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        <title>Tatra Mountains Mathematical Publications Feed</title>
        <link>https://reference-global.com/journal/TMMP</link>
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            <title>Tatra Mountains Mathematical Publications Feed</title>
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            <link>https://reference-global.com/journal/TMMP</link>
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        <copyright>All rights reserved 2026, Slovak Academy of Sciences, Mathematical Institute</copyright>
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            <title><![CDATA[Mathematical and Numerical Methods for Accurate Aorta Segmentation from Non-Enhanced CT Data Yielding Reliable Identification and Evaluation of Large Vessel Vasculitis]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0005</link>
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            <pubDate>Wed, 09 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Segmentation of the aorta is crucial for various medical analyses, such as the diagnosis and treatment of cardiovascular diseases. This work presents mathematical models and methods yielding a semi-automatic segmentation of the aorta from non-enhanced CT data. Our framework consists of three steps. First, using the minimal path approach, we extract a path within the aorta from two user-supplied points. Then, using 3D Lagrangian curve evolution, we move the initial path to the approximate centerline of the aorta. The centered path is used in the last step to construct the initial condition for the generalized subjective surface method (GSUBSURF). Applying the GSUBSURF method with this initial condition yields an accurate segmentation of the aorta. The segmentation results and the manual segmentations overlap, with a worst-case mean Hausdorff distance of 2.175 ± 0.605 mm for a voxel spacing of 0.977 mm. Using the aorta centerline and segmentation, we define precise regions of interest along the aorta to assess large-vessel vasculitis from patient FDG-PET/CT image data. The application shows promising results, as we demonstrated widespread inflammation throughout the aorta in a patient prior to treatment. After treatment, we observed a significant reduction in inflammation and accurately identified the aortic regions where it persisted. These findings also align with those of experienced medical doctors who have worked on the same cases.]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[Prediction of Depression for Inpatients with Chronic Heart Failure]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0010</link>
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            <pubDate>Wed, 09 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Depression is a common and prognostically important comorbidity of chronic heart failure (CHF). Because datasets from cohort studies in this research area are often small and strongly imbalanced, and a ready-to-apply training and evaluation procedure for binary classification in this setting is still lacking, we provide a rigorous methodological overview and elaborate it into a straightforward protocol: leave-one-out cross-validation (LOOCV) with fixed seeds and default library hyperparameters, and a full panel of confusion matrix metrics, including imbalance-adjusted summaries. As an illustration of the chosen methodology, we reformulated the 9-item Patient Health Questionnaire (PHQ-9) screening as a binary classification task and compared three deliberately chosen standard methods—ridge-regularized logistic regression, decision tree, and RUSBoost—on a public cohort published by Cheng and co-authors in 2023. These methods are evaluated at each learner’s default operating point over the range of PHQ-9 binarization thresholds θ ∈ {1, . . . , 15}.RUSBoost obtained the best results at the standard diagnostic PHQ-9 cut-off θ = 10—sensitivity 0.641, specificity 0.619, accuracy 0.621 and a sensitivity– specificity gap of 0.022. As the only learner with built-in imbalance handling, it also consistently outperforms the two observation-weighted baselines on these metrics across the entire range of thresholds. However, absolute sensitivity and specificity remain below clinically ambitious levels for all three models. We attribute part of this performance ceiling to selection bias introduced during cohort acquisition and eligibility filtering.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Mathematical Oncology: Models, Methods, and Clinical Applications]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0011</link>
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            <pubDate>Wed, 09 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Mathematical oncology integrates mechanistic modeling, experimental biology, clinical medicine, and data science to improve cancer detection, treatment planning, and understanding of tumor dynamics. This work provides a systematic review of the field, tracing its historical development from early population- level growth models and the log-kill hypothesis to contemporary spatial, evolutionary, multiscale, and data-driven approaches, supported by a large-scale bibliometric analysis of the discipline’s emergence and thematic clusters. The review surveys mechanistic descriptions of tumor growth, the tumor microenvironment, clonal evolution, and metastasis, before examining models of treatment response, optimal control of therapy, and evolutionary game theory as frameworks for understanding and counteracting drug resistance. Multiscale modeling approaches for coupling molecular, cellular, and tissue-level processes are discussed alongside data-driven methods, including genomics and bioinformatics, artificial intelligence, and mechanistic learning, which combines knowledge-driven mathematical models with data-driven machine learning. Particular attention is given to digital twins and their prospective clinical validation, and to the practical requirements for translating mathematical models into clinical implementation, including model validation, FAIR data principles, and shared benchmarking infrastructure. The review concludes by outlining future directions for the field, emphasizing that sustained interdisciplinary collaboration across mathematics, biology, data science, and clinical medicine, rather than any single modeling paradigm, will determine the extent to which mathematical oncology translates into improved patient care.]]></description>
            <category>ARTICLE</category>
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        <item>
