Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).
We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} ...We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} and Schur harmonic concave with respect to （x,y） ∈ （0,∞）×（0,∞） if and only if （a,b）∈{（a,b）：a≤0,b≤0,a｜b｜1≤0}.展开更多
This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p...This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.展开更多
Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for ...Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis. The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable com- putational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.展开更多
Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas f...Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）展开更多
在室内可见光通信中符号间干扰和噪声会严重影响系统性能,K均值(K-means)均衡方法可以抑制光无线信道的影响,但其复杂度较高,且在聚类边界处易出现误判。提出了改进聚类中心点的K-means(Improved Center K-means,IC-Kmeans)算法,通过随...在室内可见光通信中符号间干扰和噪声会严重影响系统性能,K均值(K-means)均衡方法可以抑制光无线信道的影响,但其复杂度较高,且在聚类边界处易出现误判。提出了改进聚类中心点的K-means(Improved Center K-means,IC-Kmeans)算法,通过随机生成足够长的训练序列,然后将训练序列每一簇的均值作为K-means聚类中心,避免了传统K-means反复迭代寻找聚类中心。进一步,提出了基于神经网络的IC-Kmeans(Neural Network Based IC-Kmeans,NNIC-Kmeans)算法,使用反向传播神经网络将接收端二维数据映射至三维空间,以增加不同簇之间混合数据的距离,提高了分类准确性。蒙特卡罗误码率仿真表明,IC-Kmeans均衡和传统K-means算法的误码率性能相当,但可以显著降低复杂度,特别是在信噪比较小时。同时,在室内多径信道模型下,与IC-Kmeans和传统Kmeans均衡相比,NNIC-Kmeans均衡的光正交频分复用系统误码率性能最好。展开更多
AIM: To evaluate whether preoperative mean corpuscular volume (MCV) is a prognostic indicator in patients with resectable esophageal squamous cell carcinoma (ESCC). METHODS: A total of 298 consecutive, prospectively e...AIM: To evaluate whether preoperative mean corpuscular volume (MCV) is a prognostic indicator in patients with resectable esophageal squamous cell carcinoma (ESCC). METHODS: A total of 298 consecutive, prospectively enrolled patients with histologically diagnosed ESCC who underwent surgery with curative intent from 2001 to 2011 were retrospectively evaluated. Patients were excluded if they had previous malignant disease, distant metastasis at the time of primary treatment, a history of neoadjuvant treatment, had undergone nonradical resection, or had died of a non-tumor-associated cause. Survival status was verified in September 2011. Pathological staging was performed based on the 2010 American Joint Committee on Cancer criteria. Preoperative MCV was obtained from blood counts performed routinely within 7 d prior to surgery. Receiver operating characteristic (ROC) curve analysis was used to determine a cutoff for preoperative MCV. RESULTS: The 298 patients consisted of 230 males and 68 females, with a median follow-up of 30.1 mo. ROC analysis showed an optimal cutoff for preoperative MCV of 95.6 fl. Fifty-nine patients (19.8%) had high (> 95.6 fl) and 239 (80.2%) had low (≤ 95.6 fl) preoperative MCV. Preoperative MCV was significantly associated with gender (P=0.003), body mass index (P=0.017), and preoperative red blood cell count (P<0.001). The predicted 1-, 3and 5-year overall survival (OS) rates were 72%, 60% and 52%, respectively. Median OS was significantly longer in patients with low than with high preoperative MCV (27.5 mo vs 19.4 mo, P<0.001). Multivariate analysis showed that advanced pT (P=0.018) and pN (P<0.001) stages, upper thoracic location (P=0.010), lower preoperative albumin concentration (P=0.002), and high preoperative MCV (P=0.001) were negative prognostic factors in patients with ESCC. Preoperative MCV also stratified OS in patients with T3, N1-N3, G2-G3 and stage Ⅲ tumors. CONCLUSION: Preoperative MCV is a prognostic factor in patients with ESCC.展开更多
This paper deals with the construction of Heun’s method of random initial value problems. Sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations pro...This paper deals with the construction of Heun’s method of random initial value problems. Sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples.展开更多
In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,a...In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.展开更多
For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential ...For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem.展开更多
In this paper, we introduce a new counting function a(m) related to the Lucas number, then use conjecture and induction methods to give an exact formula Ar(N)=α(n), (r=1,2,3) and prove them.
