共查询到20条相似文献,搜索用时 15 毫秒
1.
O. V. Lopotko 《Ukrainian Mathematical Journal》2010,62(2):320-324
We obtain an integral representation of even positive-definite functions of one variable for which the kernel [k
1(x + y) + k
2 (x − y)] is positive definite. 相似文献
2.
In this paper, we consider the equation y″+f(x,y)=0 with a nonresonance condition of the form A≤f
y
(x,y)≤B, where (k−1)2<A≤k
2<⋅⋅⋅<m
2≤B<(m+1)2, k,m∈ℤ+. With optimal control theory and the Schauder fixed-point theorem, by introducing a new cost functional, we obtain a new
existence and uniqueness result for the above equation with two-point boundary-value conditions.
This work was supported by NSFC Grant 10501017 and 985 Project of Jilin University. 相似文献
3.
Let R
k,s
(n) denote the number of solutions of the equation n = x2 + y1k + y2k + ?+ ysk{n= x^2 + y_1^k + y_2^k + \cdots + y_s^k} in natural numbers x, y
1, . . . , y
s
. By a straightforward application of the circle method, an asymptotic formula for R
k,s
(n) is obtained when k ≥ 3 and s ≥ 2
k–1 + 2. When k ≥ 6, work of Heath-Brown and Boklan is applied to establish the asymptotic formula under the milder constraint s ≥ 7 · 2
k–4 + 3. Although the principal conclusions provided by Heath-Brown and Boklan are not available for smaller values of k, some of the underlying ideas are still applicable for k = 5, and the main objective of this article is to establish an asymptotic formula for R
5,17(n) by this strategy. 相似文献
4.
E. P. Golubeva 《Journal of Mathematical Sciences》2009,157(4):543-552
The solvability of the equation n = x
2 + y
2 + 6pz
2 (p is a fixed large prime) is proved under some natural congruential conditions and the assumption nm
12 > p
21. As an implication, the solvability of the equation n = x
2 + y
2 + u
3 + v
3 + z
4 + w
16 + t
4k+1 for all sufficiently large n is established. Bibliography: 13 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 5–21. 相似文献
5.
We determine the general solution of the functional equation f(x + ky) + f(x-ky) = g(x + y) + g(x-y) + h(x) + h(y) for fixed integers with k ≠ 0; ±1 without assuming any regularity conditions for the unknown functions f, g, h, and0020[(h)\tilde] \tilde{h} . The method used for solving these functional equations is elementary but it exploits an important result due to Hosszú.
The solution of this functional equation can also be obtained in groups of certain type by using two important results due
to Székelyhidi. 相似文献
6.
E. Preissmann 《Aequationes Mathematicae》1987,32(1):195-212
We solve independently the equations 1/θ(x)θ(y)=ψ(x)−ψ(y)+φ(x−y)/θ(x−y) and 1/θ(x)θ(y)=σ(x)−σ(y)/θ(x−y)+τ(x)τ(y), τ(0)=0. In both cases we find θ2=aθ4+bθ2+c. We deduce estimates for the spectral radius of a matrix of type(1/θ(x
r
−x
s
)) (the accent meaning that the coefficients of the main diagonal are zero) and we study the case where thex
r
are equidistant.
Dédié to à Monsieur le Professeur Otto Haupt à l'occasion de son cententiare avec les meilleurs voeux 相似文献
7.
Yasuyo Hatano Ichizo Ninomiya Hiroshi Sugiura Takemitsu Hasegawa 《Numerical Algorithms》2009,52(2):213-224
The infinite integral ò0¥x dx/(1+x6sin2x)\int_0^{\infty}x\,dx/(1+x^6\sin^2x) converges but is hard to evaluate because the integrand f(x) = x/(1 + x
6sin2
x) is a non-convergent and unbounded function, indeed f(kπ) = kπ→ ∞ (k→ ∞). We present an efficient method to evaluate the above integral in high accuracy and actually obtain an approximate value
in up to 73 significant digits on an octuple precision system in C++. 相似文献
8.