            <title><![CDATA[A Short Overview of Cellular Automata in Mathematical Oncology]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0012</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2026-0012</guid>
            <pubDate>Wed, 09 Sep 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Mathematical oncology has developed into an increasingly active interdisciplinary field, providing quantitative tools for the study of tumor growth, invasion, metastasis, treatment response, and therapy optimization. Within this field, cellular automata form an important class of models. This overview focuses on cellular automata and their extensions in the context of mathematical oncology. We first introduce the necessary mathematical preliminaries and then present the basic formalism of cellular automata, beginning with deterministic models and elementary cellular automata. We continue with a presentation of biologically motivated extensions, including probabilistic cellular automata, lattice-gas cellular automata, Cellular Potts models, and hybrid cellular automata. Particular attention is given to focusing this survey on the reader with some background in mathematics or computer science, who is interested in first discovering the biological applications of the model. Finally, we review selected works from the recent literature.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[On the Asymptotic Behaviour of the Integral    T(x)=∫0+∞|{xt}−{xt+1}|dt T(x)=\int_0^{+\infty}\left|\left\{\frac{x}{t}\right\}-\left\{\frac{x}{t+1}\right\}\right|\,dt  ]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0009</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2026-0009</guid>
            <pubDate>Tue, 30 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[In this paper, we estimate the integral T (x) considered in the title, where {t} denote the fractional parts of the real number t,and x is any positive real number.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Expansion of a Bivariate Symmetric Mean in the Neighbourhood of the First Bisector]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0008</link>
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            <pubDate>Fri, 19 Jun 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[In this paper, we investigate the behavior of a bivariate mean M near the first bisector by establishing, in several significant cases, an important expansion of M derived from the Taylor expansion of a single-variable function. These expansions are made explicit for a number of classical means. This motivates the introduction of the concept of the characteristic function QM of a mean M, defined as the second partial derivative of M with respect to its first variable, evaluated along the diagonal. The function QM measures the proximity of M to the arithmetic mean near the first bisector and provides a univariate analytic framework for comparing and classifying means. We prove that inequalities between characteristic functions yield local inequalities between the corresponding means, and that, in the case of homogeneous means, such inequalities hold globally.We also examine several important classes of means, both classical and novel, including: normal means, additive means,and (weighted) integral means of the first and second kind. For each class, we determine the specific form taken by the characteristic functions QM of the means M contained in that class, and we then study the injectivity and the surjectivity of the mapping M ↦ QM within the class. We also use characteristic functions to investigate intersections between certain classes of means, highlighting one of the key strengths of this concept. Finally, we introduce and study, for a given mean M,the classof M-means,and show, in particular, that the arithmetic-geometric mean AGM is an M-mean for a specific weighted integral mean of the first kind M.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Small Perturbations on Means and Lateral Means]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0007</link>
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            <pubDate>Wed, 22 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[We begin by investigating how small changes in the definition of ordinary means affect their properties, particularly the property of being a mean. In this direction, we look for weakenings of the basic defining property of means. Consequently, we introduce weaker notions in two directions. We study these functions and provide many examples.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[General Framework for Intuitionistic Values and Related Fuzzy Sets Based on Automorphisms]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0004</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2026-0004</guid>
            <pubDate>Wed, 22 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[This paper introduces a novel framework for understanding intuitionistic values and fuzzy sets through the automorphism of the unit interval [0, 1]. By generalizing the concepts of classical intuitionistic sets using strong negations generated by these automorphisms, we define the φ-intuitionistic values and explore their arithmetic, establishing a comprehensive set of operations based mainly on additive generators of t-(co)norms and their properties. This approach provides greater flexibility to the modelling with these sets.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Langevin Resonance Transformer for Cross-Script Writer Identification]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0006</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2026-0006</guid>
            <pubDate>Wed, 22 Apr 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Vision Transformers (ViTs) have emerged as a powerful architecture for various computer vision tasks, including writer identification. However, like their CNN counterparts, they are susceptible to performance degradation in cross-script scenarios because their standard self-attention mechanism learns script-specific visual correlations. To overcome this, we propose a novel architecture, the Langevin Resonance Transformer (LRT). The LRT fundamentally redefines self-attention by replacing the abstract mathematical operation with a physically-grounded dynamic simulation. Each image patch is treated as a particle. The core of the LRT is a novel Langevin Attention Layer, where the interaction between pairs of particles is governed by a learnable potential energy function. The net force on each particle is aggregated from all other particles, and its state is evolved according to the Langevin equation, which models motion under both deterministic and stochastic forces. The LRT treats a writer’s style as a physical system defined by an energy landscape. Because it models biomechanics rather than just visual shapes, the resulting representation works regardless of the script. We tested this on the BRS-ID dataset using a custom augmentation strategy. The results show that LRT achieves higher accuracy than standard Vision Transformers and other top-tier models on the cross-script identification task.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[A New Class of Mean Convergence : Structured Mean Convergence]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0001</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2026-0001</guid>
