Axioms

According to the literature on innovation, several vital factors or determinants favor innovation in companies. In the case of R&D, significant advances have been made in the last two decades, which have enriched our understanding of its impact on various innovation outcomes. However, due to a lack of data availability, its study is difficult to address in emerging markets. This is why, using microdata from 5588 firms, we investigate the relationship between R&D investment and the impact on product and process innovations in different Latin American countries. We contribute to the literature by employing a machine learning methodology and comparing its results to a traditional innovation model. Our findings demonstrate the behavior of both product and process innovation methods. Full article

In this article, a new two-parameter model called the truncated Cauchy power-inverted Topp–Leone (TCP-ITL) is constructed by merging the truncated Cauchy power -G (TCP-G) family with the inverted Topp–Leone (ITL) distribution. Some structural properties of the newly suggested model are obtained. Different types of entropies are proposed under the TCP-ITL distribution. Under the complete and hybrid censored data, the maximum likelihood (ML), maximum product of spacing (MPSP), and Bayesian estimate approaches are explored. A simulation study is developed to test the proposed distribution’s restricted sample attributes. In the majority of cases, the numerical data revealed that the Bayesian estimates provided more accurate outcomes than the equivalent alternative estimates. The adaptability of the proposed approach is proven using examples from dependability, medicine, and engineering. A real-world data set is utilized to demonstrate the potential of the TCP-ITL distribution in comparison to other well-known distributions. The results of the model selection revealed that the proposed distribution is the best choice for the data sets under consideration. Full article

This paper proposes a novel approach for analyzing the stability of polynomial fractional-order systems using the frequency-distributed fractional integrator model. There are two types of frequency and temporal stabilization methods for fractional-order systems that global and semi-global stability conditions attain using the sum-of-squares (SOS) method. Substantiation conditions of global and asymptotical stability are complicated for fractional polynomial systems. According to recent studies on nonlinear fractional-order systems, this paper concentrates on polynomial fractional-order systems with any degree of nonlinearity. Global stability conditions are obtained for polynomial fractional-order systems (PFD) via the sum-of-squares approach and the frequency technique employed. This method can be effective in nonlinear systems where the linear matrix inequality (LMI) approach is incapable of response. This paper proposes to solve non-convex SOS-designed equations and design framework key ideas to avoid conservative problems. A Lyapunov polynomial function is determined to address the problem of PFD stabilization conditions and stability established using sufficiently expressed conditions. The main goal of this article is to present an analytical method based on the optimization method for fractional order models in the form of frequency response. This method can convert it into an optimization problem, and by changing the solution of the optimization problem, the stability of the fractional-order system can be improved. Full article

Environmental security is among the top priorities worldwide, and there are many difficulties in this area. The reason for this is a painful subject for society and healthcare systems. Multidimensional sensitivity analysis is fundamental in the process of validating the accuracy and reliability of large-scale computational models of air pollution. In this paper, we present an improved version of the well-known Sobol sequence, which shows a significant improvement over the best available existing sequences in the measurement of the sensitivity indices of the digital ecosystem under consideration. We performed a complicated comparison with the best available low-discrepancy sequences for multidimensional sensitivity analysis to study the model’s output with respect to variations in the input emissions of anthropogenic pollutants and to evaluate the rates of several chemical reactions. Our results, which are presented in this paper through a sensitivity analysis, will play an extremely important multi-sided role. Full article

In contemporary times, science-based technologies are needed for launching innovative products and services in the market. As technology-based management strategies are gaining importance, associated patents need to be comprehensively studied. Previous studies have proposed predictive models based on patent factors. However, technology-based management strategies can influence the growth and decline of firms. Thus, this study aims to estimate uncertainties of the factors that are frequently used in technology-based studies. Furthermore, the importance of the factors may fluctuate over time. Therefore, we propose a Bayesian neural network model based on Flipout and four research hypotheses to evaluate the validity of our method. The proposed method not only estimates the uncertainties of the factors, but also predicts the future value of technologies. Our contribution is to (i) provide a tractable Bayesian neural network applicable to big data, (ii) discover factors that affect the value of technology, and (iii) present empirical evidence for the timeliness and objectivity of technology evaluation. In our experiments, 3781 healthcare-related cases of patents were used, and we found that the proposed hypotheses were all statistically significant. Therefore, we believe that reliable and stable technology-based management strategies can be established through our method. Full article

