preservation has been demonstrated.

In this article, we first defined a stronger form of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored novel types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Thereafter, we introduced novel types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-gfsc sets and discussed some topological properties of them. Finally, some novel types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

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.

Magnetorheological fluids (MRFs) are smart materials consisting of micro-scale magnetizable particles suspended in a carrier fluid. The rheological properties of a MRF can be changed from a fluid-state to a solid-state upon the application of an external magnetic field. This study reports the development of a particle-level simulation code for magnetic solid spheres moving through an incompressible Newtonian carrier fluid. The numerical algorithm is implemented within an open-source finite-volume solver coupled with an immersed boundary method (FVM-IBM) to perform fully-resolved simulations. The particulate phase of the MRF is modeled using the discrete element method (DEM). The resultant force acting on the particles due to the external magnetic field (i.e., magnetostatic polarization force) is computed based on the Clausius-Mossotti relationship. The fixed and mutual dipole magnetic models are then used to account for the magnetic (MAG) interactions between particles. Several benchmark flows were simulated using the newly-developed FVM-IBM-DEM-MAG algorithm to assess the accuracy and robustness of the calculations. First, the sedimentation of two spheres in a rectangular duct containing a Newtonian fluid is computed without the presence of an external magnetic field, mimicking the so-called drafting-kissing-tumbling (DKT) phenomenon. The numerical results obtained for the DKT case study are verified against published data from the scientific literature. Second, we activate both the magnetostatic polarization and the dipole-dipole forces and resultant torques between the spheres for the DKT case study. Next, we study the robustness of the FVM-IBM-DEM-MAG solver by computing multi-particle chaining (i.e., particle assembly) in a two-dimensional (2D) domain for area volume fractions of 20% (260 particles) and 30% (390 particles) under vertical and horizontal magnetic fields. Finally, the fourth computational experiment describes the multi-particle chaining in a three-dimensional (3D) domain allowing to study fully-resolved MRF simulations of 580 magnetic particles under vertical and horizontal magnetic fields.

During the past few years many projects and initiatives were undertaken deploying and testing automated vehicles for public transportation and logistics. However in spite of their ambition, all of these deployments stayed on the level of elaborated experimentation deploying no more than 4 maximum 5 AVs in rather small sites (few Kms of roads) and never really reached the level of large scale “commercial” deployment of transport services. The reasons for this are many, but the most important being the lack of economically viability and commercially realistic models, the lack of scalability of the business and operating models, and the lack of inclusive citizen/user centric services required for the large end-user acceptation and adoption of the solutions. In this paper, based on the experience gained in the H2020 AVENUE project, we present the missing pieces of the puzzle, ad which will be addressed in the Horizon Europe project ULTIMO.

This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent regimes: smooth turbulent regime, partial non-fully developed turbulent and fully developed rough turbulent regime. The formula follows the inflectional form of curves as suggested in Nikuradse’s experiment rather than monotonic shape proposed by Colebrook and White. The composition of the proposed unified formula consists of switching functions and of the interchangeable formulas for laminar, smooth turbulent and fully rough turbulent flow. The proposed switching functions provide a smooth and a computationally cheap transition among hydraulic regimes. Thus, the here presented formulation represents a coherent hydraulic model suitable for engineering use. The model is compared to existing literature models, and shows smooth and computationally cheap transitions among hydraulic regimes.

The feasibility of using full ion kinetics, instead of gyrokinetics, in simulating low-frequency Ion-Temperature-Gradient (ITG) instabilities in tokamaks has recently been demonstrated by Sturdevant et al. [Physics of Plasmas 24, 081207 (2017)]. In that work, a variational integrator was developed to integrate the full orbits of ions in toroidal geometry, which proved to be accurate in capturing both the short-time scale cyclotron motion and long time scale drift motion. The present work extends that work in three aspects. First, we implement a relatively simple full orbit integrator, the Boris integrator, and demonstrate that the accuracy of this integrator is also sufficient for simulation of ITG instabilities. Second, the equilibrium magnetic configuration is extended to general toroidal configuration specified numerically, enabling simulation of realistic equilibria reconstructed from tokamak experiments. Third, we extend that work to the nonlinear regime and investigate the nonlinear saturation of ITG instabilities. To verify the new numerical implementation of the orbit integrator and magnetic configuration, the linear electrostatic ITG frequency and growth rate are compared with those given in Sturdevant's work and good agreement is found.

A key concern in an ageing society is citizens’ mobility. As populations age, disability impairments can affect active ageing, health-related wellbeing and quality of life. In this paper, we present the on-going research project SeriousGiggle—Game-based learning for triggering active ageing. Its goal is to assess the potential of game-based learning for active ageing and contribute to a sense of wellbeing and quality of life. It also seeks to improve the mobility of older adults by creating a set of journey plans with route guidance that are rated in terms of safety, community support, environment and age-friendliness. Drawn on our field work with 33 co-designers, 40 end users and 10 semi-structured interviews with Subject Matter Experts, we identify a set of necessary design requirements to an Age-friendly Playable City. This study recommends the use of gamification and playful techniques to engage the end-users to provide information about local traffic signs, pavement conditions, wayfinding and, therefore, help to create route guidance and walking assistance that are personalized to older adults’ context in terms of location, travel fitness, mobility impairments and motivations.

In this paper, we study the problem of controllability of impulsive neutral evolution integrodifferential equations with state dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii's fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.

