Search Results (1,401)

This article introduces the Index of Distributive and Developmental Outlook (IDDO), a composite indicator designed to jointly assess economic performance and income inequality across EU-27 Member States. While GDP per capita is widely used to evaluate national prosperity, and the Gini coefficient captures income distribution, their separate use often obscures the interaction between growth and equity—an essential dimension of sustainable development. To address this gap, the IDDO integrates normalized values of both indicators using arithmetic and geometric means. The study applies the IDDO to a longitudinal dataset covering the years 2005, 2014, and 2024, allowing for comparative and temporal analysis. Based on IDDO scores, countries are classified into four development types: balanced development, growth with inequality, equity with stagnation, and dual vulnerability. Results show that while some Member States, such as Luxembourg, Czechia, and Slovenia, maintain consistently high IDDO levels, others—including Bulgaria, Romania, and Latvia—exhibit persistent challenges in aligning growth with equitable outcomes. The findings underscore the need for cohesion policies that prioritize not only economic convergence but also distributive fairness. The IDDO provides a practical and adaptable tool for diagnosing development patterns, benchmarking performance, and informing policy design within the EU framework. Full article

In this paper, we propose a diffusion-type predator–prey interaction model with harvest and disease in prey, and conduct stability analysis and pattern formation analysis on the model. For the temporal model, the asymptotic stability of each equilibrium is analyzed using the linear stability method, and the conditions for Hopf bifurcation to occur near the positive equilibrium are investigated. The simulation results indicate that an increase in infection force might disrupt the stability of the model, while an increase in harvesting intensity would make the model stable. For the spatiotemporal model, a priori estimate for the positive steady state is obtained for the non-existence of the non-constant positive solution using maximum principle and Harnack inequality. The Leray–Schauder degree theory is used to study the sufficient conditions for the existence of non-constant positive steady states of the model, and pattern formation are achieved through numerical simulations. This indicates that the movement of prey and predators plays an important role in pattern formation, and different diffusions of these species may play essentially different effects. Full article

In this article, we study a double-phase variable-exponent Kirchhoff problem and show the existence of at least three solutions. The proposed model, as a generalization of the Kirchhoff equation, is interesting since it is driven by a double-phase operator that governs anisotropic and heterogeneous diffusion associated with the energy functional, as well as encapsulating two different types of elliptic behavior within the same framework. To tackle the problem, we obtain regularity results for the corresponding energy functional, which makes the problem suitable for the application of a well-known critical point result by Bonanno and Marano. We introduce an n-dimensional vector inequality, not covered in the literature, which provides a key auxiliary tool for establishing essential regularity properties of the energy functional such as $C^1$-smoothness, the $\left(S_{+}\right)$-condition, and sequential weak lower semicontinuity. Full article

This paper explores novel inequalities for statistical submanifolds within the framework of the Norden golden-like statistical manifold. By leveraging the intrinsic properties of statistical manifolds and the structural richness of Norden golden geometry, we establish fundamental relationships between the intrinsic and extrinsic invariants of submanifolds. The methodology involves deriving generalized Chen-type and $\delta (2,2)$ curvature inequalities using curvature tensor analysis and dual affine connections. A concrete example is provided to verify the theoretical framework. The novelty of this work lies in extending classical curvature inequalities to a newly introduced statistical structure, thereby opening new perspectives in the study of geometric inequalities in information geometry and related mathematical physics contexts. Full article

In this paper, we first introduce a parametric identity for generalized differentiable functions using a generalized fractal–fractional integral operators. Based on this identity, we establish several variants of parameterized inequalities for functions whose local fractional derivatives in absolute value satisfy generalized convexity conditions. Furthermore, we demonstrate that our main results reduce to well-known Ostrowski- and Simpson-type inequalities by selecting suitable parameters. These inequalities contribute to finding tight bounds for various integrals over fractal spaces. By comparing the classical Hölder and Power mean inequalities with their new generalized versions, we show that the improved forms yield sharper and more refined upper bounds. In particular, we illustrate that the generalizations of Hölder and Power mean inequalities provide better results when applied to fractal integrals, with their tighter bounds supported by graphical representations. Finally, a series of applications are discussed, including generalized special means, generalized probability density functions and generalized quadrature formulas, which highlight the practical significance of the proposed results in fractal analysis. Full article

