Let $p$ be a prime number, and let $k$ and $m$ be positive integers with $k\ge 2$. This paper studies the algebraic structure of $\lambda$-constacyclic codes of arbitrary length over the finite commutative ring $R=\frac{{\mathbb{F}}_{p^m}[u,v]}{⟨u^k,v^2,uv–vu⟩}$, where $\lambda$ is a unit in $R$ given by $\lambda =\sum _{i=0}^{k-1}{\lambda }_i{u}^i+v\sum _{i=0}^{k-1}{\lambda }_i^{\prime }{u}^i$, with ${\lambda }_i,{\lambda }_i^{\prime }\in {\mathbb{F}}_{p^m}$ and ${\lambda }_0,{\lambda }_1\ne 0$. We provide a complete classification of these constacyclic codes, determine their dual structures, and compute their Hamming distances when the code length is $p^s$.

In this paper, the hyperoctahedral group algebra $\mathcal{F}[\overrightarrow{S_n}]$ over a splitting field $\mathcal{F}$ of wreath product $\overrightarrow{S_n}$ with $\text{char}(\mathcal{F})\nmid |\overrightarrow{S_n}|$, is considered and the unique idempotents corresponding to the four linear characters of the group $\overrightarrow{S_n}$ are explored. Also, by establishing the minimum weights and dimensions, all group codes generated by the linear idempotents in the aforementioned group algebra are completely characterized for every $n$. The nonlinear idempotents corresponding to nonlinear characters of $\overrightarrow{S_3}$ are also obtained and various group codes in $\mathcal{F}[\overrightarrow{S_3}]$ generated by linear and nonlinear idempotents are examined.

Let $G=(V,E)$ be a graph with minimum degree at least one. The general inverse degree of $G$ is defined as $\sum _{v\in V}\frac{1}{d^{\alpha }(v)}$, where $\alpha$ is a real number with $\alpha >0$. In this paper, we present sufficient conditions involving the general inverse degree with $\alpha \ge 1$ for some Hamiltonian properties of graphs and upper bounds for the general inverse degree with $\alpha \ge 1$.

In today’s era, the rapid development of artificial intelligence is transforming warehousing and logistics by enhancing efficiency and reducing labor costs. In this paper, we first employ a least squares support vector machine to develop an inventory prediction model for warehousing logistics, accurately forecasting inventory values. Next, we design an automated logistics and warehousing architecture that facilitates seamless data transfer and information feedback. Finally, this architecture is used to build a comprehensive inventory management model. Our analysis shows that the AI-based prediction nearly matches the actual inventory value (229 vs. 230) and achieves an inventory turnover rate of 5 times per month, which significantly reduces backlog and improves overall management efficiency and user satisfaction.

The Cascaded Integrator Comb (CIC) decimation filter is a pivotal technology extensively employed in digital signal processing (DSP). This paper delves into a comprehensive examination of the CIC algorithm within software-defined radio (SDR) systems from the perspective of parallel computing and introduces a novel Non-Recursive Implementation (NR-I) on an NVIDIA GPU using CUDA. The NR-I approach significantly reduces computational load by unfolding the recursive CIC structure with pre-derived Unfold Factors. Further optimization was achieved through data-transfer enhancements using PM Implementation (PM-I) and ODT Implementation (ODT-I). Experimental results demonstrate that NR-I achieves a speedup of over 449.48. Additionally, the data-transfer optimizations resulted in substantial performance improvements, with PM-I and ODT-I reducing execution time by 43.24% and 64.22%, respectively. The GPU implementation’s speedup is significantly greater than that of OpenMP, ranging from 3.34 to 10.22 times. These results underscore the effectiveness of the proposed Non-Recursive Implementation in accelerating time-intensive and data-intensive computations.

This paper presents a new sequence called the $k-$division sequence. The Pell and Lehmer sequences are then used to define new sequences called the $k-$division $L-$Lehmer-Pell sequences and some properties of these sequences are determined. Then the $k-$division $L-$Lehmer-Pell sequences and corresponding self-invertible matrices are used in a new Affine-Hill cipher algorithm. The security of this cipher is examined.