We propose a new Mamdani fuzzy rule-based system in which the fuzzy sets in the antecedents and consequents are assigned in a discrete set of points and approximated by using the extended inverse fuzzy transforms, whose components are calculated by verifying that the dataset is sufficiently dense with respect to the uniform fuzzy partition. We test our system in the problem of spatial analysis consisting in the evaluation of the liveability of residential housings in all the municipalities of the district of Naples (Italy). Comparisons are done with the results obtained by using trapezoidal fuzzy numbers in the fuzzy rules.

The well-known equations for the process of powder compaction (PCP) in a rigid die published over the period from the beginning of the last century to the present are considered. Most of the considered equations are converted into the dependence of the densification pressure on the relative density. The equations were analyzed and their ability to describe PCP was assessed by determining the coefficient of determination when approximating experimental data on the compaction of various powders. It is shown that most of the equations contain two constants, the values of which are determined by fitting the mathematical dependence to the experimental curve. Such equations are able to describe PCP with high accuracy in the case of compaction of powders up to a relative density of 0.9-0.95. It is also shown that different equations can describe PCP in the range of density change from the initial to 0.9 with the same and sufficiently high accuracy, but when the process of compaction is extrapolated to higher values of density, the curves diverge. This indicates the importance of equations that can unambiguously describe PCP to a relative density equal to or close to 1.0. For an adequate description of PCP to a relative density greater than 0.95, equations containing three or four constants have proven themselves well.

The paper is considering of the basic differential equations of hydrodynamics: the equation of continuity and motion. On the simplest example, it is shown that the equation of continuity in a system with the equation of motion leads to contradictions and erroneous results of modeling. A more correct form of the continuity equation is described. It is shown that the equations of motion can be written in the form of complete differentials. Three possible integral forms of the equations of motion are presented. As a conclusion, the existence and smoothness of the solution of the Navier-Stokes equations are considered.

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. This involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We also state Abelian results which yield asymptotic formulas for weighted summatory function from that for the original summatory function

Orchids totalling close to 4000 species in Malaysia are one of the most diverse and most widespread family here had gained momentum in recognition among policy makers and guardians of the forest as one of the profiles that fit and can benefit plant conservation on a broad scale in recent years. Listed not only as conservation indicator but also as priority germplasm for sustainable floriculture industry in the country, a milestone that could safeguard wild orchids from verge of extinction in the natural habitat. Through our 30 years of studying orchids in the wild, we understand more about the distribution, rarity, threats and extinction of orchids than ever before, and we have the scientific tools to address many of the problems, yet many species face daily threats including habitat loss and unsustainable exploitation mainly via Internet trade. Prior to executing workable conservation plan, various research institutions working closely with Forestry Departments in Malaysia to first inventory and document the orchid species richness in the country. Selangor, Sarawak and Perlis Forestry Departments in collaboration with UPM have published seven orchid books that cover various habitat types. Selangor Forestry Department is leading on publishing biodiversity data in form of books for its various ecotourism’s sites and State Parks, and had published two books on orchids. Sarawak state has published one on the limestone orchids, and Perlis is the first to embark on the feat published one in 2010 and currently preparing a new book that includes other flagship wild flowers. Realizing the importance of documenting its biodiversity wealth, Malaysia has developed an information system that would be a one-stop retrieval point or repository for biodiversity facts and as a part of the commitments to CBD to facilitate reporting and the transfer of biological diversity and conservation-related information both nationally and internationally.

Maxwell’s equations are valid only for a stationary observation point, therefore, to adequately describe real processes so far we have had to move to a moving reference frame. This paper presents the equations of electrodynamics for the moving observation point, it is shown that plane and spherical electromagnetic waves are their solutions, while the spherical wave propagates only outward, which cannot be said about Maxwell’s equations. The fields of uniformly moving charges are also solutions of the equations. Now there is no need to move to a moving reference frame, to use four-dimensional space and covariant form of equations. The question of finding a universal form of the equations that allows a solution in the form of the field of an arbitrarily moving charge remains open. This raises the question of the existence of a two-parameter group of transformations of electromagnetic fields along with the known one-parameter group has been posed. The phenomena derived from the equations, which make an additional contribution to the phase overrun in the Aharonov-Bohm effect are considered. The equation of motion of a charged particle in an electromagnetic field without simplifying approximations is considered, which allows us to take into account the radiation effects. It is shown that the fields in a moving observation point depend on its velocity and acceleration. In particular, although in a constant uniform electric field a force qE acts on a motionless charged particle, but on the same motionless but not fixed particle the force 4/3qE acts already, because it has a nonzero acceleration and the electric field at this point is larger. As the speed increases, the field decreases, and when it reaches the speed of light, when the particle stops accelerating, the force again becomes equal to qE The principle of operation of an unconventional alternator in a constant electric field and its corresponding engine, as well as new types of direct and impulse current generators, predicted by the equations, are described.

The missing link between cross-sectoral resource utilisation and management, and full-scale adoption of the water-energy-food (WEF) nexus has been lack of analytical tools to support policy and decision-making. This paper defined WEF nexus sustainability indicators and developed a methodology to calculate composite indices to facilitate WEF nexus performance, monitoring and evaluation. WEF nexus indicators were integrated through the Analytic Hierarchy Process (AHP) in a multi-criteria decision-making (MCDM). Data were normalised to determine composite indices. The method established quantitative relationships among WEF nexus sectors to indicate resource utilisation and performance over time, using South Africa as a case study. A spider graph of normalised indices was used to illustrate WEF nexus indicator performance and inter-relationships, providing a synopsis of the level of interactions and inter-connectedness of WEF nexus sectors. The shape of the spider graph is determined by the level of the interdependencies and interactions among the WEF nexus sectors, whose management is viewed either as sustainable or unsustainable depending on the classification of the developed integrated index. The spider graph produced for South Africa shows an over emphasis on food self-sufficiency and water productivity at the expense of other sectors, which results from the sectoral approach in resource management. Although the calculated integrated index of 0.203 for South Africa is classified as lowly sustainable, the emphasis is on the quantitative relationships among the indicators and on how to improve them to achieve sustainability. The developed method provides evidence to decision makers, indicating priority areas for intervention. The analytical model is another niche area for the WEF nexus, as it is now capable to evaluate synergies and trade-offs in a holistic way to improve efficiency and productivity in resource use and management for sustainable development.

