Mathematics, Volume 10, Issue 4 (February-2 2022) – 139 articles

In this paper, the existence of a mild solution to the Cauchy problem for impulsive semilinear second-order differential inclusion in a Banach space is investigated in the case when the nonlinear term also depends on the first derivative. This purpose is achieved by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables obtaining the result under easily verifiable and not restrictive conditions on the impulsive terms, the cosine family generated by the linear operator and the right-hand side while avoiding any requirement for compactness. Firstly, the problems without impulses are investigated, and then their solutions are glued together to construct the solution to the impulsive problem step by step. The paper concludes with an application of the obtained results to the generalized telegraph equation with a Balakrishnan–Taylor-type damping term. Full article

In the advanced applications, based on infrared detection systems, the precise detection of small targets has become a tough work today. This becomes even more difficult when the background is highly dense in addition to the nature of small targets. The problem raised above is solved in various ways, including infrared patch image (IPI) based methods which are considered to have the best performance. In addition, the greater shrinkage of singular values in the methods based on IPI leads to the problem of nuclear norm minimization (NNM), which leads to the problem of incorrectly recognizing small targets in a highly complex background. Hence, this paper proposed a new method for infrared small target detection (ISTD) via total variation and partial sum minimization (TV-PSMSV). The proposed TV-PSMVS in this work basically replaces the IPI’s NNM with partial sum minimization (PSM) of singular values and, additionally, the total variance (TV) regularization term is inducted to the background patch image (BPI) to suppress the complex background and enhance the target object of interest. The mathematical solution of the proposed TV-PSMSV approach was performed using alternating direction multiplier (ADMM) to verify the proposed solution. The experimental evaluation using real and synthetic data set was performed, and the result revealed that the proposed TV-PSMSV outperformed existing referenced methods in the terms of background suppression factor (BSF) and the signal to gain ratio (SCRG). Full article

This paper proposes a model for brucellosis transmission. The model takes into account the age of infection and waning immunity, that is, the progressive loss of immunity after recovery. Three routes of transmissions are considered: vertical transmission, and both direct and indirect routes of horizontal transmission. According to the well-posedness results, we provide explicit formulas for the equilibria. Next, we derive the basic reproduction number ${\mathcal{R}}_0$ and prove some stability results depending on the basic reproductive number. Finally, we perform numerical simulations using model parameters estimated from biological data to confirm our theoretical results. The results of these simulations suggest that for certain values of parameters, there will be periodic outbreaks of epidemics, and the disease will not be eradicated from the population. Our results also highlight the fact that the birth rate of cattle significantly influences the dynamics of the disease. The proposed model can be of a good use in studying the effects of vaccination on the cattle population. Full article

Fractional stochastic differential equation (FSDE)-based random processes are used in a wide spectrum of scientific disciplines. However, in the majority of cases, explicit solutions for these FSDEs do not exist and approximation schemes have to be applied. In this paper, we study one-dimensional stochastic differential equations (SDEs) driven by stochastic process with Hölder continuous paths of order $1/2<\gamma <1$. Using the Lamperti transformation, we construct a backward approximation scheme for the transformed SDE. The inverse transformation provides an approximation scheme for the original SDE which converges at the rate $h^{2\gamma }$, where h is a time step size of a uniform partition of the time interval under consideration. This approximation scheme covers wider class of FSDEs and demonstrates higher convergence rate than previous schemes by other authors in the field. Full article

This work is situated at the conjunction of the fields of distributed systems, telecommunications, and mathematical modeling, aiming to offer solutions to the problem of people’s overexposure to electro-magnetic fields (EMF) radiation. In this paper, we propose a new routing scheme for wireless multi-hop networks, which seeks a fairer distribution of the exposure to electromagnetic fields, by leveraging a combination of the transmitted power and the accumulated exposure as a routing metric. We carry out a holistic approach, including: (1) an algorithmic study, (2) an analytical model of the aforementioned novel routing metric, and (3) the specification of a routing protocol. We make a performance assessment of our novel routing protocol and the corresponding algorithm, by means of an extensive simulation campaign over the NS-3 simulator. The obtained results yield that the proposed novel solution is able to not only fairly distribute the exposure, but also to reduce its average value, thus enhancing the user experience. We also show that the power consumption using the EMF-aware proposed solution, based on Cycle Canceling Algorithm (CCA), and that observed with an approach seeking power reduction are alike. Indeed, even if there exist key-differences from the user experience’s point of view between both routing approaches, there is no statistically relevant power increase between them. Thus, our solution manages to keep the consumed power at a low level, and at the same time it reduces the overall nodes’ exposure to EMF. Full article

