Search Results (2,387)

In this paper, we introduce and investigate a refined generalization of convexity, termed the multiplicatively strongly s-convex function, and establish several of its fundamental algebraic properties. Within the framework of multiplicative calculus, this generalized convexity structure is employed to derive new midpoint-, trapezoid-, and Simpson-type inequalities, thereby providing unified refinements of several classical integral inequalities. Particular choices of the underlying parameters yield a variety of meaningful special cases and corresponding novel inequalities. Furthermore, we demonstrate the applicability of the established results through inequalities involving several important special means, including the arithmetic, geometric, logarithmic, and m-logarithmic means. To complement the theoretical developments, selected consequences are illustrated numerically and graphically, providing comchosenational evidence for the validity and effectiveness of the proposed inequalities. The results contribute to the development of multiplicative convexity theory and offer a flexible framework for deriving further inequalities within multiplicative calculus. Full article

The impact resistance of thin PMMA plates in deep-sea transparent structures is important for crashworthiness safety and is governed by high-strain-rate loading and hydrostatic pressure. Conventional empirical constitutive models exhibit limited adaptability to strain ratio effects and complex energy dissipation, leading to significant deviations in anti-impact assessment. This study proposes a constitutive-aware physics-informed neural network framework that integrates a data-driven constitutive neural network with embedded physical constraints. Such a proposed constitutive network replaces the theoretical model to capture rate-dependent stress response, while a physics-informed network enforces momentum conservation, energy balance, thermodynamic dissipation inequality, and pressure-induced stress limits. A dynamically weighted multimodal loss function is proposed and is used to ensure stable constraint enforcement during data training. Experimental validation based on a high-speed impact test confirms the constitutive and physics constraint network accuracy. Numerical results demonstrate that increasing hydrostatic pressure alters energy dissipation, increasing residual projectile velocities, and degrading impact resistance. The framework provides an efficient, physically consistent method for evaluating anti-impact performance of thin-walled PMMA structures in deep-sea engineering. Full article

Reliable cooperative control of connected vehicle platoons remains challenging when stochastic communication-topology variations coexist with heterogeneous time-varying transmission delays. This study investigates a distributed consensus control problem for connected vehicle platoons subject to Markovian switching topologies and heterogeneous time-varying inter-vehicle communication delays. A third-order longitudinal vehicle model with powertrain inertial lag is combined with a continuous-time Markov chain (CTMC) to describe randomly switching communication topologies. A distributed control protocol incorporating the constant time headway policy, full velocity difference car-following behavior, and leader-pinning information is formulated, while link-dependent time-varying delays are embedded in the closed-loop error system. Based on a mode-dependent Lyapunov–Krasovskii functional, Jensen’s integral inequality, and the Schur complement, sufficient linear matrix inequality (LMI) conditions are derived for mean-square asymptotic stability of the nominal delayed system; the LMI is feasible at ${\overline{\tau }}_{\mathsf{\ell }}=0.10$ s and ${\mu }_{\mathsf{\ell }}=0.04$, remains feasible at $0.30$ s, and becomes infeasible at $0.375$ s. An input-to-state stability (ISS) corollary extends the result to bounded time-varying leader acceleration, showing that tracking errors remain bounded during dynamic EUDC phases and converge when the leader acceleration and its derivative vanish. Using the same Lyapunov–Krasovskii certificate, a mean-square $L_{\infty }$ bounded-propagation result is further established; this result characterizes uniform-in-vehicle error bounds and does not assert strict non-amplification. Numerical simulations under the Extra-Urban Driving Cycle (EUDC) show that the follower vehicles maintain cooperative tracking under topology switching and bounded communication delays, with position, velocity, and acceleration errors remaining bounded during the dynamic phases and converging as the leader acceleration vanishes. In the EUDC simulation, the largest leader-relative position error is approximately $-60.75$ m for Vehicle 10 at $t\approx 380$ s, the maximum adjacent local spacing-error peak ratio is $2.32$, and the position error returns below 1 m by $t\approx 400.8$ s. The minimum inter-vehicle gap is $5.87$ m and the minimum safety margin after the initial 10 s is $0.84$, with all safety-margin indices remaining positive; these results indicate that the proposed framework maintains platoon coordination and car-following safety under stochastic communication uncertainties. Full article