With the continuous development of deep learning, the application of object detection based on deep neural network in the coal mine has been expanding. Simultaneously, as the production applications demand higher recognition accuracy, most research chooses to enlarge the depth and parameters of the network to improve accuracy. However, due to the limited computing resources in the coal mining face, it is challenging to meet the computation demands of a large number of hardware resources. Therefore, this paper proposes a lightweight object detection algorithm designed specifically for coal mining face, referred to as CM-YOLOv8. The algorithm introduces adaptive predefined anchor boxes tailored to the coal mining face dataset to enhance the detection performance of various targets. Simultaneously, a pruning method based on the L1 norm is designed, significantly compressing the model's computation and parameter volume without compromising accuracy. The proposed algorithm is validated on the coal mining dataset DsLMF+, achieving a compression rate of 40% on the model volume with less than a 1% drop in accuracy. Comparative analysis with other existing algorithms demonstrates its efficiency and practicality in coal mining scenarios. The experiments confirm that CM-YOLOv8 significantly reduces the model's computational requirements and volume while maintaining high accuracy.

Efficient member revocation and strong security against attacks are prominent requirements in group signature schemes. Among the revocation approaches Verifier-local revocation is the most flexible and efficient method since it requires to inform only the verifiers regarding the revoked members. The verifier-local revocation technique uses a token system to manage members’ status. However, the existing group signature schemes with verifier-local revocability rely on weaker security. On the other hand, existing static group signature schemes rely on a stronger security notion called, full-anonymity. Achieving the full-anonymity for group signature schemes with verifier-local revocation is a quite challenging task. This paper aims to obtain stronger security for the lattice-based group signature schemes with verifier-local revocability, which is closer to the full-anonymity. Moreover, this paper delivers a new key-generation method which outputs revocation tokens without deriving from the users’ signing keys. By applying the tracing algorithm given in group signature schemes for static groups, this paper also outputs an efficient tracing mechanism. Thus, we deliver a new group signature scheme with verifier-local revocation that satisfies a stronger security from lattices.

In traditional finance, option prices are typically calculated using crisp sets of variables. However, in a proposed new approach, the assumption is made that these parameters have a degree of fuzziness or uncertainty associated with them. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. To determine the belief degree associated with a particular option price, an interpolation search algorithm was proposed recently[1]. Interpolation is a mathematical technique used to estimate values between known data points. In this case, the algorithm is applied to determine the belief degree associated with a specific option price within the range of possible prices. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. It allows them to consider their risk preferences and beliefs about the uncertain parameters when selecting an option price. In this paper, we will review a unified framework for combining fractional Brownian motion with fuzzy processes and obtain a joint measure space. We start by constructing a product measure space that captures the randomness and fuzziness inherent in the respective processes. We begin with the usual Kolmogorov filtered probability space (Ω, F, ℙ), where ℙ represents the probability measure, Ω is the set of all possible outcomes or states that a random process can take and {Ft, t ∈ [0, T]} is an information filtration. We will review the work of Merton (1976) on option pricing when the underlying stock returns have jumps [2] and expand it to fuzzy fractional processes.

Sentiment analysis to characterize properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy transform to capture stylized facts and mutual connections between time series having different nature. Six years of daily Bitcoin Prices and Google Trends are analyzed in order to establish new perspectives in the management of their dynamics.

Decomposed fuzzy sets are the resent extension of intuitionistic fuzzy sets by incorporating functional and dysfunctional points of views to the definition of membership functions. This paper extends the Technique of Order Preference Similarity to the Ideal Solution (TOPSIS) method to the Decomposed Fuzzy TOPSIS (DF TOPSIS) method and applies it to a multi-criteria risk-based supplier selection problem under fuzziness. DF TOPSIS involves finding a positive ideal solution and a negative ideal solution and measuring the distance of each alternative to these solutions. The final ranking is obtained based on the proportion of distances to the positive and negative ideal solutions. The developed DF TOPSIS method incorporates the accuracy and consistency of expert judgments, enhancing the decision-making process. A sensitivity analysis is also presented in order to show the robustness of the obtained rankings by DF TOPSIS.

The transformation of the states of polarization of electromagnetic waves that interact with polarimetrically linear media can be represented by means of the associated Mueller matrix. A global measure of the ability of a linear medium to modify the states of polarization of incident waves, due to any combination of enpolarizing, depolarizing and retarding properties, is introduced as a distance of the Mueller matrix to the identity matrix. This new descriptor, called the polarizing power, is applicable to any Mueller matrix and can be expressed as a function of the degree of polarimetric purity and the trace of the Mueller matrix. The graphical representation of the feasible values of the polarizing power provides a general view of its main peculiarities and features. The values of the polarizing power for several typical devices are analyzed.