            <pubDate>Tue, 17 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[In this paper, we introduce the concept of structured mean convergence (SMC), a generalization of Cesàro convergence that allows averaging over selected index subsets rather than the entire sequence. This approach provides a flexible framework for analyzing the asymptotic behaviour of sequences under customized selection criteria. We explore the fundamental properties of SMC and establish its relationships with classical, Cesàro, and statistical convergence. Additionally, we examine its connection to lacunary mean convergence, proving that lacunary mean convergence is a special case of SMC under certain density conditions. We also present counterexamples demonstrating that SMC does not necessarily imply lacunary mean convergence. These results suggest that SMC provides a broader perspective on summability theory and sequence transformations. Potential applications of SMC include functional analysis, ergodic theory, and number theory, where selective summability plays a crucial role.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[On (τ1, τ2)-Star-I Compact Spaces]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0002</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2026-0002</guid>
            <pubDate>Tue, 17 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[This paper introduces the concept of the (τ1, τ2)-star-ℐ compact space in an ideal bispace, where an ideal bispace is a quadruple (X, τ1, τ2, ℐ), τ1, τ2 being topologies defined on the set X and I being an ideal defined on X. The structure of (τ1, τ2)-star-ℐ compactness has been compared with some nearer structures like (τ1, τ2)-I compactness, strongly star-I compactness, countably I compactness, etc. With some counter examples, the distinct structures of these topological features have been validated. The nature of subspaces and the nature of functions that preserve the (τ1, τ2)-star-I compactness are revealed. It has been shown that real-valued continuous functions defined on (τ1, τ2)-star-Ifin compact spaces are bounded. A characterization of this specific topological property in terms of a finite intersection property is provided. Finally, the relation with weakly (τ1, τ2)-star compactness is established by means of co-dense ideals.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Contextualized Vision Transformers (CVT): Adaptive Spectral Embedding and Feature Gating for Precise Text-Graphics Classification]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2026-0003</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2026-0003</guid>
            <pubDate>Tue, 17 Mar 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[The accurate classification of images into graphics-only, text-only, and mixed-content categories is a critical prerequisite for building efficient, content-aware processing pipelines. This initial triage prevents the unnecessary application of computationally expensive operations, such as Optical Character Recognition (OCR), to irrelevant graphical data. To address this challenge, we introduce the Contextualized Vision Transformer (CVT), a novel architecture designed specifically for this nuanced classification task. The CVT addresses the limitations of standard Vision Transformers (ViTs) through three synergistic components. It employs a Learnable Patch Decomposition (LPD) strategy that efficiently extracts patch embeddings. To model complex spatial arrangements, it introduces an Adaptive Spectral Embedding (ASE) module, which replaces static positional encodings with a dynamic, learnable representation. Crucially, a Contextual Feature Gating (CFG) module enhances feature discriminability by adaptively recalibrating patch-level features, selectively amplifying the salient text or graphic regions. Comprehensive K-fold cross-validation demonstrates the robustness and generalizability of the proposed model. The CVT achieves statistically significant improvements in accuracy, precision, and recall compared to state-of-the-art Vision Transformer baselines. Experimental results highlight the effectiveness of this architecture in providing a fast and accurate solution for the vital task of content triage in large-scale visual processing systems.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Solving Sparse Mrhs Systems With Genetic Algorithms]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0029</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0029</guid>
            <pubDate>Tue, 20 Jan 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[Multiple Right-Hand Sides (MRHS) equations represent a mathematical formalism with applications in algebraic cryptanalysis. Solving MRHS equation systems is in general a difficult problem. In this article, we investigate the efficient use of genetic algorithms for solving random sparse MRHS systems. Our experiments suggest that the steady-state selection method with low elitism and mutation rate gives the best results. If the systems are sparse, the system size does not have a significant impact on the success of the algorithm. On the other hand, the method is very sensitive to the system density, with the success rate rapidly declining with increased system density.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Compact Implicit High Resolution Numerical Method for Solving Transport Problems with Sorption Isotherms]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0030</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0030</guid>
