共查询到19条相似文献,搜索用时 109 毫秒
1.
证明了:假设λ,μ是不全为负的非零实数,λ是无理数,k是正整数,那么存在无穷多素数p,p_1,p_2,使得[λp_1+μp_2~2]=kp.特别地,[λp_1+μp_2~2]表示无穷多素数. 相似文献
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证明了:设k是大于或等于2的正整数,η是任意给定的实数,λ_1,λ_2,λ_3是非零实数,不全同号,并且λ_1/λ_2是无理数,则不等式|λ_1p_1+λ_2p_2+λ_3p_32~k+η|(max p_j)~(-σ)有无穷多组素数解p_1,p_2,p_3,这里σ满足:当2≤k≤3时,0σ1/2(2~(k+1)+1),当4≤k≤5时,0σ5/6k2~k;当k≥6时,0σ20/21k2~k. 相似文献
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设λ_1,λ_2,λ_3,λ_4是正实数,λ_1/λ_2是无理数和代数数,V是具有良好间隔的序列,δ0.证明了:对于任意的ε0及v∈ν,v≤X,使得λ_1p_1~2+λ_2p_2~2+λ_3p_3~3+λ_4p_4~3-v|v~(-δ)没有素数解p_1,p_2,p_3,p_4的v的个数不超过O(X~((67)/(72)+2δ+ε)).这改进了之前的结果. 相似文献
6.
设λ_1,λ_2,λ_3,λ_4为不全为负的非零实数,λ_1/λ_2是无理数和代数数.■是具有良好间隔的序列,δ>0.本文证明了:对于任意ε>0及v∈■,v≤X,使得不等式|λ_1p_1~2+λ_2p_2~2+λ_3p_3~3+λ_4p_4~3-v|相似文献
7.
朱立 《数学年刊A辑(中文版)》2019,40(4):365-376
令■设λ_1,λ_2,λ_3是不全同号的非零实数,且满足λ_1/λ_2为无理数,则对于任意实数η和ε 0,不等式■有无穷多组素数解p_1,p_2,p_3.该结果改进了Gambini,Languasco和Zaccagnini的结果. 相似文献
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混合幂的素变数丢番图逼近 总被引:1,自引:0,他引:1
证明了:如果λ_1,λ_2,λ_3,λ_4是正实数,λ_1/λ_2是无理数和代数数,V是well-spaced序列,δ0,那么对于v∈V,v≤X,ε0,使得|λ_(1p_1~2)+λ_(2p_2~2)+λ_(3p_3~3)+λ_(4p_4~3)-v|v~(-δ)没有素数解p1,p2,p3,p4的v的个数不超过O(X~(20/21+21δ+ε)). 相似文献
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证明了在一定条件下, 不等式
$|\lambda_1p_1^2+\lambda_2p_2^2+\lambda_3p_3^2+\lambda_4p_4^2+\mu_12^{m_1}+\cdots+\mu_s2^{m_s}+\varpi|<\eta$关
于素数$p_1, p_2, p_3, p_4$
和正整数$m_1, \cdots, m_s$有无穷多解, 改进了之前的结果. 相似文献
12.
Quanwu Mu 《The Ramanujan Journal》2016,39(3):481-496
Let k be an integer with \(k\ge 3\) and \(\eta \) be any real number. Suppose that \(\lambda _1, \lambda _2, \lambda _3, \lambda _4, \mu \) are non-zero real numbers, not all of the same sign and \(\lambda _1/\lambda _2\) is irrational. It is proved that the inequality \(|\lambda _1p_1^2+\lambda _2p_2^2+\lambda _3p_3^2+\lambda _4p_4^2+\mu p_5^k+\eta |<(\max \ p_j)^{-\sigma }\) has infinitely many solutions in prime variables \(p_1, p_2, \ldots , p_5\), where \(0<\sigma <\frac{1}{16}\) for \(k=3,\ 0<\sigma <\frac{5}{3k2^k}\) for \(4\le k\le 5\) and \(0<\sigma <\frac{40}{21k2^k}\) for \(k\ge 6\). This gives an improvement of an earlier result. 相似文献
13.
