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1.
The following problem, arising from medical imaging, is addressed: Suppose that T is a known tetrahedron in ? 3 with centroid at the origin. Also known is the orthogonal projection U of the vertices of the image ?T of T under an unknown rotation ? about the origin. Under what circumstances can ? be determined from T and U? 相似文献
2.
Let T be a square matrix with a real spectrum, and let f be an analytic function. The problem of the approximate calculation of f(T) is discussed. Applying the Schur triangular decomposition and the reordering, one can assume that T is triangular and its diagonal entries tii are arranged in increasing order. To avoid calculations using the differences tii ? tjj with close (including equal) tii and tjj, it is proposed to represent T in a block form and calculate the two main block diagonals using interpolating polynomials. The rest of the f(T) entries can be calculated using the Parlett recurrence algorithm. It is also proposed to perform some scalar operations (such as the building of interpolating polynomials) with an enlarged number of significant decimal digits. 相似文献
3.
We obtain an exact estimate for the minimum multiplicity of a continuous finite-to-one mapping of a projective space into
a sphere for all dimensions. For finite-to-one mappings of a projective space into a Euclidean space, we obtain an exact estimate
for this multiplicity for n = 2, 3. For n ≥ 4, we prove that this estimate does not exceed 4. Several open questions are formulated. 相似文献
4.
In the paper we study the algorithmic nature of some “simple” fragments of positive theories with “few” constants for free
noncyclic semigroups.
Translated from Matematicheskie Zametki, Vol. 67, No. 2, pp. 191–200, February, 2000. 相似文献
5.
For a submanifold M
n of a Riemannian manifold M
q, the concept of a torsion bivector at the point x M
n for given one- and two-dimensional directions from T
x
M
n is introduced using only the first and second fundamental forms of M
n. Its relation to the concept of Gaussian torsion is then established. It is proved that: 1) equality to zero of the torsion bivector is necessary and, when M
n is a nondevelopable surface of a space of constant curvature with nonzero second fundamental form, is also sufficient for the "flattening" of M
n into some totally geodesic M
n+1 in M
q; 2) when n = 2, the independence of the nonzero torsion bivector of direction characterizes a minimal M
2 in M
q.Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 39–42, 1991. 相似文献
6.
In a graph G, which has a loop at every vertex, a connected subgraph H=( V( H), E( H)) is a retract if, for any a, b ∈ V( H) and for any paths P, Q in G, both joining a to b, and satisfying | Q|≧ ≧| P|, then P ⫅ V( H) whenever Q ⫅ V( H). As such subgraphs can be described by a closure operator we are led to the investigation of the corresponding complete
lattice of “closed” subgraphs. For example, in this complete lattice every element is the infimum of an irredundant family
of infimum irreducible elements.
The work presented here was supported in part by N.S.E.R.C. Operating Grant No. A4077. 相似文献
7.
The problem of the motion of a container in a curved section of a horizontal pipeline is solved using second-order Lagrange equations in the presence of nonholonous couplings. The special case of the motion of a container in a circular curve is examined.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 90–95, 1987. 相似文献
8.
We study a periodic boundary-value problem for the quasilinear equation u
tt
− u
xx
= F[ u, u
t
, u
x
], u( x, 0)= u( x, π)=0, u( x + ω, t) = u( x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1293–1296, September, 1998. 相似文献
9.
To every closed subset X of a symplectic manifold ( M, ω) we associate a natural group of Hamiltonian diffeomorphisms Ham ( X, ω). We equip this group with a semi-norm ${\Vert\cdot\Vert^{X, \omega}}$ , generalizing the Hofer norm. We discuss Ham ( X, ω) and ${\Vert\cdot\Vert^{X, \omega}}$ if X is a symplectic or isotropic submanifold. The main result involves the relative Hofer diameter of X in M. Its first part states that for the unit sphere in ${\mathbb{R}^{2n}}$ this diameter is bounded below by ${\frac{\pi}{2}}$ , if n ≥ 2. Its second part states that for n ≥ 2 and d ≥ n there exists a compact subset X of the closed unit ball in ${\mathbb{R}^{2n}}$ , such that X has Hausdorff dimension at most d + 1 and relative Hofer diameter bounded below by π / k( n, d), where k( n, d) is an explicitly defined integer. 相似文献
10.
The results of Seeley on admissible Cauchy data for the solutions of a homogeneous elliptic equation on a manifold with boundary are extended to equations with a pseudodifferential operator.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 110, pp. 217–224, 1981. 相似文献
11.
