Mathematics

Uniaxial compressive strength (UCS) is a critical parameter in the disaster prevention of engineering projects, requiring a large budget and a long time to estimate in different rocks or the early stage of a project. If predicted accurately, the UCS of rocks significantly affects geotechnical applications. This paper develops a dataset of 734 samples from previous studies on different countries’ magmatic, sedimentary, and metamorphic rocks. Within the study context, three main factors, point load index, P-wave velocity, and Schmidt hammer rebound number, are utilized to estimate UCS. Moreover, it applies extreme learning machines (ELM) to map the nonlinear relationship between the UCS and the influential factors. Five metaheuristic algorithms, particle swarm optimization (PSO), grey wolf optimization (GWO), whale optimization algorithm (WOA), butterfly optimization algorithm (BOA), and sparrow search algorithm (SSA), are used to optimize the bias and weight of ELM and thus enhance its predictability. Indeed, several performance parameters are utilized to verify the proposed models’ generalization capability and predictive performance. The minimum, maximum, and average relative errors of ELM achieved by the whale optimization algorithm (WOA-ELM) are smaller than the other models, with values of 0.22%, 72.05%, and 11.48%, respectively. In contrast, the minimum and mean residual error produced by WOA-ELM are less than the other models, with values of 0.02 and 2.64 MPa, respectively. The results show that the UCS values derived from WOA-ELM are superior to those from other models. The performance indices (coefficient of determination (R²): 0.861, mean squared error (MSE): 17.61, root mean squared error (RMSE): 4.20, and value account for (VAF): 91% obtained using the WOA-ELM model indicates high accuracy and reliability, which means that it has broad application potential for estimating UCS of different rocks. Full article

In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of $\alpha$ numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability. Full article

The temporal linear instability of a viscoelastic liquid sheet moving around an inviscid gas in a transverse electrical field is analyzed. The fluid is described by the leaky dielectric model, which is more complex than existing models and enables a characterization of the liquid electrical properties. In addition, the liquid is assumed to be viscoelastic, and the dimensionless dispersion relation of the sinuous and varicose modes between the wavenumber and the temporal growth rate can be derived as a 3 × 3 matrix. According to this relationship, the effects of the liquid properties on the sheet instability are determined. The results suggest that, as the electrical Euler number and the elasticity number increase and the time constant ratio decreases, the sheet becomes more unstable. Finally, an energy budget approach is adopted to investigate the instability mechanism for the sinuous mode. Full article

Artificial neural networks (ANNs), one of the most important artificial intelligence techniques, are used extensively in modeling many types of problems. A successful training process is required to create effective models with ANN. An effective training algorithm is essential for a successful training process. In this study, a new neural network training algorithm called the hybrid artificial bee colony algorithm based on effective scout bee stage (HABCES) was proposed. The HABCES algorithm includes four fundamental changes. Arithmetic crossover was used in the solution generation mechanisms of the employed bee and onlooker bee stages. The knowledge of the global best solution was utilized by arithmetic crossover. Again, this solution generation mechanism also has an adaptive step size. Limit is an important control parameter. In the standard ABC algorithm, it is constant throughout the optimization. In the HABCES algorithm, it was determined dynamically depending on the number of generations. Unlike the standard ABC algorithm, the HABCES algorithm used a solution generation mechanism based on the global best solution in the scout bee stage. Through these features, the HABCES algorithm has a strong local and global convergence ability. Firstly, the performance of the HABCES algorithm was analyzed on the solution of global optimization problems. Then, applications on the training of the ANN were carried out. ANN was trained using the HABCES algorithm for the identification of nonlinear static and dynamic systems. The performance of the HABCES algorithm was compared with the standard ABC, aABC and ABCES algorithms. The results showed that the performance of the HABCES algorithm was better in terms of solution quality and convergence speed. A performance increase of up to 69.57% was achieved by using the HABCES algorithm in the identification of static systems. This rate is 46.82% for the identification of dynamic systems. Full article

