Search Results (208)

A near-field is an algebraic structure akin to a division ring where distributivity is relaxed on one side. The smallest such object is the Dickson near-field of order nine. We lay the foundations of linear codes over that near-field. This includes a systematic form for their generator matrices based on a one-sided Gauss pivot algorithm. Dual codes are defined and a formula is given for the parity check matrix. LCD codes are characterized by a direct sum property. Self-orthogonal codes are classified in short lengths. Full article

Under the influence of engineering disturbances, the loading rate of surrounding rock is in a state of continuous adjustment. This study conducts experimental investigations on the mechanical response characteristics under different strain rates (10⁻⁵ s⁻¹, 10⁻⁴ s⁻¹, and 10⁻³ s⁻¹). During the uniaxial loading process of coal–rock composite specimens, multi-parameter monitoring was implemented, and a systematic study was carried out on the ring-down count induced by microcracks, the energy values of acoustic emission (AE) events, the stage-dependent strain characteristics on the specimen surface, and the surface temperature variation characteristics. Additionally, the stress–strain curve characteristics under different strain rates were comparatively analyzed in stages. The loading process of the coal–rock composite specimens was reproduced using the Particle Flow Code (PFC3D 6.0) simulation software. The simulation results indicate that the stress–strain results obtained from the simulation are in good agreement with the laboratory test results; based on these simulation results, the energy accumulation and dissipation characteristics of the coal–rock composite specimens under the influence of strain rate were revealed. Furthermore, a microscopic damage model considering strain rate was constructed based on the Weibull probability statistics theory. The results show that strain rate has a significant impact on the strength, elastic modulus, and failure mode of the coal–rock composite specimens. At low strain rates, the specimens exhibit obvious progressive failure characteristics and strain localization phenomena, while at higher strain rates, they show brittle sudden failure characteristics. Meanwhile, the thermal imaging results reveal that at high strain rates, the overall temperature rise in the composite specimens is rapid, whereas at low strain rates, the overall temperature rise is slow—but the temperature rise in the coal portion is faster than that in the rock portion. The peak temperature at high strain rates is approximately 2 °C higher than that at low strain rates. The PFC simulation results demonstrate that the larger the strain rate, the faster the growth rate of plastic energy in the post-peak stage and the faster the release rate of elastic energy. Full article

Torularhodin is the monocyclic C40 carotenoid with the β-ring and a terminal carboxyl group at the acyclic part, with long conjugated double bonds, only synthesized in fungi called red (oleaginous) yeasts, e.g., the genera Rhodotorula and Sporobolomyces. This unique red pigment with strong antioxidant properties is promising for use in food additives, nutritional supplements, and cosmetics. We aimed to produce torularhodin in Escherichia coli through the identification of the biosynthesis genes needed for its heterologous production, while no genes oxidizing torulene to torularhodin had been reported. The Rhodotorula toruloides crtI (CAR1) and crtYB (CAR2) genes, which were chemically synthesized, proved to lead to the complete conversion of phytoene into torulene when they were introduced into an E. coli cell that carried the Pantoea ananatis crtE and Haematococcus pluvialis IDI genes. We found that the Planococcus maritimus genes coding for C30 carotenoid terminal oxidase (crtP/crtNb/cruO) and aldehyde dehydrogenase (aldH/crtNc), through their introduction into the E. coli transformant synthesizing torulene, mediated the efficient oxidations of torulene to torularhodin, and resulted in the production of torularhodin as the dominant carotenoid. This is the first report of torularhodin production in a heterologous host. We also identified the aldH/crtNc gene in R. toruloides. Full article

We study UAV-assisted 5G uplink connectivity for disaster response, in which a UAV (unmanned aerial vehicle) acts as an aerial base station to restore service to ground users. We formulate a joint control problem coupling UAV kinematics (bounded acceleration and velocity), per-subchannel uplink power allocation, and uplink non-orthogonal multiple access (UL-NOMA) scheduling with adaptive successive interference cancellation (SIC) under a minimum user-rate constraint. The wireless channel follows 3GPP urban macro (UMa) with probabilistic line of sight/non-line of sight (LoS/NLoS), realistic receiver noise levels and noise figure, and user equipment (UE) transmit-power limits. We propose a bounded-action proximal policy optimization with generalized advantage estimation (PPO-GAE) agent that parameterizes acceleration and power with squashed distributions and enforces feasibility by design. Across four user distributions (clustered, uniform, ring, and edge-heavy) and multiple rate thresholds, our method increases the fraction of users meeting the target rate by 8.2–10.1 percentage points compared to strong baselines (OFDMA with heuristic placement, PSO-based placement/power, and PPO without NOMA) while reducing median UE transmit power by $64.6\%$. The results are averaged over at least five random seeds, with $95\%$ confidence intervals. Ablations isolate the gains from NOMA, adaptive SIC order, and bounded-action parameterization. We discuss robustness to imperfect SIC and CSI errors and release code/configurations to support reproducibility. Full article

