分类： 数学 >> 数学（综合） 提交时间： 2025-05-30
摘要： Keyboard-based interaction may not accommodate various needs, especially for individuals with disabilities. While inertial sensor-based writing recognition is promising due to the sensors’ small size, wearability, and low cost, accurate recognition in the Chinese context is hampered by the difficulty of collecting extensive inertial signal samples for the vast number of characters. Therefore, we design a Chinese Inertial GAN (CI-GAN) containing Chinese glyph encoding (CGE), forced optimal transport (FOT), and semantic relevance alignment (SRA) to acquire unlimited high-quality training samples. Unlike existing vectorization methods focusing on the meaning of Chinese characters, CGE represents shape and stroke features, providing glyph guidance for writing signal generation. FOT establishes a triple-consistency constraint between the input prompt, output signal features, and real signal features, ensuring the authenticity and semantic accuracy of the generated signals. SRA aligns semantic relationships between multiple outputs and their input prompts, ensuring that similar inputs correspond to similar outputs (and vice versa), alleviating model hallucination. The three modules guide the generator while also interacting with each other, forming a coupled system. By utilizing the massive training samples provided by CI-GAN, the performance of six widely used classifiers is improved from 6.7% to 98.4%, indicating that CI-GAN constructs a flexible and efficient data platform for Chinese inertial writing recognition. Furthermore, we release the first Chinese inertial writing dataset on GitHub.
分类： 数学 >> 数学（综合） 提交时间： 2025-02-15
摘要： By considering the he spectrum of the Cesaro operator on the Hilber-Polya space, we proved the Riemann hypothesis for Riemann zeta function and Dirichlet L-function.
分类： 数学 >> 数学（综合） 提交时间： 2024-11-01
摘要： 目的：探讨A,B,P是圆锥曲线C上不同的三点，探讨直线PA,PB的斜率的积（和）为定值与直线AB是否经过定点的关系.方法：设而不求，恰当转化，通过斜率齐次化简化计算，探索发现.结论：在特定条件下，直线PA,PB的斜率的和（积）为定值等价于直线AB经过定点,据此可以创编若干具体问题.
分类： 数学 >> 数学（综合） 提交时间： 2024-10-07
摘要： 本文介绍了一种改进的参数方程曲面面积计算方法，旨在解决现有教材中公式复杂、难以记忆和理解的问题。通过引入隐函数曲面面积的计算方法，并结合参数方程的特点，推导出一种新的计算公式。该公式具有形式简单、对称整齐易记、数学意义明确等优点，有利于学生掌握和理解参数方程曲面面积的计算方法。
分类： 数学 >> 数学（综合） 提交时间： 2024-09-24
摘要： 调和级数是非常重要的无穷级数，是P-级数中收敛级数与发散级数的分界点。其英文名称Harmonic series 与泛音列相同，这与它的来源有关，并且它的发散性可以应用到里拉斜塔的结论中。在教学中，讲清楚这些背景与应用，能大大激发学生对数学相关知识的兴趣和学习热情，有助于学生克服对《微积分》课程学习的畏难情绪。另一方面，这样的教学内容设计把看似不相关的内容联系了起来，体现了事物是普遍联系的观点。有鉴于此，笔者这篇文章，旨在抛砖引玉，希望有更多的老师，把自己成功的教学心得与教学发现分享出来，共同把《微积分》这门课程的思政教学建设好。
分类： 数学 >> 数学（综合） 提交时间： 2024-08-29
摘要： In this paper, the main aim is to demonstrate the boundedness for commutatorsof sharp maximal function in the context of the p-adic variable Lebesgue spaces and Morreyspaces. where the symbols of the commutators belong to the p-adic version of Lipschitz orBMO spaces. Moreover, the boundedness of commutators of fractional maximal operatorin the p-adic Morrey space is also given, where the symbols of the commutators belong tothe p-adic version of Lipschitz space, by which some new characterizations of Lipschitz andBMO spaces are obtained.
