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Locally recoverable codes (LRCs) have emerged as fundamental objects in modern coding theory, primarily due to their pivotal role in distributed and cloud storage systems. A major breakthrough in their construction was achieved by Tamo and Barg, who introduced the notion of \emph{good polynomials} as a key structural ingredient. In this article, we propose a natural generalization of this paradigm by introducing the concept of \emph{good rational functions}. Building upon this extension, we develop a unified and flexible framework for constructing optimal LRCs. To quantify the quality of a rational function, we embed the problem into the rich context of algebraic function field theory and Galois theory. This perspective allows us to extend the Galois-theoretic framework originally developed by Micheli for good polynomials. In particular, we derive structural and quantitative results on the number of totally split rational places associated with rational functions. Furthermore, we construct explicit families of good rational functions that outperform all good polynomials of the same degree. As a consequence, we obtain infinite families of optimal LRCs with improved parameters compar

Agentic AI opens new opportunities for automating Business Process (BP), enabling autonomous decision-making and dynamic adaptation. However, realising this potential requires BP entities and their interactions to be defined with formal precision. This paper presents a formal framework for Agentic BP analysis through the AGO methodology. AGO captures the modelling perspective in terms of who is acting (Agents), why it is carried out (Goals), and what the relevant entities are (Objects). Grounded in set theory and mathematical logic, we formally define the AGO entity types and their interactions, organising all definitions into a BP Knowledge Base (BPKB). The resulting BPKB supports structured querying, incremental updates, and automatic generation of BP workflows, while ensuring soundness and completeness of the derived paths.

Enterprises are currently undergoing profound transformations due to the unpostponable digital transformation. Then, to remain competitive, enterprises must adapt digital solutions, transforming their organisational structures and operations. This organisational shift is also important for small and medium-sized enterprises. A key innovation frontier is the adoption of process-oriented production models. This paper presents a knowledge-based method to support business experts in designing business processes. The method requires no prior expertise in Knowledge Engineering and guides designers through a structured sequence of steps to produce a diagrammatic workflow of the target process. The construction of the knowledge base starts from simple, text-based, knowledge artefacts and then progresses towards more structured, formal representations. The approach has been conceived to allow a shared approach for all stakeholders and actors who participate in the BP design.

This article presents numerical simulations of an iron dust Bunsen flame. The results are validated against experimental results. The burning velocity is extracted from the 3D simulation results, as in the experiments. The agreement of the burning velocity between the model and experiment is the best to date for iron dust flames. A comparison is performed between 3D and 1D simulations to improve our understanding of how the 3D Bunsen flame deviates from an ideal 1D flame. This comparison reveals that the co-flow mixes with the post-flame zone, increasing the oxygen concentration in the reaction layer, which increases the burning velocity. Moreover, the analysis also reveals that stretch and curvature affect the burning velocity. These results are valuable for the future development of experimental setups aimed at measuring the burning velocity.

This article presents numerical simulations of the response of an iron dust Bunsen flame to particle seeding changes. A validated numerical model is used to study the impact of particle seeding fluctuations on flame stability. Simulations are conducted for the Bunsen setup in the right-side up and up-side down configuration. No significant differences in flame response are identified in flame stability between the right-side up and up-side down configurations. We find that the Bunsen flame is surprisingly robust to abrupt changes in particle loading. The sudden change in particle loading does not excite any intrinsic instabilities in the flame. Based on our results, the iron dust flames are robust to imposed fluctuations. We hypothesize that this is due to the lack of a feedback mechanism between the burned temperature and the heat release rate. This mechanism is present in conventional, chemistry-driven, gaseous flames. However, such a mechanism is absent in iron dust flames because the combustion of individual iron particles is limited by oxygen diffusion, which is insensitive to temperature.

Artificial Intelligence agents represent the next major revolution in the continuous technological evolution of industrial automation. In this paper, we introduce a new approach for business process design and development that leverages the capabilities of Agentic AI. Departing from the traditional task-based approach to business process design, we propose an agent-based method, where agents contribute to the achievement of business goals, identified by a set of business objects. When a single agent cannot fulfill a goal, we have a merge goal that can be achieved through the collaboration of multiple agents. The proposed model leads to a more modular and intelligent business process development by organizing it around goals, objects, and agents. As a result, this approach enables flexible and context-aware automation in dynamic industrial environments.

We generalize the shadow codes of Cherubini and Micheli to include basic polynomials having arbitrary degree, and show that restricting basic polynomials to have degree one or less can result in improved lower bounds on the minimum distance of the code. However, even these improved lower bounds suggest that shadow codes have considerably inferior distance-rate characteristics compared with the concatenation of a Reed-Solomon outer code and a first-order Reed-Muller inner code.