This paper presents a physics-informed, tacholess pipeline for smartphone-grade Noise, Vibration, and Harshness (NVH) diagnosis in electric vehicle powertrains. A configurable generator synthesizes labeled signals with order components (1×/2×/3×), AM/FM modulation, sub-harmonics, impact-driven ring-down near resonance, and realistic white/pink/ambient noise at phone bandwidths. A ridge-guided harmonic comb recenters orders without a tachometer and splits tonal from residual content. Interpretable features—order-invariant ratios ($E_{2\times }/E_{1\times }$, ${\mathrm{S}\mathrm{B}}_1$/$E_{1\times }$, $E_{0.5\times }/E_{1\times }$) and residual descriptors (band-power, kurtosis, cepstrum/WPT)—feed light-compute models. A reproducible benchmark stresses SNR (−5…+10 dB), RPM profiles (ramp/steps/cycles), and simulated domain shift; parameter-to-feature analyses (with Sobol sensitivity and a delta-method identifiability proxy) quantify measurability under phone constraints. Across a five-fold CV, tacholess order tracking increases tonal SNR by ≥+6 dB and yields macro-F1 ≈ 0.86 with Random Forest, while ordinal severity achieves QWK ≈ 0.81 (ECE ≈ 0.06) and regression attains MAE ≈ 0.12 (R² ≈ 0.78). All code, datasets, figures, and tables regenerate from fixed seeds with one-command builds; a data card and a sim-to-real guide are included. The result is an open, low-compute standard that couples reproducibility with physics-aligned interpretability, providing a practical baseline for EV NVH diagnostics with smartphones and a common ground for future field validation. Full article

Let e be a fixed positive integer and $n_1,n_2$ be odd positive integers. The main objective of this article is to investigate the algebraic structure of double cyclic codes of length $(n_1,n_2)$ over the finite chain ring ${}_e\mathcal{R} = F_{4^e}+v{F}_{4^e}$, where $v^2=0$. Building upon this structural framework, we further demonstrate the construction of DNA codes derived from these double cyclic codes over ${}_e\mathcal{R}$. In addition, we provide the necessary and sufficient criteria showing that these codes possess reversibility and reverse-complement properties over ${}_e\mathcal{R}$. Furthermore, we introduce a generalized Gray map that extends the classical Gray map from the ring $F_2+v{F}_2$ with $v^2=0$ to the ring ${}_e\mathcal{R}$, showing a direct correspondence between elements of ${}_e\mathcal{R}$ and DNA sequences over $S=\{A,T,G,C\}$ utilizing double cyclic codes. To illustrate the applicability of our results, we present some examples demonstrating the effectiveness of the mapping in generating reversible and reverse-complement DNA codes from algebraic structures over the ring ${}_e\mathcal{R}$. Full article

To study the bearing capacity of large width-to-height ratio (LWHR) wind power spread foundations on onshore sandy soils, this study takes a 2 MW unit foundation of a specific wind farm as the object, conducts its sustainable design optimization, structural design and bearing capacity analysis, and explores internal force variation patterns of the structure and foundation. First, it investigates interactions among foundation soil stiffness, foundation deformation, and width-to-height ratio, and proposes the ratio can be slightly over 2.5 under specific geological conditions. Then, it verifies the foundation’s design and bearing capacity via code-based methods and uses ABAQUS to build an integrated finite element model (foundation, reinforcement, foundation ring, soil) for analyzing the mechanical behavior of the overall structure and key components. Finally, it focuses on bending moments of the foundation’s top/bottom slab reinforcement and reaction force distribution, and compares results from code formulas, commercial software, and finite element analysis. The results show that foundation deformation relates to the outer cantilever’s width-to-height ratio, reaction force magnitude, and soil stiffness. Soil stiffness impacts the linear distribution of reaction forces more significantly than the ratio—when soil stiffness is smaller, reaction forces still meet the linear assumption even if the ratio exceeds 2.5 within a range; when larger, they differ greatly. Under specific sandy soils (bearing stratum capacity < 300 kPa), the LWHR foundation meets wind turbine requirements, and its foundation ring’s punching shear resistance complies with standards (considering uplift-resistant reinforcement). For coarse sand bearing strata, the foundation’s bottom pressure follows linear distribution per code, and code formulas apply. However, the LWHR scheme is not fully suitable for complex geology or other foundation types, whose applicability needs comprehensive analysis. Full article

