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On the Mean Value of High-Powers of a Special Character Sum Modulo a Prime
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作者 Xiaodan Yuan Wenpeng Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第7期943-953,共11页
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
关键词 Quadratic character the classical gauss sums the mean value of high-power computational formula
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A Number Theoretic Function and Its Mean Value Computation 被引量:1
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作者 李海龙 杨倩丽 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第3期53-56,共4页
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).
关键词 number theoretic function mean value computing formula
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On the Weyl’s Lemma for Triharmonic Functions
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作者 ZHENG Run-jie ZENG Jia-min FANG Yi 《Chinese Quarterly Journal of Mathematics》 2024年第3期288-294,共7页
In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
关键词 Weyl’s lemma Harmonic functions Triharmonic functions Test functions Mean value formulas
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THE SCHUR CONVEXITY OF GINI MEAN VALUES IN THE SENSE OF HARMONIC MEAN 被引量:4
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作者 夏卫锋 褚玉明 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期1103-1112,共10页
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
关键词 Gini mean values Schur convex Schur harmonic convex
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The Asymptotic Property of Generalized Taylor Remainder "Mean Value Point" 被引量:4
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作者 RENLi-shun ZHANGCai-yu 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期314-318,共5页
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
关键词 FUNCTIONAL F-derivative Gα-derivative mean value point assymptotic property
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Some Hybrid Mean Values of a New Number Theoretic Function 被引量:1
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作者 REN Gang-lian 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期325-329,共5页
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
关键词 largest exponent asymptotic formula hybrid mean value Dirichlet divisor function d(n)
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On the Lucas Base and Computation of Counting Function Mean Value
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作者 LIHai-long LIUHua-ke 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第1期84-89,共6页
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.
关键词 Lucas sequence Fibonacci sequence mean value counting fuction
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THE MEAN VALUE THEOREM AND CONVERSE THEOREM OF ONE CLASS THE FOURTH-ORDER PARTIAL DIFFERENTIAL EQUATIONS
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作者 同小军 同登科 陈绵云 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第6期717-723,共7页
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
关键词 Asgeirsson mean value theorem generalized biaxial symmetry potential equation Jacobi polynomials
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On the Mean Value of the Infinite Order Legendre Series
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作者 王安斌 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第4期6-12, ,共7页
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
关键词 cntire function mean value order
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Hybrid Mean Value of the Hyper Cochrane Sums
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作者 ZHANG TIAN-PING 《Communications in Mathematical Research》 CSCD 2009年第4期329-339,共11页
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.
关键词 hyper Cochrane sum hyper-Kloosterman sum hybrid mean value
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A New Compound Function and Its Mean Value
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作者 MA Jin-ping GE Jian 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第2期312-316,共5页
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.
关键词 arithmetic function mean value asymptotic formula
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Mean Values of the Hardy Sum
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作者 王晓瑛 岳霞霞 《Chinese Quarterly Journal of Mathematics》 2017年第1期16-33,共18页
Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H(h,p)=sum((-1)^(j+1+[(hj)/p]))from (p-1) to (j=1) which is related to the classical Dedekind sum. The mean values of the Hardy sum in short interval... Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H(h,p)=sum((-1)^(j+1+[(hj)/p]))from (p-1) to (j=1) which is related to the classical Dedekind sum. The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions. 展开更多
关键词 Dedekind sum Hardy sum mean value Dirichlet L-function
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A Note on the Mean Value Theorems
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作者 Kung Kuen Tse 《Advances in Pure Mathematics》 2021年第5期395-399,共5页
