In this paper, we propose the partition approach and define several new classes of partitioned failure detectors weaker than existing failure detectors for the k-set agreement problem in both the shared-memory model and the message-passing model. In the shared-memory model with n + 1 processes, for any 2 ≤ k ≤ n, we first propose a partitioned failure detector ΠΩk that solves k-set agreement wi...

The problem of determining all utility measures over binary gambles that are both separable and additive leads to the functional equation f(v) = f(vw) + f [vQ(w)], v, vQ(w) ∈ [0, k), w ∈ [0, 1] . The following conditions are more or less natural to the problem: f strictly increasing, Q strictly decreasing; both map their domains onto intervals (f onto a [0, K), Q onto [0, 1]); thus both are con...

For a strictly semistable log scheme Y over a perfect field k of characteristic p we investigate the canonical Čech spectral sequence (C)T abutting the Hyodo-Kato (log crystalline) cohomologyH∗ crys(Y/T )Q of Y and beginning with the log convergent cohomology of its various component intersections Y i. We compare the filtration on H∗ crys(Y/T )Q arising from (C)T with the monodromy operator N o...

The fault exposure ratio K is an important factor that controls the per-fault hazard rate, and hence the effectiveness of testing of software. The paper examines the variations of K with fault density which declines with testing time. Because faults get harder to find, K should decline if testing is strictly random. However, it is shown that at lower fault densities K tends to increase; we expl...

Suppose X = Lp (or Ip), p > 2, and K is a nonempty closed convex bounded subset of X. Suppose T: K —* K is a Lipschitzian strictly pseudo-contractive mapping of K into itself. Let {Cn}^_0 be a real sequence satisfying: (i) 0 < C„ < 1 for all n > 1, (") Z)rT=l Cn = °°> and Then the iteration process, zn G K, Zn+l = (1 — Cn)xn + CnTXn for n > 1, converges strongly to a fixed point of T in K.

We show that general one-way trapdoor permutations are sufficient to privately retrieve an entry from a database of size n with total communication complexity strictly less than n. More specifically, we present a protocol in which the user sends O(K) bits and the server sends n− cn K bits (for any constant c), where K is the security parameter of the trapdoor permutations. Thus, for sufficientl...

Let E be a real q-uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E. We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong c...

Here are three recently-established theorems from the literature. (A) (2006) Every non-metrizable compact abelian group K has 2|K|-many proper dense pseudocompact subgroups. (B) (2003) Every non-metrizable compact abelian group K admits 22 |K| -many strictly finer pseudocompact topological group refinements. (C) (2007) Every non-metrizable pseudocompact abelian group has a proper dense pseudoco...

We show that general one-way trapdoor permutations are suucient to privately retrieve an entry from a database of size n with total communication complexity strictly less than n. More speciically, we present a protocol in which the user sends O(K 2) bits and the server sends n ? cn K bits (for any constant c), where K is the security parameter of the trapdoor permutations. Thus, for suuciently ...