In this paper, we studies the relations between the mean value and the maximun norm of the infinite order entire functions which defined by legendre series. We obtained that if f(z) is an infinite order entire functio...In this paper, we studies the relations between the mean value and the maximun norm of the infinite order entire functions which defined by legendre series. We obtained that if f(z) is an infinite order entire function with a positive exponenatial lower order. then loaM (α) ～logMδ(α) ～ logMδ(α) (α→+∞).展开更多
The main purpose of this paper is using the analytic method to study the mean value properties of the arithmetical functions δk（（m, n））, δk（[m,n]/m）,and give several interesting asymptotic formulae for them.
The main purpose of this paper is to use the analytic methods to study the hybrid mean value involving the hyper Cochrane sums, and give several sharp asymptotic formulae.
R.Witula et al obtained a stronger version of the second mean value theorem for integral with some restrictions.In this paper,the stronger version theorem is proved without any restriction.The result is first restrict...R.Witula et al obtained a stronger version of the second mean value theorem for integral with some restrictions.In this paper,the stronger version theorem is proved without any restriction.The result is first restricted to the Riemann integrable functions and can be easily generalized to L~p integrable functions by using the well-known result that continuous functions are dense in the Banach space L~p[a,b]for any p≥1.展开更多
文摘Let p be a prime, n be any positiv e integer, α(n,p) denotes the power of p in the factorization of n! . In this paper, we give an exact computing formula of the mean value ∑ n<Nα(n,p).
基金Supported by the NSFC (11071069)the NSF of Zhejiang Province (D7080080 and Y7080185)the Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)
文摘We prove that the Gini mean values S（a,b; x,y） are Schur harmonic convex with respect to （x,y）∈（0,∞）×（0,∞） if and only if （a, b） ∈{（a, b）：a≥0,a ≥ b,a＋b＋1≥0}∪{（a,b）：b≥0,b≥a,a＋b＋1≥0} and Schur harmonic concave with respect to （x,y） ∈ （0,∞）×（0,∞） if and only if （a,b）∈{（a,b）：a≤0,b≤0,a｜b｜1≤0}.
基金Supported by the Natural Seience Foundation of Henan Educational Committee(20031100036)
文摘This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.
基金Project supported by the National Basic Research Program of China(No.2010CB731503)the National Natural Science Foundation of China(Nos.11172004 and 10772004)the Beijing Municipal Natural Science Foundation(No.1102020)
文摘Mesh deformation technique is widely used in many application fields, and has re- ceived a lot of attentions in recent years. This paper focuses on the methodology and algorithm of algebraic type mesh deformation for unstructured mesh in numerical discretization. To preserve mesh quality effectively, an algebraic approach for two and three dimensional unstructured mesh is developed based on mean value coordinates interpolation combined with node visibility analysis. The proposed approach firstly performs node visibility analysis to find out the visible boundary for each grid point to be moved, then evaluates the mean value coordinates of each grid point with respect to all vertices on its visible boundary. Thus the displacements of grid points can be calculated by interpolating the boundary movement by the mean value coordinates. Compared with other methods, the proposed method has good deformation capability and predictable com- putational cost, with no need to select parameters or functions. Applications of mesh deformation in different fields are presented to demonstrate the effectiveness of the proposed approach. The results of numerical experiments exhibit not only superior deformation capability of the method in traditional applications of fluid dynamic grid, but also great potential in modeling for large deformation analysis and inverse design problems.
