In this paper, we study some of the main properties of the double base number system (DBNS), using bases 2 and 5. A simple geometric interpretation provides the implementation of the arithmetic operations and the addition and multiplication rules of this number systems have been introduced. It can also be shown that the double base number system is used in digital signal processing. Also, the s...

We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals < ω, and pseudoexponentiation with the base ω1 of the Wadge degrees. In consequence, the Wadge hierarchy of weakly recognizable tree languages has the height of at least ε0, that is the least fixed point of the exponenti...

Several experiments involving two-dimensional and axisymmetric bodies have been carried out in a Trisonic wind tunnel at supersonic speeds to investigate and analyse the measured values of base pressure and to compare them with those from the theoretical methods. The objective of the experiments was to obtain an appropriate method for processing the results of wind tunnel tests on rockets or ai...

Example 1 Let Bm = multiplication by the Schur function sm. The family {Bm} creates the homogeneous basis. Bm(sλ) is given by the Pieri rule. This implies that the homogeneous basis when expanded in terms of the Schur functions is given by bλ = ∑ μKμλsμ where the coefficients Kμλ are the column strict tableaux of shape μ and content λ. We could hope that a similar attack might work on more comp...

We show that, when the dimension N of the Hilbert space is a prime power, mutually unbiased bases are naturally related to the symmetry group that leaves (generalized) Bell states invariant. We show how the mutually unbiased bases can be expressed in terms of the (multiplication of the) associated finite field of N elements, and derive a new solution for the mean king’s problem.

The canonical bases of cluster algebras of finite types and rank 2 are given explicitly in [4] and [14] respectively. In this paper, we will deduce Z-bases for cluster algebras for affine types e An,n, e D and e E. Moreover, we give an inductive formula for computing the multiplication between two generalized cluster variables associated to objects in a tube.

Let n be a maximal nilpotent subalgebra of a complex simple Lie algebra of type A, D, E. Lusztig has introduced a basis of U(n) called the semicanonical basis, whose elements can be seen as certain constructible functions on varieties of modules over a preprojective algebra of the same Dynkin type as n. We prove a formula for the product of two elements of the dual of this semicanonical basis, ...

We prove a multiplication theorem of a quantum Caldero-Chapoton map associated to valued quivers which extends the results in [8][6]. As an application, when Q is a valued quiver of finite type or rank 2, we obtain that the algebra A H |k|(Q) generated by all cluster characters (see Definition 1) is exactly the quantum cluster algebra E H |k|(Q) and various bases of the quantum cluster algebras...

where the coefficients are real numbers and bm 6= 0. (i) Define addition and multiplication of two elements of F to be the usual addition and multiplication of functions. Show that with this addition and multiplication, F is a field. (ii) We can define an order on F as follows. A rational function like (1.1) is positive if and only if an and bn have the same sign, i.e., anbm > 0. Now given two ...

The objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a Fibonacci Hypercube structure. Most of the popular algorithms for parallel matrix multiplication can not run on Fibonacci Hypercube structure, therefore giving a method that can be run on all structures especially Fibonacci Hypercube structure is necessary for parallel matr...