In this paper after introducing a model of binary data matrix (BDM) for physical parameters of an evolving system (of particles), we develop a Hilbert space as an ambient space to derive induced metric tensor on embedded parametric manifold identified by associated joint probabilities of particles observables (parameters). Parameter manifold assumed as space-like hypersurface evolving along time axis, an approach that resembles 3+1 formalism of ADM and numerical relativity. We show the relation of endowed metric with related density matrix. Identification of system density matrix by this metric tensor, leads to the equivalence of quantum Liouville equation and metric compatibility condition while covariant derivative of metric tensor has been calculated respect to Wick rotated time or spatial coordinates. After deriving a formula for expected energy per particles, we prove the equality of this expected energy with local scalar curvature of related manifold. We show the compatibility of BDM model with Hamilton-Jacobi formalism and canonical forms. On the basis of the model, I derive the Ricci flow like dynamics as the governing dynamics and subsequently derive the action of BDM model and Einstein field equations. Given examples clarify the compatibility of the results with well-known principles such as equipartition energy principle and Landauer’s principle. This model provides a background for geometrization of quantum mechanics compatible with curved manifolds and information geometry. Finally, we conclude a “bit density principle” which predicts the Planck equation, De Broglie wave particle relation, , Beckenstein bound and Bremermann limit.

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

In this research paper an algorithm for the derivation of methods based on theorems and axioms of fuzzy logic is presented, analyzed and applied. This new proposed procedure generates fuzzy methods and evaluates the value of fuzzy propositions through fuzzy implication. The new implications of the family should satisfy a number of axioms. Also, we denote the conditions in order to satisfy the maximum number of axioms. Moreover, authors state and prove theorems focusing on fuzzy implication, observing the rule: the fuzzy function of fuzzy implication is strong and that lead to fuzzy negation. In addition, the optimal number of repetitions is calculated according to the expected truth value. The formulas produced are verified through the use of temperature and humidity values over a certain period of time and in a certain geographical area in Greece. The basic steps of the methodology are the fuzzification of the data given ​​using four membership degree functions and the application of the membership degrees of temperature and humidity values on a new type of fuzzy implication. Finally, we observed that the isosceles trapezium gave the best results and the type of fuzzy implication can be effectively applied.

The major arboviruses belong mainly to the families Bunyaviridae, Togaviridae, and Flaviviridae amongst which chikungunya virus and dengue virus have emerged as a global public health problem. The main objective of the study was to develop a specific, sensitive, and cost-effective molecular multiplex RT-PCR and RT-qPCR assay for the rapid and simultaneous detection of CHIKV and the four serotypes of DENV for arbovirus surveillance. Specific primers of all virus were designed, one step multiplex RT-PCR (mRT-PCR) and RT-qPCR (mRT-qPCR) was developed using reference strains of CHIKV and DENV serotypes. The specificity of the test for all the viruses was confirmed by sequencing. The standard curves showed a high correlation coefficient, R2= 0.99, for DENV-2 and DENV-3; R2= 0.98, for DENV-4 and CHIKV; R2= 0.93, for DENV-1. The limits of detection were calculated to be 10-2 copies/µL for all viruses. The specificity and sensitivity of the newly developed mRT-PCR and mRT-qPCR were validated using positive serum samples collected in India and Burkina Faso. The sensitivity of mRT-PCR and mRT-qPCR are 91%, and 100% respectively. The specificity of both assays was 100% specific. mRT-PCR and mRT-qPCR assays are low cost and a combination of both will be a useful tool for arbovirus surveillance.

Quantitative and qualitative fuzzy measures have been proposed to hesitant fuzzy sets (HFSs) from different points. However, few of the existing HFSs fuzzy measures refer to the grey relational analysis (GRA) theory. Actually, the GRA theory is very useful in the fuzzy measure domain, which has been developed for such the intuitionistic fuzzy sets. Therefore, in this paper, we apply the GRA theory to the HFSs and interval-valued hesitant fuzzy sets (IVHFS) domain. We propose the HFSs grey relational degree, HFSs slope grey relational degree, HFSs synthetic grey relational degree and IVHFSs grey relational degree, which describe the closeness, the variation tendency and both the closeness and variation tendency of HFSs and closeness of IVHFSs, respectively, greatly enriching the fuzzy measures of HFSs. Furthermore, with the help of the TOPSIS method, we develop the grey relational based MADM methodology to solve the HFSs and IVHFSs MADM problems. Finally, combined with two practical MADM examples about energy policy selection with HFSs information and emergency management evaluation with IVHFSs information, we obtain the most desirable decision results, and compared with the previous methods, the validity, effectiveness and accuracy of the proposed grey relational degree for HFSs and IVHFSs are demonstrated in detail.

Despite being small and simple structured in comparison to their victims, virus particles have the potential to harm severly and even kill highly developed species such as humans. To face upcoming virus pandemics, detailed quantitative biophysical understanding of intracellular virus replication mechanisms is inevitable. Unveiling the relationship of form and function might allow to determine putative attack points relevant for the systematic development of direct antiviral agents (DAA) and potent vaccines. Biophysical investigations of spatio-temporal dynamics of intracellular virus replication so far are rare. We are developing a framework to allow for fully spatio-temporal resolved virus replication dynamics simulations based on partial differential equations models (PDE) and evaluated with advanced numerical mathematical methods on leading supercomputers. This study presents an advanced highly nonlinear model of the genome replication cycle of a specific RNA virus, the Hepatitis C virus (HCV). The diffusion-reaction model mimics the interplay of the major components of the viral RNA (vRNA) cycle, namely non structural viral proteins (NSP), vRNA and a generic host factor. Technically, we couple surface PDEs (sufPDEs) on the 3D embedded 2D Endoplasmatic Reticulum (ER) manifold with PDEs in the 3D membranous web (MW) and cytosol volume. (The MWs are the replication factories growing on the ER induced by NSPs.) The sufPDE/PDE model is evaluated at realistic reconstructed cell geometries which are based on experimental data. The simulations couple the effects of NSPs which are restricted to the ER surface with effects appearing in the volume. The volume effects include the host factor supply from the cytosol and the MW dynamics. Special emphasis is put to the exchange of components between ER surface, MWs and cytosol volume. As the vRNA spatial properties are not fully understood so far in experiment, the model allows for vRNA both restricted to the ER and moving in the cytosol. The visualization of the simulation resembles a look into some sort of fully 3D resolved “in silico microscopes” to mirror and complement in vitro / in vivo experiments for the intracellular vRNA cycle dynamics. The output data are quantitatively consistent with experimental data and provoke advanced experimental studies to validate the model.

