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1.
In Cutland's construction of Wiener measure, he used the product of Gaussian measures on , where is an infinite integer. It is mentioned by Cutland and Ng that for the product measure ,
where and with any positive infinite number. We prove here that may be replaced by with any positive infinite number. This is the optimal estimation for the shell thickness. It is also proved that . And for the *Lebesgue measure , is finite and not infinitesimal iff with finite, while for the *Lebesgue area of the sphere , should be .
2.
Let and be compact Hausdorff topological spaces, and let and be real Banach algebras of all real-valued continuous functions on and , respectively. The general form of continuous multiplicative mappings is given.
3.
B. A. Sethuraman 《Proceedings of the American Mathematical Society》1998,126(1):9-14
Let , where is a prime, and . In , let be the variety defined by . We show that any subvariety of of codimension less than must have degree a multiple of . We also show that the bounds on the codimension in our results are strict by exhibiting subvarieties of the appropriate codimension whose degrees are prime to .
4.
Martin Bridgeman 《Proceedings of the American Mathematical Society》1998,126(1):221-224
A well-known result states that, if a curve in has geodesic curvature less than or equal to one at every point, then is embedded. The converse is obviously not true, but the embeddedness of a curve does give information about the curvature. We prove that, if is a convex embedded curve in , then the average curvature (curvature per unit length) of , denoted , satisfies . This bound on the average curvature is tight as for a horocycle.
5.
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 .
6.
Marjan Matvejchuk 《Proceedings of the American Mathematical Society》1998,126(4):1155-1164
Let be a real -algebra of -real bounded operators containing no central summand of type in a complex Hilbert space with conjugation . Denote by the quantum logic of all -orthogonal projections in the von Neumann algebra . Let be a probability measure. It is shown that contains a finite central summand and there exists a normal finite trace on such that , .
7.
Gabriel Navarro 《Proceedings of the American Mathematical Society》1998,126(1):65-66
Suppose that is a Sylow -subgroup of a finite -solvable group . If , then the number of -conjugates of in can be read off from the character table of .
8.
9.
D. B. Shakhmatov M. G. Tkacenko V. V. Tkachuk S. Watson R. G. Wilson 《Proceedings of the American Mathematical Society》1998,126(1):279-287
A connected Tychonoff space is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on . We show that if is a connected Tychonoff space and locally separable spaces, locally \v{C}ech-complete spaces, first countable spaces, then is not maximal Tychonoff connected. This result is new even in the cases where is compact or metrizable.
10.
Toby N. Bailey Edward G. Dunne 《Proceedings of the American Mathematical Society》1998,126(4):1245-1252
For odd-dimensional hyperbolic space , we construct transforms between the cohomology of certain line bundles on (a twistor space for ) and eigenspaces of the Laplacian and of the Dirac operator on . The transforms are isomorphisms. As a corollary we obtain that every eigenfunction of or on extends as a holomorphic eigenfunction of the corresponding holomorphic operator on a certain region of the complexification of . We also obtain vanishing theorems for the cohomology of a class of line bundles on .
11.
J. Wu 《Proceedings of the American Mathematical Society》1998,126(1):1-8
In this note, we prove that for every and , the short interval contains at least one prime number of the form with . This improves a similar result due to Huxley and Iwaniec, which requires .
12.
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.
13.
Changsun Choi 《Proceedings of the American Mathematical Society》1998,126(4):1149-1153
We prove the weak-type inequality , , between a non-negative subharmonic function and an -valued smooth function , defined on an open set containing the closure of a bounded domain in a Euclidean space , satisfying , and , where is a constant. Here is the harmonic measure on with respect to 0. This inequality extends Burkholder's inequality in which and , a Euclidean space.
14.
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.
15.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》1998,126(4):1055-1061
Let and be bounded linear operators defined on Banach spaces, , . When , then the operators and have many basic operator properties in common. This situation is studied in this paper.
16.
Dong Yujun 《Proceedings of the American Mathematical Society》1998,126(1):145-152
In this paper, based on of the concept , which is a generalized form of the first resonant point to the Picard problem , , we study the solvability of second-order Sturm-Liouville boundary value problems at resonance , , , and improve the previous results about problems derived by Chaitan P. Gupta, R.Iannacci and M. N. Nkashama, and Ma Ruyun, respectively.
17.
Keith J. Coates 《Proceedings of the American Mathematical Society》1998,126(1):159-165
For a nest with associated nest algebra , we define , the normalizer of . We develop a characterization of elements of based on certain order homomorphisms of into itself. This characterization enables us to prove several structure theorems.
18.
A. Skopenkov 《Proceedings of the American Mathematical Society》1998,126(8):2467-2476
For a space let . Let act on and on by exchanging factors and antipodes respectively. We present a new short proof of the following theorem by Weber: For an -polyhedron and , if there exists an equivariant map , then is embeddable in . We also prove this theorem for a peanian continuum and . We prove that the theorem is not true for the 3-adic solenoid and .
19.
Pawe l Kolwicz Ryszard Pluciennik 《Proceedings of the American Mathematical Society》1998,126(8):2315-2322
A characterization of -convexity of arbitrary Banach space is given. Moreover, it is proved that the Orlicz-Bochner function space is P-convex if and only if both spaces and are -convex. In particular, the Lebesgue-Bochner space with is -convex iff is -convex.
20.
Jiro Egawa 《Proceedings of the American Mathematical Society》1998,126(1):273-278
In this paper we construct distal functions of another type discussed by Salehi (1991). Let be an almost periodic function with the mean value 0, which has unbounded integral, and a continuous periodic function with the prime period 1. If satisfies some additional condition, then is a distal function, which is not almost periodic, and the set of eigenvalues of is the module of .