The modeling different data behaviour like the human development index as a function of life expectancy, the water capacity of a reservoir with respect to a certain threshold, or the percentage of death rate of an infant before his or her first birthday, are situations which a researcher can face. It is noteworthy that these problems may have in common data with excessive zeros and ones. Then, it is essential to have flexible and accuracy models to fit data with these features. Given the relevance of data modeling with excessive zeros and ones, in this paper, a mixture of discrete and continuous distributions is proposed for modeling data with these behaviors. Additionally, the Unit-Birnbaum-Saunders distribution is considered with the aim to explain the continuous component of the model and the features of a Bernoulli process. The estimation of the parameters is based on the maximum likelihood method. Observed and expected information matrices are derived, illustrating interesting aspects of the likelihood approach. Finally, with practical applications by using real data we can show the advantage of using our proposal concerning the inflated beta model. Full article

Recently Brusov et al. have developed innovative investment models that are very close to investment practice. Investment models with frequent payments of tax on profit and of interest on debt at the ends of periods have been considered. However, in practice, payments of tax on profit as well as of interest on debt could be made in advance. In the current paper, we developed, for the first time, innovative investment models with frequent advance payments of tax on profit and of interest on debt and studied the impact of these types of payments on investment project effectiveness. Numerical calculations carried out for four innovative investment models (without split flows) showed that, in the case of advance frequent payments of income tax and interest on debt, all the results related to the effect of the number of payments of income tax and interest on debt on the investment projects’ effectiveness were opposite to the results in the case of payments at the end of the periods obtained by Brusov et al. in the previous article. Thus, this means that the method of payments of tax on profit and of interest on debt (in advance or at the ends of periods) changes drastically the effect of the number of payments of income tax and interest on debt on the investment effectiveness. The verification developed by us for the new models with frequent advance payments of tax on income helps create a comprehensive system of correct valuation of the investments’ effectiveness for two schemes for payments of income tax (in advance or at the ends of periods). The obtained results help the tax regulator (Finance Ministry) understand the influence of the frequency of payments of tax on income and the credit regulator (Central Bank) understand the influence of the frequency of payments of interest on debt on the investment projects’ effectiveness. This allows them to modify and improve tax legislation and credit policy, respectively. Full article

In the current paper, we first introduce a new class of contractions via a new notion called p-cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p-cyclic contraction mappings on $D\cup E$ where $\left(D,E\right)$ is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper. Full article

With the rapid development of the tourism industry, various travel websites are emerging. The tourism question answering system explores a large amount of information from these travel websites to answer tourism questions, which is critical for providing a competitive travel experience. In this paper, we propose a framework that automatically constructs a tourism knowledge graph from a series of travel websites with regard to tourist attractions in Zhejiang province, China. Backed by this domain-specific knowledge base, we developed a tourism question answering system that also incorporates the underlying knowledge from a large-scale language model such as BERT. Experiments on real-world datasets demonstrate that the proposed method outperforms the baseline on various metrics. We also show the effectiveness of each of the question answering components in detail, including the query intent recognition and the answer generation. Full article

White light can be decomposed into different colors, and a complex sound wave can be decomposed into its partials. While the physics behind transverse and longitudinal waves is quite different and several theories have been developed to investigate the complexity of colors and timbres, we can try to model their structural similarities through the language of categories. Then, we consider color mixing and color transition in painting, comparing them with timbre superposition and timbre morphing in orchestration and computer music in light of bicategories and bigroupoids. Colors and timbres can be a probe to investigate some relevant aspects of visual and auditory perception jointly with their connections. Thus, the use of categories proposed here aims to investigate color/timbre perception, influencing the computer science developments in this area. Full article

This paper focuses on the distributed fusion estimation problem in which a signal transmitted over wireless sensor networks is subject to deception attacks and random delays. We assume that each sensor can suffer attacks that may corrupt and/or modify the output measurements. In addition, communication failures between sensors and their local processors can delay the receipt of processed measurements. The randomness of attacks and transmission delays is modelled by different Bernoulli random variables with known probabilities of success. According to these characteristics of the sensor networks and assuming that the measurement noises are cross-correlated at the same time step between sensors and are also correlated with the signal at the same and subsequent time steps, we derive a fusion estimation algorithm, including prediction and filtering, using the distributed fusion method. First, for each sensor, the local least-squares linear prediction and filtering algorithm are derived, using a covariance-based approach. Then, the distributed fusion predictor and the corresponding filter are obtained as the matrix-weighted linear combination of corresponding local estimators, checking that the mean squared error is minimised. A simulation example is then given to illustrate the effectiveness of the proposed algorithms. Full article