In this paper, we study the problem $D_{0^{+}}^{\alpha }u+f(t,u)=0$ on $(0,1)$, $u\left(0\right)=0$, $D_{0^{+}}^{\alpha -1}u\left(1\right)={\int }_0^{1}u\mathrm{d}A$, where $1<\alpha \le 2$ and the measure $\mathrm{d}A$ may change sign. For a measure made of two point masses of opposite sign, we show that the function ${\mathcal{K}}_A\left(s\right)={\int }_0^{1}G(\tau ,s)\mathrm{d}A\left(\tau \right)$, through which $\mathrm{d}A$ enters the Green function, is nonnegative exactly when the positive weight is at least ${\theta }^{*}$ times the size of the negative one, where ${\theta }^{*}$ is given in closed form. Together with a simple condition $\Delta >0$, this makes the Green function nonnegative. The threshold ${\theta }^{*}$ decreases in $\alpha$ and tends to infinity as $\alpha \to 1^{+}$. For $\alpha <2$ the Green function has no uniform Harnack estimate, so we work in a cone weighted by $\Psi \left(t\right)={\int }_0^1\mathcal{G}(t,s)\mathrm{d}s$, where Schauder’s theorem gives a positive solution with explicit bounds whenever f lies between two positive constants. For the omitted ray fixed point theorem of Avery, Henderson and Liu, we describe exactly when its key inequality holds for the two-point functional used here, and we show that the hypotheses under which we can verify it already imply the classical inward condition. Examples with $\alpha =3/2$ and $\alpha =1.08$ illustrate the results. Full article

Environmental improvements in tourism do not determine who controls assets, influences decisions, retains income, or bears transition costs. This conceptual article examines how governance can connect green tourism transitions to Sustainable Development Goal 10 (SDG 10: Reduced Inequalities). An integrative literature review and abductive theory synthesis connect justice and sustainability, political economy and access, collective governance and capability conversion, and organizational accountability. Mechanism-oriented analysis identifies eight capture pathways and develops the Equitable Green Tourism Governance Framework (EGTG). The framework links destination institutions, community entrepreneurial ecosystems, and hospitality firms and boards through six functions: rights and recognition; representative voice and decision power; capabilities and finance; fair transactions and local value capture; accountability, assurance, and remedy; and reinvestment and adaptive learning. Twelve conditional propositions explain how these functions may convert formal commitments into realized benefits and identify constraints on their effectiveness. A governance gate, readiness-based implementation sequence, responsibility matrix, and SDG-aligned diagnostics translate the framework into testable practice. The contribution is a multilevel explanation of why environmental commitments require aligned authority, capabilities, transactions, and corrective mechanisms to support equitable outcomes. The proposed relationships and implementation instruments require context-sensitive empirical validation. Full article

We study a critical homogeneous continuous-time Markov branching-immigration system whose offspring and immigration generating functions regularly vary at point 1 of orders $1+\nu$ and $\delta$ with $\nu ,\delta \in (0,1]$. The slowly varying factors are controlled through their index functions, which causes regular variation of the second order, both factors tending to finite positive limits. Two numbers govern the classification: the difference $\gamma =\delta -\nu$ of the two orders and the limit ${\Lambda }_{\infty }$ of the ratio of the immigration factor to the offspring one. We classify the state space completely: it is positive recurrent for $\gamma >0$, transient for $\gamma <0$, and on the boundary $\gamma =0$, null recurrent or transient accordingly as ${\Lambda }_{\infty }\le \nu$ or ${\Lambda }_{\infty }>\nu$; at $\nu =\delta =1$, this is the classical threshold, read under the present second-order hypotheses. In each regime, we identify the limiting generating function of the normalised transition functions, together with the leading term of the deviation from it, uniformly in the argument on compact subsets of $[0,1)$, the transient regime under two further inequalities on the parameters. Every rate is carried by a complex-analytic argument and with no monotonicity hypothesis to the individual transition probabilities as an upper bound, which for each fixed state is the exact order when $\gamma \ne 0$. An exact integral identity for the survival probability of the system without immigration makes the constants explicit and yields a three-term expansion of that probability. A numerical section on explicit models confirms the constants and the rates. Full article