设k和r是满足k≥3及r≥Ψ(k)+1的正整数,这里当3≤k≤4时,Ψ(k)=2~(k-1);而当k≥5时,Ψ(k)=1/2k(k+1).假定δ和ε是给定的足够小的正数,λ_1,λ_2,…,λ_(r+1)是不全同号且两两之比不全为有理数的非零实数.对于任意实数η与0σ2~(1-2k)/r-1,证明了:存在一个正数序列X→+∞,使得不等式|λ_1p_1~k+λ_2p_2~k+···+λ_rp_r~k+λ_(r+1)p_(r+1)+η|(max(1≤j≤r+1)p_j)~(-σ)有》■X~(■-(2~(1-2k))/(r-1)+ε组素数解(p_1,p_2,…,p_(r+1)),这里(δX)~(1/k)≤p_j≤X~(1/k)(1≤j≤r)及δX≤p_(r+1)≤X.这改进了之前的结果. 相似文献
14.
Doron S. Lubinsky 《Constructive Approximation》2016,43(2):311-336
Let \(\mu \) and \(\nu \) be measures supported on \(\left( -1,1\right) \) with corresponding orthonormal polynomials \(\left\{ p_{n}^{\mu }\right\} \) and \( \left\{ p_{n}^{\nu }\right\} \), respectively. Define the mixed kernel We establish scaling limits such as where \(S\left( t\right) =\frac{\sin t}{t}\) is the sinc kernel, and \(B\left( \xi \right) \) depends on \({\mu },\nu \) and \(\xi \). This reduces to the classical universality limit in the bulk when \(\mu =\nu \). We deduce applications to the zero distribution of \(K_{n}^{{\mu },\nu }\), and asymptotics for its derivatives.
相似文献
$$\begin{aligned} K_{n}^{{\mu },\nu }\left( x,y\right) =\sum _{j=0}^{n-1}p_{j}^{\mu }\left( x\right) p_{j}^{\nu }\left( y\right) . \end{aligned}$$
$$\begin{aligned}&\lim _{n\rightarrow \infty }\frac{\pi \sqrt{1-\xi ^{2}}\sqrt{\mu ^{\prime }\left( \xi \right) \nu ^{\prime }\left( \xi \right) }}{n}K_{n}^{\mu ,\nu }\left( \xi +\frac{a\pi \sqrt{1-\xi ^{2}}}{n},\xi +\frac{b\pi \sqrt{1-\xi ^{2}}}{n}\right) \\&\quad =S\left( \frac{\pi \left( a-b\right) }{2}\right) \cos \left( \frac{\pi \left( a-b\right) }{2}+B\left( \xi \right) \right) , \end{aligned}$$
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We consider an eigenvalue problem for a system on [0, 1]:
$$\left\{ {\begin{array}{*{20}l} {\left[ {\left( {\begin{array}{*{20}c} 0 & 1 \\ 1 & 0 \\ \end{array} } \right)\frac{{\text{d}}}
{{{\text{d}}x}} + \left( {\begin{array}{*{20}c} {p_{11} (x)} & {p_{12} (x)} \\ {p_{21} (x)} & {p_{22} (x)} \\ \end{array}
} \right)} \right]\left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(2)} (x)} \\ \end{array} } \right) =
\lambda \left( {\begin{array}{*{20}c} {\varphi ^{(1)} (x)} \\ {\varphi ^{(1)} (x)} \\ \end{array} } \right)} \\ {\varphi
^{(2)} (0)\cosh \mu - \varphi ^{(1)} (0)\sinh \mu = \varphi ^{(2)} (1)\cosh \nu + \varphi ^{(1)} (1)\sinh \nu = 0} \\ \end{array}
} \right.$$ with constants
$$\mu ,\nu \in \mathbb{C}.$$ Under the assumption that p21, p22 are known, we prove a uniqueness theorem and provide a reconstruction formula for p11 and p12 from the spectral characteristics consisting of one spectrum and the associated norming constants. 相似文献
16.
