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1.
K. V. Navickis 《Lithuanian Mathematical Journal》2000,40(2):166-175
We consider intrinsic normalizations of distributions of flags of type (m, m+1) on the Grassmann manifold ofm-planes of a (2m+2)-dimensional projective space.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 2, pp. 214–227, April–June, 2000.
Translated by V. Mackevičius 相似文献
2.
V. A. Gor'kavyi 《Mathematical Notes》1997,62(5):581-585
We present necessary and sufficient conditions for a regular three-dimensional manifold in the Grassmannian manifoldG(m, m+3) to be the Gauss image of a regular 3-submanifold in (m+3)-dimensional Euclidean space form>4.
Translated fromMatemalicheskie Zametki, Vol. 62, No. 5, pp. 694–699, November, 1997.
Translated by S. K. Lando 相似文献
3.
L. M. Samoilov 《Mathematical Notes》1999,65(2):208-213
In the paper, trinomial identities of associative algebras over an infinite field are considered (in general, the algebras
may have no unit), i.e., identities of the formα
m
1+β
m
2+γ
m
3=0, where α, β, and γ are scalars andm
1,m
2, andm
3 are different monomials. It is shown that any nontrivial identity if this kind implies a semigroup identity. The algebras
with trinomial identities are characterized in the language of varieties.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 254–260, February, 1999. 相似文献
4.
The following results are proved. In Theorem 1, it is stated that there exist both finitely presented and not finitely presented
2-generated nonfree groups which are k-free-like for any k ⩾ 2. In Theorem 2, it is claimed that every nonvirtually cyclic (resp., noncyclic and torsion-free) hyperbolic m-generated group is k-free-like for every k ⩾ m + 1 (resp., k ⩾ m). Finally, Theorem 3 asserts that there exists a 2-generated periodic group G which is k-free-like for every k ⩾ 3.
Supported by NSF (grant Nos. DMS 0455881 and DMS-0700811). (A. Yu. Olshanskii, M. V. Sapir)
Supported by RFBR project No. 08-01-00573. (A. Yu. Olshanskii)
Supported by BSF grant (USA–Israel). (M. V. Sapir)
Translated from Algebra i Logika, Vol. 48, No. 2, pp. 245–257, March–April, 2009. 相似文献
5.
We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues
and eigenfunctions of the problems asm→−0.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999. 相似文献
6.
V. N. Karpushkin 《Mathematical Notes》1997,62(6):697-700
In this paperk-harmonic polynomials in ℝ
n
, i.e. polynomials satisfying the Laplace equation with respect tok variables: ∂2/∂x
1
2
+...+∂2/∂x
k
2
F=0 are considered; here 1≤k≤n andn≥2. For a polynomialF (of degreem) of this type, it is proved that the number of components of the complements of its level sets does not exceed 2m
n−1+O(m
n−2). Under the assumptions that the singular set of the level surface is compact or that the leading homogeneous part of thek-harmonic polynomialF is nondegenerate, sharper estimates are also established.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 831–835, December, 1997
Translated by S. S. Anisov 相似文献
7.
D. V. Prokhorov 《Mathematical Notes》1997,61(5):609-613
We solve the maximal value problem for the functional
in the class of functionsf(z)=z+a
2z2+… that are holomorphic and univalent in the unit disk and satisfy the inequality |f(z)|<M. We prove that the Pick functions are extremal for this problem for sufficiently largeM whenever the set of indicesk
1,…,km contains an even number.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 728–733, May, 1997.
Translated by S. S. Anisov 相似文献
8.
It is well known that the number of isolated singular points of a hypersurface of degree d in ℂPm does not exceed the Arnol’d number Am(d), which is defined in combinatorial terms. In the paper it is proved that if b
m−1
±
(d) are the inertia indices of the intersection form of a nonsingular hypersurface of degree d in ℂPm, then the inequality Am(d)<min{b
m−1
+
(d), b
m−1
−
(d)} holds if and only if (m−5)(d−2)≥18 and (m,d)≠(7,12). The table of the Arnol’d numbers for 3≤m≤14, 3≤d≤17 and for 3≤m≤14,
d=18, 19 is given. Bibliography: 6 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 180–190.
Translated by O. A. Ivanov and N. Yu. Netsvetev. 相似文献
9.