Neculai Andrei 《Numerical Algorithms》2010,54(1):23-46
An accelerated hybrid conjugate gradient algorithm represents the subject of this paper. The parameter β
k
is computed as a convex combination of bkHS\beta_k^{HS} (Hestenes and Stiefel, J Res Nat Bur Stand 49:409–436, 1952) and bkDY\beta_k^{DY} (Dai and Yuan, SIAM J Optim 10:177–182, 1999), i.e. bkC = (1-qk)bkHS + qk bkDY\beta_k^C =\left({1-\theta_k}\right)\beta_k^{HS} + \theta_k \beta_k^{DY}. The parameter θ
k
in the convex combinaztion is computed in such a way the direction corresponding to the conjugate gradient algorithm is the
best direction we know, i.e. the Newton direction, while the pair (s
k
, y
k
) satisfies the modified secant condition given by Li et al. (J Comput Appl Math 202:523–539, 2007) B
k + 1
s
k
= z
k
, where zk = yk +(hk / || sk ||2 )skz_k =y_k +\left({{\eta_k} / {\left\| {s_k} \right\|^2}} \right)s_k, hk = 2( fk -fk+1 )+( gk +gk+1 )Tsk\eta_k =2\left( {f_k -f_{k+1}} \right)+\left( {g_k +g_{k+1}} \right)^Ts_k, s
k
= x
k + 1 − x
k
and y
k
= g
k + 1 − g
k
. It is shown that both for uniformly convex functions and for general nonlinear functions the algorithm with strong Wolfe
line search is globally convergent. The algorithm uses an acceleration scheme modifying the steplength α
k
for improving the reduction of the function values along the iterations. Numerical comparisons with conjugate gradient algorithms
show that this hybrid computational scheme outperforms a variant of the hybrid conjugate gradient algorithm given by Andrei
(Numer Algorithms 47:143–156, 2008), in which the pair (s
k
, y
k
) satisfies the classical secant condition B
k + 1
s
k
= y
k
, as well as some other conjugate gradient algorithms including Hestenes-Stiefel, Dai-Yuan, Polack-Ribière-Polyak, Liu-Storey,
hybrid Dai-Yuan, Gilbert-Nocedal etc. A set of 75 unconstrained optimization problems with 10 different dimensions is being
used (Andrei, Adv Model Optim 10:147–161, 2008). 相似文献
9.
We establish the existence of infinitely many polynomial progressions in the primes; more precisely, given any integer-valued polynomials P
1, …, P
k
∈ Z[m] in one unknown m with P
1(0) = … = P
k
(0) = 0, and given any ε > 0, we show that there are infinitely many integers x and m, with
1 \leqslant m \leqslant xe1 \leqslant m \leqslant x^\varepsilon, such that x + P
1(m), …, x + P
k
(m) are simultaneously prime. The arguments are based on those in [18], which treated the linear case P
j
= (j − 1)m and ε = 1; the main new features are a localization of the shift parameters (and the attendant Gowers norm objects) to both coarse
and fine scales, the use of PET induction to linearize the polynomial averaging, and some elementary estimates for the number
of points over finite fields in certain algebraic varieties. 相似文献
10.
Frank Uhlig 《Numerical Algorithms》2009,52(3):335-353
We use methods of geometric computing combined with hermitean matrix eigenvalue/eigenvector evaluations to find the numerical
radius w(A) of a real or complex square matrix A simply, quickly, and accurately. The numerical radius w(A) is defined as the maximal distance of points in the field of values F(A) = { x* A x | ||x||2 = 1 }F(A) = \{ x^* A x \mid \|x\|_2 = 1 \} from zero in ℂ. Its value is an indicator of the transient behavior of the discrete dynamical system f
k + 1 = Af
k
. We describe and test a MATLAB code for solving this optimization problem that can have multiple and even infinitely many
solutions with maximal distance. 相似文献
11.