Transportation systems play a key role in urban development by providing access for people to markets and education, employment, health care, recreation, and other key services. However, uncontrolled urban population and fast growth of vehicle mobility inevitably lead to unsustainable urban transportation systems in terms of economic, technical, social, and geographical aspects of sustainability. Thus, there is a need to select suitable sustainable urban transportation (SUT) alternatives, which can contributed to the technological advancement of a city and changes in societal necessities, mitigating the climate change impact from transport and transforming living habits, in the context of high urban population growth. Therefore, this paper aims to introduce an integrated multi-attribute decision analysis (MADA) framework for assessing and ranking the sustainable urban transportation (SUT) options under an intuitionistic fuzzy sets (IFSs) context. In this regard, firstly IF-distance measures and their properties are developed to obtain the criteria weight. Second, an IF-relative closeness coefficient-based model is presented to find the criteria weights. Third, the operational competitiveness rating (OCRA) model is introduced with the IF-score function-RS-based decision experts’ weighing model and the relative closeness coefficient-based criteria weight determination model under the IFSs environment. To exemplify the utility and effectiveness of the developed IF-relative closeness coefficient-based OCRA methodology, a case study ranking the different SUT bus options is presented from an intuitionistic fuzzy perspective. A comparison with different models is made to prove the superiority and solidity of the obtained outcome. Moreover, the comparative analysis outperforms the other extant MADA models, as it can provide more sound outcomes than others, and thus it is more suitable and efficient to elucidate uncertain information in handling practical MADA problems. In this study, we analyze and determine the most suitable and sustainable SUT by considering the economic, technical, environmental, and social dimensions of sustainability and also make a significant contribution to the current scientific knowledge by providing a novel decision support system from an uncertainty perspective. Full article

In this paper, we introduce the concept of orthogonal convex structure contraction mapping and prove some fixed point theorems on orthogonal ♭-metric spaces. We adopt an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of the solution for the spring-mass system via an integral equation with a numerical example. Full article

Power retail companies in the electricity market make profits through buying and selling power energy in the wholesale and retail markets, respectively. Traditionally, they are assumed to bid in the wholesale market with the same objective, i.e., maximize the profit. This paper proposes a multiagent reinforcement learning (MRL)-based model to simulate the diverse bidding decision-making concerning various operation objectives and the profit-sharing modes of power retail companies in China’s wholesale electricity market, which contributes to a more realistic modeling and simulation of the retail companies. Specifically, three types of operation objectives and five types of profit-sharing modes are mathematically formulated. After that, a complete electricity market optimization model is established, and a case study with 30 retail companies is carried out. The simulation results show that the proposed method can effectively model the diverse bidding decision-making of the power retail companies, which can further assist their decision-making and further contribute to the analysis and simulations of the electricity market. Full article

We introduce the Levinson functional on time scales using integral inequality of Levinson’s type in the terms of $\Delta$-integral for convex (concave) functions on time scale sets and investigate its properties such as superadditivity and monotonicity. The obtained properties are used to derive the bounds of the given Levinson’s functional and those results provide a refinement and the converse of the known Levinson’s inequality on time scales. Further, we define new types of functionals using weighted generalized and power means on time scales, and prove their properties which can be employed in future works to obtain refinements and converses of known integral inequalities on time scales. Full article

The present paper deals with the investigations of a Kenmotsu manifold satisfying certain curvature conditions endowed with 🟉-$\eta$-Ricci solitons. First we find some necessary conditions for such a manifold to be $\phi$-Einstein. Then, we study the notion of 🟉-$\eta$-Ricci soliton on this manifold and prove some significant results related to this notion. Finally, we construct a nontrivial example of three-dimensional Kenmotsu manifolds to verify some of our results. Full article

In this paper, we consider several classes of mappings related to the class of $\alpha$-$ϝ$-contraction mappings by introducing a convexity condition and establish some fixed-point theorems for such mappings in complete metric spaces. The present result extends and generalizes the well-known results of Singh, Khan, and Kang (Mathematics, 2018, 6(6), 105), Istr$\breve{a}$tescu (Liberta Math., 1981, 1, 151–163), and many others in the existing literature. An illustrative example is also provided to exhibit the utility of our main results. Finally, we derive the existence and uniqueness of a solution to an integral equation to support our main result and give a numerical example to validate the application of our obtained results. Full article

The goal of the present research paper is to study how a spacetime manifold evolves when thermal flux, thermal energy density and thermal stress are involved; such spacetime is called a thermodynamical fluid spacetime (TFS). We deal with some geometrical characteristics of $TFS$ and obtain the value of cosmological constant $\mathsf{\Lambda }$. The next step is to demonstrate that a relativistic $TFS$ is a generalized Ricci recurrent $TFS$. Moreover, we use $TFS$ with thermodynamic matter tensors of Codazzi type and Ricci cyclic type. In addition, we discover the solitonic significance of $TFS$ in terms of the Ricci metric (i.e., Ricci soliton $RS$). Full article

Within eye diseases, diabetic retinopathy and retinopathy of prematurity are considered one of the main causes of blindness in adults and children. In order to prevent the disease from reaching such an extreme, a timely diagnosis and effective treatment must be applied. Until now, the way to verify the state of the retina has been to make qualitative observations of fundus images, all carried out by an ophthalmological specialist; however, this is totally restricted to their experience, and some changes in the vascular structure of the retina could be omitted, in addition to the fact that very high resolution images would be needed to be able to detect significant changes. Accordingly, with the help of computational tools, this diagnostic/monitoring process can be improved. This paper presents a novel strategy for the modeling of the MTA by using an estimation of distribution algorithm (EDA) based on the probability density function in order to determine the coefficients and parameters $(\alpha ,\beta )$ of a Jacobi polynomial series. A model using polynomials is the novel aspect of this work since in the literature there are no models of the MTA of this type, in addition to seeking to better cover the profile of the retinal vein. According to the experimental results, the proposed method presents the advantage to achieve superior performance in terms of the mean distance to the closest point (4.34 pixels), and the Hausdorff distance (14.43 pixels) with respect to different state-of-the-art methods of the numerical modeling of the retina, using the DRIVE database of retinal fundus images with a manual delineation of the MTA performed by an specialist. Full article

