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...

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise inputdependant bounds on these coefficients. Such bounds are e.g. useful to perform deterministic chinese remaindering of the characteristic or minimal polynomi...

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

conclusions we can conclude that treatment of af using a right-sided minithoracotomy approach and rf energy in patients undergoing cardiac surgery for various valve diseases is feasible, safe, and reproducible. objectives our aim is to evaluate the feasibility, safety, and immediate plus medium-term results of concomitant af ablation therapy in patients undergoing minimally invasive valve surge...

background: one of the main causes of sexually transmitted diseases is group b β- hemolytic streptococci (gbs) multiplying in the genital tracts. penicillin is the most common drug for the treatment of infections caused by these bacteria, but in patients suffering from penicillin allergy, erythromycin and clindamycin are used as alternative therapeutic drugs against gbs. recently, resistance to...

Knuth and Moore presented a theoretical lower bound on the number of leaves that any fixed-depth minimax tree-search algorithm traversing a uniform tree must explore, the so-called minimal tree. Since real-life minimax trees aren’t uniform, the exact size of this tree isn’t known for most applications. Further, most games have transpositions, implying that there exists a minimal graph which is ...

Acta Crystallographica Section A: Foundations of Crystallography covers theoretical and fundamental aspects of the structure of matter. The journal is the prime forum for research in diffraction physics and the theory of crystallographic structure determination by diffraction methods using X-rays, neutrons and electrons. The structures include periodic and aperiodic crystals, and non-periodic d...