文摘Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）
文摘在室内可见光通信中符号间干扰和噪声会严重影响系统性能,K均值(K-means)均衡方法可以抑制光无线信道的影响,但其复杂度较高,且在聚类边界处易出现误判。提出了改进聚类中心点的K-means(Improved Center K-means,IC-Kmeans)算法,通过随机生成足够长的训练序列,然后将训练序列每一簇的均值作为K-means聚类中心,避免了传统K-means反复迭代寻找聚类中心。进一步,提出了基于神经网络的IC-Kmeans(Neural Network Based IC-Kmeans,NNIC-Kmeans)算法,使用反向传播神经网络将接收端二维数据映射至三维空间,以增加不同簇之间混合数据的距离,提高了分类准确性。蒙特卡罗误码率仿真表明,IC-Kmeans均衡和传统K-means算法的误码率性能相当,但可以显著降低复杂度,特别是在信噪比较小时。同时,在室内多径信道模型下,与IC-Kmeans和传统Kmeans均衡相比,NNIC-Kmeans均衡的光正交频分复用系统误码率性能最好。
文摘AIM: To evaluate whether preoperative mean corpuscular volume (MCV) is a prognostic indicator in patients with resectable esophageal squamous cell carcinoma (ESCC). METHODS: A total of 298 consecutive, prospectively enrolled patients with histologically diagnosed ESCC who underwent surgery with curative intent from 2001 to 2011 were retrospectively evaluated. Patients were excluded if they had previous malignant disease, distant metastasis at the time of primary treatment, a history of neoadjuvant treatment, had undergone nonradical resection, or had died of a non-tumor-associated cause. Survival status was verified in September 2011. Pathological staging was performed based on the 2010 American Joint Committee on Cancer criteria. Preoperative MCV was obtained from blood counts performed routinely within 7 d prior to surgery. Receiver operating characteristic (ROC) curve analysis was used to determine a cutoff for preoperative MCV. RESULTS: The 298 patients consisted of 230 males and 68 females, with a median follow-up of 30.1 mo. ROC analysis showed an optimal cutoff for preoperative MCV of 95.6 fl. Fifty-nine patients (19.8%) had high (> 95.6 fl) and 239 (80.2%) had low (≤ 95.6 fl) preoperative MCV. Preoperative MCV was significantly associated with gender (P=0.003), body mass index (P=0.017), and preoperative red blood cell count (P<0.001). The predicted 1-, 3and 5-year overall survival (OS) rates were 72%, 60% and 52%, respectively. Median OS was significantly longer in patients with low than with high preoperative MCV (27.5 mo vs 19.4 mo, P<0.001). Multivariate analysis showed that advanced pT (P=0.018) and pN (P<0.001) stages, upper thoracic location (P=0.010), lower preoperative albumin concentration (P=0.002), and high preoperative MCV (P=0.001) were negative prognostic factors in patients with ESCC. Preoperative MCV also stratified OS in patients with T3, N1-N3, G2-G3 and stage Ⅲ tumors. CONCLUSION: Preoperative MCV is a prognostic factor in patients with ESCC.
文摘This paper deals with the construction of Heun’s method of random initial value problems. Sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples.
文摘In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.
文摘For the formal presentation about the definite problems of ultra-hyperbolic equations, the famous Asgeirsson mean value theorem has answered that Cauchy problems are ill-posed to ultra-hyperbolic partial differential equations of the second-order. So it is important to develop Asgeirsson mean value theorem. The mean value of solution for the higher order equation hay been discussed primarily and has no exact result at present. The mean value theorem for the higher order equation can be deduced and satisfied generalized biaxial symmetry potential equation by using the result of Asgeirsson mean value theorem and the properties of derivation and integration. Moreover, the mean value formula can be obtained by using the regular solutions of potential equation and the special properties of Jacobi polynomials. Its converse theorem is also proved. The obtained results make it possible to discuss on continuation of the solutions and well posed problem.
基金Supported by the Education Department Foundation of Shaanxi Province(03JK213) Supported by the Weinan Teacher's College Foundation(03YKF001)
文摘In this paper, we introduce a new counting function a(m) related to the Lucas number, then use conjecture and induction methods to give an exact formula Ar(N)=α(n), (r=1,2,3) and prove them.
文摘In this paper, we studies the relations between the mean value and the maximun norm of the infinite order entire functions which defined by legendre series. We obtained that if f(z) is an infinite order entire function with a positive exponenatial lower order. then loaM (α) ～logMδ(α) ～ logMδ(α) (α→+∞).
基金Supported by NSF of China(10671155)Supported by SF of Education Department of Shannxi Province(08JK291)
文摘The main purpose of this paper is using the analytic method to study the mean value properties of the arithmetical functions δk（（m, n））, δk（[m,n]/m）,and give several interesting asymptotic formulae for them.
文摘The main purpose of this paper is to use the analytic methods to study the hybrid mean value involving the hyper Cochrane sums, and give several sharp asymptotic formulae.
基金Supported by Natural Science Basic Research Program of Shaanxi(Program No.2021JM-487)the Special Scientific Research Program of the Education Department of Shaanxi Province(Grant No.18JK0161)the Scientific Research Foundation of Shaanxi University of Technology(Grant No.SLGQD1807)。
文摘R.Witula et al obtained a stronger version of the second mean value theorem for integral with some restrictions.In this paper,the stronger version theorem is proved without any restriction.The result is first restricted to the Riemann integrable functions and can be easily generalized to L~p integrable functions by using the well-known result that continuous functions are dense in the Banach space L~p[a,b]for any p≥1.