In the era of globalization and intense market competition, strategic human resource management (SHRM) is critical for boosting corporate competitiveness. This study employs structural equation modeling (SEM) and multiple linear regression to uncover the complex influence of SHRM perceptions on employee proactive behaviors, and uses a convolutional neural network (CNN) to explore nonlinear relationships and validate the SEM findings. Results reveal that SHRM perception has a significant positive effect on employee proactive behavior ($\beta =0.254$, $p<0.001$). Mediators such as job self-efficacy and conceptual psychological contract play a positive role, with indirect effects of 0.1043 and 0.1726, respectively, while insider identity perception significantly moderates the relationship ($\beta =0.09$, $p<0.01$). The CNN model ranks the importance of variables in descending order as: conceptual psychological contract, job self-efficacy, SHRM perception, job category, and insider identity perception, consistent with the SEM results. These findings highlight the potential of CNNs to optimize HR strategies and enhance employee motivation.

One of the urgent challenges in auditing today is preventing accounting management risk. This study integrates big data auditing technology to enhance audit quality by developing an audit risk assessment index system based on material misstatement risk and inspection risk. By combining the hierarchical analysis and entropy weighting methods to assign risk indicators, the accounting audit risk index for Company Z was calculated using a multi-level fuzzy comprehensive evaluation method and regression analysis to examine impact factors. Empirical evidence shows that the overall expected audit risk is 0.412—indicating a low to average risk level—with significant correlations between the previous year’s audit opinion, audit fee, and other factors such as the largest shareholder’s holding, board size, percentage of independent directors, operating income growth, net profit, and the audit environment. The study focuses on developing effective prevention and response strategies in the era of big data and offers recommendations to reduce potential auditing risks.

Let $\mathcal{F}$ be a family of graphs, and $H$ a “host” graph. A spanning subgraph $G$ of $H$ is called $\mathcal{F}$- saturated in $H$ if $G$ contains no member of $\mathcal{F}$ as a subgraph, but $G+e$ contains a member of $\mathcal{F}$ for any edge $e\in E(H)–E(G)$. We let $Sat(H,\mathcal{F})$ be the minimum number of edges in any graph $G$ which is $\mathcal{F}$-saturated in $H$, where $Sat(H,\mathcal{F})=|E(H)|$ if $H$ contains no member of $\mathcal{F}$ as a subgraph. Let $P_m^r$ be the $r$-dimensional grid, with entries in each coordinate taken from $\{1,2,\cdots ,m\}$, and $K_t$ the complete graph on $t$ vertices. Also let $S(F)$ be the family of all subdivisions of a graph $F$. There has been substantial previous work on extremal questions involving subdivisions of graphs, involving both $Sat(K_n,S(F))$ and the Turan function $ex(K_n,S(F))$, for $F=K_t$ or $F$ a complete bipartite graph. In this paper we study $Sat(H,S(F))$ for the host graph $H=P_m^r$, and $F=K_4$, motivated by previous work on $Sat(K_n,S(K_t))$. Our main results are the following; 1) If at least one of $m$ or $n$ is odd with $m\ge 5$ and $n\ge 5$, then $Sat(P_m\times P_n,S(K_4))=mn+1.$ 2) For $m$ even and $m\ge 4$, we have $m^3+1\le Sat(P_m^3,S(K_4))\le m^3+2.$ 3) For $r\ge 3$ with $m$ even and $m\ge 4$, we have $Sat(P_m^r,S(K_4))\le m^r+2^{r-1}–2$.

An undirected graph is said to be cordial if there is a friendly (0,1)-labeling of the vertices that induces a friendly (0,1)-labeling of the edges. An undirected graph $G$ is said to be $(2,3)$-orientable if there exists a friendly (0,1)-labeling of the vertices of $G$ such that about one-third of the edges are incident to vertices labeled the same. That is, there is some digraph that is an orientation of $G$ that is $(2,3)$-cordial. Examples of the smallest noncordial/non-$(2,3)$-orientable graphs are given, and upper bounds on the possible number of edges in a cordial/$(2,3)$-orientable graph are presented. It is also shown that if $T$ is a linear operator on the set of all undirected graphs on $n$ vertices that strongly preserves the set of cordial graphs or the set of $(2,3)$-orientable graphs, then $T$ is a vertex permutation.