Abstract: In this paper, we move beyond the classical setting by redefining the Chebyshev functional in the context of q-circles situated within Minkowski space, rather than the standard Euclidean circles in R². This approach introduces a new theoretical framework suitable for non-Euclidean geometries. We derive sharp estimates for the functional when applied to functions on q-circles that adhere to Hölder-type continuity conditions.

Abstract: Time series data, characterized by temporal dependencies, seasonality, and noise, are prevalent in domains such as healthcare, finance, energy, and transportation. Effective clustering of time series enables the discovery of patterns, supports forecasting, and facilitates data-driven decision-making. This paper provides a comprehensive review of time series clustering techniques, including conventional methods (e.g., k-means, hierarchical, and fuzzy clustering), similarity-based approaches (e.g., Dynamic Time Warping), feature-based methods, and deep learning models (e.g., autoencoders, convolutional and recurrent neural networks). The review analyzes tasks, application domains, performance outcomes, and key limitations, highlighting common challenges such as computational complexity, sensitivity to noise, and scalability issues. A particular focus is given to transport-related time series, including traffic flow, travel time, and congestion patterns, demonstrating how clustering can support traffic state classification, anomaly detection, and infrastructure planning. The analysis reveals a trade-off between accuracy, interpretability, and computational efficiency, emphasizing the need for scalable, robust, and domain-aware clustering frameworks. Finally, practical directions for future research are discussed, including lightweight hybrid approaches and transport-specific feature engineering to enhance clustering performance in real-world applications.

Abstract: This study presents the development and verification of CUPID-MSR, an extended thermal-hydraulics code incorporating temperature-dependent properties of two chloride-based molten salts, KCl–UCl3 and NaCl–MgCl2–TRUCl3. Verification against the de Vahl Davis natural-convection benchmark across Rayleigh numbers 1,000–1,000,000 showed agreement within 0.4–3.9%, accurately capturing reference Nusselt numbers, flow structures, and thermal boundary layers. Additional temperature-variation studies confirmed stable and consistent performance of the implemented material correlations. The applicability of the Boussinesq approximation was assessed by comparing full variable-density and Boussinesq formulations, revealing that the approximation remains accurate for βΔT ≲ 0.1. Since this threshold depends only on relative density change, it is broadly relevant for natural-convection flows in Newtonian fluids.

Abstract: This paper addresses the failure of major digital investments to achieve sustained technology adoption in developing countries, hindering their business growth. While existing research identifies institutional drawbacks as a key problem, it offers limited guidance on progress within these constraints. To address this gap, the new Institutional Framework for Smart Technology Adoption (IFSTA), pronounced Eye-f-sta, is developed as a contingent institutional framework connecting digital transformation theory with practical assessment tools. IFSTA argues that adoption success depends not on technology alone, but on strategic alignment with specific institutional contexts. Built around three core pillars, governance, socio-technical infrastructure, and adaptive capacity, the framework explains how their interactions shape adoption. Three questions are addressed: (1) how local conditions moderate infrastructure impact; (2) what workarounds enable progress amid fragile systems; and (3) how digital investments can be sequenced based on institutional starting points. A central insight is the critical role of localization, adapting standards, platforms, and partnerships to local context as a fundamental mechanism. Contributions are threefold: addressing the gap between diagnosis and implementation by developing effective guidance for developing economies; methodologically bridging static assessments with actionable diagnostics; and practically providing a structured framework and Performance-Knowledge Index (PKI) tool to diagnose contexts and prioritize interventions, moving from agnostic best practices to local strategies.

Abstract: Topic modeling plays an essential role in extracting latent structures from large text corpora. The choice of model and the number of topics which can strongly influence the performance and interpretability of the outcomes. In this work, I compare three widely used models in topic modeling: Latent Dirichlet Allocation, Non-Negative Matrix Factorization, and Bidirectional Encoder Representations from Transformers. The outcomes of the models are studied using Entropy, Jaccard similarity, Coherence, and Silhouette over a wide number of topics. The results show that NMF consistently produces the most interpretable and distinct topics, achieving the highest coherence score, with optimal performance observed at k = 15. LDA yields broader and less coherent topics. In contrast, BERT-based clustering shows low Silhouette scores, indicating weak cluster separation.

