Search Results (143)

The q-calculus framework has emerged as a powerful tool in geometric function theory, enabling refined analysis of analytic and bi-univalent functions. Inspired by the versatility of the q-derivative operator, this paper introduces a new generalized subclass of bi-univalent functions defined via the q-derivative in combination with generalized bivariate Fibonacci polynomials, which have recently gained significant attention in mathematical research. For functions in this class, we establish bounds on the initial coefficients and provide estimates for the corresponding Fekete–Szegö functional. By appropriate specialization of parameters, our results recover several known findings and, importantly, produce bounds for new subclasses of bi-univalent functions not previously studied. This framework unifies earlier developments while extending the theory to novel, analytically meaningful classes. Full article

This paper presents a newly defined subclass of analytic functions and explores several significant properties within the class, which use for their definitions the q-analogues of the derivative and the subordinations. Thus, we tried to connect different notions of the q-calculus with those of the Geometric Function Theory of one variable function. We identify the bounds of the initial coefficients and found upper bounds of the Fekete–Szegő functional for these classes. We investigate the relationship between the coefficients of an univalent function and those of its inverse by examining the difference between their second Hankel determinants. Furthermore, we analyze the behavior of the quantity module of the difference between the second Hankel determinant of a function and the same determinant for its inverse. To improve the obtained results by finding sharp estimations remains an interesting open question. Full article

Background/Objectives: The segmentation of three-dimensional radiological images constitutes a fundamental task in medical image processing for isolating tumors from complex datasets in computed tomography or magnetic resonance imaging. Precise visualization, volumetry, and treatment monitoring are enabled, which are critical for oncology diagnostics and planning. Volumetric analysis surpasses standard criteria by detecting subtle tumor changes, thereby aiding adaptive therapies. The objective of this study was to develop an enhanced, interactive Graphcut algorithm for 3D DICOM segmentation, specifically designed to improve boundary accuracy and 3D modeling of breast and brain tumors in datasets with heterogeneous tissue intensities. Methods: The standard Graphcut algorithm was augmented with a clustering mechanism (utilizing k = 2–5 clusters) to refine boundary detection in tissues with varying intensities. DICOM datasets were processed into 3D volumes using pixel spacing and slice thickness metadata. User-defined seeds were utilized for tumor and background initialization, constrained by bounding boxes. The method was implemented in Python 3.13 using the PyMaxflow library for graph optimization and pydicom for data transformation. Results: The proposed segmentation method outperformed standard thresholding and region growing techniques, demonstrating reduced noise sensitivity and improved boundary definition. An average Dice Similarity Coefficient (DSC) of 0.92 ± 0.07 was achieved for brain tumors and 0.90 ± 0.05 for breast tumors. These results were found to be comparable to state-of-the-art deep learning benchmarks (typically ranging from 0.84 to 0.95), achieved without the need for extensive pre-training. Boundary edge errors were reduced by a mean of 7.5% through the integration of clustering. Therapeutic changes were quantified accurately (e.g., a reduction from 22,106 mm³ to 14,270 mm³ post-treatment) with an average processing time of 12–15 s per stack. Conclusions: An efficient, precise 3D tumor segmentation tool suitable for diagnostics and planning is presented. This approach is demonstrated to be a robust, data-efficient alternative to deep learning, particularly advantageous in clinical settings where the large annotated datasets required for training neural networks are unavailable. Full article

This paper introduces novel subfamilies of analytic and bi-univalent functions in $\mathrm{\Omega }=\left\{\varsigma \in \mathbb{C}:\left|\varsigma \right|<1\right\}$, defined by applying a linear operator associated with the Mittag–Leffler function and requiring subordination to domains related to generalized bivariate Fibonacci polynomials. The proposed framework provides a unified treatment that generalizes numerous earlier studies by incorporating parameters controlling both the operator’s fractional calculus features and the domain’s combinatorial geometry. For these subfamilies, we establish initial coefficient bounds ($\left|d_2\right|$, $\left|d_3\right|$) and solve the Fekete–Szegö problem ($\left|d_3-\xi d_2^2\right|$). The derived inequalities are interesting, and their proofs leverage the intricate interplay between the series expansions of the Mittag–Leffler function and the generating function of the Fibonacci polynomials. By specializing the parameters governing the operator and the polynomial domain, we show how our main theorems systematically recover and extend a wide range of known results from the literature, thereby demonstrating the generality and unifying power of our approach. Full article

The study explores analytic, geometric and algebaraic properties of two subclasses of analytic functions: the class of Bounded Radius Rotation denoted by ${\mathcal{R}}_{\mathfrak{s}}{,}_{\varrho }(\mathcal{A},\mathcal{B},z)$, and the class of Bounded Boundary Rotation denoted by ${\mathcal{V}}_{\mathfrak{s}}{,}_{\varrho }(\mathcal{A},\mathcal{B},z)$, both associated with strongly Janowski type functions. In particular, we obtain upper bounds for the third-order Hankel determinant $|{\mathcal{H}}_{3,1}f\left(z\right)|$ and concentrate on functions displaying 2- and 3-fold symmetry. We also provide estimates for the initial logarithmic coefficients ${\eta }_1,{\eta }_2,{\eta }_3$ and the Zalcman functional $|t_3^2-t_5|$ for each class. These findings provide fresh insights into the behavior of generalized subclasses of univalent function. Full article

