Aura-CAPTCHA was developed as a multi-modal CAPTCHA system to address vulnerabilities in traditional methods that are increasingly bypassed by AI technologies, such as Optical Character Recognition (OCR) and adversarial image processing. The design integrated Generative Adversarial Networks (GANs) for generating dynamic image challenges, Reinforcement Learning (RL) for adaptive difficulty tuning, and Large Language Models (LLMs) for creating text and audio prompts. Visual challenges included 3x3 grid selections with at least three correct images, while audio challenges combined randomized numbers and words into a single task. RL adjusted difficulty based on incorrect attempts, response time, and suspicious user behavior. Evaluations on real-world traffic demonstrated a 92% human success rate and a 10% bot bypass rate, significantly outperforming existing CAPTCHA systems. The system provided a robust and scalable approach for securing online applications while remaining accessible to users, addressing gaps highlighted in previous research.

In the age of open and free information, a concerning trend of reliance on AI is emerging. However, existing AI tools struggle to evaluate the credibility of information and to justify their assessments. Hence, there is a growing need for systems that can help users evaluate the trustworthiness of online information. Although major search engines incorporate AI features, they often lack clear reliability indicators. We present TrueGL, a model that makes trustworthy search results more accessible. The model is a fine-tuned version of IBM's Granite-1B, trained on the custom dataset and integrated into a search engine with a reliability scoring system. We evaluate the system using prompt engineering and assigning each statement a continuous reliability score from 0.1 to 1, then instructing the model to return a textual explanation alongside the score. Each model's predicted scores are measured against real scores using standard evaluation metrics. TrueGL consistently outperforms other small-scale LLMs and rule-based approaches across all experiments on key evaluation metrics, including MAE, RMSE, and R2. The model's high accuracy, broad content coverage, and ease of use make trustworthy information more accessible and help reduce the spread of false or misleading content online. Our code is publicly available at this https URL, and our model is publicly released at this https URL.

Symmetric teleparallel gravity and its $f(Q)$ extensions have emerged as promising alternatives to General Relativity (GR), yet the role of explicit geometry-matter couplings remains largely unexplored. In this work, we address this gap by proposing a generalized $f(Q,\mathcal{L}_m)$ theory, where the gravitational Lagrangian density depends on both the non-metricity scalar $Q$ and the matter Lagrangian $\mathcal{L}_m$. This formulation naturally includes Coincident GR and the Symmetric Teleparallel Equivalent of GR as special cases. Working in the metric formalism, we derive the corresponding field equations, which generalize those of the standard $f(Q)$ gravity, and obtain the modified Klein-Gordon equation for scenarios involving scalar fields. The cosmological implications of the theory are explored in the context of the Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. As a first step, we obtain the modified Friedmann equations for $f(Q,\mathcal{L}_m)$ gravity in full generality. We then investigate specific cosmological models arising from both linear and non-linear choices of $f(Q,\mathcal{L}_m)$, performing detailed comparisons with the standard $\Lambda$CDM scenario and examining their observational consequences.

The right kind of theoretical treatment of direct Coulomb ionization of inner-shell of target atoms including multiple ionization of their outer-shells by using accurate x-ray fluorescence yield data and electron capture by projectile ions from inner-shell electrons of target atoms enables us to fully understand the complex physics issues with the heavy-ion-induced inner-shell ionization phenomenon. Such great success has only been achieved recently [Phys. Rev. A 111 (2025) 042827]. Aftermath, further investigations exhibit such a picture only if the Fermi velocity of the elemental target is accurate, as it takes a significant role in correct evaluation of charge-state distribution of the projectile ions inside the target, which contributes an invaluable share in calculating the electron capture-induced ionization cross section correctly. In this work, we devise a powerful method that enables us to measure the correct and accurate Fermi velocity for almost every elemental metal in the periodic table. As per our present knowledge, this in turn not only improves our understanding of the said complex physics issues one step ahead but also helps move toward further miniaturization of integrated circuits and use the heavy-ion-induced X-ray emission in impurity analysis more reliable and accurate.

In this work we study the E1 decay processes, $^3P_1$ $\rightarrow$ $^3S_1\gamma$, and $^3S_1$ $\rightarrow$ $^3P_1\gamma$ in the framework of Bethe-Salpeter equation and calculate their decay widths. We have used algebraic forms of Salpeter wave functions obtained through analytic solutions of mass spectral equations for ground and excited states of $^3S_1$, and $^3P_1$ equal mass quarkonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. These decay widths have been compared with data and other models.

Low-dimensional materials with broken inversion symmetry and strong spin-orbit coupling can give rise to fascinating quantum phases and phase transitions. Here we report coexistence of superconductivity and ferromagnetism below 2.5\,K in the quasi-one dimensional crystals of non-centrosymmetric (TaSe$_4$)$_3$I (space group: $P\bar{4}2_1c$). The unique phase is a direct consequence of inversion symmetry breaking as the same material also stabilizes in a centro-symmetric structure (space group: $P4/mnc$) where it behaves like a non-magnetic insulator. The coexistence here upfront contradicts the popular belief that superconductivity and ferromagnetism are two apparently antagonistic phenomena. Notably, here, for the first time, we have clearly detected Meissner effect in the superconducting state despite the coexisting ferromagnetic order. The coexistence of superconductivity and ferromagnetism projects non-centrosymmetric (TaSe$_4$)$_3$I as a host for complex ground states of quantum matter including possible unconventional superconductivity with elusive spin-triplet pairing.