We establish necessary and sufficient conditions under which a sequence x
0 = y
0 , x
n+1 = Ax
n
+ y
n+1 , n ≥ 0, is bounded for each bounded sequence
{ yn :n \geqslant 0 } ì { x ? èn = 1¥ D( An ) |supn \geqslant 0 || An x || < ¥ }\left\{ {y_n :n \geqslant 0} \right\} \subset \left\{ {\left. {x \in \bigcup\nolimits_{n = 1}^\infty {D\left( {A^n } \right)} } \right|\sup _{n \geqslant 0} \left\| {A^n x} \right\| < \infty } \right\}, where A is a closed operator in a complex Banach space with domain of definition D(A) . 相似文献
12.
Jorge J. Betancor Juan C. Fariña Teresa Martinez Lourdes Rodríguez-Mesa 《Arkiv f?r Matematik》2008,46(2):219-250
In this paper we investigate Riesz transforms R
μ
(k) of order k≥1 related to the Bessel operator Δμ
f(x)=-f”(x)-((2μ+1)/x)f’(x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We
obtain that for every k≥1, R
μ
(k) is a principal value operator of strong type (p,p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ(x)=x
2μ+1
dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R
μ
(k) maps L
p
(ω) into itself and L
1(ω) into L
1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman. 相似文献
13.
We consider an Abel equation (*)y’=p(x)y
2 +q(x)y
3 withp(x), q(x) polynomials inx. A center condition for (*) (closely related to the classical center condition for polynomial vector fields on the plane)
is thaty
0=y(0)≡y(1) for any solutiony(x) of (*).
Folowing [7], we consider a parametric version of this condition: an equation (**)y’=p(x)y
2 +εq(x)y
3
p, q as above, ε ∈ ℂ, is said to have a parametric center, if for any ɛ and for any solutiony(ɛ,x) of (**)y(ɛ, 0)≡y(ɛ, 1)..
We give another proof of the fact, shown in [6], that the parametric center condition implies vanishing of all the momentsm
k
(1), wherem
k
(x)=∫
0
x
pk
(t)q(t)(dt),P(x)=∫
0
x
p(t)dt. We investigate the structure of zeroes ofm
k
(x) and generalize a “canonical representation” ofm
k
(x) given in [7]. On this base we prove in some additional cases a composition conjecture, stated in [6, 7] for a parametric
center problem.
The research of the first and the third author was supported by the Israel Science Foundation, Grant No. 101/95-1 and by the
Minerva Foundation. 相似文献
14.
For a finite poset P = (V, ≤ ), let _s(P){\cal B}_s(P) consist of all triples (x,y,z) ∈ V
3 such that either x < y < z or z < y < x. Similarly, for every finite, simple, and undirected graph G = (V,E), let Bs(G){\cal B}_s(G) consist of all triples (x,y,z) ∈ V
3 such that y is an internal vertex on an induced path in G between x and z. The ternary relations Bs(P){\cal B}_s(P) and Bs(G){\cal B}_s(G) are well-known examples of so-called strict betweennesses. We characterize the pairs (P,G) of posets P and graphs G on the same ground set V which induce the same strict betweenness relation Bs(P)=Bs(G){\cal B}_s(P)={\cal B}_s(G). 相似文献
15.
We consider an Abel equation (*)y’=p(x)y
2 +q(x)y
3 withp(x), q(x) polynomials inx. A center condition for (*) (closely related to the classical center condition for polynomial vector fields on the plane)
is thaty
0=y(0)≡y(1) for any solutiony(x) of (*).
We introduce a parametric version of this condition: an equation (**)y’=p(x)y
2 +εq(x)y
3
p, q as above, ℂ, is said to have a parametric center, if for any ε and for any solutiony(ε,x) of (**),y(ε,0)≡y(ε,1).
We show that the parametric center condition implies vanishing of all the momentsm
k
(1), wherem
k
(x)=∫
0
x
pk
(t)q(t)(dt),P(x)=∫
0
x
p(t)dt. We investigate the structure of zeroes ofm
k
(x) and on this base prove in some special cases a composition conjecture, stated in [10], for a parametric center problem.
The research of the first and the third author was supported by the Israel Science Foundation, Grant No. 101/95-1 and by the
Minerva Foundation. 相似文献
16.
M. Eshaghi Gordji H. Khodaei 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5629-5643
In this paper, we achieve the general solution and the generalized Hyers–Ulam–Rassias stability of the following functional equation
f(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x)