分类： 数学 >> 数学（综合） 提交时间： 2024-06-14
摘要： In the case of external force $f in C_0^ infty( 0, infty);C_{0}^ infty( Omega)^3)$ and the initial data $u^0 in W_{0, sigma}^{1,2}( Omega)$ without the Serrin’s condition,we show the uniqueness of { it Leray-Hopf solution} to incompressible Navier-Stokes Equations in Theorem 3.1
分类： 数学 >> 数学（综合） 提交时间： 2024-05-16
摘要： 五千年的我国传统文化是国家与民族继承与发展的基础。弘扬我国优秀的传统文化有利于增进当代大学生的文化自信。如何将我国灿烂的传统文化有机地融入到《高等数学》的枯燥的学习中去，如何提高当代大学生对这门课程的兴趣，以及树立他们的文化自信，上述种种，在当前都值得我们去探究。本文基于此出发点，以一个重要的知识点——分部积分的思政教学为例，我们给出了中国传统文化中的若干典型形象在《高等数学》课程中的一个应用。另外，可以发现笔者的思政教学，有效地提高了学生对这门课的学习兴趣和学习效果。
分类： 数学 >> 数学（综合） 提交时间： 2024-03-01
摘要： In this paper, the main aim is to demonstrate the boundedness for commutators of fractional maximal function and sharp maximal function in the context of the p-adic version of Orlicz spaces, where the symbols of the commutators belong to the p-adic version of Lipschitz space, whereby some new characterizations for Λβ(Qnp) spaces are given.
分类： 数学 >> 数学（综合） 提交时间： 2024-03-01
摘要： In this article, the main aim is to introduce the grand variable Herz space over the p-adic fields and demonstrate the boundedness for fractional integral operator, fractional maximal operator in the context of the grand p-adic version of Herz-Morrey spaces with variable exponent, as well as the Lipschitz estimates for the commutators of fractional integral operator, fractional maximal operator, and sharp maximal function on the grand p-adic version of Herz-Morrey spaces with variable exponent.
分类： 数学 >> 数学（综合） 提交时间： 2024-02-17
摘要： 本文利用拉格朗日反演级数方法，研究了形如级数y=a1x+a2x2+a3x3++anxn+的在x=0的邻域内单调区间，然后针对更一般形式的级数方程，给出了其中一个非零实根的一个计算方法。
分类： 数学 >> 数学（综合） 分类： 数学 >> 逻辑 提交时间： 2023-06-20
摘要： The aim of this paper is to study well-connected residuated lattices and residually finite residuated lattices. So far, well-connected residuated lattices not only a main tool for studying RLsi but also a subdirect irreducible representation object of residuated lattices. In this paper we both investigate the above two aspects by using some di#11;erent methods. Finally, we introduce the residually finite residuated lattices and characterize them from algebraic, logical and topological perspectives, respectively.
分类： 数学 >> 数学（综合） 分类： 水利工程 >> 水利工程基础学科 提交时间： 2023-04-28
摘要： In this paper, we mainly provide a proper maintenance plan for the Kariba Dam in Africa which falls into disrepair and is facing to collapse. Firstly, we make a threshold analysis of the three options about their costs which include peoples moving, old dams removing, new dams building, later repairing, ecological destruction and their incomes which include generation energy, avoiding of flood disasters loss, providing employment, tourism resources and ecological protection. Then we get the specific relationship between benefits and years with some collected data. Both of the results show that the third option is the best choice from the economic view. And the result is completely as same as the conclusion we get after studying deeply on Option 3. Secondly, we regard water management capabilities as the safety coefficient of dams. We select 30 seed points along the riverbank for preparing the establishment of dams. With flow-between-riverway model, Manning equations, large Cauchy distribute function we get the scores of the seed points. We give an advice that the number of dams should be more and the positions of dams should be well-distributed. Then, we build an assessment model by analytic hierarchy process. We select three factors among all the factors, safety, economy and population. After testing the consistency, we get the weights of each factor: 0.6442, 0.2705, 0.0852. Then we value the factors and get an optimal scheme during the assessment with 0-1 integer programming: the number of dams is 17 and the longitude and latitude of them are shown in Table 17. The sensitivity of the result is tested as well. We also provide some strategies for the managers of ZRA to use. We suggest that they should use the dams normally in general. With the Dam-break model, we find 13 points among 17 points which are shown in Table 20. The dams at the 13 points need to be closed when there is a flood and it is just the opposite when the drought happens. For the extreme water flow, we assume an ideal water flow at first. The extreme water flow has to be adjusted to satisfy the ideal one. As for the restrictions in extreme conditions, the biggest impact happens at the 8th point among the 17 points. If the duration of maximum flow is t0, the drainage time t to make the water flow return to the normal level equals to 4.95t0.
