共查询到20条相似文献,搜索用时 109 毫秒
1.
Bruno Pini 《Annali di Matematica Pura ed Applicata》1959,48(1):305-332
Sunto Si studia il problema della determinazione di una soluzione dell'equazione
ak(x)∂ku/∂xk=f(x, y) entro la semistriscia a≤x≤b, y≥0, che assuma assegnati valori per y=0 e per x=a, x1, x2, b (a<x1<x2<b). Analogamente si studia il problema della determinazione di una soluzione dell' equazione
ak(x)∂ku/∂xk+b(x)∂u/∂y=f(x,y), entro la medesima semistriscia, cha assuma assegnati valori per y=0 e per x=a, x1, x2, b e la cui ∂/∂y assuma assegnati valori per y=0.
A Giovanni Sansone nel suo 70mo compleanno. 相似文献
2.
Let X, X1 , X2 , . . . be i.i.d. random variables, and set Sn = X1 +···+Xn , Mn = maxk≤n |Sk|, n ≥1. Let an = o( (n)(1/2)/logn). By using the strong approximation, we prove that, if EX = 0, VarX = σ2 0 and E|X| 2+ε ∞ for some ε 0, then for any r 1, lim ε1/(r-1)(1/2) [ε-2-(r-1)]∞∑n=1 nr-2 P{Mn ≤εσ (π2n/(8log n))(1/2) + an } = 4/π . We also show that the widest a n is o( n(1/2)/logn). 相似文献
3.
Forn a positive integer letp(n) denote the number of partitions ofn into positive integers and letp(n,k) denote the number of partitions ofn into exactlyk parts. Let
, thenP(n) represents the total number of parts in all the partitions ofn. In this paper we obtain the following asymptotic formula for
. 相似文献
4.
It is proposed that the Gaussian type distribution constantb
qi in the Gaussian model depends on the coordination numberq
i of sitei, and that the relation
holds amongb
qi
’s. The Gaussian model is then studied on a family of the diamond-type hierarchical (or DH) lattices, by the decimation real-space
renormalization group following spin-rescaling method. It is found that the magnetic property of the Gaussian model belongs
to the same universal class, and that the critical pointK* and the critical exponentv are given by
and
, respectively.
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research
Project supported by the National Natural Science Foundation of China (Grant No. 19775008), the National Basic Research 相似文献
5.
V. A. Yudin 《Proceedings of the Steklov Institute of Mathematics》2011,273(1):188-189
It is established that H. Bohr’s inequality \(\sum\nolimits_{k = 0}^\infty {\left| {{{f^{\left( k \right)} \left( 0 \right)} \mathord{\left/ {\vphantom {{f^{\left( k \right)} \left( 0 \right)} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2^{{k \mathord{\left/ {\vphantom {k 2}} \right. \kern-\nulldelimiterspace} 2}} k!} \right)}}} \right| \leqslant \sqrt 2 \left\| f \right\|_\infty }\) is sharp on the class H ∞. 相似文献
6.
Xn(d1, . . . , dr-1, dr; w) and Xn(e1, . . . , er-1, dr; w) are two complex odd-dimensional smooth weighted complete intersections defined in a smooth weighted hypersurface Xn+r-1(dr; w). We prove that they are diffeomorphic if and only if they have the same total degree d, the Pontrjagin classes and the Euler characteristic, under the following assumptions: the weights w = (ω0, . . . , ωn+r) are pairwise relatively prime and odd, νp(d/dr) ≥ 2n+1/ 2(p-1) + 1 for all primes p with p(p-1) ≤ n + 1, where νp(d/dr) satisfies d/dr =Ⅱp prime pνp (d/dr). 相似文献
7.
K. F. Cheng 《Periodica Mathematica Hungarica》1983,14(2):177-187
The nonparametric regression problem has the objective of estimating conditional expectation. Consider the model $$Y = R(X) + Z$$ , where the random variableZ has mean zero and is independent ofX. The regression functionR(x) is the conditional expectation ofY givenX = x. For an estimator of the form $$R_n (x) = \sum\limits_{i = 1}^n {Y_i K{{\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} \mathord{\left/ {\vphantom {{\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} {\sum\limits_{i = 1}^n {K\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} }}} \right. \kern-\nulldelimiterspace} {\sum\limits_{i = 1}^n {K\left[ {{{\left( {x - X_i } \right)} \mathord{\left/ {\vphantom {{\left( {x - X_i } \right)} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}} \right]} }}} $$ , we obtain the rate of strong uniform convergence $$\mathop {\sup }\limits_{x\varepsilon C} \left| {R_n (x) - R(x)} \right|\mathop {w \cdot p \cdot 1}\limits_ = o({{n^{{1 \mathord{\left/ {\vphantom {1 {(2 + d)}}} \right. \kern-\nulldelimiterspace} {(2 + d)}}} } \mathord{\left/ {\vphantom {{n^{{1 \mathord{\left/ {\vphantom {1 {(2 + d)}}} \right. \kern-\nulldelimiterspace} {(2 + d)}}} } {\beta _n \log n}}} \right. \kern-\nulldelimiterspace} {\beta _n \log n}}),\beta _n \to \infty $$ . HereX is ad-dimensional variable andC is a suitable subset ofR d . 相似文献
8.
