With the increasing scale of college enrollment and the increasing complexity of college teaching management, college finance department should innovate the traditional financial management mode while adapting to the reform of teaching management, and make use of the openness and real-time characteristics of Internet to improve the quality of college financial management and reduce the risk of college financial management. To this end, this paper designs a university financial system based on multi-scale deep learning. In the hardware design, the system adds multiple sensors and scans all the information in the financial database using a coordinator. In the software design, the weights that can connect the financial information of the same attribute are set by establishing a database form; according to the multilayer perceptual network topology, a full interconnection model based on multi-scale deep learning is designed to realize the system’s deep extraction of data. The experimental results show that the financial risk is based on the risk warning capability for university finance, and compared with the system under the traditional design, the university finance system designed in this time has the most categories of financial information parameters extracted.

This work suggests predicting student performance using a Gaussian process model classification in order to address the issue that the prediction approach is too complex and the data set involved is too huge in the process of predicting students’ performance. In order to prevent overfitting, a sample set consisting of the three typical test outcomes from 465 undergraduate College English students is divided into training and test sets. The cross-validation technique is used in this study. According to the findings, Gaussian process model classification can accurately predict 92% of the test set with a prediction model, and it can also forecast students’ final exam marks based on their typical quiz scores. Furthermore, it is discovered that the prediction accuracy increases with the sample set’s distance from the normal distribution; this prediction accuracy rises to 96% when test scores with less than 60 points are taken out of the analysis.

Fix integers \(k, b, q\) with \(k \ge 2\), \(b \ge 0\), \(q \ge 2\). Define the function \(p\) to be: \(p(x) = kx + b\). We call a set \(S\) of integers \emph{\((k, b, q)\)-linear-free} if \(x \in S\) implies \(p^i(x) \notin S\) for all \(i = 1, 2, \dots, q-1\), where \(p^i(x) = p(p^{i-1}(x))\) and \(p^0(x) = x\). Such a set \(S\) is maximal in \([n] := \{1, 2, \dots, n\}\) if \(S \cup \{t\}, \forall t \in [n] \setminus S\) is not \((k, b, q)\)-linear-free. Let \(M_{k, b, q}(n)\) be the set of all maximal \((k, b, q)\)-linear-free subsets of \([n]\), and define \(g_{k, b, q}(n) = \min_{S \in M_{k, b, q}(n)} |S|\) and \(f_{k, b, q}(n) = \max_{S \in M_{k, b, q}(n)} |S|\). In this paper, formulae for \(g_{k, b, q}(n)\) and \(f_{k, b, q}(n)\) are proposed. Also, it is proven that there is at least one maximal \((k, b, q)\)-linear-free subset of \([n]\) with exactly \(x\) elements for any integer \(x\) between \(g_{k, b, q}(n)\) and \(f_{k, b, q}(n)\), inclusively.

Nanoparticles have potential applications in a wide range of fields, including electronics, medicine and material research, because of their remarkable and exceptional attributes. Carbon nanocones are planar carbon networks with mostly hexagonal faces and a few non-hexagonal faces (mostly pentagons) in the core. Two types of nanocone configurations are possible: symmetric and asymmetric, depending on where the pentagons are positioned within the structure. In addition to being a good substitute for carbon nanotubes, carbon nanocones have made an identity for themselves in a number of fields, including biosensing, electrochemical sensing, biofuel cells, supercapacitors, gas storage devices, and biomedical applications. Their astonishing chemical and physical attributes have made them well-known and widely accepted in the fields of condensed matter physics, chemistry, material science, and nanotechnology. Mathematical and chemical breakthroughs were made possible by the concept of modeling a chemical structure as a chemical graph and quantitatively analyzing the related graph using molecular descriptors. Molecular descriptors are useful in many areas of chemistry, biology, computer science, and other sciences because they allow for the analysis of chemical structures without the need for experiments. In this work, the quotient graph approach is used to establish the distance based descriptors of symmetrically configured two-pentagonal and three-pentagonal carbon nanocones.

