While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure ...

Objectives: Different treatment approaches have been introduced for children with Speech Sound Disorders (SSD). Minimal pair intervention, Metaphon therapy, and parents and children together approach as linguistically-based approaches are routinely utilized in this population and both of them shared minimal pairs as a common component. The purpose of the current study was to develop and investi...

We study the sizes of minimal finite state machines associated with linear cellular automata. In particular, we construct a class of binary linear cellular automata whose corresponding minimal automata exhibit full exponential blow-up. These cellular automata have Hamming distance 1 to a permutation automaton. Moreover, the corresponding minimal Fischer automata as well as the minimal DFAs have...

We find the minimal number of links in an embedding of any complete k-partite graph on 7 vertices (including K 7 , which has at least 21 links). We give either exact values or upper and lower bounds for the minimal number of links for all complete k-partite graphs on 8 vertices. We also look at larger complete bipartite graphs, and state a conjecture relating minimal linking embeddings with min...

The paper arose from the fact that the smallest element of the set of Salem numbers is not known. Indeed, it is not even known whether this set has a smallest element. The aim of this paper is to prove that the minimal polynomial of the smallest Salem series of degree n in the field of formal power series over a finite field is given by P (Y ) = Y n −XY n−1 − Y + X − 1, where we suppose that 1 ...

Throughout the text, let R be a commutative ring with identity (often called a commutative unital ring) and with multiplicative group of units R∗. Likewise, let f(x) = a0x +a1x n−1+ · · ·+an−1x+an be a polynomial of the variable x over R such that a0 ∈ R∗. Traditionally, R[x] is the ring of all polynomials of x over R; thereby f(x) ∈ R[x]. For an arbitrary but fixed element α, suppose f(x) is t...

We prove that for all algebraic number β > 1 the strings of zeros in the Rényi βexpansion dβ(1) of 1 exhibit a lacunarity bounded above by log(s(Pβ))/ log(β), where s(Pβ) is the size of the minimal polynomial of β. The conjecture about the specification of the β-shift, equivalently the uniform discreteness of the sets Zβ of β-integers, for β a Perron number is discussed. We propose a classifica...

has some ei greater than 1. If every ei equals 1, we say p is unramified in K. Example 1.1. In Z[i], the only prime which ramifies is 2: (2) = (1 + i)2. Example 1.2. Let K = Q(α) where α is a root of f(X) = T 3 − 9T − 6. Then 6 = α3 − 9α = α(α− 3)(α+ 3). For m ∈ Z, α+m has minimal polynomial f(T −m) in Q[T ], so NK/Q(α+m) = −f(−m) = m3 − 9m+ 6 and the principal ideal (α−m) has norm N(α−m) = |m ...

We derive the linear complexity and the minimal polynomial over the finite fields of order two and p of series of binary sequences with a period 4p and optimal autocorrelation value/magnitude. These sequences are constructed by cyclotomic classes of order two, four and six by methods proposed by K.T. Arasu et al. and Y. Sun et al. We define the parameters of sequences with optimal autocorrelati...