Masahide Kuwada 《Annals of the Institute of Statistical Mathematics》1987,39(1):649-659
Summary By use of the algebraic structure, we obtain a simplified expression for the outlier-insensitivity factor for balanced fractional
2m factorial (2m-BFF) designs of resolution 2l+1 derived from simple arrays (S-arrays), whose measure has been introduced by Ghosh and Kipnegeno (1985,J. Statist. Plann. Inference,11, 119–129). It is defined by use of the measure suggested by Box and Draper (1975,Biometrika, 62 (2), 347–352). As examples, we study the sensitivity ofA-optimal 2m-BFF designs of resolution VII (i.e.,l=3) given by Shirakura (1976,Ann. Statist.,4, 515–531; 1977,Hiroshima Math. J.,7, 217–285). We observe that these designs are robust in the sense that they have low sensitivities.
Research supported in part by Grant 59530012 (C) and 60530014 (C), Japan. 相似文献
10.
E. A. Rovba 《Mathematical Notes》1997,61(2):221-226
Summation rational positive operatorsD
4n−n(x; f) of the Jackson type are constructed on the real axis. The corresponding approximations of continuous functionsf onℝwith coinciding finite limits limx→−∞
f(x) and limx→+∞
f(x) are estimated.
Translated fromMatematischeskie Zametki, Vol. 61, No. 2, pp. 270–277, February, 1997.
Translated by N. K. Kulman 相似文献
11.
Masahide Kuwada 《Annals of the Institute of Statistical Mathematics》1986,38(1):343-351
Summary This paper investigates some partially balanced fractional 2
m
1+m
2 factorial designs of resolution IV derived from partially balanced arrays, which permit estimation of the general mean, all
main effects, all two-factor interactions within each set of them
k
factors (k=1, 2) and some linear combinations of the two-factor interactions between the sets of them
k
ones. In addition, optimal designs with respect to the generalized trace criterion defined by Shirakura (1976,Ann. Statist.,4, 723–735) are presented for each pair (m
1,m
2) with 2≦m
1≦m
2 andm
1+m
2≦6, and for values ofN (the number of observations) in a reasonable range.
Partially supported in part by Grants 56530009 (C) and 57530010 (C). 相似文献
12.
We introduce modified Lagrange–Galerkin (MLG) methods of order one and two with respect to time to integrate convection–diffusion
equations. As numerical tests show, the new methods are more efficient, but maintaining the same order of convergence, than
the conventional Lagrange–Galerkin (LG) methods when they are used with either P
1 or P
2 finite elements. The error analysis reveals that: (1) when the problem is diffusion dominated the convergence of the modified
LG methods is of the form O(h
m+1 + h
2 + Δt
q
), q = 1 or 2 and m being the degree of the polynomials of the finite elements; (2) when the problem is convection dominated and the time step
Δt is large enough the convergence is of the form
O(\frachm+1Dt+h2+Dtq){O(\frac{h^{m+1}}{\Delta t}+h^{2}+\Delta t^{q})} ; (3) as in case (2) but with Δt small, then the order of convergence is now O(h
m
+ h
2 + Δt
q
); (4) when the problem is convection dominated the convergence is uniform with respect to the diffusion parameter ν (x, t), so that when ν → 0 and the forcing term is also equal to zero the error tends to that of the pure convection problem. Our error analysis
shows that the conventional LG methods exhibit the same error behavior as the MLG methods but without the term h
2. Numerical experiments support these theoretical results. 相似文献
13.
The computation of the Legendre functions Pv(x) for −1 < x ≤ 1, v ∈ ℂ and of the adjoint Legendre functions P
v
−m
(x) for −1 < x ≤ 1, v ∈ ℂ, and m ∈ ℤ+ is the subject of the paper. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 14–30. 相似文献
14.
Yoshinobu Kamishima 《Central European Journal of Mathematics》2012,10(5):1771-1788
An (m+2)-dimensional Lorentzian similarity manifold M is an affine flat manifold locally modeled on (G,ℝ m+2), where G = ℝ m+2 ⋊ (O(m+1, 1)×ℝ+). M is also a conformally flat Lorentzian manifold because G is isomorphic to the stabilizer of the Lorentzian group PO(m+2, 2) of the Lorentz model S m+1,1. We discuss the properties of compact Lorentzian similarity manifolds using developing maps and holonomy representations. 相似文献
15.