Depending on the factors to which the soils are exposed, many properties and engineering parameters may change. In particular, the temperature parameter affects the strength of the soils, the degree of compressibility, permeability, void ratio, Atterberg limits, and many other parameters. In areas where high temperatures occur, such as heat piles and nuclear waste storage areas, alternative soil mixtures are needed that can stabilize or better optimize the behavior of the soils. For this purpose, additives with high heat transfer capacity and symmetry can be used. In this study, aluminum additive, which is known to have high conductivity, was used together with zeolite–bentonite mixtures. Aluminum-added mixtures were kept at different temperatures, and their thermal conductivity values were measured at the end of different periods. Measurements were first carried out at room temperature for all mixtures. Then, measurements were repeated at the end of 1, 3, and 10 days for 55 °C and 80 °C temperature values. At the end of the heating periods, the samples were left to cool to room temperature, and the thermal conductivity values were examined at the end of the heating–cooling cycle. Experimental results showed that thermal conductivity increased as temperature increased when the same period was taken as a basis, but an increase was observed for 1 and 3 day heating periods, while the thermal conductivity values for the 10th day decreased. The initial increase is attributed to the densification of the material due to the removal of free and weakly bound water or to the improvement of solid–solid contact paths. The subsequent decrease is due to microstructural deterioration, such as increased air-filled porosity, drying shrinkage, and microcracking due to thermal stresses, and material degradation caused by prolonged heating. In addition, thermal conductivity values of the mixtures under high temperature were estimated for days 100 and 365 using the DeepSeek method. The results showed that the thermal conductivity coefficients symmetrically decreased with increasing time. Full article

In this investigation, two new subfamilies of bi-univalent functions defined on the open unit disk are presented using Liouville–Caputo fractional derivatives. We determine bounds on the initial Maclaurin coefficients $|a_2|$ and $|a_3|,$ as well as Fekete–Szegö inequality results based on the bonds of $a_2$ and $a_3$ for functions belonging to certain bi-univalent function subfamilies. Additionally, some novel subfamilies are inferred that have not yet been examined within the context of Liouville–Caputo fractional derivatives. Full article

Regional economic diversity and unevenly allocated space-based resources have created unprecedented difficulties for collaborative and innovative supply chain construction. This paper sets up a tripartite evolutionary model of the government, upstream companies, and downstream companies to explore dynamic processes of regional supply chain collaborative innovation with bounded rationality. Through incorporation of hierarchical space organizations and policy incentive differentiation mechanisms, the model discerns actors’ behavioral evolution and strategic adjustment in a geographically divided structure. Adopting evolutionary game theory and numerical simulation, this paper includes crucial parameters like the conversion efficiency of return conversion, information-sharing coefficient, mutual trust coefficient, and fiscal subsidy coefficient for examining policy and spatial heterogeneity effects on information collaborative innovations. The results reveal that fiscal incentives are the primary driving factor for collaborative evolution across local supply chains. Adaptive profit-sharing and subsidy intensities both stimulate upstream innovation investments and downstream cooperation adoption efficiently, stimulating a shift out of inefficient equilibrium states towards sustainable high-cooperation states. Furthermore, the restructuring of space accelerates hierarchical differentiation—core region companies are able to act like initiators and leaders for collaborative innovations, while periphery companies encounter participatory barriers in terms of elevated coordination costs and incentive shortages. In light of this, it is therefore crucial to have a “core-driven, periphery-subsidized” policy system for eliminating spatial gaps, stimulating cross-regional information exchange, and building systemic robustness. These findings contribute to enhancing the overall efficiency, stability, and innovation capacity of regional supply chain systems. They also provide a theoretical basis for policy decision making and industrial upgrading across regions of varying scales and environments. Full article

In this paper, we introduce and investigate new subclasses of analytic bi-univalent functions defined via Caputo fractional derivatives with boundary rotation constraints. Utilizing the generalized operator ${\mathcal{C}}_{\mathsf{ȷ}}^{\varrho }$, which encompasses and extends classical operators such as the Salagean differential operator and the Libera–Bernardi integral operator, we establish sharp coefficient estimates for the initial Taylor Maclaurin coefficients of functions within these subclasses. Furthermore, we derive Fekete–Szegö-type inequalities that provide bounds on the second and third coefficients and their linear combinations involving a real parameter. Our approach leverages subordination principles through analytic functions associated with the classes ${\mathcal{T}}_{\varsigma }\left(\xi \right)$ and ${\mathcal{R}}_{\Omega }^{\mathsf{ȷ},\varrho }(\vartheta ,\varsigma ,\xi )$, allowing a unified treatment of fractional differential operators in geometric function theory. The results generalize several known cases and open avenues for further exploration in fractional calculus applied to analytic function theory. Full article