We explore the ground states of strongly interacting bosons in the vanishingly small and weak lattices using the multiconfiguration time-dependent Hartree method for bosons (MCTDHB) which calculate numerically exact many-body wave function. Two new many-body phases: fragmented or quasi superfluid (QSF) and incomplete fragmented Mott or quasi Mott insulator (QMI) are emerged due to the strong interplay between interaction and lattice depth. Fragmentation is utilized as a figure of merit to distinguish these two new phases. We utilize the eigenvalues of the reduced one-body density matrix and define an order parameter that characterizes the pathway from a very weak lattice to a deep lattice. We provide a detailed investigation through the measures of one- and two-body correlations and information entropy. We find that the structures in one- and two-body coherence are good markers to understand the gradual built-up of intra-well correlation and decay of inter-well correlation with increase in lattice depth.

In this work, we explore the behavior of interacting dark energy and dark matter within a model of $f(Q)$ gravity, employing a standard framework of dynamical system analysis. We consider the power-law $f(Q)$ model incorporating with two different forms of interacting dark energy and dark matter: $3\alpha H\rho_m$and$\frac{\alpha}{3H}\rho_m \rho_{DE}$. The evolution of$\Omega_m, \Omega_r, \Omega_{DE}, q$, and$\omega$ for different values of the model parameter $n$ and the interaction parameter $\alpha$ has been examined. Our results show that the universe was dominated by matter in the early stages and will be dominated by dark energy in later stages. Using the observational data, the fixed points are found to be stable and can be represented the de Sitter and quintessence acceleration solutions. We discover that the dynamical profiles of the universe in $f(Q)$ dark energy models are influenced by both the interaction term and the relevant model parameters.

This paper studies the thermodynamic topology through the bulk-boundary and restricted phase space (RPS) frameworks. In bulk-boundary framework, we observe two topological charges $(\omega = +1, -1)$ concerning the non-extensive Barrow parameter and with ($\delta=0$) in Bekenstein-Hawking entropy. For Renyi entropy, different topological charges are observed depending on the value of the $\lambda$ with a notable transition from three topological charges $(\omega = +1, -1, +1)$ to a single topological charge $(\omega = +1)$ as $\lambda$ increases. Also, by setting $\lambda$ to zero results in two topological charges $(\omega = +1, -1)$. Sharma-Mittal entropy exhibits three distinct ranges of topological charges influenced by the $\alpha$ and $\beta$ with different classifications viz $\beta$ exceeds $\alpha$, we will have $(\omega = +1, -1, +1)$, $\beta = \alpha$, we have $(\omega = +1, -1)$ and for $\alpha$ exceeds $\beta$ we face $(\omega = -1)$. Also, Kaniadakis entropy shows variations in topological charges viz we observe $(\omega = +1, -1)$ for any acceptable value of $K$, except when $K = 0$, where a single topological charge $(\omega = -1)$. In the case of Tsallis-Cirto entropy, for small parameter $\Delta$ values, we have $(\omega = +1)$ and when $\Delta$ increases to 0.9, we will have $(\omega = +1, -1)$. When we extend our analysis to the RPS framework, we find that the topological charge consistently remains $(\omega = +1)$ independent of the specific values of the free parameters for Renyi, Sharma-Mittal, and Tsallis-Cirto. Additionally, for Barrow entropy in RPS, the number of topological charges rises when $\delta$ increases from 0 to 0.8. Finally for Kaniadakis entropy, at small values of $K$, we observe $(\omega = +1)$. However, as the non-extensive parameter $K$ increases, we encounter different topological charges and classifications with $(\omega = +1, -1)$.

Multi-core quantum computing architectures offer a promising and scalable solution to the challenges of integrating large number of qubits into existing monolithic chip design. However, the issue of transferring quantum information across the cores remains unresolved. Quantum Teleportation offers a potential approach for efficient qubit transfer, but existing methods primarily rely on centralized interconnection mechanisms for teleportation, which may limit scalability and parallel communication. We proposes a decentralized framework for teleportation in multi-core quantum computing systems, aiming to address these limitations. We introduce two variants of teleportation within the decentralized framework and evaluate their impact on reducing end-to-end communication delay and quantum circuit depth. Our findings demonstrate that the optimized teleportation strategy, termed two-way teleportation, results in a substantial 40% reduction in end-to-end communication latency for synthetic benchmarks and a 30% reduction for real benchmark applications, and 24% decrease in circuit depth compared to the baseline teleportation strategy. These results highlight the significant potential of decentralized teleportation to improve the performance of large-scale quantum systems, offering a scalable and efficient solution for future quantum architectures.

The paper introduce a new type of partitions where the largest part appears exactly once, and the remaining parts constitute a partition of that largest part. We derive the generating function associated with these partitions and subsequently explore several variations, providing the corresponding generating functions for each variant.