Objective: To explore the relationship between type of grocery store used (chain vs. independent), transportation access, food insecurity, and fruit and vegetable intake in Detroit, Michigan, USA, during the COVID-19 pandemic. Design: A cross-sectional online survey was conducted from December 2021 to May 2022. Setting: Detroit, Michigan. Participants: 656 Detroit residents aged 18 and older. Results: Bivariate analyses showed that chain grocery store shoppers reported significantly greater fruit and vegetable intake (2.42 vs. 2.14 times/day for independent grocery store shoppers, p < 0.001) and lower rates of food insecurity compared to independent store shoppers (45.9% vs. 65.3% for independent grocery store shoppers, p < 0.001). Fewer independent store shoppers used their own vehicle (52.9% vs. 76.2% for chain store shoppers, p < 0.001). After adjusting for socioeconomic and demographic variables transportation access was strongly associated with increased odds of shopping at chain stores (OR = 1.89, 95% CI [1.21,2.95], p = 0.005) but food insecurity was no longer associated with grocery store type. Shopping at chain grocery stores was associated with higher fruit and vegetable intake after adjusting for covariates (1.18 times more per day, p = 0.042). Qualitative responses highlighted systemic barriers, including poor food quality, high costs, and limited transportation options, exacerbating food access inequities. Conclusions: These disparities underscore the need for targeted interventions to improve transportation options and support food security in vulnerable populations, particularly in urban areas like Detroit. Addressing these structural challenges is essential for reducing food insecurity and promoting equitable access to nutritious foods. Full article

The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions for total geodesicity with adequate restrictions on some smooth functions using mathematical operators. Furthermore, we go over some natural conclusions in which the gradient k-almost Newton-conformal Ricci soliton on the hypersurface of the Golden Riemannian manifold becomes compact. Finally, we establish a Schur’s type inequality in terms of k-almost Newton-conformal Ricci solitons immersed in Golden Riemannian manifolds with constant golden sectional curvature. Full article

This research investigates higher education admission outcomes at Hungarian universities for ethnic Hungarian minority students residing in countries within the Carpathian Basin. The region is distinguished by a variety of national policies that impact minority education. By analyzing extensive data on the availability of mother tongue education, the status of minority rights, advanced level examination performance, and types of settlement using a wide range of statistical methods, our study reveals significant cross-national differences in the distribution of admission scores and central tendencies. Compared to lower and more varied scores for students from Ukraine and Romania, ethnic Hungarian students from Serbia and Slovakia achieved high average admission scores. Performance was notably more consistent among students from EU member states compared to non-EU regions, strongly linking outcomes to the more robust implementation of minority rights and better access to mother-tongue education within the EU framework. A critical finding is the strong positive correlation (Pearson r = 0.837) between admission scores and advanced level examination results, highlighting the pivotal role of these exams for the academic progression of these minority students. The Jonckheere-Terpstra test (p < 0.05) further confirmed significant performance differences between ranked country groups, with Serbian and Slovak students generally outperforming their Ukrainian and Romanian counterparts. Counterintuitively, settlement type (urban vs. rural) exhibited a negligible relationship with admission scores (r = 0.150), explaining only 2% of score variability. This challenges common assumptions and suggests other factors specific to the Hungarian minority context are more influential. This study provides crucial insights into the complex dynamics influencing Hungarian minority students’ access to higher education, underscoring cross-country educational inequalities, and informing the development of equitable minority rights and mother-tongue education policies in Central Europe for these often-marginalized communities. Full article

A refined version of the q-Hermite–Hadamard inequalities for strongly convex functions is introduced in this paper, utilizing both left and right q-integrals. Tighter bounds and more accurate estimates are derived by incorporating strong convexity. New q-trapezoidal and q-midpoint estimates are also presented to enhance the precision of the results. The improvements in the results compared to previous work are demonstrated through numerical examples in terms of precision and tighter bounds, and the advantages of using strongly convex functions are showcased. Full article

