Search

With the development of society and economy, higher education has new requirements in the new era, under the background of the new media era, colleges and universities throughout the country have continuously strengthened innovation and entrepreneurship education, run through innovation and entrepreneurship ideas throughout the whole process of talent training, colleges and universities should use scientific and reasonable methods develop talents in order to promote college students’ entrepreneurial and innovative ability. The rapid development of Internet technology and the changeable new media have brought new opportunities and challenges to college students' innovation and entrepreneurship education. This paper studies and analyzes the cultivation of college students' innovation and entrepreneurship education under the background of the new media era, and provides suggestions for new media to better serve college students' innovation and entrepreneurship education.

Catalan-Daehee numbers and polynomials, generating functions of which can be expressed as p-adic Volkenborn integrals on Zp, were studied previously. The aim of this paper is to introduce qanalogues of the Catalan-Daehee numbers and polynomials with the help of p-adic q-integrals on Zp. We derive, among other things, some explicit expressions for the q-analogues of the Catalan-Daehee numbers and polynomials.

In this paper, we define the multi-Stirling numbers of the first kind by means of the multiple logarithm and as a generalization of the Stirling numbers of the first kind. Then we introduce two additional special numbers by using the multiple logarithm, namely the modified multi-Bernoulli numbers as a generalization of the higher-order Bernoulli numbers and the multi-Lah numbers of type 2 as a generalization of the Lah numbers. For both of these special numbers, we derive explicit expressions for them which involve the multi-Stirling numbers of the first kind.

The main purpose of this paper is to obtain some exact computational formulas or upper bounds for hybrid mean value involving Hardy sums $S_{3}(h, p)$ and general Kloosterman sums $K(r, l, \lambda; p)$. By applying the properties of Gauss sums and the mean value theorems of Dirichlet $L$-function, we derive some new identities. As the special cases, we also deduce some exact computational formulas for hybrid mean value involving $S_{3}(h, p)$ and classical Kloosterman sums $K(n, p)$.

We show how to decompose all separable ultrametric spaces into a "Lego" combinations of scaled versions of full simplices. To do this we introduce metric resolutions of large scale metric spaces, which describe how a space can be broken up into roughly independent pieces. We use these metric resolutions to define the coarse disjoint union of large scale metric spaces, which provides a way of attaching large scale metric spaces to each other in a "coarsely independent way". We use these notions to construct universal spaces in the categories of separable and proper metric spaces of asymptotic dimension $0$, respectively. In doing so we generalize a similar result of Dranishnikov and Zarichnyi as well as Nag\'orko and Bell. However, the new application is a universal space for proper metric spaces of asymptotic dimension $0$, something that eluded those authors. We finish with a description of some countable groups that can serve as such universal spaces., Comment: 14 pages, overrides 2110.08929. arXiv admin note: substantial text overlap with arXiv:2110.08929 The 2nd version contains fixes for several errors and gaps pointed out by an excellent referee

The main aim of this paper is to use the analytic methods and the properties of the classical Gauss sums to research the computational problem of one kind hybrid power mean containing the character sums of polynomials and two-term exponential sums modulo p, an odd prime, and acquire several accurate asymptotic formulas for them.

Recently, Kim-Kim introduced the lambda-umbral calculus, in which the lambda-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate some properties and identities relating to those polynomials with the help oflambda-umbral calculus. Here we note that the fully degenerate Bell poynomials and the fully degenerate Dowling polynomials are respectively degenerate versions of the Bell polynomials and the Dowling polynomials, of which the latters are the natural extension of the Whitney numbers of the second kind., Comment: 14 pages

Apostol considered generalized Dedekind sums by replacing the first Bernoulli function appearing in Dedekind sums by any Bernoulli functions and derived a reciprocity relation for them. Recently, poly-Dedekind sums were introduced by replacing the first Bernoulli function appearing in Dedekind sums by any type 2 poly-Bernoulli functions of arbitrary indices and were shown to satisfy a reciprocity relation. In this paper, we consider other poly-Dedekind sums that are obtained by replacing the first Bernoulli function appearing in Dedekind sums by any poly-Bernoulli functions of arbitrary indices. We derive a reciprocity relation for these poly-Dedekind sums.

Recently, the nth Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for any nonnegative integer n. Further, as natural extensions of the Lah–Bell numbers, Lah–Bell polynomials are defined. We study Lah–Bell polynomials with and without the help of umbral calculus. Notably, we use three different formulas in order to express various known families of polynomials such as higher-order Bernoulli polynomials and poly-Bernoulli polynomials in terms of the Lah–Bell polynomials. In addition, we obtain several properties of Lah–Bell polynomials.

By using the properties of Kloosterman sum and Dirichlet character, an optimal upper bound estimate of incomplete Cochrane sum is given.

We use the elementary and analytic methods and the properties of Chebyshev polynomials to study the computational problem of the reciprocal sums of one-kind Chebyshev polynomials and give several interesting identities for them. At the same time, we also give a general computational method for this kind of reciprocal sums.

A new representation of 3D shapes is proposed using spherical hybrid curvature images. Signals like normals and curvatures are stored in spherical hybrid curvature images using spherical parameterization and partition of a sphere. The generation depends on several geometric signals, not one single geometric signal. So its colors reflect the properties of 3D shapes more clearly. With simple arrays similar to 2D image, the spherical hybrid curvature image can be post-processed easily using sophisticated image processing algorithms. Applications include segmentation, editing and model retrieval etc. Experimental results show that our method is better than other geometry image algorithms. The algorithm is simple and practical especially for models in engineering.

The representation of triangular mesh surface is proposed using spherical image. Surface signals like normals and curvatures are stored in spherical images using spherical parameterization and partition of the sphere. The generation depends on several geometric signals, not one single geometric signal. So its color reflects the properties of the triangular mesh surface more clearly. With simple arrays similar to 2D image, the spherical image can be post-processed easily using sophisticated image processing algorithms. Applications include segmentation, editing and model retrieval.

A reverse engineering innovative design method is proposed in this paper. The core of this method is mesh editing, namely, blending the features from multiple objects together to construct a new model. Firstly, the parts of interest to users are divided from the existing meshes, then mesh fusion, and finally local deformation of the fused mesh is implemented according to some constraints. This method facilitates design and knowledge reuse by leveraging 3D digital design applications. So the difficulty of modeling and development costs of new products can be reduced, the efficiency of modeling can be improved.

Protein structure comparison is one of the most important problems in computational biology and plays a key role in protein structure prediction. A new method based on the shape distribution of Calpha representation of the backbone is proposed for evaluating structural similarity between protein pairs. The method is completely independent of sequence information. By examining the 3D proteins structural data from Protein Data Bank (PDB) using the method, strong shape distribution similarity is detected between protein pairs with close structures and functions. It provides a helpful method to measure protein pairspsila similarity when sequence similarity is not enough.

Let q > 2 $q>2$ be an integer, n ⩾ 2 $n\geqslant2$ be a fixed integer with ( n , q ) = 1 $(n,q)=1$ , ψ be a non-principal Dirichlet character modq. An upper bound estimate for character sums of the form ∑ a ∈ C ( 1 , q ) ψ ( a ) $$\sum_{a\in\textit{C}(1,q)}\psi(a) $$ is given, where C ( 1 , q ) = { a ∣ 1 ⩽ a ⩽ q − 1 , a a ‾ ≡ 1 ( mod q ) , n ∤ ( a + a ‾ ) } $\mathcal{C}(1,q)=\{a \mid 1\leqslant a\leqslant q-1, a\overline{a}\equiv1 (\bmod q), n\nmid(a+\overline{a})\}$ .