The trigonometric polynomials of Fejér and Young are defined by $S_n (x) = \sum\nolimits_{k = 1}^n {\tfrac{{\sin (kx)}}
{k}}$S_n (x) = \sum\nolimits_{k = 1}^n {\tfrac{{\sin (kx)}}
{k}} and $C_n (x) = 1 + \sum\nolimits_{k = 1}^n {\tfrac{{\cos (kx)}}
{k}}$C_n (x) = 1 + \sum\nolimits_{k = 1}^n {\tfrac{{\cos (kx)}}
{k}}, respectively. We prove that the inequality $\left( {{1 \mathord{\left/
{\vphantom {1 9}} \right.
\kern-\nulldelimiterspace} 9}} \right)\sqrt {15} \leqslant {{C_n \left( x \right)} \mathord{\left/
{\vphantom {{C_n \left( x \right)} {S_n \left( x \right)}}} \right.
\kern-\nulldelimiterspace} {S_n \left( x \right)}}$\left( {{1 \mathord{\left/
{\vphantom {1 9}} \right.
\kern-\nulldelimiterspace} 9}} \right)\sqrt {15} \leqslant {{C_n \left( x \right)} \mathord{\left/
{\vphantom {{C_n \left( x \right)} {S_n \left( x \right)}}} \right.
\kern-\nulldelimiterspace} {S_n \left( x \right)}} holds for all n ≥ 2 and x ∈ (0, π). The lower bound is sharp. 相似文献
9.
O. V. Kulikova 《Journal of Mathematical Sciences》2007,142(2):1942-1948
Under the condition of asphericity of a quotient group
, mutual commutants of the form
in hyperbolic groups G are investigated together with the structure of central subgroups
in central extensions
of
. In particular, quotients of the form G/[g
m
, G] are considered, where g is an element of infinite order from a hyperbolic group G and m is sufficiently large (depending on g).
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 115–125, 2005. 相似文献
10.
D. V. Goryashin 《Moscow University Mathematics Bulletin》2011,66(3):125-128
For the number N(x) of solutions to the equation aq − bc = 1 in positive integers a, b, c and square-free numbers q satisfying the condition aq ≤ x the asymptotic formula
$N\left( x \right) = \sum\limits_{n \leqslant x} {2^{\omega \left( n \right)} \tau \left( {n - 1} \right) = \xi _0 x\ln ^2 x + \xi _1 x\ln x + \xi _2 x + O\left( {x^{{5 \mathord{\left/
{\vphantom {5 {6 + \varepsilon }}} \right.
\kern-\nulldelimiterspace} {6 + \varepsilon }}} } \right)}$N\left( x \right) = \sum\limits_{n \leqslant x} {2^{\omega \left( n \right)} \tau \left( {n - 1} \right) = \xi _0 x\ln ^2 x + \xi _1 x\ln x + \xi _2 x + O\left( {x^{{5 \mathord{\left/
{\vphantom {5 {6 + \varepsilon }}} \right.
\kern-\nulldelimiterspace} {6 + \varepsilon }}} } \right)} 相似文献
11.
If P(z) is a polynomial of degree n which does not vanish in |z| 1,then it is recently proved by Rather [Jour.Ineq.Pure and Appl.Math.,9 (2008),Issue 4,Art.103] that for every γ 0 and every real or complex number α with |α|≥ 1,{∫02π |D α P(e iθ)| γ dθ}1/γ≤ n(|α| + 1)C γ{∫02π|P(eiθ)| γ dθ}1/γ,C γ ={1/2π∫0 2π|1+eiβ|γdβ}-1/γ,where D α P(z) denotes the polar derivative of P(z) with respect to α.In this paper we prove a result which not only provides a refinement of the above inequality but also gives a result of Aziz and Dawood [J.Approx.Theory,54 (1988),306-313] as a special case. 相似文献
12.
G. Kuba 《Acta Mathematica Hungarica》2001,91(4):325-332
For a large real parameter t and 0 a b
we consider sums
where is the rounding error function, i.e. (z) = z - [z] - 1/2. We generalize Huxley's well known estimate
by showing that
holds uniformly in 0 a b
. Fruther, we investigate an analogous question related to the divisor problem and show that the inequality
, which (due to Huxley) holds uniformly in 0 a b
, and which is in general not true for 1 a b t, is true uniformly in 0 a b
. 相似文献
13.
We demonstrate how a well studied combinatorial optimizationproblem may be used as a new cryptographic primitive. The problemin question is that of finding a "large" clique in a randomgraph. While the largest clique in a random graph with nvertices and edge probability p is very likely tobe of size about
, it is widely conjecturedthat no polynomial-time algorithm exists which finds a cliqueof size
with significantprobability for any constant > 0. We presenta very simple method of exploiting this conjecture by hidinglarge cliques in random graphs. In particular, we show that ifthe conjecture is true, then when a large clique—of size,say,
is randomlyinserted (hidden) in a random graph, finding a clique ofsize
remains hard.Our analysis also covers the case of high edge probabilitieswhich allows us to insert cliques of size up to
. Our result suggests several cryptographicapplications, such as a simple one-way function. 相似文献
14.