Abstract: We prove that the Riemann Hypothesis (RH) admits a theorem-level stagewise arithmetical normal form of type $\Pi^0_2$, obtained from a single fixed terminating certificate calculus for the Riemann $\Xi$--function. Let \[ \xi(s):=\tfrac12\,s(s-1)\,\pi^{-s/2}\Gamma\!\Bigl(\frac{s}{2}\Bigr)\zeta(s), \qquad \Xi(z):=\xi\!\left(\tfrac12+\ii z\right), \] and let \[ \U:=\{z=x+\ii y\in\CC:\ x>0,\ 0<y<\tfrac12\}. \] Then RH is equivalent to $Z(\Xi;\U)=\varnothing$.We construct a countable family of rational stage rectangles $\{\Omega_{j,k}\}_{j\ge1,k\in\ZZ}$ with $\overline{\Omega_{j,k}}\subset\U$ and $\U\subseteq\bigcup_{j,k}\Omega_{j,k}$, and we define an explicit predicate \[ \Cert(j,k,c)\ \subseteq\ \NN_{\ge1}\times\ZZ\times\NN \] whose truth asserts that the code $c$ is a mechanically checkable certificate that $\Xi$ is zero-free on $\Omega_{j,k}$. Soundness is proved via certified boundary nonvanishing, a certified winding computation, and the argument principle.Decidability of $\Cert$ is proved by a terminating verifier based on rational disk arithmetic together with explicit rational remainder bounds for special-function evaluations (Euler--Maclaurin for $\zeta,\zeta',\zeta''$ and Stirling-type bounds for $\Gamma,\psi,\psi'$). The verifier uses only rational computations and certified rational upper bounds; external libraries (e.g.\ Arb) may be used to \emph{discover} certificates but are not trusted by the formal predicate.Define the sweep sentence \[ \CS:\Longleftrightarrow\ \forall j\ge1\ \forall k\in\ZZ\ \exists c\in\NN\ \Cert(j,k,c). \] We prove $\RH\iff\CS$. Since $\Cert$ is decidable, $\CS$ is a $\Pi^0_2$ sentence; thus RH is $\Pi^0_2$.

Abstract: We develop a comprehensive Lagrangian framework for the analysis of singularities in the threedimensional chemotaxis–Navier–Stokes system. Focusing on suitable weak solutions, we introduce the notion of Lagrangian singular trajectories and establish a geometric characterization of the space–time blow-up set. Our main theoretical advance shows that singularities are confined to a low-dimensional Lagrangian structure transported by the flow. More precisely, we prove that the space–time singular set S is contained in a countable union of Lagrangian trajectories associated with the velocity field and satisfies the sharp estimate dim_H(S) ≤ 1. This result constitutes a substantial refinement of classical Eulerian partial regularity bounds of Caffarelli–Kohn–Nirenberg type and provides a genuinely geometric interpretation of singularity formation in coupled fluid–chemotaxis models. The proof combines global energy inequalities, compactness methods, and partial regularity theory with a refined analysis of the Lagrangian flow map in the DiPerna–Lions–Ambrosio setting. A key feature of our approach is the propagation of regularity along particle trajectories, which allows singularities to be tracked dynamically and yields improved dimensional estimates via tools from geometric measure theory. Beyond the dimensional bound, the proposed Lagrangian formulation clarifies the mechanism by which chemotactic forcing interacts with fluid transport to produce potential blow-up and establishes a direct connection between singularity formation and low-dimensional invariant structures. These results open new perspectives for the geometric analysis of singularities in active fluid systems and related nonlinear PDEs.

