Abstract: This paper presents a novel framework for real-time detection of anomalous trading patterns in financial markets using Generative Adversarial Networks (GANs). The proposed system integrates advanced deep learning techniques with specialised temporal attention mechanisms to identify complex market manipulation schemes while maintaining low latency requirements essential for high-frequency trading environments. The framework implements a multi-scale architecture that processes market data streams at multiple time horizons, incorporating market microstructure features and order book dynamics. Experimental evaluation on a comprehensive dataset spanning 24 months of trading data from various markets demonstrates the framework's superior performance, achieving 94.7% detection accuracy with sub-3ms latency. The system processes up to 150,000 transactions per second while maintaining stable performance across market conditions. The framework's adaptive threshold mechanism and hierarchical feature fusion approach significantly reduce false positives during periods of high market volatility. Comparative analysis shows a 15.5% improvement in detection accuracy over traditional methods. The implementation incorporates robust data preprocessing pipelines and efficient computational architectures, enabling practical deployment in production environments. The research contributes to the advancement of financial market surveillance technology by introducing innovative applications of GANs in real-time anomaly detection while addressing critical challenges in processing high-frequency trading data.

Abstract: We will show, in any space dimension d≥1, the decay and scattering in the energy space for the solution to the damped nonlinear Schrödinger equation posed on R^d×T and initial data in H¹(R^d×T). We will derive also new bilinear Morawetz identities and corresponding localized Morawetz estimates.

Abstract: This study proposes a deep learning-driven stock market sentiment analysis and prediction framework based on the fusion model of convolutional neural network (CNN) and long short-term memory network (LSTM). Natural language processing (NLP) technology is used to extract the sentiment features of financial news and social media texts, and a high-dimensional feature space is constructed by combining the market transaction data.CNN is responsible for local feature extraction, and LSTM is used for time-series modeling to realize the accurate prediction of market sentiment. Experimental results show that the model outperforms a single deep learning model in terms of mean square error (MSE), coefficient of determination ( ) and F1-score, which proves the effectiveness of the fusion method. The research results provide scientific support for financial market prediction and investment decision-making.

Abstract: This paper presents a novel mathematical framework for addressing the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. We introduce new mathematical tools that extend beyond traditional partial differential equation theory to establish the global existence and uniqueness of smooth solutions to the three-dimensional Navier-Stokes equations. Our approach combines advanced functional analysis with innovative harmonic analysis techniques to overcome the longstanding difficulties associated with the nonlinear term and pressure. The theoretical results are validated through numerical simula- tions and demonstrate practical applications in turbulence prediction for aircraft design, weather forecasting, and blood flow modeling.

Abstract: This research introduces the concept of harmonically m-convex set-valued functions, combining harmonically m-convex functions and set-valued mappings. We establish fundamental properties and derive a Hermite-Hadamard-type inequality for these functions, generalizing classical results in convex analysis. The study provides a theoretical foundation with potential applications in optimization, variational analysis, and mathematical economics, where set-valued mappings are essential. This work advances the understanding of harmonic convexity in the context of set-valued analysis, offering new insights for both theoretical and applied mathematics.

Abstract: Synthesizing climate change impacts on agriculture requires integrating diverse climate projections, spatial data, multiple process-based crop models, and various management scenarios. Existing approaches often rely on cumbersome, specific scripting, hindering scalability, reproducibility, and the robust exploration of uncertainty through multi-model ensembles. We present PyCIAT (Python Climate Impact and Adaptation Toolkit for Agriculture), an open-source, configuration-driven framework designed to orchestrate complex agricultural impact assessments. PyCIAT utilizes a modular Python architecture, driven by a central YAML configuration file, to manage workflows encompassing climate data processing (GCMs/RCMs), soil data integration, simulation setup across multiple locations, parallelized execution of crop simulation models via standardized interfaces (placeholders for DSSAT, APSIM, STICS provided), and automated post-processing for impact and adaptation analysis. Key features include explicit handling of multi-model ensembles, HPC-readiness via support for cluster job arrays, standardized output variable mapping, and optional integration points for advanced modules (e.g., detailed water dynamics, biotic stress) and machine learning surrogates potentially leveraging advances in AI for agriculture [1]. This framework significantly reduces boilerplate code, enhances reproducibility, and facilitates large-scale, systematic exploration of climate impacts [2] and adaptation strategy effectiveness across diverse agricultural systems. PyCIAT provides a scalable and extensible platform for advancing agricultural modeling under climate change.