Femur length (FL) is a biometric measurement of ultrasound images used to identify the growth patterns and abnormalities of the foetus. Automatic segmentation of FL can improve the efficiency and convenience of inexperienced users. The femur region in a low-cost ultrasound image is a small area with low contrast intensity compared with the non-femur region. This study proposed a fully automated framework for segmenting and measuring the FL in a portable ultrasound image. We utilized statistical modeling, employing Gaussian mixture functions for thresholding to extract the femur area from the background. We also used the localizing region-based active contour method to segment the femur region accurately. We also proposed a refinement step in this framework to obtain a more accurate femur area in the ultrasound image. Because the length and position of the femur are the main factors affecting foetal biometric measurement accuracy, we not only evaluated segmentation results using region-based methods, such as sensitivity, specificity, and dice similarity. We also applied the FL measurement approach to evaluate the angle and length accuracy relative to the ground truth. In terms of region-based segmentation performance, the proposed method provided the best average performance with a sensitivity of 0.78, specificity of 0.87, and dice similarity of 0.81. For FL measurement performance, the proposed framework achieved an average angle accuracy of 0.99, distance accuracy of 0.88, and length accuracy of 0.93.

This document presents the design and manufacture of a reflectarray (RA) antenna for the Ku-band, based on a fully-metallic 3D architecture. The reflectarray unit cell is formed by a square-shaped waveguide section ended in a short circuit, that is the reflectarray back ground plane. Each cell has the ability of configuring the phase of its own reflected field by means of resonators perforated on the walls of the cell waveguide section. The resonator-based waveguide cell introduces the 3D character to the design. The geometry of the resonators and its size variation introduces the phase behaviour of each cell, conforming the radiation pattern of the reflectarray. This design explores the potential of phase value truncation (6 states and 2 states), and demonstrates that proper pattern results can be obtained with this phase truncation.

Microwave Power Modules (MPM) are high power devices largely used for radar applications. An MPM is a hybrid combination of a Solid-State Power Amplifier (SSPA) as a driver and a Traveling wave tube amplifier (TWT) as the final high power stage. Power equalizer is often used to flat the TWT output power gain owing to its big gain fluctuations in the operating frequency range. This paper deals with an optimal design and development of a fully-coaxial easy-tunable power equalizer for an X-band MPM. The structure utilizes a coaxial waveguide as the main transmission line and a coaxial cavity loaded with absorbing material as the resonant unit. A sensitivity analysis of the coaxial cavity length, the thickness of the absorbing disc and inserted depth of the probe on the attenuation amplitude and resonant frequency is carried out. The transmission characteristic curves and the voltage standing wave ratio curves show a good compromise in terms of transferred power and adaptive matching impedance at the input and output ports. The measured results show that the equalization curve meets the requirements well and prove that this structure is practical and effective.

This paper proposes a novel micro-grid structure, which can operate fully-autonomously with inherent seamless switching. It can operate independently in both grid-connected and islanded mode as a self-governed entity without relying on the utility grid. An AC/DC/AC converter is employed as the interface between the micro-grid and the utility grid, which enables the two entities to have different voltages in grid-connected mode. Seamless switching between operation modes can be achieved naturally. The micro-grid is regulated to exchange predefined amount of power with the utility grid in grid-connected mode. This will benefit the power dispatching algorithm of the power system. The predefined power is estimated based on power forecasting of local renewable generations and loads with consideration of the Sate of Charge (SOC) of the battery, and is updated and broadcasted every certain period. A small scale AC micro-grid with a rotating generator, battery storage and solar arrays etc. is built for investigation. Matlab/Simulink results are provided to validate the robustness and flexibility of proposed micro-grid and its operation strategy.

In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.

The ordinary continuity equation relating the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The horizontal and transverse currents and the densities associated with them are found to be coupled to each other. Each of these quantities are found to obey a wave equation traveling at the velocity of light in vacuum. London's equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London's equations are symmetric and are shown to be dual to each other. It is shown that London's equations are Maxwell's equations with massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

In this paper, we define Tetranacci and Tetranacci-Lucas matrix sequences and investigate their properties.

Hydrogels can be considered as mimics of extracellular matrix (ECM).Cytoskeleton through integrins is connected with ECM and cytoskeleton tension depends on ECM stiffness.A number of age-related diseases depend on cellular processes related with cytoskeleton function.Some examples of cancer initiation and progression and heart disease in relationship with ECM stiffness has been analysed.Incorporation of rigid particles in ECM can increase ECM stifness and to promote formation of internal residual stresses. Water migration, changes of water binding energy to biomactomolecules, changes of the state of water from tightly bound water to free and loosely bound water changes stiffness of ECM. Risks related with rigid particles incorporation into ECM have been also iscussed.