The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point <em>P</em> on the graph such that the tangent at <em>P</em> is paralle... The mean value theorem for derivatives says that for a given function over a closed and bounded interval, there is a point <em>P</em> on the graph such that the tangent at <em>P</em> is parallel to the secant through the two endpoints. The mean value theorem for definite integrals says that the area under the function is equal to the area of a rectangle whose base is the length of the interval and height of some point <em>Q</em> on the graph. These two theorems have been studied and utilized extensively and they form the backbone of many important theorems in different branches of mathematics. In this note, we pose the question: for what functions do the two points <em>P </em>and <em>Q</em> always coincide? We find that the only analytic functions satisfying this condition are linear or exponential functions. 展开更多
关键词 Mean value Theorem Real Analytic Functions Identity Theorem Power Series
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Image Feature Computation in Encrypted Domain Based on Mean Value
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作者 Xiangshu Ou Mingfang Jiang +1 位作者 Shuai Li Yao Bai 《Journal of Cyber Security》 2020年第3期123-130,共8页
In smart environments,more and more teaching data sources are uploaded to remote cloud centers which promote the development of the smart campus.The outsourcing of massive teaching data can reduce storage burden and c... In smart environments,more and more teaching data sources are uploaded to remote cloud centers which promote the development of the smart campus.The outsourcing of massive teaching data can reduce storage burden and computational cost,but causes some privacy concerns because those teaching data(especially personal image data)may contain personal private information.In this paper,a privacy-preserving image feature extraction algorithm is proposed by using mean value features.Clients use block scrambling and chaotic map to encrypt original images before uploading to the remote servers.Cloud servers can directly extract image mean value features from encrypted images.Experiments show the effectiveness and security of our algorithm.It can achieve information search over the encrypted images on the smart campus. 展开更多
关键词 PRIVACY-PRESERVING image encryption cloud computing mean value
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Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces
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作者 Akachukwu Offia Ugochukwu Osisiogu +4 位作者 Theresa Efor Friday Oyakhire Monday Ekhator Friday Nkume Sunday Aloke 《Open Journal of Optimization》 2023年第3期99-108,共10页
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su... In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces. 展开更多
关键词 Real Banach Spaces Pseudo-Convex Functions Pseudo-Monotone Maps Sub-Differentials Lower Semi-Continuous Functions and Approximate Mean value Inequality
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Adaptive Active Control of Low Frequency Noise in a Duct
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作者 李传光 李悟 韩秀苓 《Journal of Beijing Institute of Technology》 EI CAS 1999年第3期318-323,共6页
Aim To study a method realizing noise control for a physical model of progressive wave in a duct. Methods A mathematical model was constructed and a transfer function of the adaptive system for noise control was als... Aim To study a method realizing noise control for a physical model of progressive wave in a duct. Methods A mathematical model was constructed and a transfer function of the adaptive system for noise control was also worked out; moreover, the effects of some algorithms such as RLS,LMS and LSL on noise control were analyzed and compared. Results Without the feedback of sound, the mean noise reduce value(MNRV) of 27 5 dB for broadband noise from 0 to 500?Hz in frequency were achieved. When acoustic feedback took place and an air stream loudspeaker was used, the MNRV was only about 4 9?dB. But if the loudspeaker had a plain frequency feature, MNRV was improved by 10 2?dB. Conclusion The technique is applied to ruducing the noise from engines' exhausted gas pipes. It is, in principle, used for noise cancelling in a closed three dimensional space. 展开更多
关键词 noise control ADAPTIVE mean noise reduce value(MNRV)
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AN APPROXIMATE EXPRESSION RELATED WITH RSA FIXED POINTS 被引量:4
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作者 YuXiuyuan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期1-8,共8页
Let T=T(n,e,α) be the number of fixed points o f RSA(n,e) that a re co prime with n=pq,and A,B be sets of prime numbers in (1,x) and (1,y) respectively. An estimation on the mean value M(A,B,e,α)=1 (#A)(#B)∑p∈... Let T=T(n,e,α) be the number of fixed points o f RSA(n,e) that a re co prime with n=pq,and A,B be sets of prime numbers in (1,x) and (1,y) respectively. An estimation on the mean value M(A,B,e,α)=1 (#A)(#B)∑p∈A,q∈B,(p,q)=1logT(pq,e,α) is given. 展开更多
关键词 RSA fixed point mean value.