A novel utility model of the daily electricity consumption patterns of any residential unit is proposed. The model is semi-parametric—its internal parameters are tractable to straightforward interpretations from the standpoints of microeconomics as well as game theory. The model considers fixed and shiftable loads. A modified Cobb–Douglas preference function is applied to incorporate utility tradeoffs in operating shiftable loads at different hours of the day based on the consumer’s intrinsic preference and time-of-use pricing. Model parameter estimation is formulated as a quadratic optimization problem with inequality constraints. The existence of a global optimum that is unique except under a very specific circumstance is theoretically established. A dual-gradient-ascent learning algorithm was developed to train the parameters that best fit real time-series load data. For units with single-point monitoring, an optional unsupervised learning algorithm for partial load disaggregation was developed. As a case study, the proposed model was trained with load profiles of two real-world residential units. The trained model is able to faithfully reproduce typical electricity consumption characteristics. Model interpretability was demonstrated by numerically evaluating the utility and cost functions with varying loads. These results illustrate the effectiveness of the proposed methodology. Full article

By means of weight functions, the introduction of parameters and Hardy’s integral inequality, a new special kind of multidimensional Hilbert-type integral inequality with the general nonhomogeneous kernel and one multiple lower limit function is obtained. The equivalent statements of the best value in the new inequality related to several parameters are considered, and some corollaries are deduced. Full article

This paper generalizes stochastic sampled-data synchronization of reaction–diffusion neural networks (RDNNs) from sampling distributions with finite support to infinite discrete distributions, whose sampling intervals are drawn from a countably infinite set ${\left\{q_i\right\}}_{i=1}^{\infty }$ with probabilities ${\left\{{\alpha }_i\right\}}_{i=1}^{\infty }$. Four regularity conditions are identified—finite interval mean, summability of the weighted absolute decay parameters, strict positivity of the probability-averaged decay rate, and boundedness above of the decay parameters, which makes the Lyapunov–Krasovskii functional (LKF) mode-independent in its delay weight and hence continuous across sampling instants. A mode-dependent LKF is constructed, the weak-law step is replaced by the strong law of large numbers combined with a Cesàro-type argument, and the infinite family of design linear matrix inequalities (LMIs) is handled by a truncation-with-tail-verification procedure, for which a rigorous certificate is given: when the tail decay parameters are non-positive, the tail conditions are affine and are certified by corner-point feasibility checks with shared variables; otherwise, a convergent-tail argument applies. Almost-sure exponential synchronization with an explicit rate is established, which implies synchronization in probability, and controller design conditions are derived in terms of LMIs; three examples (two neural networks and one reaction–diffusion neural network) corroborate the design through computed gains, verified tail conditions, stochastic closed-loop simulations, an N-sensitivity analysis, and a comparison with a fixed-period controller. The proposed framework removes the finite-support restriction on the sampling distribution and yields an almost-sure, rate-explicit synchronization guarantee with a numerically verifiable LMI design. Full article