Abstract: Determining whether a piece of text was used to pretrain a large language model (LLM) is a critical challenge in understanding model behavior and ensuring data privacy. In this paper, I propose a novel Semantic Echo Analysis approach to detect pretraining text usage by analyzing the LLM’s output for semantic and stylistic "echoes" of the input text. My method is manual, requiring no access to the model’s internals, and leverages statistical and linguistic analysis to identify overfamiliarity in the LLM’s responses. I compare my approach to existing methods like membership inference attacks, watermarking, and text memorization detection, highlighting its unique focus on semantic patterns. A detailed experimental evaluation, theoretical analysis, and practical insights demonstrate the feasibility of my method for academic and ethical applications, such as data privacy audits and intellectual property protection.

Abstract: This paper is mainly to do in-depth research on inequalities on symmetric cones. We will conduct further analysis and discussion based on the inequalities we have developed on the second-order cone, and develop more inequalities. According to our past research in dealing with second-order cone inequalities, we derive more inequalities concerning eigenvalue version of Young inequality and trace version of inverse Young inequality. These results coincide with the conclusions on the positive semidefinite cone, which is also a symmetric cone. It is of considerable help to the establishment of inequalities on symmetric cones and the analysis of their derivative algorithms.

Abstract: In this article, we are devoted to investigating a class of fractional differential inclusions with impulses in a concrete ordered Banach algebra. The existence results of solutions for the considered problem are derived by applying related hybrid fixed point theorem of multi-valued maps. A simple example is provided to illustrate and validate our proposed results.

Abstract:

This paper introduce a fractional-fractal ψ-Fueter operator in the quaternionic context inspired in the concepts of proportional fractional derivative and Hausdorff derivative of a function with respect to a fractal measure. Moreover, we establish the corresponding Stokes and Borel-Pompeiu formulas associated to this generalized fractional-fractal ψ-Fueter operator.

Abstract:

Among the equivalents of the Riemann Hypothesis (RH), a millennium unsolved problem ([7]), the Alcantara-Bode equivalent ([2]) is of a particular interest due to its formulation: the Riemann Hypothesis holds iff the null space of the integral operator on L2(0, 1) having the kernel function the fractional part of the ratio (y/x), contains only the element 0 ([2]), i.e. iff the operator is injective. This equivalent formulation allows us to use techniques outside of the number theory field in order to prove it and so, to show that RH holds. We introduced in this article a functional analysis - numerical method for investigating the injectivity of the linear bounded operators on separable Hilbert spaces, updating and extending the result from [1]. The method is built around the result obtained (Theorem 1) saying that if a linear bounded operator is strict positive on a dense set, then it is injective. When the operator - or its associated Hermitian replacing it if needed, is only positive definite on a dense set, additional operator properties should be considered. Dealing with this case, two are the directions we choose for obtaining the corresponding criteria, using the operator approximations over finite dimension subspaces in L2(0, 1) whose union is dense: · involving the operator finite rank approximations on subspaces or, · involving its adjoint restrictions on subspaces. (Injectivity Criteria [1]). Applying both versions of the method on the dense set of indicator interval functions, we proved the Alcantara-Bode equivalent is true so, that RH holds. This solution for RH is not one in pure math. field as seems to have been expected since 1859. However, it is in line with the Clay Math Inst. principle that has been expressed (citing [7]) by: "A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers."

