We show that, for every orthogonally additive homogeneous polynomial P on a space of continuous functions C(K) with values in a Banach space Y , there exists a linear operator S : C(K) −→ Y such that P (f) = S(f). This is the C(K) version of a related result of Sundaresam for polynomials on Lp spaces.

Background: Lumbar puncture (LP) is a worth procedure in diagnosis of oncological diseases and intrathecal administration of antineoplastic drugs. The effort should be to minimize pain of LP in children with cancers. This clinical trial was done to compare success rates in performing LP and reducing anxiety and pain of LP in sitting and lateral decubitus positions in 1 to 5-year-old children. ...

In this paper, we give a characterization of compact sets in Lp-spaces on metric measure spaces, which is generalization the Kolmogorov-Riesz theorem. Using criterion, investigate topological type space consisting Lipschitz maps with bounded supports.

We prove that the first reduced cohomology with values in a mixing Lp-representation, 1 < p < ∞, vanishes for a class of amenable groups including amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, th...

A multi-valued Non-Impeding Noisy-AND (NIN-AND) tree model has the linear complexity and is more expressive than common Causal Independence Models (CIMs). We formulate a Multiplicative Factorization (MF) for multi-valued NIN-AND Tree (NAT) models. In comparison with the MF for binary NAT models (of a undirected tree structure), the proposed MF is a hybrid and multiply connected graphical model....

Fliess operators as input–output mappings are particularly useful in a number of fundamental problems concerning nonlinear realization theory. In the classical analysis of these operators, certain growth conditions on the coe3cients in their series representations insure uniform and absolute convergence, provided every input is uniformly bounded by some 4xed upperbound. In some emerging applica...

In this paper, it is proved that every non-zero continuous operator with modulus on an lp-space whose modulus is quasinilpotent at a non-zero positive vector has a non-trivial modulus hyperinvariant closed ideal. AMS Subject Classification: 47A15

and Applied Analysis 3 satisfy the critical growth condition ũ ∈ LpLq, for 2 p 3 q 1, 3 < q ≤ ∞. 1.9 It should be mentioned that the weak solution remains regular if the single velocity component satisfies the higher subcritical growth conditions see Zhou 9 , Penel and Pokorný 10 , Kukavica and Ziane 11 , and Cao and Titi 12 . One may also refer to some interesting regularity criteria 13–15 for...