In the military field, decision making has become the core of the new operational concept, known as the “kill web”. Although the theory of kill web has been widely recognized by many countries, the decision-making methods for the kill web are still in the early stage. Therefore, there is a need for a new decision-making method for the kill web. Firstly, different from the traditional scheme decision, the kill web is a complex system. The method of complex network provides a new perspective on complex systems, so the kill web was modeled based on complex network. Secondly, the kill web relies on artificial intelligence to provide decision-makers with operation loop solutions, and then decision-makers rely on the experience to make a final decision. However, the current decision-making methods only consider one of the intelligent and human decision-making methods, while the kill web needs to consider both. Hence, we combined intelligent decision making with human decision making through multi-objective optimization and the prospect theory. Finally, we designed a nondominated sorting ant colony genetic algorithm-II (NSACGA-II) to solve large-scale problems, since the kill web is a large-scale system. In addition, an illustrative case was used to verify the feasibility and effectiveness of the proposed model. The results showed that, compared with other classical multi-objective optimization algorithms, the NSACGA-II is superior to other superior algorithms in terms of the hypervolume (HV) and spacing (SP), which verifies the effectiveness of the method and greatly improves the quality of commanders’ decision-making. Full article

This research studies a metapopulation model where each patch is considered a form of fragmentation of the environment produced by the spatio-temporal variability of anthropogenic noise. A deterministic mathematical model is proposed that describes two processes of migration between patches. The first process consists of migration due to chronic critical noise produced by an anthropogenic and biological source (self-generated acoustic signals of higher intensity, due to the Lombard effect). The second process consists of migration due to a higher level of stain occupancy. A simple and classical analysis of the local stability of the model is performed. The results indicate that no subpopulation goes extinct; in fact, a necessary condition for long-term stabilization of the size of the subpopulations is that the noise attenuation rate is higher. Moreover, as long as the noise is of low intensity the differences in the carrying capacity of each patch do not produce substantial, long-term differences in the sizes of the subpopulations. However, as the noise intensity increases, the difference in carrying capacities produce noticeable, long-term differences between subpopulation sizes. Finally, the results are corroborated by numerical simulations. Full article

Computer-aided diagnosis/detection (CADx) systems have been used to help doctors in improving the quality of diagnosis and treatment processes in many serious diseases such as breast cancer, brain stroke, lung cancer, and bone fracture. However, the performance of such systems has not been completely accurate. The key factor in CADx systems is to localize positive disease lesions from the captured medical images. This step is important as it is used not only to localize lesions but also to reduce the effect of noise and normal regions on the overall CADx system. In this research, we proposed a method to enhance the segmentation performance of thyroid nodules in ultrasound images based on information fusion of suggestion and enhancement segmentation networks. Experimental results with two open databases of thyroid digital image databases and 3DThyroid databases showed that our method resulted in a higher performance compared to current up-to-date methods. Full article

Damage to the surface construction of reinforced concrete (RC) will impact the security of the facility’s structure. Deep learning can effectively identify various types of damage, which is useful for taking protective measures to avoid further deterioration of the structure. Based on deep learning, the multi-convolutional neural network (MCNN) has the potential for identifying multiple RC damage images. The MCNN6 of this study was evaluated by indicators (accuracy, loss, and efficiency), and the optimized architecture was confirmed. The results show that the identification performance for “crack and rebar exposure” (Type B) by MCNN6 is the best, with an accuracy of 96.81% and a loss of 0.07. The accuracy of the other five types of damage combinations is also higher than 80.0%, and the loss is less than 0.44. Finally, the MCNN6 model can be used in the detection of various damage to achieve automated assessment for RC facility surface conditions. Full article

