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1.
Victoria Paolantoni 《Proceedings of the American Mathematical Society》1998,126(6):1733-1738
Let be a smooth real hypersurface of and a compact submanifold of . We generalize a result of A. Boggess and R. Dwilewicz giving, under some geometric conditions on and , an estimate of the submeanvalue on of any function on a neighbourhood of , by the norm of on a neighbourhood of in .
2.
It is shown that the suspension order of the -fold cartesian product of real projective -space is less than or equal to the suspension order of the -fold symmetric product of and greater than or equal to , where and satisfy and . In particular has suspension order , and for fixed the suspension orders of the spaces are unbounded while their stable suspension orders are constant and equal to .
3.
Pietro Poggi-Corradini 《Proceedings of the American Mathematical Society》1998,126(6):1697-1708
Let be a one-to-one analytic function of the unit disk into itself, with . The origin is an attracting fixed point for , if is not a rotation. In addition, there can be fixed points on where has a finite angular derivative. These boundary fixed points must be repelling (abbreviated b.r.f.p.). The Koenigs function of is a one-to-one analytic function defined on such that , where . If is the first iterate of that does have b.r.f.p., we compute the Hardy number of , , in terms of the smallest angular derivative of at its b.r.f.p.. In the case when no iterate of has b.r.f.p., then , and vice versa. This has applications to composition operators, since is a formal eigenfunction of the operator . When acts on , by a result of C. Cowen and B. MacCluer, the spectrum of is determined by and the essential spectral radius of , . Also, by a result of P. Bourdon and J. Shapiro, and our earlier work, can be computed in terms of . Hence, our result implies that the spectrum of is determined by the derivative of at the fixed point and the angular derivatives at b.r.f.p. of or some iterate of .
4.
Jeffrey Bergen D. S. Passman 《Proceedings of the American Mathematical Society》1998,126(6):1627-1635
Let be a finite abelian group and let be a, possibly restricted, -graded Lie color algebra. Then the enveloping algebra is also -graded, and we consider the question of whether being graded-prime implies that it is prime. The first section of this paper is devoted to the special case of Lie superalgebras over a field of characteristic . Specifically, we show that if and if has a unique minimal graded-prime ideal, then this ideal is necessarily prime. As will be apparent, the latter result follows quickly from the existence of an anti-automorphism of whose square is the automorphism of the enveloping algebra associated with its -grading. The second section, which is independent of the first, studies more general Lie color algebras and shows that if is graded-prime and if most homogeneous components of are infinite dimensional over , then is prime. Here we use -methods to study the grading on the extended centroid of . In particular, if is generated by the infinite support of , then we prove that is homogeneous.
5.
Chih-Nung Hsu 《Proceedings of the American Mathematical Society》1998,126(3):647-652
Let be the finite field with elements and let denote the ring of polynomials in one variable with coefficients in . Let be a monic polynomial irreducible in . We obtain a bound for the least degree of a monic polynomial irreducible in ( odd) which is a quadratic non-residue modulo . We also find a bound for the least degree of a monic polynomial irreducible in which is a primitive root modulo .
6.
Salvador Garcia-Ferreira Claude Laflamme 《Proceedings of the American Mathematical Society》1998,126(6):1791-1798
The property may be generalized by using filters on in a very natural way. We analyze the necessary requirements for a space to have property for a filter . We construct special filters for which has the property, in particular a P-point and a Q-point.
7.
Sufficient conditions for one domain to contain another in a space of constant curvature 总被引:4,自引:0,他引:4
Jiazu Zhou 《Proceedings of the American Mathematical Society》1998,126(9):2797-2803
As an application of the analogue of C-S. Chen's kinematic formula in the 3-dimensional space of constant curvature , that is, Euclidean space , -sphere , hyperbolic space (, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space , or a -sphere or a hyperbolic space .
8.
Peter B. Gilkey John V. Leahy Jeong Hyeong Park 《Proceedings of the American Mathematical Society》1998,126(6):1845-1850
Let be a Riemannian submersion of closed manifolds. Let be an eigen -form of the Laplacian on with eigenvalue which pulls back to an eigen -form of the Laplacian on with eigenvalue . We are interested in when the eigenvalue can change. We show that , so the eigenvalue can only increase; and we give some examples where , so the eigenvalue changes. If the horizontal distribution is integrable and if is simply connected, then , so the eigenvalue does not change.
9.
Zbigniew S. Marciniak Sudarshan K. Sehgal 《Proceedings of the American Mathematical Society》1998,126(2):343-348
Let be an arbitrary group. If satisfies , , then the units , generate a nonabelian free subgroup of units. As an application we show that if is contained in an almost subnormal subgroup of units in then either contains a nonabelian free subgroup or all finite subgroups of are normal. This was known before to be true for finite groups only.
10.