During the evolution of the COVID-19 pandemic, each country has adopted different control measures to contrast the epidemic’s diffusion. Restrictions to mobility, public transport, and social life in general have been actuated to contain the spread of the pandemic. In this paper, we consider the deterministic SIRD model with delays proposed by Calleri et al., which is improved by adding the vaccinated compartment V (SIRDV model) and considering a time-dependent contact frequency. The three delays take into account the incubation time of the disease, the healing time, and the death time. The aim of this work is to study the effect of the vaccination campaigns in Great Britain (GBR) and Israel (ISR) during the pandemic period. The different restriction periods are included by fitting the contact frequency on real datasets as a piecewise constant function. As expected, the vaccination campaign reduces the amount of deaths and infected people. Furthermore, for the different levels of restriction policy, we find specific values of the contact frequency that can be used to predict the trend of the pandemic. Full article

The aim of this article was to provide analytical and numerical approaches to a one-dimensional Eyring–Powell flow. First of all, the regularity, existence, and uniqueness of the solutions were explored making use of a variational weak formulation. Then, the Eyring–Powell equation was transformed into the travelling wave domain, where analytical solutions were obtained supported by the geometric perturbation theory. Such analytical solutions were validated with a numerical exercise. The main finding reported is the existence of a particular travelling wave speed $a=1.212$ for which the analytical solution is close to the actual numerical solution with an accumulative error of <${10}^{-3}$. Full article

Deprivation is associated with an increased risk of developing chronic health conditions and with worse outcomes in multimorbidity. The goal of our study was to develop an integrated population index of deprivation (IPID) to observe the influence of deprivation on morbidity and the subsequent use of healthcare resources in one health district, using the socioeconomic, clinical and geographical data from its administrative health records. Eight socioeconomic indicators were identified and weighted using the methodology of two-phase principal component analysis, providing an index that allowed each census section to be classified into seven deprivation groups. Secondly, the possible relation between the IPID and the variables for multimorbidity and healthcare resources was analysed using the theory of multiple comparisons. It was observed that places with a greater proportion of healthy people presented lower values of deprivation and that, at lower levels of deprivation, there were fewer hospital admissions. The results show that living in an area with a higher deprivation index is associated with greater consumption of healthcare resources and disease burden. Identifying areas of sociosanitary vulnerability can help to identify health inequalities and allow intervention by clinical practices and healthcare management to reduce them. Full article

A Yamabe soliton is defined on an arbitrary almost-contact B-metric manifold, which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The cases when the given manifold is cosymplectic or Sasaki-like are studied. In this manner, manifolds are obtained that belong to one of the main classes of the studied manifolds. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the B-metric on contact distribution. In both cases, explicit five-dimensional examples are given, which are characterized in relation to the results obtained. Full article

This paper addresses a batch loading and scheduling problem of minimizing the makespan on parallel batch processing machines. For batch loading, jobs with compatible families can be assigned to the same batch process even if they differ in size; however, batches can only be formed from jobs within the same family, and the batch production time is determined by the family. During the batch scheduling, the deterioration effects are continuously added to batches processed in each parallel machine so that the batch production times become deteriorated. The deteriorated processing time of batches can be recovered to the original processing times of batches by a maintenance or cleaning process of machines. In this problem, we sequentially determine the batching of jobs and the scheduling of batches. Due to the complexity of the problem, we proposed a three-stage ant colony optimization algorithm. The proposed algorithm found an optimal solution for small-sized problems and achieved near-optimal solutions and better performance than a genetic algorithm or a particle swarm optimization for large-sized problems. Full article

This work addresses the suitability of using structured meshes composed of quadrilateral finite elements, instead of the classical unstructured meshes made of triangular elements. These meshes are used in the modal analysis of waveguides with Manhattan-like cross-sections. For this problem, solved with the two-dimensional Finite Element Method, there are two main quality metrics: eigenvalue and eigenvector accuracy. The eigenvalue accuracy is first considered, showing how the proposed structured meshes are, given comparable densities, better, especially when dealing with waveguides presenting pairs of modes with the same cutoff frequency. The second metric is measured through a practical problem, which commonly appears in microwave engineering: discontinuity analysis. In this problem, for which the Mode-Matching technique is used, eigenvectors are needed to compute the coupling between the modes in the discontinuities, directly influencing the quality of the transmission and reflection parameters. In this case, it is found that the proposed analysis performs better given low-density meshes and mode counts, thus proving that quadrilateral-element structured meshes are more resilient than their triangular counterparts to higher-order eigenvectors. Full article