Abstract: We consider the Fisher–KPP equation with Neumann boundary conditions on the real half line. We claim that the Fisher-KPP equation with Neumann boundary conditions is well-posed only for odd positive stationary solutions. We begin by proving that the Fisher-KPP equation with a Dirichlet boundary condition is stable, and with a Robin condition is stable only for odd positive stationary solutions. Then we inferred and proved that the Fisher-KPP equation with Neumann boundary conditions is stable only for odd positive stationary solutions. We solved the Fisher–KPP equation with Neumann boundary conditions to demonstrate the existence of the solution. In addition, we proved the uniqueness of the solution. Moreover, we proved the the solution of Fisher-Kpp equation with Dirichlet condition is stable. We also showed that the Fisher-KPP equation with Robin boundary conditions is stable only for odd positive stationary solutions. The uniqueness and existence proof of the Fisher-KPP equation with Robin condition are similar to the Neumann condition. Hence, we conclude that the Fisher-KPP equation on the real line is well-posed for the Dirichlet condition, and well-posed only for odd positive stationary solutions for both the Neumann condition and the Robin condition.

Abstract: We present a study to assess the feasibility and implications of replacing internal combustion engine vehicles with battery-powered electric vehicles (EVs) in a car-sharing fleet. For the analysis, we used operational data from a local car-sharing company, which encompasses various aspects such as trip distance, start and duration, vehicle type, and pickup and return locations. To evaluate the impact of transitioning the entire fleet to EVs, we used EV and charger models to simulate the battery-powered trips and also the necessary post-trip recharging. Both could affect the service quality of car sharing services, as the requested trip distance might not be covered by an electric vehicle due to range or charging time limitations. Specifically, in our simulation-based analysis, we identified chains of consecutive bookings as a critical factor for car-sharing electrification. Furthermore, to assess the potential impact of electrification on the energy grid, we used data about the local grid load and its composition to relate it to the predicted vehicle charging times.

Abstract: The rapid expansion of artificial intelligence (AI) technologies has led to an increasing demand for skilled professionals across various industries. Understanding job market dynamics such as salary distribution, experience requirements, employment types, and remote work opportunities is crucial for students, job seekers, educators, and policymakers. This research presents a comprehensive visual analytics study of the global AI job market using a real-world dataset consisting of approximately 15,000 job postings. The dataset includes variables such as job titles, salaries in USD, experience levels, employment types, company locations, employee residence, remote work ratios, industry sectors, and benefits scores. Building on established visual analytics practices in employment and public-health data analysis, this study applies a range of exploratory tasks used in prior research, including trend identification, comparison across categories, correlation analysis, and outlier detection. Visualization techniques such as bar charts, box plots, scatter plots, line graphs, violin plots, and heatmaps are employed to explore patterns and relationships within the data. The analysis shows that salary is strongly correlated with experience level and geographic location. Senior-level professionals earn significantly more than entry-level employees, while countries such as the United States, Switzerland, and Canada offer the highest compensation. In addition, remote and hybrid work arrangements are increasingly prevalent and, in some cases, associated with higher average salaries. The study supports career decision-making by enabling stakeholders to identify high-paying regions, realistic experience pathways, and industries with strong AI demand.

Abstract: Minesweeper has been a traditional puzzle game based on numeric patterns to indicate the presence of hidden mines. Despite being a game with simple gameplay patterns, its algorithmic structure has been well defined in terms of a set of predefined rules to deduce safe and harmful cells. This research aims to perform an algorithmic analysis of Minesweeper instead of being a traditional game analysis approach. Several player-based tests have been developed for evaluating the algorithmic performance in different sizes of game boards. Black-box and user-based testing techniques have been employed in this research as used in traditional game analysis frameworks. The experiment outcomes indicate good algorithmic performance for smaller game boards but poor performance for larger boards under conditions of uncertain game data.

Abstract: The type of AI used to design video game enemies greatly affects the gameplay experience of speed, difficulty, and enjoyment. In most cases, the majority of developers who create 2D platforming games will choose to implement a simple but efficient AI design over an advanced AI model that learns based on experience. One of these simpler AI models that is frequently utilized by 2D platforming game developers is the Finite State Machine (FSM) model. The FSM model creates an organization of the enemy's actions into a limited number of well-defined behaviours, while also indicating how these behaviours relate to one another. We look at how AI uses the FSM method in the 2D platform game "Kirby: Nightmare in Dreamland," which first came out on the Game Boy Advance. The analysis of FSM models enemy AI behaviors and how those behaviors change and when they do so affects how hard the game is. Simulated experiments were conducted on how state time is spread out and how to make things harder by changing the attack cooldown. The results show that FSM-based AI is easy to control, doesn't need a lot of processing power, and has behavior that can be predicted. This makes it a good choice for platform games that are easy to get into. The results show that FSMs are still important in AI research and game design today.