Let D be a Dedekind domain with quotient field K. Let Cp be the completion of the localisation Dp , of D at a nonzero prime ideal p, of D. Let rp be the rank of Cp as a D-module, ie rp , is the dimension of the K-vector space Kp , = K? DCp . The following results on rp are deduced from well-known theorems: if rp is finite for at least one prime ideal p, then D is a discrete valuation ring; and D = Cp if p = 1. If D is a discrete valuation ring, then rp = dimExt( K, D) + 1. A module M is extensionless if every extension of M by M splits. The D-module rC is an estensionless indecomposable module. If rC is infinite for every nonzero prime ideal, it is shown that an estensionless D-module of finite rank is a direct sum or certain rank one modulcs. 相似文献
12.
Summary The problem of selecting a subpopulation from a given population II is to be, on the basis of measurements of members of II, achieved by choosing those members of II who satisfy the standards determined by a given selection cirterion and rejecting those who do not.
Since the optimum selection depends on the unknown parameter of the probability distribution of II, it is here considered how to construct a decision function from the space of subsidiary sample having infor-mation on θ
to the space of selections. Thus the existence of Bayes and minimax decision functions under the constraint defined by the
selection criterion is proved. A necessary and sufficient condition for a decision function satisfying the constraint to be
a Bayes decision function is also obtained.
The Institute of Statistical Mathematics 相似文献
14.
We present two conjectures concerning the diameter of a direct power of a finite group. The first conjecture states that the diameter of Gn with respect to each generating set is at most n(| G|? rank( G)); and the second one states that there exists a generating set 𝒜, of minimum size, for Gn such that the diameter of Gn with respect to 𝒜 is at most n(| G|? rank( G)). We will establish evidence for each of the above mentioned conjectures. 相似文献
15.
Let A denote an n× n matrix with all its elements real and non-negative, and let ri be the sum of the elements in the ith row of A, i=1,…, n. Let B= A? D( r1,…, rn), where D( r1,…, rn) is the diagonal matrix with ri at the position ( i, i). Then it is proved that A is irreducible if and only if rank B= n?1 and the null space of BT contains a vector d whose entries are all non-null. 相似文献
16.
Let V be a semigroup variety containing all commutative semigroups such that the law of exponents ( xy)
n
=x ny n fails in V for every n > 1. For every semigroup S V such that the reflection of the semigroup obtained from S by an adding unity has only one idempotent there exists a semigroup T
V extending S without non-trivial endomorphisms. In more general, the full subcategory of V formed by all extensions of S within V is universal.Presented by B. M. Schein. 相似文献
17.
We define strong and weak affinities of a number a for a sequence ( xk ) denoted by L ( a,( xk )) and U ( a, ( xk )) respectively. We show U ( a,( xk )) > 0 if and only if the number a is a statistical limit point of the sequence ( xk ). We consider the distribution of sequences with positive weak and strong measures of affinity within the space l ∞ of bounded sequences. The main result is that the set of bounded sequences with U ( a,( xk )) > 0, that is, the set of sequences with statistical limit points, is a dense subset in l ∞ of the first category. We also show the set of sequences with positive strong affinities is a nowhere dense subset of l ∞. 相似文献
18.
The problem has a large parameter, the number N of particles (outside the condensate), and a small parameter, Planck’s constant
ħ (more precisely, a dimensionless parameter containing ħ in the numerator). They turn out to be interrelated for Bose particles.
Using the exact solution of the variational equation for a bosonic system in a capillary, we can obtain precise criteria restricting
the superfluidity of a classical liquid in the capillary.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 524–528, June, 2008. 相似文献
19.
Given the function f and the vector-statistic t N which is a mean square consistent estimator of a parameter a, the problem is to estimate f(a). The criteria for the mean
square consistency of the estimator f(t N) are considered. In the case where the estimator f(t N) is not mean square consistent, a class of estimators of f(a) is proposed, and it is proved that the estimators of the class
are mean square consistent for all distribution of t N.
Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 44–55, Perm, 1990. 相似文献
20.
Necessary and sufficient conditions are given on a family A
r
r>0 of subsets of a real linear space X under which inf r > 0 x A
r
is a quasinorm [l] on X. It is shown that for any symmetric (about zero) closed set A in a normed space X containing the ball {x X: x l there exists a quasinorm ¦·¦ on X such that A = {x X ¦x¦ 1}. Examples are constructed of linear metric spaces in which there exists a Chebyshev line which is not an approximately compact set.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 237–246, February, 1976. 相似文献
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