In this paper, we generalize an inequality for a convex function in one dimension ${\mathbb{R}}^1$ on three intervals to a function with nondecreasing increments in k dimensions ${\mathbb{R}}^k$ on $(2n+1)$ intervals. We prove all the situations when $n=1,2$ and prove a very special case for a general n as well as the discrete version. The proofs are based on a general conclusion for convex functions, and analogues of this conclusion are established. We apply the discrete case of the inequality to Csiszár $\varphi$-divergence $I_{\varphi }(p,q)$ in information theory, and the continuous case $I_{\varphi }(p_1,q_1)\le I_{\varphi }(p_2,q_2)$ on a measurable set is also established. The same inequality for an $ϵ$-approximately convex function on a discrete set is also established and can be used to prove a similar Landau–Kolmogorov-type inequality. Full article

Urban green spaces (UGS) are essential for residents’ well-being, environmental quality, and social cohesion. However, previous studies have typically employed undifferentiated analytical frameworks, overlooking UGS types and failing to adequately measure the structural disparities of different UGS types within residents’ walking distance. To address this, this study integrates Gaussian Two-Step Floating Catchment Area models, Simpson’s index, and the Gini coefficient to construct an accessibility–diversity–equality assessment framework for UGS. This study conducted an analysis of accessibility, diversity, and equity for various types of UGSs under pedestrian conditions, using the high-density city of Shenzhen, China as a case study. Results reveal high inequality in accessibility to most UGS types within 15 min to 30 min walking range, except residential green spaces, which show moderate-high inequality (Gini coefficient: 0.4–0.6). Encouragingly, UGS diversity performs well, with over 80% of residents able to access three or more UGS types within walking distance. These findings highlight the heterogeneous UGS supply and provide actionable insights for optimizing green space allocation to support healthy urban development. Full article

In this short note, we focus on complete translating solitons with a bounded $L_f^n$-norm of the second fundamental form and obtain two results. First, based on a Sobolev-type inequality and a Simons-type inequality, we establish a rigidity theorem of complete translating solitons. Second, based on the same Sobolev-type inequality and a Bochner-type inequality, a vanishing theorem regarding $L_f^p$ weighted harmonic 1-forms is proved. Full article

This paper investigates a new class of fractional integral operators, namely, the exponentially damped Riesz-type operators within the framework of variable exponent Lebesgue spaces $L^{\mathtt{p}(·)}$. To the best of our knowledge, the boundedness of such operators has not been addressed in any existing functional setting. We establish their boundedness under appropriate log-Hölder continuity and growth conditions on the exponent function $\mathtt{p}(·)$. To highlight the novelty and practical relevance of the proposed operator, we conduct a comparative analysis demonstrating its effectiveness in addressing convergence, regularity, and stability of solutions to partial differential equations. We also provide non-trivial examples that illustrate not only these properties but also show that, under this operator, a broader class of functions becomes locally integrable. The exponential decay factor notably broadens the domain of boundedness compared to classical Riesz and Bessel–Riesz potentials, making the operator more versatile and robust. Additionally, we generalize earlier results on Sobolev-type inequalities previously studied in constant exponent spaces by extending them to the variable exponent setting through our fractional operator, which reduces to the classical Riesz potential when the decay parameter $\lambda =0$. Applications to elliptic PDEs are provided to illustrate the functional impact of our results. Furthermore, we develop several new structural properties tailored to variable exponent frameworks, reinforcing the strength and applicability of the proposed theory. Full article