分类： 数学 >> 数学（综合） 提交时间： 2023-04-27
摘要： This paper demonstrates the invariant distribution of a stochastic dynamical system. We give the invariant distribution and numerical examples. We also present a further discussion on the computation details.
分类： 数学 >> 数学（综合） 分类： 信息科学与系统科学 >> 信息安全技术 提交时间： 2023-02-18
摘要： 构造线性码是编码密码理论中的重要研究课题.码的重量分布和重量谱的决定在编码理论中也有着基本的理论意义，而且在保密通信中有重要作用.本文构造了一类3-重和一类4-重二元线性码，并完全确定了它们的重量分布和重量谱.
分类： 数学 >> 数学（综合） 提交时间： 2023-01-14
摘要： In this paper, we present the characterizations of total boundedness, relative compactness and compactness in fuzzy set spaces equipped with the endograph metric.The conclusions in this papersignificantly improvethe corresponding conclusions given in our previous paper H. Huang, Characterizations of endograph metric and $ Gamma$-convergence on fuzzy sets, Fuzzy Sets and Systems 350 (2018), 55-84 . The results in this paper are applicable tofuzzy sets in a general metric space. The results in our previous paper are applicable tofuzzy sets in the $m$-dimensional Euclidean space $ mathbb{R}^m$,which is a special type of metric space.Furthermore, based on the above results,wegivethe characterizations of relative compactness,total boundedness and compactness in a kind of common subspaces of general fuzzy sets according to the endograph metric.As an application, we investigate some relationship betweenthe endograph metric and the $ Gamma$-convergence on fuzzy sets.
分类： 物理学 >> 气体、等离子体、放电物理 分类： 数学 >> 数学（综合） 提交时间： 2022-12-27
摘要： 对三维向量场中的双曲环的不变流形，本文给出其柱坐标下的生长公式。其流形初始生长方向取决于 Poincar 映射的 Jacobian 矩阵，文中给出这一矩阵在环上的演化公式。这一演化公式也适用于任意有限维的自治连续时间动力系统。本文构造有非莫比乌斯型、莫比乌斯型的鞍环，以及仿造的 X-环，以演示公式的使用方法。 对于真实的数值例子，取东方超环运行中的一磁场时间切片作为演示。
分类： 数学 >> 数学（综合） 提交时间： 2022-12-04
摘要： 本文通过严格数学分析找出了交叉熵过拟合的成因：边界样本的损失贡献比重大且随法向量增长而加速增大、边界样本分布散乱，顺便理清了正则项的作用机理。
分类： 数学 >> 数学（综合） 提交时间： 2022-10-10
摘要： 微博平台上的大量图片几乎相同，差别仅在于水印和清晰度。为了从海量图片中找出几乎相同的图片，本文提出一种称为多层指纹的新算法。多层指纹包含5个字符串和3种实数向量，其中一个字符串用于快速召回，剩余字符串、向量用于计算指纹间相似度。多层指纹的算力需求很小，准确率高。在微博百万级图片库上测试结果表明，多层指纹的检索速度达到QPS 345，准确率达到 97.69%。
分类： 数学 >> 数学（综合） 提交时间： 2022-08-13
摘要： This paper shows thatthe endograph metric and the $\Gamma$-convergenceare compatible on a large classof fuzzy set in $\mathbb{R}^m$.
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