Fractional derivatives can express anomalous diffusion in brain tissue. Various brain diseases such as Alzheimer’s disease, multiple sclerosis, and Parkinson’s disease are attributed to the accumulation of proteins in axons. Discrete swellings along the axons cause other neuro diseases. To model the propagation of voltage in axons with all those causes, a fractional cable geometry has been adopted. Although a fractional cable model has already been presented, the non-existence of fractional differential geometry based on the well-known fractional derivatives raises questions. These minute parts of the human neural system are modeled as cables that function with a non-uniform cross-section in the fractional realm based upon the Λ-fractional derivative (Λ-FD). That derivative is considered the unique fractional derivative generating differential geometry. Examples are presented so that fruitful conclusions can be made. The present work is going to help medical and bioengineering scientists in controlling various brain diseases. Full article

This paper classifies the exact solutions of the Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group $G_3\left(IX\right)$. All the appropriate non-equivalent exact solutions of the Maxwell vacuum equations are found. Full article

We consider a data-driven method, which combines Koopman operator theory with Extended Dynamic Mode Decomposition. We apply this method to the hypergeometric equation which is the Fuchsian equation with three regular singular points. The space of solutions at any of its singular points is a two-dimensional linear vector space on the field of reals when the independent variable is restricted to take values in the real axis and the unknown function is restricted to be a real-valued function of a real variable. A basis of the linear vector space of solutions is spanned by the hypergeometric function and its products with appropriate powers of the independent variable or the logarithmic function depending on the roots of the indicial equation of the hypergeometric equation. With our work, we obtain a new representation of the fundamental solutions of the hypergeometric equation and relate them to the spectral analysis of the finite approximation of the Koopman operator associated with the hypergeometric equation. We expect that the usefulness of our results will come more to the fore when we extend our study into the complex domain. Full article

Sanford S. Miller and Petru T. Mocanu’s theory of second-order differential subordinations was extended for the case of third-order differential subordinations by José A. Antonino and Sanford S. Miller in 2011. In this paper, new results are proved regarding third-order differential subordinations that extend the ones involving the classical second-order differential subordination theory. A method for finding a dominant of a third-order differential subordination is provided when the behavior of the function is not known on the boundary of the unit disc. Additionally, a new method for obtaining the best dominant of a third-order differential subordination is presented. This newly proposed method essentially consists of finding the univalent solution for the differential equation that corresponds to the differential subordination considered in the investigation; previous results involving third-order differential subordinations have been obtained mainly by investigating specific classes of admissible functions. The fractional integral of the Gaussian hypergeometric function, previously associated with the theory of fuzzy differential subordination, is used in this paper to obtain an interesting third-order differential subordination by involving a specific convex function. The best dominant is also provided, and the example presented proves the importance of the theoretical results involving the fractional integral of the Gaussian hypergeometric function. Full article

The importance of inland ports in promoting current cross-border trade is increasingly recognized. In this work, we aim to design the entire network for the cross-border multimodal container transport system based on inland ports. Unlike previous studies, we consider strong uncertainty in cross-border transportation demand to be caused by a variety of realistic factors such as the global economic situation, trade policies among countries, and global epidemics, etc. To handle the demand uncertainty, we develop an uncertain programming model for the considered cross-border multimodal container transportation network design problem to minimize the expectation of the total costs, including carbon emissions, by imposing two types of chance constraints for capacity limitations. Under mild assumptions, we further convert the proposed uncertain model into its equivalent deterministic one, which can be solved by off-the-shelf solvers such as CPLEX, Gurobi, and Lingo. Finally, we illustrate the applicability of the proposed model by taking the Huaihai Economic Zone-Europe multimodal container transport system as a real-world case study. The computational results provide valuable suggestions and policy guidance regarding four issues: the inland port locations, the transportation route choices, the strategies for reducing the total cost, and the schemes for improving network performance against uncertain demand. Full article

Let the class of functions of $f\left(z\right)$ of the form $f\left(z\right)=z+{\sum }_{k=2}^{\infty }{a}_k{z}^k$, which are denoted by $\mathcal{A}$ and called analytic functions in the open-unit disk. There are many interesting properties of the functions $f\left(z\right)$ in the class $\mathcal{A}$ concerning the subordinations. Applying the three lemmas for $f\left(z\right)\in \mathcal{A}$ provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of $f\left(z\right)\in \mathcal{A}$ with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results. Full article