Abstract: Concerns about hardware security are raised by the increasing dependence on third-party Semiconductor Intellectual Property in system-on-chip design, especially during physical design verification. Traditional rule-based verification methods, such as Design Rule Checking (DRC) and Layout vs. Schematic (LVS) checking, together with side-channel analysis, indicated apparent deficiencies in dealing with new forms of threat. The impossibility of distinguishing dependable from malicious insertions in ICs makes it hard to prevent such dangers as hardware Trojans (HTs); side-channel vulnerabilities remain everywhere, and modifications at various stages of the manufacturing process can be hard to detect. This thesis addresses these security challenges by defining a theoretical AI-driven framework for secure physical design verification that couples graph neural network models (GNNs) and probabilistic modeling with constraints optimized to maximize IC security. This approach views physical design verification as graph-based machine learning: GNNs identify unauthorized modifications or discrepancies between the layout and circuit netlist through the acquisition of behavioral metrics and structural feature extraction of netlist data. A probabilistic DRC model is derived after processing some learning data using recurrent algorithms. This model departs from the rigid rules of traditional deterministic DRC in that it uses machine learning-based predictions to estimate the likelihood that design rules will be violated. Also, we can model mathematical foundations for the secure routing as a constrained pathfinding problem for all myths addressed above concerning these different methods— moves are optimized to avoid sources of security problems. These problems might include crosstalk-induced leakage and electromagnetic side-channel threats. Lagrange multipliers and Karush-Kuhn-Tucker (KKT) conditions are included in verification to maintain security constraints while ensuring efficient use of resources. Then, HT detection is reformulated as GNN-based node embeddings, whose information propagation throughout the circuit graph picks up modifications at boundary nodes and those less deep in the structure. As an alternative to experience-based anomaly detection proposed in earlier work, a theoretical softmax-based anomaly classification framework is put forward here to model HT insertion probabilities, gathering acceptable anomalies at various levels of circuit design from RTL-level to Gate-level as necessary. The capturing of side-channel signals becomes the focus of a deep learning-based theoretical run-time anomaly detection model, aiming at power and electromagnetic (EM) leakage patterns so that all potential threats can be detected early on. This theoretical framework provides a conceptual methodology for scalable, automated, and robust security verification in modern ICs through graph-based learning, and constrained optimization methods. It lays a foundation to advance secure semiconductor designs further using AI-driven techniques without recourse to benchmarks or empirical validations.

Abstract: Machine learning (ML) is becoming more common in the insurance industry to predict costs and help set prices. Accurate predictions help insurance companies set fair prices while keeping insurance affordable for customers. However, many ML models are difficult to understand, making it unclear how they make decisions. This study focuses on improving prediction accuracy and making models easier to interpret by using hyperparameter tuning with Optuna and feature importance analysis with SHAP (SHapley Additive Explanations). Three models—Ridge Regression, Random Forest, and XGBoost—were optimized and tested. The results show that XGBoost performed the best, with a median Rsquared of \textbf{0.8655} and RMSE of \textbf{4136.59}. SHAP analysis found that \textbf{smoking status, BMI, and age} were the most important factors affecting insurance costs. These findings show that using both model tuning and explainability tools helps improve ML models for insurance pricing.

Abstract: On the basis of the isomorphic algebraic structures of the field of complex numbers ℂ and the 2-dimensional Euclidean field of vectors V₂, in terms of identical geometric products of elements, in this paper vector integral identities have been derived for scalar and vector fields in V₂, which are vector analogues of the well-known integral identities of complex analysis. In doing so, special attention is given to the vector analogue in V₂ of Cauchy's calculus of residues.