In recent years, with the rapid development of Internet services in all walks of life, a large number of malicious acts such as network attacks, data leakage, and information theft have become major challenges for network security. Due to the difficulty of malicious traffic collection and labeling, the distribution of various samples in the existing dataset is seriously imbalanced, resulting in low accuracy of malicious traffic classification based on machine learning and deep learning, and poor model generalization ability. In this paper, a feature image representation method and Adversarial Generative Network with Filter (Filter-GAN) are proposed to solve these problems. First, the feature image representation method divides the original session traffic into three parts. The Markov matrix is extracted from each part to form a three-channel feature image. This method can transform the original session traffic format into a uniform-length matrix and fully characterize the network traffic. Then, Filter-GAN uses the feature images to generate few attack samples. Compared with general methods, Filter-GAN can generate more efficient samples. Experiments were conducted on public datasets. The results show that the feature image representation method can effectively characterize the original session traffic. When the number of samples is sufficient, the classification accuracy can reach 99%. Compared with unbalanced datasets, Filter-GAN has significantly improved the recognition accuracy of small-sample datasets, with a maximum improvement of 6%. Full article

Transfer theorems for combined logics provide essential tools and insight for reasoning about complex logical systems. In this paper, we present the first sufficient criterion (contextual extensibility) for decidability to be preserved through combination of propositional logics, and we study the complexity upper bounds induced by the method. In order to assess the scope and usability of our criterion, we illustrate its use in re-obtaining two standard important (though partial) results of the area: the preservation of decidability for disjoint combinations of logics, and the preservation of decidability for fusions of modal logics. Due to the very abstract nature and generality of the idea underlying contextual extensibility, we further explore its applicability beyond propositional logics. Namely, we explore the particular case of 2-deductive systems, and as a byproduct, we obtain the preservation of decidability for disjoint combinations of equational logics and discuss the relationship of this result and of our criterion with several related results with meaningful applications in satisfiability modulo theories. Full article

In this paper we study the magnetic trajectories as the solutions of the Lorentz equation defined by the cross product corresponding to the $7-$dimensional Euclidean space. We find several examples of such trajectories and moreover, we strongly motivate our results making a comparison with the $3-$dimensional Euclidean case, ambient space which was among the first ones approached in the study of magnetic trajectories. Full article

Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored. Here, we present a description of the prime spectrum of this ring and study some of the algebraic and topological properties of these prime ideals. We also study how they behave under separable extensions of the base field and give an indication of how this study can be applied in adele rings not of number fields. Full article

This paper studies the problem of target control and how a virtual ellipsoid can avoid the static obstacle. During the motion to the target set, the virtual ellipsoid can achieve a motion under collision avoidance by keeping the distance between the ellipsoid and obstacle. We present solutions to this problem in the class of closed-loop (feedback) controls based on Hamilton–Jacobi–Bellman (HJB) equation. Simulation results verify the validity and effectiveness of our algorithm. Full article

Squeezed light—nonclassical multiphoton states with fluctuations in one of the quadrature field components below the vacuum level—has found applications in quantum light spectroscopy, quantum telecommunications, quantum computing, precision quantum metrology, detecting gravitational waves, and biological measurements. At present, quantum noise squeezing with optical fiber systems operating in the range near 1.5 μm has been mastered relatively well, but there are no fiber sources of nonclassical squeezed light beyond this range. Silica fibers are not suitable for strong noise suppression for 2 µm continuous-wave (CW) light since their losses dramatically deteriorate the squeezed state of required lengths longer than 100 m. We propose the generation multiphoton states of 2-micron 10-W class CW light with squeezed quantum fluctuations stronger than −15 dB in chalcogenide and tellurite soft glass fibers with large Kerr nonlinearities. Using a realistic theoretical model, we numerically study squeezing for 2-micron light in step-index soft glass fibers by taking into account Kerr nonlinearity, distributed losses, and inelastic light scattering processes. Quantum noise squeezing stronger than −20 dB is numerically attained for a customized As₂Se₃ fibers with realistic parameters for the optimal fiber lengths shorter than 1 m. For commercial As₂S₃ and customized tellurite glass fibers, the expected squeezing in the −20–−15 dB range can be reached for fiber lengths of the order of 1 m. Full article

