For a nonincreasing function $\psi$, let $\textrm{Exact}(\psi)$ be the set of complex numbers that are approximable by rational to order $\psi$ but no better order. In this paper, we obtain Hausdorff dimension and packing when $\psi(x)=o(x^{-2})$. We also prove lower bound is greater than $2-\tau/(1-2\tau)$ $\tau=\limsup_{x\to\infty}\psi(x)x^2$ small enough.

‎ Let $(X,d)$ be a metric space and $Jsubseteq (0,infty)$ be a nonempty set. We study the structure of the arbitrary intersection of vector-valued Lipschitz algebras, and define a special Banach subalgebra of $cap{Lip_gamma (X,E):gammain J}$, where $E$ is a Banach algebra, denoted by $ILip_J (X,E)$. Mainly, we investigate $C-$character amenability of $ILip_J (X,E)$.

In the Näıve Bayes classification problem using a vertically partitioned dataset, the conventional scheme to preserve privacy of each partition uses a secure scalar product and is based on the assumption that the data is synchronised amongst common unique identities. In this paper, we attempt to discard this assumption in order to develop a more efficient and secure scheme to perform classifica...

Let F be a k-uniform set system defined on a ground set of size n with no singleton intersection; i.e., no pair A,B ∈ F has |A ∩ B| = 1. Frankl showed that |F| ≤ (n−2 k−2 ) for k ≥ 4 and n sufficiently large, confirming a conjecture of Erdős and Sós. We determine the maximum size of F for k = 4 and all n, and also establish a stability result for general k, showing that any F with size asymptot...

In this paper we present a new problem, the fast set intersection problem, which is to preprocess a collection of sets in order to efficiently report the intersection of any two sets in the collection. In addition we suggest new solutions for the two-dimensional substring indexing problem and the document listing problem for two patterns by reduction to the fast set intersection problem.