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1.
Turgut Önder 《manuscripta mathematica》1995,86(1):393-407
LetG be a finite group and letM be a unitary representation space ofG. We consider the existence problem of equivariant frame fields on the unit sphereS(M) whose orthogonal complements in the tangent bundleT(S(M)) admitG-equivariant complex structures. Under mild fixed point conditions we give a complete solution for this problem whenG is either ℤ/2ℤ or a finite group of odd order.
This article was processed by the author using theLaTEX style filecljourl from Springer-Verlag. 相似文献
2.
Let {Ai }and {Bi } be two given families of n-by-n matrices. We give conditions under which there is a unitary U such that every matrix UAiU 1 is upper triangular. We give conditions, weaker than the classical conditions of commutativity of the whole family, under which there is a unitary U such that every matrix UAjU ? is upper triangular. We also give conditions under which there is one single unitary U such that every UAiU 1 and every UBjU ? is upper triangular. We give necessary and sufficient conditions for simultaneous unitary reduction to diagonal form in this way when all the Aj's are complex symmetric and all theBj 's are Hermitian. 相似文献
3.
Prof. Dr. R. Bulirsch 《Numerische Mathematik》1969,13(4):305-315
Summary This paper is a continuation of [2, 3]. It contains anALGOL program for the incomplete elliptic integral of the third kind based on a theory described in [4]. This program replaces the inadequate one based on the Gauß-transformation which was published in [2]. In addition, anAlgol program for a general complete elliptic integral is presented.
Editor's note. In this fascicle, prepublication of algorithms from the Special Functions Series of the Handbook for Automatic Computation is continued. Algorithms are published inAlgol 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones.This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the U. S. Army Research Office —Durham under Contract DA-31-124-ARO-D-257. 相似文献
4.
Adolf Grünbaum 《Annali di Matematica Pura ed Applicata》1962,57(1):257-282
Summary
1. The philosophical justification of Einstein's conception of distant simultaneity as conventional depends on two cardinal
physical assumptions which are stated. Awareness of these two assumptions poses the following historical problem: On what
grounds didEinstein feel entitled to make them in 1905? In an endeavor to answer this question, the contribution of experimental results to Einstein's
postulational achievement in the Special Theory of Relativity (?RT?) is examined. As a consequence, the author rejects (i)M. Polanyi's recent citation of the history of RT as evidence against an empiricist account of scientific knowledge, and (ii)G. Holton's assessment of the relevance of knowledge of the history of RT to the philosophical mastery of its logical foundations.
2. An analysis of theKennedy-Thorndike experiment is used to provide a refutation of the widespread belief that the aether-theoreticLorentz-Fitzgerald contraction hypothesis was ad hoc in the logical sense. A distinction is drawn between a logical and a psychological sense
in which an auxiliary hypothesis can be ad hoc.
3.
E. T. Whittaker's disparaging estimate ofEinstein's contributions to RT vis -à -vis those ofLorentz andPoincare is shown to rest on fundamental philosophical misunderstandings ofEinstein's conception of theLorentz transformations.Holton's maxim for the study of the history of RT is then tested in the light of his evaluation ofWhittaker's belittlement ofEinstein's role.
To Enrico Bompiani on his scientific Jubilee 相似文献
5.
Summary A bilinear divergence identity is obtained, which differs from the usualLagrange divergence identity employed byRiemann. In the case of two independent variables, this new identity is used to unify the treatment ofCauchy's problem for hyperbolic equations, the initial value problem for parabolic equations, and theDirichlet problem for elliptic equations.
This research was supported in whole or in part by the United States Air Force under Contract No. AF18(600)-573 monitored by the Office of Scientific Research, Air Research and Development Command. 相似文献
6.
Summary In this paper we study the stability(1) of linear inviscid fluid mixtures. In particular, we show that thestatical stability criterion of Gibbs is both necessary and sufficient for thedynamical stability of the mixture(2), using, as our main hypotheses, only those inequalities and symmetries which are consequences of the second law of thermodynamics(3).