In this article, we present an efficient and highly accurate numerical scheme that achieves exponential convergence for solving nonlinear Riesz distributed-order fractional differential equations (RDFDEs) in one- and two-dimensional initial–boundary value problems. The proposed method is based on a two-stage collocation framework. In the first stage, spatial discretization is performed using the shifted Legendre–Gauss–Lobatto (SL-G-L) collocation method, where the approximate solutions and spatial derivatives are expressed in terms of shifted Legendre polynomial expansions. This reduces the original problem to a system of fractional differential equations (FDEs) for the expansion coefficients. Then, the temporal discretization is achieved in the second stage via Romanovski–Gauss–Radau collocation approach, which converts the system into a system of algebraic equations that can be solved efficiently. The method is applied to one- and two-dimensional nonlinear RDFDEs, and numerical experiments confirm its spectral accuracy, computational efficiency, and reliability. Existing numerical approaches to distributed-order fractional models often suffer from poor accuracy, instability in nonlinear settings, and high computational costs. By combining the efficiency of Legendre polynomials for bounded spatial domains with the stability of Romanovski polynomials for temporal discretization, the proposed two-stage framework effectively overcomes these limitations and achieves superior accuracy and stability. Full article

The central focus of this study is the development and investigation of a generalized subclass of bi-univalent functions, defined using the $q^2$-Srivastava–Attiya operator in conjunction with Bernoulli polynomials. We derive initial coefficient estimates for functions in the newly proposed class and also provide bounds for the Fekete–Szegö functional. In addition to presenting several new findings, we also explore meaningful connections with previously established results in the theory of bi-univalent and subordinate functions, thereby extending and unifying the existing literature in a novel direction. Full article

This paper presents Rain-Cloud Condensation Optimizer (RCCO), a nature-inspired metaheuristic that maps cloud microphysics to population-based search. Candidate solutions (“droplets”) evolve under a dual-attractor dynamic toward both a global leader and a rank-weighted cloud core, with time-decaying coefficients that progressively shift emphasis from exploration to exploitation. Diversity is preserved via domain-aware coalescence and opposition-based mirroring sampled within the coordinate-wise band defined by two parents. Rare heavy-tailed “turbulence gusts” (Cauchy perturbations) enable long jumps, while a wrap-and-reflect scheme enforces feasibility near the bounds. A sine-map initializer improves early coverage with negligible overhead. RCCO exposes a small hyperparameter set, and its per-iteration time and memory scale linearly with population size and problem dimension. RCOO has been compared with 21 state-of-the-art optimizers, over the CEC 2022 benchmark suite, where it achieves competitive to superior accuracy and stability, and achieves the top results over eight functions, including in high-dimensional regimes. We further demonstrate constrained, real-world effectiveness on five structural engineering problems—cantilever stepped beam, pressure vessel, planetary gear train, ten-bar planar truss, and three-bar truss. These results suggest that a hydrology-inspired search framework, coupled with simple state-dependent schedules, yields a robust, low-tuning optimizer for black-box, nonconvex problems. Full article

In recent years, special functions have played a significant role in the investigation of different subclasses within the class of bi-univalent functions. In this work, we present and investigate two new subclasses of bi-univalent functions defined in $\mathfrak{U}=$$\{\varsigma \in \mathbb{C}:|\varsigma |<1\}$, characterized by Bernoulli polynomials associated with imaginary error functions. For functions belonging to these subclasses, we establish bounds for their initial coefficients. For these classes, we also tackle the Fekete–Szegö problem. Several new results are also obtained as special cases by specifying certain parameter values in the general findings. Full article

In the present work, we define certain families, ${\mathbb{M}}_{\Sigma }\left(\mu ,{\rm Y},\gimel ,q; x\right)$ and ${\mathbb{N}}_{\Sigma }\left(\mu ,{\rm Y},\gimel ,q; x\right)$, of normalized holomorphic and bi-univalent functions associated with Bazilevič functions and $\gimel$-pseudo functions involving the $q$-Bernoulli polynomial, which is defined by the symmetric nature of quantum calculus in the open unit disk $U$. We determine the upper bounds for the initial symmetry Taylor–Maclaurin coefficients and the Fekete–Szegö-type inequalities of functions in the families we have introduced here. In addition, we indicate certain special cases and consequences for our results. Full article

This paper investigates a new subclass of bi-univalent analytic functions defined on the open unit disk in the complex plane, associated with the subordination to $1+\mathrm{s}\mathrm{i}\mathrm{n}z$. Coefficient bounds are obtained for the initial Taylor–Maclaurin coefficients, with a particular focus on the second- and third-order Hankel determinants. To illustrate the non-emptiness of the proposed class, we consider the function $\sqrt{1+tanhz}$, which maps the unit disk onto a bean-shaped domain. This function satisfies the required subordination condition and hence serves as an explicit member of the class. A graphical depiction of the image domain is provided to highlight its geometric characteristics. The results obtained in this work confirm that the class under study is non-trivial and possesses rich geometric structure, making it suitable for further development in the theory of geometric function classes and coefficient estimation problems. Full article