In this paper, we consider a predator–prey model, in which the prey’s growth is affected by the additive predation of its potential predators. Due to the additive predation term in prey, the model may exhibit the cases of the strong Allee effect, weak Allee effect and no Allee effect. In each case, the dynamics of global features of the model are investigated. Compared to the well-known Lotka–Volterra type model, the model proposed in this paper exhibits much richer and more complex dynamic behaviors, such as the Allee effect, the sensitivity to the initial conditions caused by the strong Allee effect, the oscillatory behavior and the Hopf and heteroclinic bifurcations. Furthermore, the stability and Hopf bifurcation of the model with the density dependent feedback time delay in prey are investigated. By the normal form method and center manifold theory, the explicit formulas are presented to determine the direction of Hopf bifurcation and the stability and period of Hopf-bifurcating periodic solutions. Theoretical analysis and numerical simulation indicate that the delay may destabilize the model, and cause the Hopf bifurcation not only at the interior equilibrium but also at a boundary equilibrium. Full article

In this study, we consider eight stages per step family of explicit Runge-Kutta-Nyström pairs of orders eight and six. The pairs from this family effectively use eight stages for each step. The coefficients provided by such a method are much less than the number of non linear order conditions required to be solved. Thus, we traditionally apply various simplified assumptions in order to address this drawback. The assumptions taken in the family we consider here deliver a subsystem where all the coefficients are evaluated successively and explicitly with respect to five free parameters. We train (adjust) these free parameters in order to derive a certain pair that outperforms other similar pairs of orders $8(6)$ in Keplerian type orbits, e.g., Kepler, perturbed Kepler, Arenstorf orbit, or Pleiades. Differential evolution technique is used for the training. The pair that we finally present offers about an additional digit of accuracy in a variety of orbits. Full article

In this paper, we propose an end-to-end single-image super-resolution neural network by leveraging hybrid multi-scale features of images. Different from most existing convolutional neural network (CNN) based solutions, our proposed network depends on the observation that image features extracted by CNN contain hybrid multi-scale features: both multi-scale local texture features and global structural features. By effectively exploiting these multi-scale and local-global features, our network involves far fewer parameters, leading to a large decrease in memory usage and computation during inference. Our network benefits from three key modules: (1) an efficient and lightweight feature extraction module (EFblock); (2) a hybrid multi-scale feature enhancement module (HMblock); and (3) a reconstruction–restoration module (DRblock). Experiments on five popular benchmarks demonstrate that our super-resolution approach achieves better performance with fewer parameters and less memory consumption, compared to more than 20 SOTAs. In summary, we propose a novel multi-scale super-resolution neural network (HMSF), which is more lightweight, has fewer parameters, and requires less execution time, but has better performance than the state-of-the-art methods. Compared to SOTAs, this method is more practical and better suited to run on constrained devices, such as PCs and mobile devices, without the need for a high-performance server. Full article

An analysis of the didactic-mathematical knowledge put into play by a sample of 30 prospective primary teachers during their participation in a Service-Learning program focused on mathematical stimulation as a measure of attention to adolescents at risk of social exclusion is presented. The program aimed to respond to current training demands by promoting the development of mathematics-specific professional competencies, as well as social skills to interact with students, and to positively influence the prospective teachers’ affection towards mathematics and its teaching. It was developed during three academic years in two phases: the learning module was oriented to the presentation of the mathematical stimulus program and the didactical analysis of the STEAM activities knocking it into shape; in the service module, the participants implemented the activities in an educational center with students at risk of social exclusion. The analysis was carried out from the video recordings of the sessions, the future teachers’ written reports with the analysis of the activities, questionnaires on the didactic-mathematical knowledge and a satisfaction test. The results show difficulties on the part of the future teachers to analyze some of the activities of the program, which seems to have its origin in their poor command of the common knowledge of the mathematical content, which also limits them when it comes to managing the activities in the way expected for the stimulus program. All in all, participation in the program was positively assessed by them in relation to its usefulness for their training. The potential benefit of Service-Learning programs such as the one addressed here in the face of a positive impact on the affections towards mathematics is concluded, as a necessary step for a more effective acquisition of didactic-mathematical knowledge and skills in the initial training. Full article

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $\Pi$-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of both metrics. Thus, the corresponding scalar curvatures of both considered metrics are equal and constant. An explicit example of the Lie group as the manifold under study is presented. Full article