A Dario Graffi nel suo 70° compleanno
Entrata in Redazione il 28 giugno 1975. 相似文献
7.
K. K. Dube 《Periodica Mathematica Hungarica》1982,13(4):267-271
The purpose of the present note is to give a number of characterizations of theR
1-axiom and to show that theR
1-axiom is equivalent to the weakly Hausdorff axiom introduced byB. Banaschewski andJ. M. Maranda [2]. In anR
1-space it is shown that the locally compactness property is also open hereditary and that the closure of an almost compact set is the union of the closures of its points. A necessary and sufficient condition is obtained under which a locally compact set dense in anR
1-space is open. Finally a variant of a well-known theorem regarding two continuous functions of a topological space into aT
2-space is formulated forR
1-spaces. 相似文献
8.
A. M. Gavrilik 《Theoretical and Mathematical Physics》1993,95(2):546-551
Summary We have considered here the (unitary) irreducible representations of theq-deformed algebraU
q(SO4) and of theq-deformed Lorentz algebraU
q(SO3,1). Both of them contain, as subalgebra, the algebraU
q(SO3) which is shown to be isomorphic to the Fairlie-Odesskii algebra. As the list of pairwise nonequivalent irreps of theU
q(SO3,1) demonstrates, the set of the parameters, which characterize such irreps is somewhat reduced (due to periodicity properties of the function w(z)=[z]q) in comparison with that of theq=1 (classical) case. From another side, the list of unitary irreps of theU
q(SO3,1) contains the strange series which has no classical counterpart (disappears at q=1).Published in Teoreticheskaya i Matematicheskaya Fizika. Vol. 95, No. 2, pp. 251–257, May, 1993. 相似文献
9.
Roger Alperin 《Monatshefte für Mathematik》1982,93(4):261-265
FollowingKazhdan, a separable locally compact groupG is said to have propertyT if the trivial representation is isolated in the dual space,, of equivalence classes of continuous irreducible unitary representations ofG. We generalize results ofMargulis—Tits by showing that groups which have propertyT can not be amalgams.Research supported by NSF. 相似文献
10.
P. L. Sharma 《Annali di Matematica Pura ed Applicata》1961,56(1):159-175
Summary The author studies a problem relating Harmonic Summability of doubleFourier serie analogous to theGergen's criteria for convergence. 相似文献
11.
Sahib Ram Mandan 《Annali di Matematica Pura ed Applicata》1961,53(1):45-55
Summary A simplex in an n-space and its tangential simplex formed of the n+1 tangent hyperplanes of its circumhypersphere (0) at its vertices are polar reciprocal of each other w. r. t. (0). The n+1 joins of their corresponding vertices, in general, do not concur [3, p.41, Ex.7;4;18;24;25]. But when n=2, the3 joins of the corresponding vertices of a triangle and its tangential triangle always concur at itsLemoine point L as its3 symmedians which are the isogonal conjugates of its medians w. r. it [7] such that its circumcircle coincides with the polar conic of L w. r. t. it [9]. For n=3, the4 joins of the corresponding vertices of a tetrahedron and its tangential tetrahedron concur at itsLemoine point L, if and only if it is isodynamic [5], as its4 Lemoinians [17] (called symmedians byCourt [6] which join its vertices to theLemoine points of its opposite faces (but not as the isogonal conjugates of its medians w. r. t. it) such that its circumsphere coincides
with the polar quadric [16] of L w. r. t. it. The purpose of this paper is to develope analogonsly the theory of an isodynamic simplex, in an n-space
(n>3), which is in rerspective with its tangential simplex, called isogonic under the circumstances. Their relationship as
cevian & anticevian simplexes, and their association with S-configurations and related cevian quadrics are also pointed out.
To Eurico Bompiani on his scientific Jubilee 相似文献
12.