The construction of self-dual and linear complementary dual (LCD) codes over finite rings, particularly over semi-local and local structures, is an active area of research due to their algebraic richness and applications in communications and cryptography. In this paper, we investigate double circulant and double negacirculant codes over the local ring $R_{q,u,v}={\mathbb{F}}_q+u{\mathbb{F}}_q+v{\mathbb{F}}_q,u^2=v^2=uv=vu=0,$ where $q=p^m$ is an odd prime power. Unlike the semi-local case, where decomposition via non-trivial idempotents simplifies analysis, the local structure of $R_{q,u,v}$ (with only trivial idempotents) makes enumeration and classification significantly more challenging. We first establish necessary and sufficient conditions for such codes to be self-dual or LCD; we then count the solutions to key equations over ${\mathbb{F}}_q$, including $a{b}^q+b{a}^q=0,$ to enable their enumeration. We further show that Gray images preserve these properties, leading to good self-dual and LCD codes over ${\mathbb{F}}_q$, and present optimal examples over ${\mathbb{F}}_7$. Our results extend double circulant constructions to a new algebraic setting, providing both theoretical advancements and practically relevant code designs. Full article

Let p be a prime and ${\mathbb{F}}_p$ a finite field of order p. This paper investigates cyclic codes over the ring $R_{p^2,u}={\mathbb{Z}}_{p^2}+u{\mathbb{Z}}_{p^2}$ of order $p^4$, where the nilpotent element u satisfies $u^2=0$ and $pu\ne 0.$ The condition $u^2=0$ with $pu\ne 0$ is crucial, as it creates a nontrivial interaction between the components of the ring, allowing the construction of new codes with enhanced structural and distance properties. We provide explicit generating sets for cyclic codes over $R_{p^2,u}$ and study fundamental parameters such as their rank and Hamming distance. In the case $\gcd (n,p)=1$, we show that cyclic codes can be generated by just two polynomials, which allows a complete determination of their rank and minimal Hamming distance distributions. Furthermore, using the Gray map from $R_{p^2,u}$ to ${\mathbb{F}}_p^4$, we construct all but one of the ternary optimal codes of length 12 as images of cyclic codes over $R_{3^2,u}$, with computations verified using the Magma system. Full article

This paper investigates whether ChatGPT, a large language model, can assist in the implementation of lattice-based cryptography and fully homomorphic encryption algorithms, specifically the Ring Learning-with-Errors encryption scheme and the Brakerski–Fan–Vercauteren FHE scheme. To the best of our knowledge, this study represents the first systematic exploration of ChatGPT’s ability to implement these cryptographic algorithms. Fully homomorphic encryption, despite its theoretical and practical significance, poses significant challenges due to its computational complexity and efficiency requirements. This study evaluates ChatGPT’s capability as a development tool from both algorithmic and implementation perspectives. At the algorithmic level, ChatGPT demonstrates a solid understanding of the Rring Learning-with-Errors lattice encryption scheme but faces limitations in comprehending the intricate structure of the Brakerski–Fan–Vercauteren FHE scheme. At the code level, ChatGPT can generate functional C++ implementations of both encryption schemes, significantly reducing manual coding effort. However, debugging and corrections remain necessary, particularly for the more complex Brakerski–Fan–Vercauteren scheme, where additional effort is required to ensure correctness. The findings highlight ChatGPT’s potential and limitations in supporting cryptographic algorithm development, offering insights into its application for advancing implementations of complex cryptographic systems. Full article