The operators $Λ_m$ ($m\in\mathbb{N}\cup \{0\}$) arise when one studies the action of the Beurling-Ahlfors transform on certain radial function subspaces. It is known that the weak-type $(1,1)$ constant of $Λ_0$ is equal to $1/\ln(2)\approx 1.44$. We construct examples showing that the weak-type $(1,1)$ constant of $Λ_1$ is larger than $1.38$ and that the weak-type $(1,1)$ constant of $Λ_m$ does not tend to $1$ when $m\to\infty$. This disproves a conjecture of Gill [Mich. Math. J. 59 (2010), No. 2, 353-363]. We also prove a companion result for the adjoint operators. This is the arXiv version of the paper - it includes some additional discussion in the appendices.

Three-dimensional CP-DNS of reacting iron particle dust clouds in a turbulent mixing layer are conducted. The simulation approach considers the Eulerian transport equations for the reacting gas phase and resolves all scales of turbulence, whereas the particle boundary layers are modelled employing the Lagrangian point-particle framework for the dispersed phase. The CP-DNS employs an existing sub-model for iron particle combustion that considers the oxidation of iron to FeO and that accounts for both diffusion- and kinetically-limited combustion. At first, the particle sub-model is validated against experimental results for single iron particle combustion considering various particle diameters and ambient oxygen concentrations. Subsequently, the CP-DNS approach is employed to predict iron particle cloud ignition and combustion in a turbulent mixing layer. The upper stream of the mixing layer is initialised with cold particles in air, while the lower stream consists of hot air flowing in the opposite direction. Simulation results show that turbulent mixing induces heating, ignition and combustion of the iron particles. Significant increases in gas temperature and oxygen consumption o

This paper is the English translation of the first 4 sections of the article ``Dimension de Heitmann des treillis distributifs et des anneaux commutatifs. Publications Mathématiques de Besançon. Algèbre et théorie des nombres, 2006'', after some corrections. Sections 5-7 of the original article are treated a bit more simply in the book ``Henri Lombardi and Claude Quitté. Commutative algebra: constructive methods. Finite projective modules. Springer, 2015.'' We study the notion of dimension introduced by Heitmann in his remarkable article ``Generating non-Noetherian modules efficiently, Mich. Math. J., 31, (1084)'' as well as a related notion, only implicit in his proofs. We first develop this within the general framework of the theory of distributive lattices and spectral spaces. -- Cet article est une version corrigée des 4 premières sections de l'article ``Dimension de Heitmann des treillis distributifs et des anneaux commutatifs. Publications Mathématiques de Besançon. Algèbre et théorie des nombres, 2006'' Les sections 5 à 7 de l'article original sont traitées de manière un peu plus simple dans ``Henri Lombardi and Claude Quitté. Commutative algebra: constructive methods. Finit

Biometric based authentication is currently playing an essential role over conventional authentication system; however, the risk of presentation attacks subsequently rising. Our research aims at identifying the areas where presentation attack can be prevented even though adequate biometric image samples of users are limited. Our work focusses on generating photorealistic synthetic images from the real image sets by implementing Deep Convolution Generative Adversarial Net (DCGAN). We have implemented the temporal and spatial augmentation during the fake image generation. Our work detects the presentation attacks on facial and iris images using our deep CNN, inspired by VGGNet [1]. We applied the deep neural net techniques on three different biometric image datasets, namely MICHE I [2], VISOB [3], and UBIPr [4]. The datasets, used in this research, contain images that are captured both in controlled and uncontrolled environment along with different resolutions and sizes. We obtained the best test accuracy of 97% on UBI-Pr [4] Iris datasets. For MICHE-I [2] and VISOB [3] datasets, we achieved the test accuracies of 95% and 96% respectively.

Fix a smooth projective family of curves $C \to S$ and a split reductive group scheme $G$ over a Noetherian base scheme $S$. For any (possibly nonreduced) fixed relative Cartier divisor $D$, we provide a treatment of the moduli of $G$-bundles on the fibers of $C$ equipped with $t$-connections with pole orders bounded by $D$. Under mild assumptions on the characteristics of all the residue fields of $S$, we construct a Hodge moduli space $M_{Hod, G} \to \mathbb{A}^1_S$ for the semistable locus, construct a Harder-Narasimhan stratification, and thus obtain a semistable reduction theorem. If all the fibers of the divisor of poles $D$ are nonempty, then we show that the stack of semistable objects is smooth over $\mathbb{A}^1_{S}$. We also define a Hodge-Hitchin morphism in positive characteristic and prove that it is proper.