The charged particles are tracked in the high energy physics detectors to provide the information of their properties. One of the tracking detector is straw tube detector that has been used by many experiments. The motivation behind the current work is to study the primary ionization and particle identification using straw tube detectors. Additionally, we report the decay of $^{60}$CO for the study of gamma peaks since these are used in cobalt therapy, that is beneficial for cancer/tumor treatment. The various studies like primary ionization, spatial co-ordinate distributions in the different gas mixtures, transition radiation, drift velocities of electrons and diffusion coefficients using different xenon-based gas mixtures have been obtained. These studies have been done after the optimization of xenon-based gas mixtures for a deeper understanding. The gas mixture that shows maximum transition radiation among the xenon-based gas mixtures was found to be $Xe:He:CH_{4}$ :: 30:55:15. The gas mixture that posses maximum primary ionization has been observed to be $Xe:CO_{2}$ :: 70:30. Finally, the simulations have been carried out for the particle identification in the straw tube detectors with different particles i.e., muons, pions and kaons.

In this review paper, we explore operator aspects in extremal properties of Bernstein-type polynomial inequalities. We shall also see that a linear operator which send polynomials to polynomials and have zero-preserving property naturally preserve Bernstein's inequality.

Antennas are known to radiate and absorb radiation. We can use this property of antennas in microwave imaging. In microwave imaging the dielectric of the surrounding objects is considered. The S11 parameters are studied. These parameters are different for cells with tumor and without. This helps us in distinguishing between normal and cancerous cells. So this is a property utilized in brain tumor detection.

The charge state distributions (CSDs) of the projectile ions through gaseous or solid targets in the energy range of tandem accelerators (1 MeV/u < E < 5 MeV/u) have a major impact on ion-atom collision and accelerator physics. Theoretically it is possible to generate the CSDs for up to Ni-like ions, but empirical models have no such bounds. In the recent decades, the mean charge states are mostly obtained from an empirical formula [Schiwietz et al., Nucl. Inst. Meths. 225, 4(2004)]. But no description on CSDs is found there. To estimate the CSDs, we have used Gaussian distribution function having distribution width given by [Novikov and Teplove, Phys. Lett. 378, 1286(2014)]. The results obtained have been compared with the experimentally measured CSDs for the heavy projectile ions. The merits and demerits of such empirical formulae have been discussed.

Radiation hard n-Fz Double Sided Silicon microstrip Detectors are used at the Silicon Tracker for the detection of two-dimensional position and energy measurement of the incident protons in the R3B experiment at FAIR, Darmstadt, Germany. For the development of the detectors for the R3B Silicon Tracker, the macroscopic analysis is conducted on the test structure of n-Fz Double Sided Silicon microstrip Detector, which was fabricated by BEL, Bengaluru, India, and the SRH results on the non-irradiated test structure detectors are compared with the experimental data. The SRH and CCE modeling is used to extrapolate the results up to the proton fluence of 8E14 neq cm-2 for the proton irradiated detectors. This experience is used in the designing of the detectors for the phase 1 upgrade of the experiment and the proposed Double Sided Silicon microstrip Detector equipped with Wider Guard Ring design is simulated by 2-D Silvaco ATLAS device TCAD. To evaluate the breakdown performance of the proton irradiated detectors, the inner and the outer sides (towards the cut edge of the detector) of the detector are simulated to extract the electric field distribution up to an applied bias of -1000 V. In order to observe the effect of the interstrip capacitances on the noise of the readout system of the proton irradiated (back side) detectors, SPICE simulation is performed. The results reveal that a new radiation hard 200 {\mu}m ac coupled Double Sided Silicon microstrip Detector (with an intra guard ring) having an outer edge wider guard ring (dead space of 450 {\mu}m) structure has been proposed for the phase 1 upgrade of the R3B Silicon Tracker.

The complex physics of inner shell ionization of target atoms by heavy ion impact has remained only partially solved for decades. Recently, agreement between theory and experiment has been achieved by considering inner shell ionization of target atoms due to projectile electron capture in addition to direct Coulomb ionization including multiple ionization effects. A thorough investigation exhibits such a picture only if the atomic parameters of the target atoms are correct. In fact, the theoretical approach is found to be right, but the problem arises with the faulty atomic parameters. Furthermore, we show that fluorescence yields play a major role among the atomic parameters. We explore such a powerful method that enables us to measure the correct and accurate fluorescence yields for almost every element in the periodic table. As per our present knowledge, this in turn not only solves the said complex issue fully but also makes the PIXE analysis more reliable and accurate using both light and heavy ions.

In high energy physics experiments, the numerical estimation of primary ionization is crucial. An advance study on primary ionization can help in minimizing the effects such as electrical discharges that can damage the gaseous detectors used in high energy physics experiments. The simulation of primary ionization of electrons and positrons with the noble gases using the geant4 toolkit have been presented. The obtained primaries have been separated from secondaries as the later contribute towards electrical discharges and further damage the detectors. The xenon gas shows highest primary ionization among the noble gases.