Due to their potential to reduce greenhouse gas emissions, light-frame timber buildings (LFTBs) are widely used in seismically active regions. However, their construction in these areas remains limited, primarily due to the high costs associated with continuous anchor tie systems (ATSs), which are required to withstand significant seismic forces. To address this challenge, frictional seismic isolation offers an alternative by enhancing seismic protection. Although frictional base isolation is an effective mitigation strategy, its performance can be compromised by extreme ground motions that induce large lateral displacements, resulting in impacts between the sliders and the perimeter protection ring. The effects of these internal lateral impacts on base-isolated LFTBs remain largely unexplored. To fill this knowledge gap, this study evaluates the collapse capacity of a set of base-isolated LFTBs representative of Chilean real estate developments. Nonlinear numerical models were developed in the OpenSeesPy platform to capture the nonlinear behavior of the superstructure, including the impact effects within the frictional isolation system. Incremental dynamic analyses following the FEMA P695 methodology were performed using subduction ground motions. Collapse margin ratios (CMRs) and fragility curves were derived to quantify seismic performance. Results indicate that frictional base-isolated LFTBs can achieve acceptable collapse safety without ATS, even with compact-size bearings. Code-conforming archetypes achieved CMRs ranging from 1.24 to 1.55, indicating sufficient safety margins. These findings support the cost-effective implementation of frictional base isolation in mid-rise timber construction for high-seismic regions. Full article

Let p be a prime number and m be a positive integer. In this paper, we investigate cyclic codes of length n over the local non-Frobenius ring $R=GR(p^2,m)\left[u\right]$, where $u^2=0$ and $pu=0$. We first determine the algebraic structure of cyclic codes of arbitrary length n. For the case $\gcd (n,p)=1$, we explicitly describe the generators of cyclic codes over R. Moreover, we establish necessary and sufficient conditions for the existence of self-dual and LCD codes, together with their enumeration. Several illustrative examples and tables are presented, highlighting the mass formula for cyclic self-orthogonal codes, cyclic LCD codes, and families of new cyclic codes that arise from our results. Full article

The problem of cybersecurity of vehicular ad hoc network (VANET) is far from being fully solved. This is due to the fact that when exchanging data between On Board Units (OBUs) and Roadside Units (RSUs) a wireless channel is used, which is subject to many cyberattacks. It is known that the use of encryption algorithms, particularly Advanced Encryption Standard (AES), can effectively counter many of them. However, during the operation of AES encryption systems, failures may occur, as a result of which closed communication channels may become open and accessible to attackers. Therefore, giving the property of fault tolerance to the used encryption systems is an urgent task. To solve this problem, the article proposes to use redundant residue codes in the polynomial ring (RCPR). The article describes a method of providing fault tolerance of AES encryption systems based on RCPR. Using the developed error correction algorithm for RCPR with one control module, the redundant RCPR can detect 100% of single and double errors, as well as correct 100% of single and 75% of double errors that occur during encryption and decryption. Thus, the developed method based on error correction of AES encryption system allows to parry cyberattacks on vehicles and ensure a higher level of cyber security of VANET. Full article

To reveal the meso-mechanical essence of deep rock mass failure and capture precursor information, this study focuses on soft rock failure mechanisms. Based on the discontinuous medium discrete element method (DEM), we employed digital image correlation (DIC) technology, acoustic emission (AE) monitoring, and particle flow code (PFC) numerical simulation to investigate the failure evolution characteristics and AE quantitative representation of soft rocks. Key findings include the following: Localized high-strain zones emerge on specimen surfaces before macroscopic crack visualization, with crack tip positions guiding both high-strain zones and crack propagation directions. Strong force chain evolution exhibits high consistency with the macroscopic stress response—as stress increases and damage progresses, force chains concentrate near macroscopic fracture surfaces, aligning with crack propagation directions, while numerous short force chains coalesce into longer chains. The spatial and temporal distribution characteristics of acoustic emissions were explored, and the damage types were quantitatively characterized, with ring-down counts demonstrating four distinct stages: sporadic, gradual increase, stepwise growth, and surge. Shear failures predominantly occurred along macroscopic fracture surfaces. At the same time, there is a phenomenon of acoustic emission silence in front of the stress peak in the surrounding rock of deep soft rock roadway, as a potential precursor indicator for engineering disaster early warning. These findings provide critical theoretical support for deep engineering disaster prediction. Full article