We obtain the new exact Kolmogorov-type inequality
15.
Nariaki Sugiura 《Annals of the Institute of Statistical Mathematics》1974,26(1):117-125
Summary LetS
i have the Wishart distributionW
p(∑i,ni) fori=1,2. An asymptotic expansion of the distribution of
for large n=n1+n2 is derived, when∑
1∑
2
−1
=I+n−1/2θ, based on an asymptotic solution of the system of partial differential equations for the hypergeometric function2
F
1, obtained recently by Muirhead [2]. Another asymptotic formula is also applied to the distributions of −2 log λ and −log|S
2(S
1+S
2)−1| under fixed∑
1∑
2
−1
, which gives the earlier results by Nagao [4]. Some useful asymptotic formulas for1
F
1 were investigated by Sugiura [7]. 相似文献
16.
In this paper, we consider the problem of computing the real dimension of a given semi-algebraic subset of R
k, where R is a real closed field. We prove that the dimension k′ of a semi-algebraic set described by s polynomials of degree d in
k variables can be computed in time
17.
We investigate the relationship between the constants K(R) and K(T), where
is the exact constant in the Kolmogorov inequality, R is the real axis, T is a unit circle,
18.
Prof. Dr. Dieter Wolke 《Monatshefte für Mathematik》1977,83(2):163-166
By means of the Hoheisel—Montgomery prime number theorem it is shown that for every α≥1 the inequality $$|(\sigma (n)/n) - \alpha | \leqslant {1 \mathord{\left/ {\vphantom {1 {n^{({2 \mathord{\left/ {\vphantom {2 5}} \right. \kern-\nulldelimiterspace} 5}) - \varepsilon } }}} \right. \kern-\nulldelimiterspace} {n^{({2 \mathord{\left/ {\vphantom {2 5}} \right. \kern-\nulldelimiterspace} 5}) - \varepsilon } }}(\varepsilon > 0,\sigma (n) = \sum\limits_{d/n} d )$$ has infinitely many solutionsn∈N. It is highly probable that the exponent 2/5 can be replaced by 1. 相似文献
19.
We construct the solution of the loop equations of the β-ensemble model in a form analogous to the solution in the case of the Hermitian matrices β = 1. The solution for β = 1 is expressed in terms of the algebraic spectral curve given by y2 = U(x). The spectral curve for arbitrary β converts into the Schrödinger equation (??)2 ? U(x) ψ(x) = 0, where ? ∝ \({{\left( {{{\sqrt \beta - 1} \mathord{\left/ {\vphantom {{\sqrt \beta - 1} {\sqrt \beta }}} \right. \kern-\nulldelimiterspace} {\sqrt \beta }}} \right)} \mathord{\left/ {\vphantom {{\left( {{{\sqrt \beta - 1} \mathord{\left/ {\vphantom {{\sqrt \beta - 1} {\sqrt \beta }}} \right. \kern-\nulldelimiterspace} {\sqrt \beta }}} \right)} N}} \right. \kern-\nulldelimiterspace} N}\). The basic ingredients of the method based on the algebraic solution retain their meaning, but we use an alternative approach to construct a solution of the loop equations in which the resolvents are given separately in each sector. Although this approach turns out to be more involved technically, it allows consistently defining the B-cycle structure for constructing the quantum algebraic curve (a D-module of the form y2 ? U(x), where [y, x] = ?) and explicitly writing the correlation functions and the corresponding symplectic invariants Fh or the terms of the free energy in an 1/N2-expansion at arbitrary ?. The set of “flat” coordinates includes the potential times tk and the occupation numbers \(\tilde \varepsilon _\alpha \). We define and investigate the properties of the A- and B-cycles, forms of the first, second, and third kinds, and the Riemann bilinear identities. These identities allow finding the singular part of \(\mathcal{F}_0 \), which depends only on \(\tilde \varepsilon _\alpha \). 相似文献
20.
Tadej Kotnik 《Advances in Computational Mathematics》2008,29(1):55-70
The paper describes a systematic computational study of the prime counting function π(x) and three of its analytic approximations: the logarithmic integral \({\text{li}}{\left( x \right)}: = {\int_0^x {\frac{{dt}}{{\log \,t}}} }\), \({\text{li}}{\left( x \right)} - \frac{1}{2}{\text{li}}{\left( {{\sqrt x }} \right)}\), and \(R{\left( x \right)}: = {\sum\nolimits_{k = 1}^\infty {{\mu {\left( k \right)}{\text{li}}{\left( {x^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} } \right)}} \mathord{\left/ {\vphantom {{\mu {\left( k \right)}{\text{li}}{\left( {x^{{1 \mathord{\left/ {\vphantom {1 k}} \right. \kern-\nulldelimiterspace} k}} } \right)}} k}} \right. \kern-\nulldelimiterspace} k} }\), where μ is the Möbius function. The results show that π(x)
|