Mountain Pass Theorem (MPT) is an important result in variational methods with multiple applications in partial differential equations involved in mathematical physics. Starting from a variant of MPT, a new result concerning the existence of the solution for certain mathematical physics problems involving p-Laplacian and p-pseudo-Laplacian has been obtained. Based on the main theorem, the existence, possibly the uniqueness, and characterization of solutions for models such as nonlinear elastic membrane, glacier sliding, and pseudo torsion problem have been obtained. The novelty of the work consists of the formulation of the central result under weaker conditions requested by the chosen variant of MPT, the proof of this statement, and its application in solving above mentioned problems. While the expressions of such Dirichlet and/or von Neumann problems were already completed, this proposed solving method suggests some specific numerical methods to construct the appropriate solution. A general goal of this paper is the extension of the applicative pallet of this way to construct the solutions encountered in modeling real processes developed within new emerging technologies. Full article

Extra edge connectivity and diagnosability have been employed to investigate the fault tolerance properties of network structures. The p-extra edge connectivity ${\lambda }_p\left(\Gamma \right)$ of a graph $\Gamma$ was introduced by Fàbrega and Fiol in 1996. In this paper, we find the exact values of p-extra edge connectivity of some special graphs. Moreover, we give some upper and lower bounds for ${\lambda }_p\left(\Gamma \right)$, and graphs with ${\lambda }_p\left(\Gamma \right)=1,2,⌈\frac{n}{2}⌉⌊\frac{n}{2}⌋-1,⌈\frac{n}{2}⌉⌊\frac{n}{2}⌋$ are characterized. Finally, we obtain the three extremal results for the p-extra edge connectivity. Full article

Heat treatment on shale reservoirs can promote the development of secondary fractures in a matrix on the basis of hydraulic fracturing, forming multi-scale gas–water seepage channels and strengthening the gas desorption. Experimental evidence shows that heat treatment can enhance gas recovery in the same mining life. Heat treatment on a shale gas reservoir is a multi-physical and multi-phase coupling process. However, how the thermal stimulation interacts with nonlinear two-phase flow in heterogeneous shale volume fracturing has not been clear. In this paper, a fully coupled THGM model for heating-enhanced shale-gas recovery in heterogeneous shale reservoirs is proposed. First, the governing equations are formulated for the shale-reservoir deformation involving both gas adsorption and thermal expansion, the permeability evolution model for the cracking process of fractured shale, the gas–water two-phase continuity equation considering the effects of gas solubility and the heat transfer equation for heat conduction and convection. The interactions among stress, temperature and seepage in a heterogeneous shale reservoir were studied. Secondly, a test on shale permeability after 50 °C temperature treatment was conducted. The evolution of temperature, capillary pressure, water and gas saturation and the permeability of shale during the heat treatment of the reservoir were numerically analyzed. Finally, the gas production from a shale gas reservoir was numerically simulated with this THGM model. The numerical results indicated that the thermal-induced fracturing, gas desorption and separation from water make predominant contributions to the evolution of permeability. The heat treatment can enhance cumulative gas production by 58.7% after 27.4 years of heat injection through promoting gas desorption and matrix diffusion. Full article

Considering the influences of uncertain factors on the reproduction of virus in vivo, a stochastic HIV model with CTLs’ immune response and logistic growth was developed to research the dynamics of HIV, where uncertain factors are white noise and telegraph noise. which are described by Brownian motion and Markovian switching, respectively. We show, firstly, the existence of global positive solutions of this model. Further, by constructing suitable stochastic Lyapunov functions with regime switching, some sufficient conditions for the existence and uniqueness of the stationary distribution and the conditions for extinction are obtained. Finally, the main results are explained by some numerical examples. Theoretical analysis and numerical simulation show that low-intensity white noise can maintain the persistence of the virus, and high intensity white noise can make the virus extinct after a period of time with multi-states. Full article