Background: Orofacial clefts are one of the most common congenital anomalies worldwide. Comprehensive cleft care interventions aim to address the complex surgical, nutritional, dental, speech, audiology, and psychosocial needs of patients with clefts. While studies from other countries have identified various implementation barriers and facilitators, evidence from Ethiopia remains limited, particularly regarding caregivers’ experiences accessing comprehensive cleft care. This study explored caregivers’ lived experiences of accessing comprehensive cleft care at Jimma University Medical Center in southwestern Ethiopia. Methods: We conducted a phenomenological study at the Comprehensive Cleft Care Center of Jimma University Medical Center. Participants were purposively selected from caregivers of children with orofacial clefts who had received at least two components of comprehensive cleft care. Data were collected through in-depth semi-structured interviews. Data collection continued until thematic saturation was achieved. Audio recordings were transcribed verbatim, translated into English, and managed in ATLAS.ti version 7.5.18. Data were analyzed inductively using Colaizzi’s seven-step descriptive phenomenological method. Trustworthiness was enhanced through member checking, reflexive bracketing, and systematic procedures. Results: Twelve caregivers of children with orofacial clefts participated in the study. The analysis generated eight overarching themes. Participants reported limited initial awareness of cleft conditions, cultural misconceptions, stigma, emotional distress, and delayed care-seeking. Key barriers included poor referral linkages, transportation difficulties, financial constraints, and geographic inaccessibility. Participants reported that engagement with comprehensive cleft care was associated with increased knowledge, caregiving confidence and skills, and trust in healthcare providers. They also described perceived improvements in feeding, nutritional status, speech development, physical appearance, and social integration, alongside reduced stigma and increased caregiver advocacy and community awareness of cleft conditions. Conclusions: Caregivers described a transition from limited awareness of orofacial clefts, emotional distress, stigma, and challenges accessing care toward greater knowledge, confidence, trust in healthcare providers, and perceived improvements in their children’s health, functional abilities, and social participation. Persistent barriers related to poverty, transportation difficulties, referral delays, and limited community awareness remained. These findings can inform policy and program planning to strengthen comprehensive cleft care and address inequities in access to care for children with orofacial clefts and their families in similar settings in Ethiopia. Full article

The objective of this article is to examine how gendered institutional practices constrain the substantive political participation of Amazigh-speaking women elected to local councils in Morocco. Although constitutional reforms, gender quotas, and the official recognition of Amazigh have expanded women’s formal political representation, less attention has been paid to the institutional processes that continue to restrict their effective participation in local governance. Existing studies have primarily attributed women’s political marginalization to sociocultural and structural factors, while paying comparatively limited attention to how everyday institutional arrangements reproduce unequal opportunities for political participation. Drawing on Feminist Institutionalism, the Capability Approach, Bourdieu’s concept of linguistic capital, Spivak’s notion of subaltern silencing, and intersectionality, this study examines how linguistic, spatial, and temporal arrangements operate as interconnected mechanisms of exclusion. Focusing on the Beni Mellal-Khenifra region as a case study, the analysis draws on semi-structured interviews with elected women councilors and local government officials. The findings indicate that the institutional dominance of Arabic in council deliberations, the organization of meetings in male-dominated spaces such as rural cafés, and the scheduling of meetings at times that conflict with women’s social responsibilities can collectively constrain Amazigh-speaking women’s ability to understand political debates, participate effectively in deliberations, and influence decision-making processes. These practices suggest that gendered institutional inequalities can be reproduced not only through explicit legal discrimination, but also through routine institutional arrangements embedded in the everyday functioning of local councils. The article argues that substantive political participation depends not only on formal legal representation but also on equitable access to the linguistic, spatial, and temporal conditions required for meaningful democratic deliberation. It contributes to the debate on women’s political participation by showing how apparently ordinary institutional rules, routines, spaces, and practices can reproduce gendered inequalities and thereby contribute to the persistence of institutionalized patriarchal relations. Full article

This paper investigates how the phases, or arguments, of coefficients in multiple power series influence the maximum modulus of entire functions of several complex variables. While classical complex analysis often emphasizes the absolute sizes of these coefficients, this study highlights that altering only the angles of Taylor coefficients can radically accelerate or amplify a function’s overall growth. To explore this phenomenon, we analyze the relationship between the actual maximum modulus of a function and its majorant. The majorant is defined mathematically as some power series constructed from primary series where every coefficient is replaced by its absolute value. This represents the “maximum possible” growth a function when all coefficients are strictly positive and add together at a given point without any mutual cancellation. The study establishes precise necessary and sufficient conditions under which specific asymptotic inequalities comparing these two distinct growth measures hold true. The main result establishes the sufficient conditions required to bound the growth of the majorant relative to the maximum modulus. Complementing this, other result demonstrates the exactness of these boundaries by proving that if the sufficient conditions are not met, an entire function can be explicitly constructed that strictly exceeds those growth constraints. The research generalizes known mathematical theorems from one-variable case into multidimensional contexts. The exact dependence of a function’s asymptotic growth rate on its coefficient phases is detailed and formulated for broad classes of multivariate transcendental entire functions. Furthermore, the paper establishes the relationship between the function’s maximum value and its majorant while systematically excluding specific, negligible intervals of radii where abnormal growth spikes might otherwise complicate the analysis. Such excluded intervals are a set of finite logarithmic measure. These generalized multidimensional estimates provide a base for controlling the behavior of analytic solutions to partial differential equations when their coefficient phases are perturbed. Full article