Cells actively sense differences in topology, matrix elasticity and protein composition of the extracellular microenvironment and adapt their function and morphology. In this study, we focus on the cross-talk between matrix stiffness and protein coating density that regulate morphology and proliferation dynamics of single myocytes. For this, C2C12 myocytes were monitored on L-DOPA functionalized hydrogels of 22 different elasticity and fibronectin density compositions. Static images were recorded and statistically analyzed to determine morphological differences and to identify the optimized extracellular matrix (ECM). Using that information, selected ECMs were used to study the dynamics before and after cell proliferation by statistical comparison of distinct cell states. We observed a fibronectin density independent increase of the projected cell area until 12 kPa. Additionally, changes in the fibronectin density led to an area optimum at about 2.6 μg/cm, which was confirmed by an independent F-actin analysis, revealing a maximum actin filament to cell area ratio of 7.5 %. The proliferation evaluation showed an opposite correlation between cell spreading duration and speed to the matrix elasticity and protein density, which did not affect the cell cycle duration. In summary, we identified an optimized ECM composition, while independent matrix properties regulate distinct cell characteristics.

The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as "Kannan-graph-fuzzy contraction." This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

Bonchev and Trinajstic defined two distance based entropy measures to measure the molecular branching of molecular graphs in 1977 [Information theory, distance matrix, and molecular branching, J. Chem. Phys., 38 (1977), 4517–4533]. In this paper we use these entropy measures which are based on distance matrices of graphs. The first one is based on distribution of distances in distance matrix and the second one is based on distribution of distances in upper triangular submatrix. We obtain the two entropy measures of paths, stars, complete graphs, cycles and complete bipartite graphs. Finally we obtain the minimal trees with respect to these entropy measures with fixed diameter.

The lab-on-a-chip concept, enabled by microfluidic technology, promises the integration of multi-ple discrete laboratory techniques into a miniaturised system. Research into microfluidics has generally focused on the development of individual elements of the total system (often with rela-tively limited functionality), without full consideration for integration into a complete fully opti-mised and miniaturised system. Typically, the operation of many of the reported lab-on-a-chip devices is dependent on the support of a laboratory framework. In this paper, a demonstrator platform for routine laboratory analysis is designed and built, which fully integrates a number of technologies into a single device with multiple domains such as fluidics, electronics, pneumatics, hydraulics, and photonics. This facilitates the delivery of breakthroughs in research, by incorpo-rating all physical requirements into a single device. To highlight this proposed approach, this demonstrator microsystem acts as a fully integrated biochemical assay reaction system. The re-sulting design determines enzyme kinetics in an automated process and combines reservoirs, three-dimensional fluidic channels, optical sensing, and electronics in a low-cost, low-power and portable package.

Given a fuzzy normed space $ \left( X,N \right) $‎, ‎we will introduce the notion of fuzzy near best approximation within a relative distance $ \rho \geq 0 $‎. ‎Some basic properties are characterized and also many examples for illustration are presented‎.

In this paper, the concept of fuzzy locally convex spaces generated by a family of fuzzy seminorms is introduced. We prove that a Minkowski functional of zero neighborhoods generates a seminorm and finally deduce that the topology generated by the family of seminorms coincides with that of the Minkowski functional.

The aim of this expository article is to present recent developments in the centuries-old discussion on the interrelations between several types of domination in graphs. However, the novelty even more prominent in the newly discovered simplified presentations of several older results. Domination can be seen as arising from real-world application and extracting classical results as first described by this article.The main part of this article, concerning a new domination and older one, is presented in a narrative that answers two classical questions: (i) To what extend must closing set be dominating? (ii) How strong is the assumption of domination of a closing set? In a addition, we give an overview of the results concerning domination. The problem asks how small can a subset of vertices be and contain no edges or, more generally how can small a subset of vertices be and contain other ones. Our work was as elegant as it was unexpected being a departure from the tried and true methods of this theory that had dominated the field for one fifth a century. This expository article covers all previous definitions. The inability of previous definitions in solving even one case of real-world problems due to the lack of simultaneous attentions to the worthy both of vertices and edges causing us to make the new one. The concept of domination in a variety of graphs models such as crisp, weighted and fuzzy, has been in a spotlight. We turn our attention to sets of vertices in a fuzzy graph that are so close to all vertices, in a variety of ways, and study minimum such sets and their cardinality. A natural way to introduce and motivate our subject is to view it as a real-world problem. In its most elementary form, we consider the problem of reducing waste of time in transport planning. Our goal here is to first describe the previous definitions and the results, and then to provide an overview of the flows ideas in their articles. The final outcome of this article is twofold: (i) Solving the problem of reducing waste of time in transport planning at static state; (ii) Solving and having a gentle discussions on problem of reducing waste of time in transport planning at dynamic state. Finally, we discuss the results concerning holding domination that are independent of fuzzy graphs. We close with a list of currently open problems related to this subject. Most of our exposition assumes only familiarity with basic linear algebra, polynomials, fuzzy graph theory and graph theory.

We introduce a new variation on the domination theme which we call vertex domination as reducing waste of time in transportation planning and optimization of transport routes. We determine the vertex domination number $\gamma_v$ for several classes of fuzzy graphs. The bounds is obtained for it. In fuzzy graphs, monotone decreasing property and monotone increasing property are introduced. We prove both of the vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for vertex domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. The relationship between several classes of operations on fuzzy graphs with the vertex domination number of them is studied. Finally, we discuss about vertex dominating set of a fuzzy tree by using the bridges and $\alpha$-strong edges equivalence.