This paper presents some of the most significant findings in the design of a hydraulic servomechanism for flight controls, which were primarily achieved by the first author during his activity in an aviation institute. These results are grouped into four main topics. The first one outlines a classical theory, from the 1950s–1970s, of the analysis of nonlinear automatic systems and namely the issue of absolute stability. The uninformed public may be misled by the adjective “absolute”. This is not a “maximalist” solution of stability but rather highlights in the system of equations a nonlinear function that describes, for the case of hydraulic servomechanisms, the flow-control dependence in the distributor spool. This function is odd, and it is therefore located in quadrants 1 and 3. The decision regarding stability is made within the so-called Lurie problem and is materialized by a matrix inequality, called the Lefschetz condition, which must be satisfied by the parameters of the electrohydraulic servomechanism and also by the components of the control feedback vector. Another approach starts from a classical theorem of V. M. Popov, extended in a stochastic framework by T. Morozan and I. Ursu, which ends with the description of the local and global spool valve flow-control characteristics that ensure stability in the large with respect to bounded perturbations for the mechano-hydraulic servomechanism. We add that a conjecture regarding the more pronounced flexibility of mathematical models in relation to mathematical instruments (theories) was used. Furthermore, the second topic concerns, the importance of the impedance characteristic of the mechano-hydraulic servomechanism in preventing flutter of the flight controls is emphasized. Impedance, also called dynamic stiffness, is defined as the ratio, in a dynamic regime, between the output exerted force (at the actuator rod of the servomechanism) and the displacement induced by this force under the assumption of a blocked input. It is demonstrated in the paper that there are two forms of the impedance function: one that favors the appearance of flutter and another that allows for flutter damping. It is interesting to note that these theoretical considerations were established in the institute’s reports some time before their introduction in the Aviation Regulation AvP.970. However, it was precisely the absence of the impedance criterion in the regulation at the appropriate time that ultimately led, by chance or not, to a disaster: the crash of a prototype due to tailplane flutter. A third topic shows how an important problem in the theory of automatic systems of the 1970s–1980s, namely the robust synthesis of the servomechanism, is formulated, applied and solved in the case of an electrohydraulic servomechanism. In general, the solution of a robust servomechanism problem consists of two distinct components: a servo-compensator, in fact an internal model of the exogenous dynamics, and a stabilizing compensator. These components are adapted in the case of an electrohydraulic servomechanism. In addition to the classical case mentioned above, a synthesis problem of an anti-windup (anti-saturation) compensator is formulated and solved. The fourth topic, and the last one presented in detail, is the synthesis of a fuzzy supervised neurocontrol (FSNC) for the position tracking of an electrohydraulic servomechanism, with experimental validation, in the laboratory, of this control law. The neurocontrol module is designed using a single-layered perceptron architecture. Neurocontrol is in principle optimal, but it is not free from saturation. To this end, in order to counteract saturation, a Mamdani-type fuzzy logic was developed, which takes control when neurocontrol has saturated. It returns to neurocontrol when it returns to normal, respectively, when saturation is eliminated. What distinguishes this FSNC law is its simplicity and efficiency and especially the fact that against quite a few opponents in the field, it still works very well on quite complicated physical systems. Finally, a brief section reviews some recent works by the authors, in which current approaches to hydraulic servomechanisms are presented: the backstepping control synthesis technique, input delay treated with Lyapunov–Krasovskii functionals, and critical stability treated with Lyapunov–Malkin theory. Full article

This paper provides a comparative review of digital and human (face-to-face) innovation platforms and their roles in promoting innovation and sustainability. These platforms are particularly significant in advancing sustainability objectives as outlined in Sustainable Development Goal 17, (SDG17) which emphasizes the importance of knowledge and technology partnerships to address sustainability challenges, foster innovation, and enhance scientific collaboration. Through a systematic literature review of organizational and management research over the past decade, the study identifies key features, benefits, and limitations of each platform type. Digital platforms offer scalability, asynchronous collaboration, and data-driven innovation, yet face challenges such as trust deficits, cybersecurity risks, and digital inequality. In contrast, human (face-to-face) platforms facilitate trust, emotional communication, and spontaneous idea generation, but are limited in scalability and resource efficiency. By categorizing insights into thematic tables and evaluating implications for organizations, the paper highlights how the integration of both platform types can optimize innovation outcomes. The authors argue that hybrid models—combining the scalability and efficiency of digital platforms with the relational depth of human (face-to-face) platforms—offer a promising path toward sustainable innovation ecosystems. The paper concludes with a call for future empirical research on platform integration strategies and sector-specific applications. Full article