N. Bertoglio Servet Martí nez Jaime San Martí n 《Proceedings of the American Mathematical Society》1998,126(2):375-382
For a self-adjoint operator commuting with an increasing family of projections we study the multifunction an open set of the topology containing , where is the spectrum of on . Let be the measure of maximal spectral type. We study the condition that is essentially a singleton, is not a singleton. We show that if is the density topology and if satisfies the density theorem, in particular if it is absolutely continuous with respect to the Lebesgue measure, then this condition is equivalent to the fact that is a Borel function of . If is the usual topology then the condition is equivalent to the fact that is approched in norm by step functions , where the set of intervals covers the set where is a singleton.
11.
Every complete doubling metric space carries a doubling measure 总被引:4,自引:0,他引:4
We prove that a complete metric space carries a doubling measure if and only if is doubling and that more precisely the infima of the homogeneity exponents of the doubling measures on and of the homogeneity exponents of are equal. We also show that a closed subset of carries a measure of homogeneity exponent . These results are based on the case of compact due to Volberg and Konyagin.
12.
Mark L. Lewis 《Proceedings of the American Mathematical Society》1998,126(7):1915-1921
Let be a finite solvable group. Assume that the degree graph of has exactly two connected components that do not contain . Suppose that one of these connected components contains the subset , where and are coprime when . Then the derived length of is less than or equal to .
13.
Hisao Kato 《Proceedings of the American Mathematical Society》1998,126(7):2151-2157
The measure of scrambled sets of interval self-maps was studied by many authors, including Smítal, Misiurewicz, Bruckner and Hu, and Xiong and Yang. In this note, first we introduce the notion of ``-chaos" which is related to chaos in the sense of Li-Yorke, and we prove a general theorem which is an improvement of a theorem of Kuratowski on independent sets. Second, we apply the result to scrambled sets of higher dimensional cases. In particular, we show that if a map of the unit -cube is -chaotic on , then for any there is a map such that and are topologically conjugate, and has a scrambled set which has Lebesgue measure 1, and hence if , then there is a homeomorphism with a scrambled set satisfying that is an -set in and has Lebesgue measure 1.
14.
We prove that every analytic proper subgroup of the reals can be covered by an null set. We also construct a proper Borel subgroup of the reals that cannot be covered by countably many sets such that is nowhere dense for every
15.
Let be a finitely generated non-PI Ore domain and the quotient division algebra of . If is the center of , then .
16.
Dave Witte 《Proceedings of the American Mathematical Society》1998,126(4):1005-1015
Let and be matrices of determinant over a field , with or . We show that if is not a scalar matrix, then is a product of matrices similar to . Analogously, we conjecture that if and are elements of a semisimple algebraic group over a field of characteristic zero, and if there is no normal subgroup of containing but not , then is a product of conjugates of . The conjecture is verified for orthogonal groups and symplectic groups, and for all semisimple groups over local fields. Thus, in a connected, semisimple Lie group with finite center, the only conjugation-invariant subsemigroups are the normal subgroups.
17.
Chengwen Wang 《Proceedings of the American Mathematical Society》1998,126(6):1725-1732
This paper is devoted to the study of multiple -periodic solutions for Duffing equations
under the condition of nonuniform non-resonance related to the positive asymptotic behavior of at the first two eigenvalues and of the periodic BVP on for the linear operator , and the condition on the negative asymptotic behavior of at infinity. The techniques we use are degree theory and the upper and lower solution method.
18.
Chih-Nung Hsu 《Proceedings of the American Mathematical Society》1998,126(7):1955-1961
Let be a global function field, a degree one prime divisor of and let be the Dedekind domain of functions in regular outside . Let be the Hilbert class field of , the integral closure of in . Let be a rank one normalized Drinfeld -module and let be a prime ideal in . We explicitly determine the finite -module structure of . In particular, if , is an odd prime number and is the Carlitz -module, then the finite -module is always cyclic.
19.
Tadashi Yanai 《Proceedings of the American Mathematical Society》1998,126(8):2221-2228
In this paper, we prove the following two results which generalize the theorem concerning automorphic-differential endomorphisms asserted by J. Bergen. Let be a ring, its left Martindale quotient ring and a right ideal of having no nonzero left annihilator. (1) Let be a pointed coalgebra which measures such that the group-like elements of act as automorphisms of . If is prime and for , then . Furthermore, if the action of extends to and if such that , then . (2) Let be an endomorphism of given as a sum of composition maps of left multiplications, right multiplications, automorphisms and skew-derivations. If is semiprime and , then .
20.
Eiji Ogasa 《Proceedings of the American Mathematical Society》1998,126(7):2175-2182
We prove that, for any ordinary sense slice 1-link , we can define the Arf invariant, and Arf()=0. We prove that, for any -component 1-link , there exists a -component ordinary sense slice 1-link of which is a sublink.