We prove that there is no sparse hard set for P under logspace computable bounded truthtable reductions unless P = L. In case of reductions computable in NC1, the collapse goes down to P = NC1. We parameterize this result and obtain a generic theorem allowing to vary the sparseness condition, the space bound and the number of queries of the truth-table reduction. Another instantiation yields th...

Logic programming has traditionally lacked devices for expressing iterative tasks. To overcome this problem, this paper proposes iterative goal formulas of the form ∧LxG where G is a goal, x is a variable, and L is a list. ∧Lx is called a parallel bounded quantifier. These goals allow us to specify the following task: iterate G with x ranging over all the elements of L. keywords: for-loop, iter...

X (F ωM ) , 2 we have the following: (1) (Apriori estimate) Suppose u is a weak solution in PSHF∗ωM (X) ∩ L(X) of the equation with the normalization supX u = 0, then there is a constant C such that ‖u‖L∞ ≤ C‖f‖Lp where C only depend on F , ω and p; (2) There would always be a bounded solution for this equation; (3) If F is locally birational, then any bounded solution is actually the unique co...

Let L ∗ M denote the coproduct of the bounded distributive lattices L and M . At the 1981 Banff Conference on Ordered Sets, the following question was posed: What is the largest class L of finite distributive lattices such that, for every non-trivial Boolean lattice B and every L ∈ L, B ∗ L = B ∗ L′ implies L = L′? In this note, the problem is solved.

To all youngsters and villagers of the municipality St John the Baptist (St. Johann im Walde), East Tyrol for warmth, sense of humour and tenderness of ~. Abstract. Let B n denote the open unit ball in R n : For t 2 R; 2 R n and m 2 L 1 ? R 2 deene a linear mapping Sm : S (R n) ?! L 2 (B n ; L 1 (B)) by (Smf)(t)^() = m(t; jj) b f(); f 2 S (R n) : The main results in this paper concern the case ...

We completely (that is, up to a logarithmic factor) characterize the bounded-error quantum communication complexity of every predicate f(x, y) depending only on |x∩y| (x, y ⊆ [n]). Namely, for a predicateD on {0, 1, . . . , n} let l0(D) def = max {l | 1 ≤ l ≤ n/2 ∧D(l) 6≡ D(l− 1)} and l1(D) def = max {n− l | n/2 ≤ l < n ∧D(l) 6≡ D(l+ 1)}. Then the bounded-error quantum communication complexity ...

We investigate the problem of existence a bounded extension to $C(K)$ $c_0(I)$-valued operator $T$ defined on subalgebra induced by continuous increasing surjection $\phi :K\to L$, where $K$ and $L$ are compact lines. Gener

In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups  including, n$-$Bourbaki-bounded homomorphisms and$hspace{1mm}$ B$-$Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous homomorphisms. So, two topologies are presented on them a...

First, we recall some notations and definitions which will be used throughout the paper (cf. [12]). A double sequence x = (xjk) of real or complex numbers is said to be bounded if ‖x‖∞ = supj,k |xjk| < ∞. We denote the space of all bounded double sequences by L. A double sequence x = (xjk) is said to converge to the limit L in Pringsheims sense (shortly, p-convergent to L) if for every ε > 0 th...