Metals can serve as carbon-free energy carriers, e. g. in innovative metal-metal oxide cycles as proposed by Bergthorson (Prog. Energy Combust. Sci., 2018). Iron powder is a suitable candidate since it can be oxidized with air. Nevertheless, the combustion of iron powder in air is challenging especially with respect to flame stabilization which depends on the particle size distribution among other factors. Models for the prediction of reaction front speed in iron-air suspensions can contribute to overcoming this challenge. To this end, three different models for iron particle oxidation are integrated into a laminar flame solver for simulating reaction fronts. The scientific objective of this work is to elucidate the influence of polydispersity on the reaction front speed, which is still not satisfactorily understood. In a systematic approach, cases with successively increasing complexity are considered: From single particle combustion to iron-air suspensions prescribing binary particle size distributions (PSDs), generic PSDs, and a PSD measured for a real iron powder sample. The simulations show that, dependent on the PSD, particles undergo thermochemical conversion in a sequential

Accurate extraction of the Region of Interest is critical for successful ocular region-based biometrics. In this direction, we propose a new context-based segmentation approach, entitled Ocular Region Context Network (ORCNet), introducing a specific loss function, i.e., he Punish Context Loss (PC-Loss). The PC-Loss punishes the segmentation losses of a network by using a percentage difference value between the ground truth and the segmented masks. We obtain the percentage difference by taking into account Biederman's semantic relationship concepts, in which we use three contexts (semantic, spatial, and scale) to evaluate the relationships of the objects in an image. Our proposal achieved promising results in the evaluated scenarios: iris, sclera, and ALL (iris + sclera) segmentations, utperforming the literature baseline techniques. The ORCNet with ResNet-152 outperforms the best baseline (EncNet with ResNet-152) on average by 2.27%, 28.26% and 6.43% in terms of F-Score, Error Rate and Intersection Over Union, respectively. We also provide (for research purposes) 3,191 manually labeled masks for the MICHE-I database, as another contribution of our work.

Scattered polynomials over finite fields attracted an increasing attention in the last years. One of the reasons is their deep connection with Maximum Rank Distance (MRD) codes. Known classification results for exceptional scattered polynomials, i.e. polynomials which are scattered over infinite field extensions, are limited to the cases where their index $\ell$ is small, or a prime number larger than the $q$-degree $k$ of the polynomial, or an integer smaller than the $k$ in the case where $k$ is a prime. In this paper we completely classify exceptional scattered polynomials when the maximum between $\ell$ and $k$ is odd, and give partial results when it is even, extending a result of Ferraguti and Micheli in 2021.

In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring $R$ defining a surface in affine three-space over a field of characteristic zero. With this method, we construct an explicit minimal generating set for the modules of differential operators of order two and three, as well as their minimal free resolutions; this expands results of Bernstein, Gel'fand, and Gel'fand and of Vigué. Our construction relies, in part, on a description of these modules that we derive in the singularity category of $R$. Namely, we build explicit matrix factorizations starting from that of the residue field.

We define a notion of Hodge modules with rational singularities. A variety has rational singularities in the usual sense, if it is normal and the Hodge module related to intersection cohomology has rational singularities in the present sense. Our main result is a generalization of Boutot's theorem that if a reductive group acts on an affine variety with a stable point, and $H$ is an equivariant Hodge module with rational singularities, then the induced module on the GIT quotient also has rational singularities.

We first, introduce a deep learning based framework named as DeepIrisNet2 for visible spectrum and NIR Iris representation. The framework can work without classical iris normalization step or very accurate iris segmentation; allowing to work under non-ideal situation. The framework contains spatial transformer layers to handle deformation and supervision branches after certain intermediate layers to mitigate overfitting. In addition, we present a dual CNN iris segmentation pipeline comprising of a iris/pupil bounding boxes detection network and a semantic pixel-wise segmentation network. Furthermore, to get compact templates, we present a strategy to generate binary iris codes using DeepIrisNet2. Since, no ground truth dataset are available for CNN training for iris segmentation, We build large scale hand labeled datasets and make them public; i) iris, pupil bounding boxes, ii) labeled iris texture. The networks are evaluated on challenging ND-IRIS-0405, UBIRIS.v2, MICHE-I, and CASIA v4 Interval datasets. Proposed approach significantly improves the state-of-the-art and achieve outstanding performance surpassing all previous methods.

Observations of the first interstellar minor object 1I/2017 'Oumuamua did not reveal direct signs of outgassing that would have been natural if it had volatile-rich composition. However, a recent measurement by Micheli et al (2018) of a substantial non-gravitational acceleration affecting the orbit of this object has been interpreted as resulting from its cometary activity, which must be rather vigorous. Here we critically re-assess this interpretation by exploring the implications of measured non-gravitational acceleration for the 'Oumuamua's rotational state. We show that outgassing torques should drive rapid evolution of 'Oumuamua's spin (on a timescale of a few days), assuming torque asymmetry typical for the Solar System comets. However, given the highly elongated shape of the object, its torque asymmetry is likely higher, implying even faster evolution. This would have resulted in rapid rotational fission of 'Oumuamua during its journey through the Solar System and is clearly incompatible with the relative stability of its rotational state inferred from photometric variability. Based on these arguments, as well as the lack of direct signs of outgassing, we conclude that the c