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Torben Maack Bisgaard 《Semigroup Forum》2004,68(1):25-46
There is a countable cancellative commutative *-semigroup S withzero (in fact, a *-subsemigroup of G × N0 for some abelian group G carrying the inverse involution) such that the answer to the question “if f is a function on S , with values in Md(C) (the square matrices of order d) and such that $\sum^{n}_{j,k=1} \lbrak f(s^*_k s_j)\xi_j, \xi_k \rbrak \ge 0$ for all n in N, s1, . . . , sn in S , and $\xi_1$, . . . , $\xi_n$ in Cd, does it follow that $f(s) = \int_{S^*}\sigma (s) d\mu(\sigma) (s \memb S)$ for some measure $\mu$ (with values in Md(C)+ , the positive semidenite matrices) on the space S of hermitian multiplicative functions on S?” is “yes” if d = 1 but “no” if d = 2 (hence also for d > 2). 相似文献
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The extraction parameters pH and Kex for Mn, Fe, Co, Ni, Cu, Zn, Cd, and Pb with N-thiobenzoyl-N-phenylhydroxylamine are reported. N-Thiobenzoyl-N-phenylhydroxylamine extracts metals from more strongly acidic solutions than does N-benzoyl-N-phenylhydroxylamine. Iron(III) is extracted as a 1:2 chelate with the extracant, whereas iron(II) forms the expected tris chelate by oxidation. The other bivalent ions are extracted as their bis chelates. 相似文献
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Torben Maack Bisgaard 《Analysis Mathematica》2001,27(1):37-54
For >2, let Q
+() be the infimum of those q>0 for which the function n epn is positive definite on N
0 for every pq. We shall prove that Q
+()0 as 2. 相似文献
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Torben Maack Bisgaard 《Czechoslovak Mathematical Journal》2002,52(1):155-196
We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters). 相似文献
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Torben Maack Bisgaard 《Mathematische Nachrichten》2000,210(1):67-83
For every a > 1, there is a function f : N20 → R, which is positive semidefinite but not a moment sequence, such that |f(m, n)| ≥ m+ na(m+n) for all (m, n). The constant 1 is the best possible. 相似文献
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For a coinmutative senugoup (S, +, *) with involution and a function f : S → [0, ∞), the set S(f) of those p ≥ 0 such that fP is a positive definite function on S is a closed subsemigroup of [0, ∞) containing 0. For S = (IR, +, x* = -x) it may happen that S(f) = { kd : k ∈ N0 } for some d > 0, and it may happen that S(f) = {0} ? [d, ∞) for some d > O. If α > 2 and if S = (?, +, n* = -n) and f(n) = e?[n]α or S = (IN0, +, n* = n) and f(n) = enα, then S(f) ∪ (0, c) = ? and [d, ∞) ? S(f) for some d ≥; c > 0. Although (with c maximal and d minimal) we have not been able to show c = d in all cases, this equality does hold if S = ? and α ≥ 3.4. In the last section we give sinipler proofs of previously known results concerning the positive definiteness of x → e?||x||α on normed spaces. 相似文献
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Torben Maack Bisgaard 《Journal of Theoretical Probability》1990,3(1):71-80
A sequence : 0 satisfiesHoeffding's inequality of order n if wheneverX
1,...,X
n are independent nonnegative integer-valued elementary random variables and
are independent identically distributed nonnegative integer-valued elementary random variables, the common distribution of which is the average of those ofX
1,...,X
n. We show that for each integerm greater than 2 there exists a sequence satisfying Hoeffding's inequality of every order greater thanm but not that of orderm. This answers a question raised by Berg, Christensen, and Ressel. 相似文献
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