Abstract: Unmanned Aerial Vehicle (UAV), when equipped as communication relays, offer a flexible solution to extend Vehicle-to-Vehicle (V2V) communications beyond fixed infrastructure and Non-Line-of-Sight constraints. In this setting, the allocation of radio resources, across time, frequency and space through beamforming, is challenged by the mobility of Connected and Autonomous Vehicles (CAVs) and their temporal dependencies, as access opportunities depend on prior transmission outcomes such as queue backlog or failed attempts. This paper proposes a Radio Resource Assignment (RRA) framework for UAV-aided V2V networks with beamforming-capable UAV relays. The model discretizes time and space to account for mobility and to track the movement of groups of CAVs across beam segments. The model also incorporates Time Division Multiple Access (TDMA)-based scheduling, beam activation constraints, and realistic traffic generation patterns. Analytical expressions are derived for per-user success probability and system throughput under both, ideal and realistic conditions, and they are validated against simulations, confirming the accuracy of the proposed approximations. Numerical results highlight trade-offs involving UAV altitude and resource allocation interval, while a heuristic beam-activation optimization strategy is shown to further enhance performance, achieving up to 12\% throughput gain over uniform activation.

Abstract: The standard $\varepsilon$--$\delta$ definition of continuity is inherently quantitative, yet the precise dependence of the admissible radius $\delta$ on the accuracy $\varepsilon$ and the base point $x_0$ is rarely treated as an independent mathematical object. In this paper, we introduce the \textit{radius of continuity} through two variants: the radius of pointwise continuity and the radius of uniform continuity, defined as explicit numerical invariants that capture the maximal symmetric neighborhood on which a real-valued function maintains a prescribed tolerance. We establish the fundamental structural properties of these radii, including their behavior under algebraic operations such as sums, products, and compositions, and demonstrate their inverse relationship to the classical modulus of continuity. Furthermore, we prove that the finiteness pattern of these radii characterizes constant versus non-constant functions. To illustrate the utility of this framework, we derive closed-form expressions for the pointwise radius of quadratic polynomials and the uniform radius of the normal probability density function. These examples highlight how the radius of continuity encodes geometric and probabilistic features, such as local curvature and global scale parameters. Ultimately, this perspective bridges the gap between real analysis and quantitative methods in metric geometry, offering a concrete measure of the stability of a function's continuity.

Abstract: This study was inspired by Alcantara-Bode’s equivalent to the Riemann Hypothesis published in 1993, the equivalent formulation consisting in the injectivity of an integral operator connected to Riemann Zeta function. Surprisingly, the research on this line has not continued, an explanation would be the lack of criteria for the injectivity of integral operators. This paper aims to fill this gap by proposing a functional-numerical analysis solution exploiting the operator positivity properties on dense sets. The main theorem says that a linear, bounded operator strict positive definite on a dense set of a separable Hilbert space, has its null space containing only the null element, equivalently, it is injective. Having in mind to obtain a generic and useful criterion, we gradually changed the hypothesis of the strict positivity of the operator on a dense set to the involvement at the end, of the associated Hermitian operator that is semi positive on the whole space requesting additional properties related to the positivity of operator approximations on finite dimension subspaces. Then, in order to apply the criterion for Hermitian Hilbert-Schmidt operators, we choose an adequate dense set allowing to obtain operator sparse matrix representations. The criterion applied to the associated Hermitian of the Alcantara-Bode integral operator, showed that the equivalent holds, so the Riemann Hypothesis is true.

