安道什猜想推广的全相等正奇数解问题

本文研究了安道什猜想推广问题 ,并给出了其全相等正奇数解的公式 .

指数Diophantine方程9^x＋242^y=323^z的奇数解

运用初等数论方法讨论了指数Diophantine方程9x+242y=323z的奇数解,证明了该方程无奇数解(x,y,z)。

方程x^y+y^x=z^2的奇数解

证明了:如果(x,y,z)是方程xy+yx=z2的一组适合min(x,y)>1,gcd(x,y)=1且xy为奇数的正整数解,则x和y都不是平方数.

数论函数方程φ(φ(n))=2^(ω(n))3^(ω(n))的奇数解

讨论了方程φ(φ(n))=2^(ω(n))3^(ω(n))的可解问题,利用初等方法给出了当n为奇数时该方程的奇数解,确定了该方程共有5个奇数解,其中ω(n)为正整数n的不同质因数的个数.

关于丢番图方程multiply from i=1 to k(x_i^(x_i))=Z^z的相等奇数解

本文讨论了丢番图方程multiply from i=1 to kx_i^(x_i)=Z^Z的相等奇数,确定了方程在2×k时有全相等奇数解的全部k值,解决了文〔4〕中提出的一个问题。

方程n^x+(3n^2-1)~y=(4n^2-1)~z的奇数解(英文)

设n是大于3的正整数.运用Gel'fond-Baker方法证明了:方程n^x+(3n^2-1)~y=(4n^2-1)~z没有可使x是奇数的正整数解(x,y,z).

安道什猜想推广奇数解问题的几个新结论

安道什猜想的推广没有正奇数适合方程：ｘｘ１１·ｘｘ２２…ｘｘｋｋ＝ｚｚ（ｋ≥２）①当ｋ＝２时，即为安道什猜想：没有正奇数适合方程ｘｘ·ｙｙ＝ｚｚ．文［１］中笔者已给出了①的反例，此后笔者对此又作了进一步的研究，虽没能完全解决这一问题，但从不同的角度得...

再论非退化方程的整数解

给出非退化型方程multiply from i=1 to k x_i^xi=z^z新的偶数解和k=4时的奇数解.

关于Euler函数方程φ(x)=m的解

研究了Ｅｕｌｅｒ函数方程φ（ｘ）＝ｍ的解。当ｍ＝２ｐ，２ｐｎ，２ｐｑ（ｐ，ｑ为素数，ｎ为正整数）时，给出了方程φ（ｘ）＝ｍ的所有解。当ｍ＝２ｒ，２ｎｒ（ｒ为奇数）时，给出了方程φ（ｘ）＝ｍ的解结构。这一结果可以应用在有限群论的结构研究中（见文［４－６］）。

关于非退化方程∏ki=1x_i^x_i=z^z的整数解

给出了非退化型方程：∏ｋｉ＝１ｘｉｘｉ＝ｚｚ的新偶数解和ｋ＝４时的奇数解

方程x^p±y^(2p)=z^2与广义费尔马猜想

设p为奇素数,证明了丢番图方程x4 -y4 =zp 与x2p±y2p=z2 均无正整数解;方程xp+y2p=z2 仅有整数解 16+2 3 =32 ;方程x2p+2 kyp =z2 (k≥ 1)仅有整数解 12p+2 3 · 1p =32 ;同时还获得了方程x2 ±y4 =zp与x2 ±y4 =±z2p 的深刻结果,从而很大程度地支持广义Fermat猜想.

Zimian问题与叙拉古算子方程初探

Zimian问题实质上是叙拉古算子方程 xi = S xi(xi >1)的解的存在性问题,Erd?s给出长度 m i =1 i = 1= 8的一组解.本文不仅给出了叙拉古算子方程有解的一个必要条件,指出了方程不存在长度 m = 1的解,还给出了方程在长度 m = 18, m = 13, = 10, = 8 和 m = 5 的若干组解.