A kite \(K\) is a graph which can be obtained by joining an edge to any vertex of \(K_3\). A kite with edge set \(\{ab,\,bc,\,ca,\,cd\}\) can be denoted as \((a,\,b,\,c;\,cd)\). If every vertex of a kite in the decomposition lies in different partite sets, then we say that a kite decomposition of a multipartite graph is a gregarious kite decomposition. In this manuscript, it is shown that there exists a decomposition of \((K_m \otimes \overline{K}_n) \times (K_r \otimes \overline{K}_s) \) into gregarious kites if and only if
\[
n^2 s^2 m(m-1)r(r-1) \equiv 0 \pmod{8},
\]
where \(\otimes\) and \(\times\) denote the wreath product and tensor product of graphs respectively. We denote a gregarious kite decomposition as \(\it GK\)-decomposition.

With the rapid development of my country’s socialist market economy, the system of joint and several liability has been established in my country’s civil and commercial law and is playing an increasingly important role. There are also problems such as scattered regulations and contradictory laws and regulations at the level. Since there is no unified application principle established in judicial practice, the litigation burden caused by the recovery lawsuit also wastes a lot of trial resources. Dimensional key features distinguish confusing charges. Use regular expression technology to extract key content such as fact descriptions, defendants’ charges, relevant laws and regulations in legal documents and create JSON format documents; use stammer word segmentation and stop word list to remove stop words; use Word2Vec algorithm to represent text into vector form , establish a judicial judgment prediction model and an optimization model, and through experimental comparison, it is concluded that the performance of the model after adding focal loss is improved by 1.82%, 0.45%, 1.62%, and 1.62% compared with the cross entropy loss, and the final accuracy of the optimized model is 84.78%. , the precision rate is 87%, the recall rate is 85%, and the F1 value is 85%. The system is expected to assist judicial workers in classifying crimes with joint liability and reduce the burden of judicial workers reading many legal documents to classify crimes.

The evolution of computer science and the innovations in language teaching methodologies have paved the way for computer-assisted language learning (CALL) technology to tackle pertinent challenges. While existing CALL systems primarily emphasize vocabulary and grammar acquisition, their evaluation mechanisms often rely on a limited set of criteria, resulting in a simplistic assessment of learners’ pronunciation skills. This oversight underscores the need for a more comprehensive approach. In response, this study targets Chinese college students’ English oral proficiency and aims to enhance the conventional computerized evaluation method. Our approach involves integrating multiple assessment parameters, including pitch, speed, rhythm, and intonation. For instance, pitch assessment is grounded on frequency central feature parameters, while speech speed evaluation considers speech duration, thus enriching the evaluation framework. Through experimental validation, the efficacy of our method in evaluating pitch, speed, rhythm, and intonation has been substantiated, reaffirming its reliability.

The common bills in life include VAT invoices, taxi invoices, train invoices, plane itineraries, machine-printed invoices, etc. Most of these common bills are presented in the form of fixed form templates, so template matching can be used. , for a certain fixed template bill, manually set the rules to determine the spatial position of the key area, extract the corresponding text information, or build a model with logical semantic relationship and spatial relative relationship between the bill texts of different attributes, from the global image of the image. Identify the required key text information in the text information. However, these methods are either limited by fixed ticket templates, or cannot guarantee considerable accuracy. The electronicization of paper invoices mainly needs to go through the steps of text detection, bill recognition and text recognition. Based on this, this paper adopts the DL method. Construct a financial bill recognition model and combine experiments to explore the effectiveness and superiority of the model. The results show that our model can achieve a recognition accuracy rate of up to 91\%, and also achieve a 26\% improvement in recognition speed.

The maximum-weight perfect matching inverse issue in graph theory and text clustering are the two primary topics of this study. We suggest a novel approach to text clustering that makes use of self-encoders and BERT embeddings for feature extraction in order to increase clustering accuracy. According to experimental results, our technique enhances the clustering results greatly and performs well on numerous short text datasets. In the context of graph theory, we examine the unit paradigm inverse issue of maximum-weight perfect matching with value constraints and provide a robust polynomial-time method for its solution. In addition to effectively solving the maximum-weight perfect matching inverse issue, our technique can also produce the best weight vector configuration scheme for real-world uses. In conclusion, our work has advanced the domains of text clustering and graph theory significantly, offering fresh approaches and theoretical underpinnings for future investigations.