Jiafa Xu Zhongli Wei Donal O Regan Donal O''Regan Yujun Cui 《Journal of Applied Analysis & Computation》2019,9(3):1165-1182
In this paper using fountain theorems we study the existence of infinitely many solutions for fractional Schr\"{o}dinger-Maxwell equations
\[\begin{cases}
(-\Delta)^\alpha u+\lambda V(x)u+\phi u=f(x,u)-\mu g(x)|u|^{q-2}u, \text{ in } \mathbb R^3,\(-\Delta)^\alpha \phi=K_\alpha u^2, \text{ in } \mathbb R^3,
\end{cases}\]
where $\lambda,\mu >0$ are two parameters, $\alpha\in (0,1]$, $K_\alpha=\frac{\pi^{-\alpha}\Gamma(\alpha)}{\pi^{-(3-2\alpha)/2}\Gamma((3-2\alpha)/2)}$ and $(-\Delta)^\alpha$ is the fractional Laplacian. Under appropriate assumptions on $f$ and $g$ we obtain an existence theorem for this system. 相似文献
17.
In this paper,we obtain that b∈ BMO(R~n) if and only if the commutator[b,I_α]is bounded from the Morrey spaces L~(p_1,λ_1)(R~n)×L~(p_2,λ_2)(R~n) to L~(q,λ)(R~n),for some appropriate indices p,q,λ,μ.Also we show that b ∈ Lip_β(R~n) if and only if the commutator[b,I_α]is bounded from the Morrey spaces L~(p_1,λ_1)(R~n)×L~(p_2,λ_2)(R~n) to L~(q,λ)(R~n),for some appropriate indices p,q,λ,μ. 相似文献
18.
Uniqueness and existence of solutions for a singular system with nonlocal operator via perturbation method 下载免费PDF全文
Kamel Saoudi Mouna Kratou Eadah AlZahrani 《Journal of Applied Analysis & Computation》2020,10(4):1311-1325
In this work, we investigate the existence and the uniqueness of solutions for the nonlocal elliptic system involving a singular nonlinearity as follows:
$$
\left\{\begin{array}{ll}
(-\Delta_p)^su = a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad
\text{in }\Omega,\ (-\Delta_p)^s v= b(x)|v|^{q-2}v +\frac{1-\beta}{2-\alpha-\beta} c(x)|u|^{1-\alpha}|v|^{-\beta}, \quad
\text{in }\Omega,\ u=v
= 0 ,\;\;\mbox{ in }\,\mathbb{R}^N\setminus\Omega,
\end{array}
\right.
$$
where $\Omega $ is a bounded domain in $\mathbb{R}^{n}$ with smooth boundary, $0<\alpha <1,$ $0<\beta <1,$ $2-\alpha -\beta
相似文献
19.
Qian Tao 《数学年刊B辑(英文版)》1985,6(2):229-240
In this paper the following result is established: For a_i,f\in \phi(R^K),i=1,\cdots,n and $T(a,f)(x)=w(x,D)()[\prod\limits_{i = 1}^n {{P_{{m_i}}}({a_i},x, \cdot )f( \cdot )} \]$
It holds that
$||T(a,f)||_q\leq C||f||_p_0[\prod\limits_{i = 1}^n {||{\nabla ^{{m_i}}}|{|_{{p_i}}}} \]$
where a=(a_1,\cdots,a_n), q^-1=p^-1_0+[\sum\limits_{i = 1}^n {p_i^{ - 1} \in (0,1),\forall i,{p_i} \in (1,\infty )} \] or \forall i,p_i=\infinity,p_0\in (1,\infinity),
for an integer m_i\geq 0,
$P_m_m(a_i,x,y)=a_i(x)-[\sum\limits_{|\beta | < {m_i}} {\frac{{a_i^{(\beta )}(y)}}{{\beta !}}} {(x - y)^\beta }\]$
w(x,\xi) is a classical symbol of order |m|, m=(m_1,\cdots, m_n), |m|=m_1+\cdots+m_n, m_i are nonnegative integers. Besides, a representation theorem is given.
The methods used here closely follow those developed by Coifman, R. and Meyer, Y. in [5] and by Cohen, J. in [3]. 相似文献