关于安道什猜想的推广

关于方程multiply from i=1 to k x_i^z_1=Z^z的奇数解问题,文献[4]证明了对k>3的所有k,方程(1)都有奇数解,本文再给出几组新的奇数解。

On the Problem of All Equal Positive Odd Number Solutions of the Dissemination of the Ends' Guess

The thesis is concerned with the problem of the dissemination of the Ends’ guess and offers the formula of all equal positive odd number solutions.

另一种求勾股数的方法

对于a^2+b^2=c^2(a、b、c为自然数),若已知a可求出b和c,见[文1].本文讨论在已知c值的情况下如何求a与b的值.显然a≠b,我们约定当a与b互换时所得为同一解答.

Singular Solutions of the Cauchy Problem for SemilinearParabolic Equations with Singular Potentions

In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.

Research on multiple elimination methods in inverse data space based on randomized singular value decomposition

Based on surfaced-related multiple elimination （SRME） , this research has derived the methods on multiples elimination in the inverse data space. Inverse data processing means moving seismic data from forward data space （FDS） to inverse data space （ IDS） . The surface-related multiples and primaries can then be sepa-rated in the IDS, since surface-related multiples wi l l form a focus region in the IDS. Muting the multiples ener-gy can achieve the purpose of multiples elimination and avoid the damage to primaries energy during the process of adaptive subtraction. Randomized singular value decomposition （ RSYD） is used to enhance calculation speed and improve the accuracy in the conversion of FDS to IDS. The synthetic shot record of the salt dome model shows that the relationship between primaries and multiples is simple and clear, and RSVD can easily eliminate multiples and save primaries energy. Compared with conventional multiples elimination methods and ordinary methods of multiples elimination in the inverse data space, this technique has an advantage of high cal-culation speed and reliable outcomes.

INTERPOLATION OF HEAD-RELATED TRANSFER FUNCTIONS USING SPHERICAL FOURIER EXPANSION

A new interpolation algorithm for Head-Related Transfer Function （HRTF） is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition （SVD） is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance.

Random seismic noise attenuation by learning-type overcomplete dictionary based on K-singular value decomposition algorithm

The transformation of basic functions is one of the most commonly used techniques for seismic denoising,which employs sparse representation of seismic data in the transform domain. The choice of transform base functions has an influence on denoising results. We propose a learning-type overcomplete dictionary based on the K-singular value decomposition( K-SVD) algorithm. To construct the dictionary and use it for random seismic noise attenuation,we replace fixed transform base functions with an overcomplete redundancy function library. Owing to the adaptability to data characteristics,the learning-type dictionary describes essential data characteristics much better than conventional denoising methods. The sparsest representation of signals is obtained by the learning and training of seismic data. By comparing the same seismic data obtained using the learning-type overcomplete dictionary based on K-SVD and the data obtained using other denoising methods,we find that the learning-type overcomplete dictionary based on the K-SVD algorithm represents the seismic data more sparsely,effectively suppressing the random noise and improving the signal-to-noise ratio.

A New Statistical Downscaling Scheme for Predicting Winter Precipitation in China

An effective statistical downscaling scheme was developed on the basis of singular value decomposition to predict boreal winter(December-January-February)precipitation over China.The variable geopotential height at 500 hPa(GH5)over East Asia,which was obtained from National Centers for Environmental Prediction’s Coupled Forecast System(NCEP CFS),was used as one predictor for the scheme.The preceding sea ice concentration(SIC)signal obtained from observed data over high latitudes of the Northern Hemisphere was chosen as an additional predictor.This downscaling scheme showed significantly improvement in predictability over the original CFS general circulation model(GCM)output in cross validation.The multi-year average spatial anomaly correlation coefficient increased from–0.03 to 0.31,and the downscaling temporal root-mean-square-error(RMSE)decreased significantly over that of the original CFS GCM for most China stations.Furthermore,large precipitation anomaly centers were reproduced with greater accuracy in the downscaling scheme than those in the original CFS GCM,and the anomaly correlation coefficient between the observation and downscaling results reached～0.6 in the winter of 2008.