The research paper provides a mathematical framework for understanding phase shift in wave phenomena, bridging theoretical foundations with real-world applications. It emphasizes the importance of phase shift in physics and engineering, particularly in fields like telecommunications and acoustics. Key equations are introduced to explain phase angle, time delay, frequency, and wavelength relationships. The study also introduces the concept of time distortion due to a 1° phase shift, crucial for precise time measurements in precision instruments. The research also addresses infinitesimal wave energy loss related to phase shift, enriching our understanding of wave behavior, and impacting scientific and engineering disciplines.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

Motivated by the intriguing discovery of $X(6900)$ by LHCb Collaboration, we undertake a comprehensive study of the $s\bar{s}s\bar{s}$ tetraquark system in positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, diquark-antidiquark ($ss$-$\bar{s}\bar{s}$) structure and meson-meson ($s\bar{s}$-$s\bar{s}$)strcuture, encompassing all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with $J^P=0^{+}$, namely $R(0,2150)$ and $R(0,2915)$, as well as a resonant state with $J^P=1^{+}$ denoted as $R(1,2950)$, and a resonant state with $J^P=2^{+}$ denoted as $R(2,2850)$, utilizing the real-scaling method. Through a comparison of their energies and widths, we propose that $R(0,2915)$ and $R(1,2950)$ may share characteristics with $X(6900)$, while $R(0,2150)$ could be a promising experimental candidate for $f_0(2100)$. We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.

Early detection improves prognosis in pancreatic ductal adenocarcinoma (PDAC) but is challenging as lesions are often small and poorly defined on contrast-enhanced computed tomography scans (CE-CT). Deep learning can facilitate PDAC diagnosis, however current models still fail to identify small (&lt;2cm) lesions. In this study, state-of-the-art deep learning models were used to develop an automatic framework for PDAC detection, focusing on small lesions. Additionally, the impact of integrating surrounding anatomy was investigated. CE-CT scans from a cohort of 119 pathology-proven PDAC patients and a cohort of 123 patients without PDAC were used to train a nnUnet for automatic lesion detection and segmentation (nnUnet_T). Two additional nnUnets were trained to investigate the impact of anatomy integration: (1) segmenting the pancreas and tumor (nnUnet_TP), (2) segmenting the pancreas, tumor, and multiple surrounding anatomical structures (nnUnet_MS). An external, publicly available test set was used to compare the performance of the three networks. The nnUnet_MS achieved the best performance, with an area under the receiver operating characteristic curve of 0.91 for the whole test set and 0.88 for tumors &lt;2cm, showing that state-of-the-art deep learning can detect small PDAC and benefits from anatomy information.

The development of printing technologies has enabled the realization of electric circuit fabrication on flexible substrate. However, the current technique remains restricted to single-layer patterning. In this paper, we demonstrate a fully solution-processable patterning approach for multi-layer circuits using a combined method of laser sintering and ablation. Selective laser sintering of silver (Ag) nanoparticle-based ink is applied to make conductive patterns on a heat-sensitive substrate and insulating layer. The laser beam path and irradiation fluence are controlled to create circuit patterns for flexible electronics. Microvia drilling using femtosecond laser through the polyvinylphenol-film insulating layer by laser ablation, as well as sequential coating of Ag ink and laser sintering, achieves an interlayer interconnection between multi-layer circuits. The dimension of microvia is determined by a sophisticated adjustment of laser focal position and intensity. Based on these methods, the flexible electronic circuit with chip-size-package light-emitting diodes was successfully fabricated and demonstrated with functional operations.

This work is mainly focused on improving the differential evolution algorithm with the utilization of shadowed and general type 2 fuzzy systems to dynamically adapt one of the parameters of the evolutionary method. In this case, the mutation parameter is dynamically moved during the evolution process by using a shadowed and general type-2 fuzzy systems. The main idea of this work is to make a performance comparison between using shadowed and general type 2 fuzzy systems as controllers of the mutation parameter in differential evolution. The performance is compared with the problem of optimizing fuzzy controllers for a D.C. Motor. Simulation results show that general type-2 fuzzy systems are better when higher levels of noise are considered in the controller.

Matrix metalloproteinases (MMPs) have been demonstrated to have both detrimental and protective functions in inflammatory diseases. Several MMP inhibitors, with the exception of Periostat®, have failed in Phase III clinical trials. As an alternative strategy, recent efforts have been focussed on the development of more selective inhibitors or targeting other domains than their active sites (e.g., exosites, ectosites) through specific small molecule inhibitors or monoclonal antibodies. Here, we present some examples that aim to better understand the mechanisms of conformational changes/allosteric control of MMPs functions. In addition to MMP inhibitors, we discuss unbiased global approaches such as proteomics and N-terminomics to identify new MMP substrates and achieve a better understanding of the roles of these proteases in diseases.

The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

The paper considers the physical consequences of bimetric geodesically (pro jectively) invariant equations of gravitation. The correct expression for the energy- impulse tensor of the gravitational field is obtained and with its help the key role of the gravitational defect of mass-energy for the energy of the newborn universe is shown..

Most fully developed galaxies have vivid spiral structure, but the formation and evolution of spiral structure is still a mystery that is not fully understood in astrophysics. We find that the currently used equations of galactic dynamics contain some unreasonable components. In this paper, the following three working assumptions are introduced to simplify the galactic structural equations. 1. In the research of large-scale structure, the retarded potential of the gravitational field should be taken into account. The propagating time of the gravitational field from center to border is longer than the revolution periods of the stars near the center of galaxy. Newton's gravitational potential is unreasonable for such case, and the weak field and low velocity approximation of Einstein's field equation should be adopted. 2. The stars in a fully developed galaxy should be zero-pressure and inviscid fluid, and the equation of motion is different from that of ordinary continuum mechanics. Stars move along geodesics. 3. The structure of the galaxy is only related to the total mass density distribution. The equation of state of dark halo is different from that of ordinary luminous interstellar matter, so their trajectories are also very different. Dark halo and ordinary matter in galaxy are automatically separated. The total mass density distribution can be presupposed according to the observation data, and then it can be determined by comparing the solution of the equations with the observed data. These assumptions and treatments are supported by theory and observation. The variables of the equations of simplified galactic dynamics are separated from each other, and the equations are well-posed and can be solved according to a definite procedure. Therefore, this simplified dynamic equation system provides a more reasonable and practical framework for the further study of galactic structure, and can solve many practical problems. Besides, it is closely related to the study of dark energy and dark matter.