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Target reliability index for serviceability limit state of single piles 被引量:3
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作者 边晓亚 郑俊杰 +1 位作者 徐志军 章荣军 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第1期310-316,共7页
The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) o... The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index. 展开更多
关键词 single pile serviceability limit state target reliability index mean value first order second moment method Monte Carlo simulation
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Meridional Distributions of Historical Zonal Averages and Their Use to Quantify the Global and Spheroidal Mean Near-Surface Temperature of the Terrestrial Atmosphere 被引量:1
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作者 Gerhard Kramm Martina Berger +1 位作者 Ralph Dlugi Nicole Molders 《Natural Science》 2020年第3期80-124,共45页
The zonal averages of temperature (the so-called normal temperatures) for numerous parallels of latitude published between 1852 and 1913 by Dove, Forbes, Ferrel, Spitaler, Batchelder, Arrhenius, von Bezold, Hopfner, v... The zonal averages of temperature (the so-called normal temperatures) for numerous parallels of latitude published between 1852 and 1913 by Dove, Forbes, Ferrel, Spitaler, Batchelder, Arrhenius, von Bezold, Hopfner, von Hann, and B&ouml;rnstein were used to quantify the global (spherical) and spheroidal mean near-surface temperature of the terrestrial atmosphere. Only the datasets of Dove and Forbes published in the 1850s provided global averages below 〈T〉=14°C, mainly due to the poor coverage of the Southern Hemisphere by observations during that time. The global averages derived from the distributions of normal temperatures published between 1877 and 1913 ranged from 〈T〉=14.0°C (Batchelder) to 〈T〉=15.1°C (Ferrel). The differences between the global and the spheroidal mean near-surface air temperature are marginal. To examine the uncertainty due to interannual variability and different years considered in the historic zonal mean temperature distributions, the historical normal temperatures were perturbed within ±2σ to obtain ensembles of 50 realizations for each dataset. Numerical integrations of the perturbed distributions indicate uncertainties in the global averages in the range of ±0.3°C to ±0.6°C and depended on the number of available normal temperatures. Compared to our results, the global mean temperature of 〈T〉=15.0°C published by von Hann in 1897 and von Bezold in 1901 and 1906 is notably too high, while 〈T〉=14.4°C published by von Hann in 1908 seems to be more adequate within the range of uncertainty. The HadCRUT4 record provided 〈T〉≌?13.7°C for 1851-1880 and 〈T〉=13.6°C for 1881-1910. The Berkeley record provided 〈T〉=13.6°C and 〈T〉≌?13.5°C for these periods, respectively. The NASA GISS record yielded 〈T〉=13.6°C for 1881-1910 as well. These results are notably lower than those based on the historic zonal means. For 1991-2018, the HadCRUT4, Berkeley, and NASA GISS records provided 〈T〉=14.4°C, 〈T〉=14.5°C, and 〈T〉=14.5°C, respectively. The comparison of the 1991-2018 globally averaged near-surface temperature with those derived from distributions of zonal temperature averages for numerous parallels of latitude suggests no change for the past 100 years. 展开更多
关键词 Global Mean Temperature Spheroidal Mean Temperature Climatological Mean values for the Parallels of Latitude Zonal Averages Normal Temperature Temperature Anomaly Isothermal Charts Solar Climate
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CHARACTERISTICS OF SUBDIFFERENTIALS OF FUNCTIONS
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作者 郭兴明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第5期445-450,共6页
In the presem paper, some important characteristics of Fenchel-, Frechet-,Hademard-, and Gateaux-Subdifferentials are showed up, and properties of functions, especially. convexity of functions, are described by subdif... In the presem paper, some important characteristics of Fenchel-, Frechet-,Hademard-, and Gateaux-Subdifferentials are showed up, and properties of functions, especially. convexity of functions, are described by subdifferentials. 展开更多
关键词 SUBDIFFERENTIAL generalized mean value theorem CONVEXITY LIPSCHITZ MONOTONE
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