I. A. Sagirov 《Mathematical Notes》1999,66(2):203-207
The degrees of the irreducible characters of the Suzuki 2-groupsA(m,ϕ) are described. Assume that the order of an automorphism ϕ of the fieldGF (2
m
) isk>1,G=A(m,ϕ), and cd (G) is the set of degrees of the irreducible characters ofG. Ifk is odd, then cd(G)={1, 2(
m−m/k)/2
}, and ifk=2, then cd(G)={1, 2
m/2
}. Ifk is even andk≠2 then cd(G)={1,2
m/2
, 2
m/2−m/k
}, and the groupG has (2
m
−1)2
m/k
/(2
m/k
+1) characters of degree2
m/2
and (2m−1)22m/k/(2m/k+1) characters of degree 2m/2−m/k.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 258–263, August, 1999. 相似文献
16.
R. D. Baker 《Combinatorica》1982,2(2):103-109
IfP is a finite projective plane of ordern with a proper subplaneQ of orderm which is not a Baer subplane, then a theorem of Bruck [Trans. AMS 78(1955), 464–481] asserts thatn≧m
2+m. If the equalityn=m
2+m were to occur thenP would be of composite order andQ should be called a Bruck subplane. It can be shown that if a projective planeP contains a Bruck subplaneQ, then in factP contains a designQ′ which has the parameters of the lines in a three dimensional projective geometry of orderm. A well known scheme of Bruck suggests using such aQ′ to constructP. Bruck’s theorem readily extends to symmetric designs [Kantor, Trans. AMS 146 (1969), 1–28], hence the concept of a Bruck
subdesign. This paper develops the analoque ofQ′ and shows (by example) that the analogous construction scheme can be used to find symmetric designs. 相似文献
17.
In this paper we consider elliptic equations of order 2m in a bounded domainQ є R
n
with boundaryδQ and nonlocal conditions relating the traces of the solution and its derivatives on (n − 1)-dimensional smooth manifolds Γ
i
(∪
i
=∂δQ) to their values on some compact setF ⊂Q, whereF ∩δQ ≠ Φ. The Fredholm solvability of these problems in the weight spacesV
p, a
/l+2m
(Q) is proved for arbitrary 1<p <∞.
Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 882–898, June, 2000.
This research was supported by the Russian Foundation for Basic Research under grant No. 99-01-00028. 相似文献
18.
I. I. Sharapudinov 《Mathematical Notes》2000,67(3):389-397
Let
N+2m
={−m, −m+1, …, −1, 0, 1, …,N−1,N, …,N−1+m}. The present paper is devoted to the approximation of discrete functions of the formf :
N+2m
→ ℝ by algebraic polynomials on the grid Ω
N
={0, 1, …,N−1}. On the basis of two systems of Chebyshev polynomials orthogonal on the sets Ω
N+m
and Ω
N
, respectively, we construct a linear operatorY
n+2m, N
=Y
n+2m, N
(f), acting in the space of discrete functions as an algebraic polynomial of degree at mostn+2m for which the following estimate holds (x ε Ω
N
):
whereE
n+m[g,l
2(Ω
N+m
)] is the best approximation of the function
by algebraic polynomials of degree at mostn+m in the spacel
2 (Ω
N+m
) and the function Θ
N, α
(x) depends only on the weighted estimate for the Chebyshev polynomialsτ
k
α,α
(x, N).
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 460–470, March, 2000. 相似文献
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19.
A. P. Oskolkov 《Journal of Mathematical Sciences》1997,83(2):320-326
In this paper, we study some nonlocal problems for the Kelvin-Voight equations (1) and the penalized Kelvin-Voight equations
(2): the first and second initial boundary-value problems and the first and second time periodic boundary problems. We prove
that these problems have global smooth solutions of the classW
∞
1
(ℝ+;W
2
2+k
(Ω)),k=1,2,...;Ω⊂ℝ3. Bibliography: 25 titles.
Dedicated to N. N. Uraltseva on her jubilee
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 185–207.
Translated by N. A. Karazeeva. 相似文献
20.
Approximation by harmonic functions in theC
m
-Norm and harmonicC
m
-capacity of compact sets in ℝ
n
Yu. A. Gorokhov 《Mathematical Notes》1997,62(3):314-322
We study the function Λ
m
(X), 0<m<1, of compact setsX in ℝ
n
, n≥2, defined as the distance in the spaceC
m
(X)≡lip
m(X) from the function |x|2 to the subspaceH
m
(X) which is the closure inC
m
(X) of the class of functions harmonic in the neighborhood ofX (each function in its own neighborhood). We prove the equivalence of the conditions Λ
m
(X)=0 andC
m
(X)=H
m
(X). We derive an estimate from above that depends only on the geometrical properties of the setX (on its volume).
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 372–382, September, 1997.
Translated by I. P. Zvyagin 相似文献