A hybrid fuzzy MADM method is proposed in this paper for evaluating airline service quality. Fuzzy set theory is used since it helps in measuring the ambiguity of concepts associated with human being’s subjective judgment. After reviewing service quality evaluation models especially in airline industry, SSQAI model was adopted as a construct for evaluating airline service quality in Iran. Fuzzy DEMATEL was applied to determine the degree of influence and impact of criteria on each other and extract cause and effect relations between them that helped in ranking criteria based on degree of relationship. Then, ANP network map was constructed based on the relation map generated from Fuzzy DEMATEL analysis. Fuzzy ANP approach assisted in prioritizing criteria based on the need for improvement and enabled in a more accurate measurement in decision making process taking the advantage of using linguistic variables. Fuzzy DEMATEL results demonstrates that expertise, Problem-solving, and conduct has the most influence on other factors and in opposite Valence, Waiting Time, Comfort are the factors which get the most impact from other factors and according to Fuzzy ANP analysis Valence, Convenience, Problem-solving, and Safety&Security are the factors with most priorities that need improvement.

A multiscale modeling concept for numerical simulation of multiphysics turbulent flow utilizing map-based advection is described. The approach is outlined with emphasis on its theoretical foundations and physical interpretations in order to establish the context for subsequent presentation of the associated numerical algorithms and the results of validation studies. The model formulation is a synthesis of existing methods, modified and extended in order to obtain a qualitatively new capability. The salient feature of the approach is that time advancement of the flow is fully resolved both spatially and temporally, albeit with modeled advancement processes restricted to one spatial dimension. This one-dimensional advancement is the basis of a bottom-up modeling approach in which three-dimensional space is discretized into under-resolved mesh cells, each of which contains an instantiation of the modeled one-dimensional advancement. Filtering is done only to provide inputs to a pressure correction that enforces continuity and to obtain mesh-scale-filtered outputs if desired. The one-dimensional advancement, the pressure correction, and coupling of one-dimensional instantiations using a Lagrangian implementation of mesh-resolved volume fluxes is sufficient to advance the three-dimensional flow without time advancing coarse-grained equations, a feature that motivates the designation of the approach as autonomous microscale evolution (AME). In this sense, the one-dimensional treatment is not a closure because there are no unclosed terms to evaluate. However, the approach is additionally suitable for use as a subgrid-scale closure of existing large-eddy-simulation methods. The potential capabilities and limitations of both of these implementations of the approach are assessed conceptually and with reference to demonstrated capabilities of related methods.

Even today, the automatic digitisation of scanned documents in general but especially the automatic optical music recognition (OMR) of historical manuscripts still remain an enormous challenge, since both handwritten musical symbols and text have to be identified. This paper focuses on the Medieval so-called square notation developed in the 11th-12th century, which is already composed of staff lines, staves, clefs, accidentals, and neumes, that are roughly spoken connected single notes. The aim is to develop an algorithm that captures both the neume and pitch, that is melody information that can be used to reconstruct the original writing. Our pipeline is similar to the standard OMR approach and comprises a novel staff line and symbol detection algorithm, based on deep Fully Convolutional Networks (FCN), which perform pixel-based predictions for either staff lines or symbols and their respective types. Then, the staff line detection combines the extracted lines to staves and yields an F1-score of over 99% for both detecting lines and complete staves. For the music symbol detection we choose a novel approach that skips the step to identify neumes and instead directly predicts note components (NCs) and their respective affiliation to a neume. Furthermore, the algorithm detects clefs and accidentals. Our algorithm recognises these symbols with an F1-score of over 96% if the type is ignored and predicts the true symbol sequence of a staff with a diplomatic symbol accuracy rate (dSAR) of about 87%. If only the NCs without their respective connection to a neume, all clefs, and accidentals are of interest the algorithm reaches an harmonic symbol accuracy rate (hSAR) of approximately 90%.

This study employed the Fully Modified Ordinary Least Squares (FMOLS) and the Error Correction Model (ECM) to investigate the long-run and short-run determinants of unemployment rate in Nigeria. To achieve this annual data on unemployment rate, inflation rate, interest rate, exchange rate and population growth from 1981 to 2016 was collected from Central Bank Statistical Bulletins and the World Bank website. The ADF test revealed that the macroeconomic variables are stationary at first difference while the Cointegration test revealed that the variables are cointegrated. Using unemployment rate as dependent variable, the FMOLS model revealed that exchange rate and population growth are positively significantly related to unemployment rate, interest rate and inflation rate were negatively related to unemployment rate but only interest rate was significant. The short run relationship revealed that the coefficient of the ecm(-1) is negative and statistically significant at 5% level indicating that the system corrects its previous period disequilibrium at the speed of 48.93% yearly. This study concludes that high exchange rate and population growth can lead to increase in unemployment rate in Nigeria while the government should develop the industrial sector and non-oil sector in order to generate employment and boost export in Nigeria.