‎we investigate graham higman's paper enumerating $p$-groups‎, ‎ii‎, ‎in which he formulated his famous porc conjecture‎. ‎we are able to simplify some of the theory‎. ‎in particular‎, ‎higman's paper contains five pages of homological algebra which he uses in‎ ‎his proof that the number of solutions in a finite field to a finite set of‎ ‎monomial equations is porc‎. ‎it turns out tha...

Here we consider the p-center problem on different types of fuzzy networks. In particular, we are interested in the networks with interval and triangular fuzzy arc lengths and vertex-weights. A methodology to obtain the best satisfaction level of the decision maker who wishes to reduce the cost within the tolerance limits is proposed. Illustrative examples are provided.

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.

Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$, where $alpha>-frac{1}{2}$ and $1

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.