We prove, using a decision procedure based on finite automata, that every natural number>686 is the sum of at most 4 natural numbers whose canonical base-2 representation is a binary square, that is, a string of the form xx for some block of bits x.

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time τ and the lattice spacing. The analytic solutions are the exact representation of these two flows without an...

A recent paper of Church, Ellenberg, and Farb uses topology and representation theory of the symmetric group to prove enumerative results about square-free polynomials and F -stable maximal tori of GLn(Fq). In this note, we use generating functions to give short, elementary proofs of some of their results, and some extensions.

This paper describes a general framework for designing purely functional datatypes that automatically satisfy given size or structural constraints. Using the framework we develop implementations of different matrix types (eg square matrices) and implementations of several tree types (eg Braun trees, 2-3 trees). Consider, for instance, representing square /102/ matrices. The usual representation...

We study the 3-state square-lattice Potts antiferromagnet at zero temperature by a Monte Carlo simulation using the Wang-Swendsen-Kotecký cluster algorithm, on lattices up to 1024 × 1024. We confirm the critical exponents predicted by Burton and Henley based on the height representation of this model.

It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e., the integrated uniform Bahadur–Kiefer process properly normalized, behaves like the square of the uniform empirical process. We give a complete description of the strong and weak asymptotic behaviour in sup-norm of this representation of the Vervaat process and, likewise, we study also its pointwi...

We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be performed by combinational logic networks with linear size and logarithmic depth. The implications of these results for multiplication, division and square-root extraction are also discussed.

We present an efficient architecture for the implementation of delayed least mean square adaptive filter. We use a novel partial product generator and propose a strategy for optimized balanced pipelining across the time consuming combinational blocks of the structure .An efficient systolic architecture of the delayed least mean square adaptive filter based on the processing element .We propose ...

A square-contact representation of a planar graph G = (V,E) maps vertices in V to interiordisjoint axis-aligned squares in the plane and edges in E to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points. We characterize the partial ...