In this work, the effect of the fractional time derivative on the piezo-thermo-elastic medium is studied, using the hybrid Laplace transform and finite element methods (LFEM). The generalized fractional piezoelectric–thermoelastic basic equations for piezo-thermo-elastic medium are formulated. The Laplace transforms are used for the time derivatives, and the finite element method is used to discretize for the space derivatives. The inversions process is performed using the Stehfest numerical technique. The finite element approach is used to obtain the solutions of complex coupled formulations of this problem. The effects of fractional time derivative and thermal relaxation time on piezoelectric–thermoelastic mediums are studied. It can be seen from the distribution that the thermal-induced displacement, the temperature and the stress of the medium increase at a high fractional parameter. Full article

In this article, the formulation of first-order approximate Mei symmetries and Mei invariants of the corresponding Lagrangian is presented. Theorems and determining equations are given to evaluate approximate Mei symmetries, as well as approximate first integrals corresponding to each symmetry of the associated Lagrangian. The formulated procedure is explained with the help of the linear equation of motion of a damped harmonic oscillator (DHO). The Mei symmetries corresponding to the Lagrangian and Hamiltonian of DHO are compared. Full article

The distance between successive zeros of all solutions of first-order differential equations with several delays is studied in this work. Many new estimations for the upper bound of the distance between zeros are obtained. Our results improve many-well known results in the literature. We also obtain some fundamental results for the lower bound of the distance between adjacent zeros. Some illustrative examples are introduced to show the accuracy and efficiency of the obtained results. Full article

In multi-hop question answering (MH-QA), the machine needs to infer the answer to a given question from multiple documents. Existing models usually apply entities as basic units in the reasoning path. Then they use relevant entities (in the same sentence or document) to expand the path and update the information of these entities to finish the QA. The process might add an entity irrelevant to the answer to the graph and then lead to incorrect predictions. It is further observed that state-of-the-art methods are susceptible to reasoning chains that pivot on compound entities. To make up the deficiency, we present a viable solution, i.e., incorporate phrases in the latent query reformulation method (IP-LQR), which incorporates phrases in the latent query reformulation to improve the cognitive ability of the proposed method for multi-hop question answering. Specifically, IP-LQR utilizes information from relevant contexts to reformulate the question in the semantic space. Then the updated query representations interact with contexts within which the answer is hidden. We also design a semantic-augmented fusion method based on the phrase graph, which is then used to propagate the information. IP-LQR is empirically evaluated on a popular MH-QA benchmark, HotpotQA, and the results of IP-LQR consistently outperform those of the state of the art, verifying its superiority. In summary, by incorporating phrases in the latent query reformulation and employing semantic-augmented embedding fusion, our proposed model can lead to better performance on MH-QA. Full article

Edutainment applications are a type of software that is designed to be entertaining while also being educational. In the current COVID-19 pandemic context, when children have to stay home due to the social distancing rules, edutainment applications for young children are more and more used each day. However, are these applications ready to take the place of an in-person teacher? In this paper, we propose a new generation of edutainment applications that are more suitable for preschoolers (aged 3–6 years old in our country) and closer to the in-person student–teacher interaction: emotions aware edutainment applications. We discuss the most important challenges that must be overcome in developing this kind of applications (i.e., recognizing children’s emotions, enhancing the edutainment application with emotion awareness, and adapting the interaction flow) and the first steps that we have taken for developing them. Full article

We address two mathematical aspects of the Biró–Néda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions. Full article

This paper deals with the creation of parallel algorithms implementing macro-and microscopic traffic flow models on modern supercomputers. High-performance computing contributes to the development of intelligent transportation systems based on information technologies and aimed at the effective regulation of traffic in large cities. As a macroscopic approach, the quasi-gas-dynamic traffic model approximated by explicit finite-difference schemes is proposed. One- and two-dimensional variants of the system are considered, and the concept of lateral velocity and different equations for obtaining it are discussed. The microscopic approach is represented by the multilane cellular automata model. The previously developed model is extended to reproduce synchronized flow in accordance with Kerner’s three-phase theory. The new version starts from the Kerner–Klenov–Schreckenberg–Wolf model and operates with the concept of the synchronization gap. Macroscopic models are relevant for determining the common characteristics of road traffic, while microscopic models are useful for a detailed description of cars’ movement. Both approaches possess inner parallelism. The parallel algorithms are based on the geometrical parallelism principle with different boundary conditions at interfaces of the subdomains. Sufficiently high speedups were reached when up to 100 processors were involved in calculations. The proposed algorithms can serve as the core of ITS. Full article