Abstract: On the basis of the isomorphic algebraic structures of the field of complex numbers ℂ and the 2-dimensional Euclidean field of real vectors V₂, in terms of identical geometric products of elements, this paper brings integral identities for scalar and vector fields in V₂, which are vector analogues of the well-known integral identities of complex analysis. Consequently, in this paper, Theorem 1., which is a generalized fundamental theorem of integral calculus in the field V₂, is the vector analogue of the Cauchy theorem of complex analysis. Therefore, special attention is paid to the vector analogue of Cauchy's calculus of residues in the field V₂. Finally, at the very end of the paper, the algebraic structure of the 3D field of vectors V₃ is presented, as well as the corresponding fundamental integral identities.

Abstract: Background: In Japan, the number of older adults living alone has been increasing, raising the risk of unnoticed health decline or solitary death. Continuous monitoring using sensors can help detect behavioral changes indicating health issues and has the potential to support both older adults and their families. Methods: We obtained behavior and temperature data, continuously recorded over a long period at 15-min intervals from sensors installed in the homes of nine older adults living alone. After data cleaning, behavioral signals were analyzed using Fourier spectral analysis and multiple regression to extract 13-dimensional behavioral characteristic vectors. We whitened a portion of these behavioral characteristic vectors as benchmark data. We applied the same whitening process to the comparing data using the matrix obtained during this whitening process. By analyzing misclassification rates using boundary variance for benchmark and comparing data, we attempted to detect temporal changes in user behavior and differences between individuals. Results: Spectral analysis revealed 24-hour periodicity in all users’ behavior. By analyzing the misclassification rate using boundary variance for long-term signals, we identified users who maintain consistent behavioral patterns and those exhibiting significant temporal variation. We were also able to detect differences in these behavioral patterns. Conclusions: This study demonstrates that long-term temporal changes in the daily behavior of older adults living alone can be detected using simple continuous sensor data. Our approach is applicable not only for monitoring behavior changes in older adults living alone, but also for observing behavior changes in people with disabilities and children within the home environment.

Abstract: The Green Tech Revolution is humanity’s answer to climate change, featuring game-changing advances in renewable energy, smart infrastructure and circular economies. Successes like Denmark’s wind energy dominance and Norway’s electric vehicle adoption provide proof that scalable, meaningful solutions are attainable. Nevertheless, this revolution in power generation has brought with it major ethical and logistical problems. The environmental impact of mining, global concerns over e-waste, and social risks, including the digital divide and job displacement, reveal a complicated terrain in which innovation can unwittingly exacerbate existing inequities. To manage this, we require a multidimensional Balancing act between Progress and equity. This involves supporting next-generation technologies such as hydrogen fuel and perovskite solar cells, implementing strong policies for sustainable production and recycling, and encouraging individual responsibility via greener consumption. In the end, a truly sustainable future is not going to be delivered by technology; it has to be a imperative and equitable partnership between governments, corporations and citizens. It is only through such concerted efforts that the gains of the green transition can be shared universally, so that planetary health and social justice march forward hand in hand.

Abstract: The semantic interpretation of actions is deeply intertwined with how change unfolds over time, space, and interaction. Prior theoretical and computational work has suggested that explicitly modeling three-dimensional motion---including object positions and orientations evolving through time---should offer a privileged pathway for encoding fine-grained verb meaning, especially for distinctions such as \textit{roll} versus \textit{slide}. At the same time, the vast majority of multimodal language models rely almost exclusively on two-dimensional visual inputs, implicitly assuming that such projections suffice to ground linguistic meaning. In this work, we revisit this assumption through a systematic and tightly controlled comparison of visual and motion-based modalities. We construct self-supervised encoders over both 2D video observations and 3D trajectory data, and probe the resulting representations for their capacity to discriminate verb-level semantic categories. Contrary to prevailing intuition, our empirical analysis reveals that representations learned from 2D visual streams are competitive with, and in some cases indistinguishable from, those derived from explicit 3D trajectories. These findings complicate the widely held belief that richer environmental encodings automatically lead to superior semantic representations, and suggest that the relationship between perceptual fidelity and linguistic abstraction is more nuanced than often assumed. Our study offers early evidence that effective verb representation may emerge from multiple perceptual pathways, motivating a rethinking of how embodiment and modality interact in multimodal language learning.

Abstract: We will prove the generalized stability of an additive-quadratic-cubic functional equation in the sprit of Găvruţa.