            <pubDate>Tue, 20 Jan 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[This study investigates numerical methods for solving nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We describe and compare second order accurate numerical schemes, focusing on implicit methods, to effectively model transport phenomena without stability restriction on the choice of time steps. Furthermore, a high resolution form of the method is proposed that limits a priori the second order accurate scheme towards first order accuracy to keep the values of numerical solutions in a physically acceptable range.Through numerical experiments, we demonstrate the effectiveness of high resolution methods in minimizing oscillations near discontinuities, thereby enhancing solution plausibility. The observed convergence rates confirm that the second order accurate schemes achieve expected accuracy for smooth solutions and that they yield significant improvements when compared with the results of the first order scheme. As the computational cost of the compact implicit method seems to be comparable to similar explicit ones with a clear profit of unconditional stability, this research provides a practical tool toward numerical simulations of nonlinear transport phenomena applicable in various fields such as contaminant transport in porous media or column liquid chromatography.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Conjunctive and Disjunctive Compartmented Secret Sharing Schemes Using Elliptic Curves]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0028</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0028</guid>
            <pubDate>Tue, 20 Jan 2026 00:00:00 GMT</pubDate>
            <description><![CDATA[This article considers two secret sharing schemes, namely, conjunctive compartmented and disjunctive compartmented. Suppose a group of companies having many compartments is working on a project. In the conjunctive compartmented scheme, a specified number of users from each compartment of every company has to collaborate to access the secret key. While in a disjunctive compartmented scheme, any company with a predetermined number of users from each compartment can get the secret key. The schemes we have proposed use elliptic curves and bilinear pairings. Our schemes are verifiable and efficient. The proposed schemes are illustrated in full detail by concrete examples using SageMath.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Existence Results of Mild Solutions for Second Order Perturbed Pseudo Integro-Differential Evolution Equations with Infinite State-Dependent delay in Fréchet Spaces]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0023</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0023</guid>
            <pubDate>Thu, 18 Dec 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[This paper is concerned with the existence of mild solutions in Fréchet spaces combined with semigroup theory, using Avramescu’s nonlinear alternative for the sum of compact operators and contraction maps, to the second order perturbed pseudo integro-differential evolution equations with state-dependent delay.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Neumann Problem with a Nonlinear p(x)-Elliptic Equation Solved by Topological Degree Methods]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0021</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0021</guid>
            <pubDate>Thu, 18 Dec 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[In this paper, we prove the existence of weak solutions to Neumann boundary value problems for a nonlinear p(x)-elliptic equation of the form



-div a(x,u,∇u)=b(x)| u |p(x)-2u+λH(x,u, ∇u).
 - {\rm{div}}\,a(x,u,\nabla u) = b\left( x \right){\left| u \right|^{p\left( x \right) - 2}}u + \lambda H\left( {x,u,\,\nabla u} \right).


We established the existence result by using the topological degree introduced by Berkovits.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Weyl’s Classification of Singular Impulsive q-Sturm-Liouville Equations]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0007</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0007</guid>
            <pubDate>Thu, 18 Dec 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[In this work, the singular impulsive q-Sturm-Liouville equations are studied. Weyl’s famous classification was made for equations of this type.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[Fourth-Order Nonlinear Neutral Difference Equations: Oscillation via New Canonical Transforms]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0025</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0025</guid>
            <pubDate>Thu, 18 Dec 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[This paper presents a new method of transforming fourth-order nonlinear semi-canonical neutral difference equations into canonical type equations. This technique reduces the set of nonoscillatory solutions to only two. By eliminating these two remaining types of nonoscillatory solutions, the authors are able to obtain new criteria for the oscillation of all solutions of the equation under investigation. Examples are provided to demonstrate the significance and novelty of the main results.]]></description>
            <category>ARTICLE</category>
        </item>
        <item>
            <title><![CDATA[An Unconventional Finite Difference Technique for the Solution of Two-Point Third-Order Boundary Value Problems in ODEs]]></title>
            <link>https://reference-global.com/article/10.2478/tmmp-2025-0020</link>
            <guid isPermaLink="false">/article/10.2478/tmmp-2025-0020</guid>
            <pubDate>Thu, 18 Dec 2025 00:00:00 GMT</pubDate>
            <description><![CDATA[In this paper, we propose a numerical method to solve the boundary value problem involving third-order differential equations in ODEs in a closed--open domain, where the boundary conditions are prescribed at the closed and open end points. An application of interpolation and the smooth function method to incorporate the boundary condition at the open end point implied an unconventional finite difference method for the approximate numerical solution of the problem. Hence, the proposed method uses the boundary conditions in an exact and natural way. The method is simple in application and solves the problem directly. We have established the quadratic order of the accuracy and convergence of the proposed method analytically. The numerical results of computational experiments on model test problems, both nonlinear and linear, confirm the competency and the theoretical discussion on the order of convergence of the method. A singular problem is considered, and satisfying numerical results obtained in computational experiments is an extended application of the method.]]></description>
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