Abstract: This paper, by constructing a fractional epidemic model, analyzes the transmission dynamics of some infectious diseases under the effect of vaccination, which is one of the most effective and common control measures. In the model, with reference that antibody formation by vaccination may not cause permanent immunity, it has been taken into account that the protection period provided by the vaccine may be finite in addition the fact that this period may change according to individuals. The model differs from other SVIR models given in the literature in terms of its progressive process with a distributed delay in losing of the protective effect provided by the vaccine. To explain this process, the model has been constructed by using a system of distributed delay nonlinear fractional integro-differential equations. Thus, the model aims to present a realistic approach to following the course of the disease.

Abstract:

In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the b-metric setting: fixed-point theorems, stability results, and a variant of Ekeland’s variational principle. As a consequence, we also derive a variant of Caristi’s fixed-point theorem.

Abstract: In this work, by using one dynamic Gronwall-Bihari type integral inequality on time scales, an interesting asymptotic behavior property of high-order nonlinear dynamic equations on time scales was obtained, which also generalized two classical results belong to Mate and Neval’s and Agarwal and Bohner’s respectively.

Abstract: This paper aims to explore the sufficient conditions for assuring that, the set of mild solutions to two types of non-local semilinear fractional differential inclusions involving the conformable derivative, in the existence of non-instantaneous impulses, is not empty and compact. We will consider the case when the linear part in the studied problem is the infinitesimal generator of a C₀ - semigroup or a sectorial operator. We give the definition of mild solutions, and then, by using appropriate fixed point theorems for multi-valued functions and the properties of both the conformable derivative, and the measure of noncompactness, we achieve to our findings. Since the most of the known fractional derivatives do not satisfy many basic properties that usual derivatives have, the conformable derivative is introduced in a previous paper, and it is shows that it is the most natural definition. Therefore, many works have been done on differential equation with the conformable. But, works on semilinear differential inclusions are not reported until now. We will do not assume that the semigroup generated by the linear term is not compact,also, we will examine the case when the values of the multi-valued function are convex, also nonconvex. So, our work is novel, and interested. We give examples of the application of our theoretical resultsThis paper aims to explore the sufficient conditions for assuring that, the set of mild solutions to two types of non-local semilinear fractional differential inclusions involving the conformable derivative, in the existence of non-instantaneous impulses, is not empty and compact. We will consider the case when the linear part in the studied problem is the infinitesimal generator of a C₀ - semigroup or a sectorial operator. We give the definition of mild solutions, and then, by using appropriate fixed point theorems for multi-valued functions and the properties of both the conformable derivative, and the measure of noncompactness, we achieve to our findings. Since the most of the known fractional derivatives do not satisfy many basic properties that usual derivatives have, the conformable derivative is introduced in a previous paper, and it is shows that it is the most natural definition. Therefore, many works have been done on differential equation with the conformable. But, works on semilinear differential inclusions are not reported until now. We will do not assume that the semigroup generated by the linear term is not compact,also, we will examine the case when the values of the multi-valued function are convex, also nonconvex. So, our work is novel, and interested. We give examples of the application of our theoretical results.

Abstract:

We consider a generalization of the evolution equation for wave fronts in chemical reactions. For this equation, we establish global well-posedness in weighted Sobolev spaces, Z_s,1/2(R), s ≥ 1, and prove the existence of a global attractor in these spaces. In particular, our results also imply the existence of a global attractor for the Kuramoto-Sivashinsky (KS) equation in these spaces.

Abstract: In this paper, we investigate the existence and uniqueness of solutions for the viscous Burgers’ equation for the isothermal flow of power-law non-Newtonian fluids $$\rho (\partial_t u + u \partial_x u)=\mu \partial_x \left(\left|\partial_x u \right|^{p-2} \partial_x u\right),$$ augmented with the initial condition $u(0, x)=u_0$, $0<x<L$ and the boundary condition $u(t, 0)=u(t, L)=0$, where $\rho$ is the density, $\mu$ the viscosity, $u$ the velocity of the fluid and $p$, $1<p<2$, $L, T>0$. Moreover, numerical solutions to the problem are constructed by applying the high-level modeling and simulation package COMSOL Multiphysics at small and large Reynold's numbers.