E. J. Pellicciaro 《Annali di Matematica Pura ed Applicata》1956,41(1):289-300
Summary With the introduction of an alternate definition for critical point, this paper studies critical sets, as defined byW. M. Whyburn, in terms of certain related domains. Critical sets are divided into four classes. Type0 has the limit point property with respect to critical sets which are not type0; type1 and2 critical sets compare, respectively, to classical minimum and maximum points; type3 includes themin-max and flex type.
This paper is a result of a study of critical sets made as a dissertation problem under the direction ofW. M. Whyburn, to whom the author is indebted for many helpful suggestions. 相似文献
13.
Iserles [1] constructed symplectic Runge-Kutta methods with real eigenvalues with the help of perturbed collocation. This note shows that such methods can comfortably be obtained using theW-transformation of [2]. 相似文献
14.
Palle E. T. Jorgensen 《Israel Journal of Mathematics》1986,56(2):129-142
LetH be an infinite-dimensional separable Hilbert space, and letS=(S
ij)∈teB(H)⊗M
2 be a unitary 2 × 2 matrix with operator entries. We study theC*-algebra generated by the operatorsS
ij, and show that the study of unitary dilations of isometriesT inH reduces to the special case whereS
11 =T, andS
21 = 0. We useC*-algebraic techniques to obtain detailed results about the set of all unitary dilations ofT.
Work supported in part by NSF. 相似文献
15.
Beresford Parlett 《Numerische Mathematik》1965,7(2):187-193
TheQR algorithm ofJ. G. F. Francis is used in computing matrix eigenvalues. The convergence proof given here is an analogue ofRutishauser's proof of the convergence of theLR algorithm, but our proof covers the case of disorder of the eigenvalues.The work presented in this paper was supported by the AEC Computing and Applied Mathematics Center, Courant Institute of Mathematical Sciences, New York University, under contract AT(30-1)-1480 with the U.S.Atomic Energy Commission. 相似文献
16.
D.R. Farenick 《Linear and Multilinear Algebra》2013,61(1-2):1-4
The unitary orbit of a complex n × n matrix A is simply connected if and only if the portion of the commutant {A} which resides in the special unitary group is path connected. 相似文献
17.
Summary Conditions on a linear algebraic eigenvalue problem are given, under which there are exactlyk–1 changes of sign in the sequence of components of thek-th eigenvector. This is analogous to the oscillation theorems of differential equations. A class of difference equations which satisfies these conditions is defined. Finally a modification of a method ofCollatz is given, by means of which upper and lower bounds for thek-th eigenvalue may be derived from a trial vector havingk–1 sign changes in the sequence of its components. This paper is merely a summary of results; no proofs are given. 相似文献
18.
A new recurrence for the number of subgroups of given index in the modular group is derived. The proof requires the derivation of a recurrence for a sequencea
nbn from recurrences for thea
n andb
n. We show that this is always possible if thea
n andb
n satisfy polynomial recurrences. We also include a short proof of a result ofW. W. Stothers on the parity of the number of subgroups of given index in the modular group. 相似文献
19.
Aurel Wintner 《Annali di Matematica Pura ed Applicata》1956,41(1):257-268
Summary At the end of his classical paper on convex surfaces in thelarge,H. Weyl (1916) gave an identity connecting the first and second fundamental forms of a surface. The identity is, however, a purelylocal relation and it holds also when the Gaussian curvature, instead of being positive, is negative. The present paper centers
around this identity. Various applications of it are considered and the conditions of validity are specified. 相似文献
20.
Buchin Su 《Annali di Matematica Pura ed Applicata》1940,19(1):289-313
Sunto. The paper deals with many projective properties of the neighbourhoods of the third,4th, 5th order of a point on a non-holonome surfaceV
3
2
inS
3. Chiefly two remarkable projective correspondences are studied, between the tangent plane and the bundle of directions, with
his contact point as centre. Many generalizations are obtained of geometrical loci (so as lines, planes, quadrics) projectively
associated with the neighbourhoods of a point on an ordinary (holonome) surface. The last sections are concerned with the
extension to theV
3
2
of the quadric ofMoutard and theSegre's correspondence.
相似文献