The spatial allocation of urban functional resources is closely linked to residents’ well-being. However, conventional macro-level approaches that emphasize the equalization of aggregate resource provision may not fully capture inequalities in the spatial distribution of functional resources relative to population within cities. To address this limitation, this study combines large-scale point-of-interest data from Amap with gridded population data to construct an index of urban functional spatial inequality, capturing the spatial alignment between resource provision and population distribution within the urban functional system, and examines its association with residents’ subjective well-being. The results show that greater urban functional spatial inequality is significantly associated with lower levels of residents’ subjective well-being. This association remains robust across a series of sensitivity tests, while instrumental-variable estimates have the same direction. Moreover, subgroup analyses suggest that the association may vary by socioeconomic resources, childcare responsibilities, and health status. Further analyses show that greater urban functional spatial inequality is associated with stronger perceived inequality of opportunity, lower satisfaction with public services, and weaker social capital. These findings suggest that the welfare performance of urban functional systems depends not only on aggregate resource provision but also on its spatial coordination with population distribution. Accordingly, efforts to enhance residents’ well-being should consider a more equitable spatial distribution of functional resources, better spatial coordination between functional resources and population distribution, and broader sharing of the benefits of urban development. Full article

We introduce and analyze a two-step inertial viscosity-type algorithm for approximating a common solution of a generalized mixed equilibrium problem and the fixed-point problems associated with a family of quasi-nonexpansive mappings in a real Hilbert space. The generalized mixed equilibrium model contains a monotone operator and a proper convex lower semicontinuous function inside an implicit equilibrium resolvent, while a second inverse strongly monotone operator is treated explicitly through two successive forward–resolvent steps. The method further incorporates two inertial corrections, a family-dependent fixed-point step, and viscosity regularization by a contraction. We first establish boundedness of the generated sequence under summability conditions on the inertial parameters. We then derive a uniform descent inequality that simultaneously controls the two equilibrium residuals and the fixed-point residual. Using a residual-based sequence convergence criterion and an appropriate weak regularity condition for the mapping family, we prove that the iterates converge strongly to the unique point $q^{*}$ of the common solution set $\mathrm{\Omega }$ satisfying $q^{*}=P_{\mathrm{\Omega }}f\left(q^{*}\right)$. The abstract theorem is specialized to composite convex minimization, mixed variational inequalities, countable convex feasibility problems, and finite families under cyclic control. A five-dimensional example verifies the assumptions explicitly and illustrates convergence to the viscosity-selected solution. Full article

In this paper, we introduce and study a normalized four-parameter Le Roy-type q-Mittag–Leffler (LR-q-ML) function defined by means of the q-Pochhammer symbol, the q-Gamma function, and the q-factorial, whose parameters directly influence the associated coefficient sequence and its growth behavior. We establish monotonicity properties of the related coefficient sequences, which are then used to derive coefficient estimates, Fekete–Szegö inequalities, upper bounds for the normalized function and its q-difference operator, and lower bounds for the real parts of the ratios involving the normalized function and its partial sums. Numerical computations together with graphical illustrations verify the theoretical estimates and show that the partial sums provide accurate approximation to the complete function as the number of terms increases. The obtained results provide a unified framework for investigating geometric properties and coefficient results of higher-parameter q-special functions in geometric function theory. Full article