In the study of substitutative dynamical systems and Pisot number systems, an algebraic condition, which we call ‘weak finiteness’, plays a fundamental role. It is expected that all Pisot numbers would have this property. In this paper, we prove some basic facts about ‘weak finiteness’. We show that this property is valid for cubic Pisot units and for Pisot numbers of higher degree under a domi...

On claw free families Abstract This paper points out that there are two types of claw free families with respect to a level of claw freeness. We formulate them as weak claw free families and strong claw free families. Then, we present suucient conditions for each type of claw free families. (A similar result is known for weak claw free families.) They are represented as some algebraic forms of ...

In this paper we define strong and weak common quadratic Lyapunov functions (CQLF’s) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the non-existence of a strong CQLF, for a pair of LTI systems, is characterised by easily verifiable algebraic conditions. These conditions are found to play an important role in provin...

In this paper we extend to algebraic extensions of local and global fields their completions some classical results due Borel-Serre, Tits, Conrad, Douai, Kneser Sansuc concerning the finiteness, surjectivity maps between Galois cohomology groups obstruction weak approximation related connected linear groups.

Heim [9] notes certain restrictions on quantifier intervention in comparatives and proposes an LF-constraint to account for this. I show that these restrictions are identical to constraints on intervention in wh-questions widely discussed under the heading of weak islands. I also show that Heim’s proposal is too restrictive: existential quantifiers can intervene. Both of these facts follow from...

We will construct an algebraic weak factorisation system on the category of 01-substitution sets such that the R-algebras are precisely the Kan fibrations together with a choice of Kan filling operation. The proof is based on Garner’s small object argument for algebraic weak factorisation systems. In order to ensure the proof is valid constructively, rather than applying the general small objec...

In this paper, we apply Legendre wavelet collocation method to obtain the approximate solution of nonlinear Stratonovich Volterra integral equations. The main advantage of this method is that Legendre wavelet has orthogonality property and therefore coefficients of expansion are easily calculated. By using this method, the solution of nonlinear Stratonovich Volterra integral equation reduces to...

In a recent paper, Bruinier and Ono proved that certain harmonic weak Maass forms have the property that the Fourier coefficients of their holomorphic parts are algebraic traces of weak Maass forms evaluated on Heegner points. As a special case they obtained a remarkable finite algebraic formula for the Hardy-Ramanujan partition function p(n), which counts the number of partitions of a positive...