A pseudo [2, b]-factor of a graph G is a spanning subgraph in which each component C on at least three vertices verifies 2 ≤ dC(x) ≤ b, for every vertex x in C. The main contibution of this paper, is to give an upper bound to the number of components that are edges or vertices in a pseudo [2, b]-factor of a graph G. Given an integer b ≥ 4, we show that a graph G with minimum degree δ, independe...

BACKGROUND In designing phase III randomized clinical trials (RCTs), the expected magnitude of the benefit of the experimental therapy (δ) determines the number of patients required and the number of person-years of follow-up. We conducted a systematic review to evaluate how reliably δ approximates the observed benefit (B) in RCTs that evaluated cancer treatment. METHODS RCTs evaluating syste...

We perform a statistical analysis and describe the asymptotic behavior of the frequency and size distribution of δoccurrent, minimal δ-occurrent, and maximal δ-occurrent itemsets occurring in random datasets across the entire spectrum of δ. We also describe the probability distribution of the support of an n-element itemset in a random dataset. We find that for small values of δ relative to num...

Definition 1 (K-function). A K-function is a function defined on a nonempty interval [0, b] with b > 0, γ : R[0:b] → R≥0 that is continuous, strictly increasing, and zero at zero. Note that we require γ(·) to be defined only on some nonzero interval, not [0,∞). As a motivating example, consider the standard -δ definition of continuity of a function f(·) at a point x. Definition 2 (Continuity: -...

We first give a proof of Lemma 2.1 which bounds the error of the (t + 1)-st iterate (ψ(X t+1)) in terms of the error incurred by the t-th iterate and the optimal solution. Proof of Lemma 2.1 Recall that ψ(X) = 1 2 ∥A(X) − b∥ 2 2. Since ψ(·) is a quadratic function, we have ψ(X t+1) − ψ(X t) = ⟨∇ψ(X t), X t+1 − X t ⟩ + 1 2 ∥A(X t+1 − X t)∥ 2 2 ≤ ⟨A T (A(X t) − b), X t+1 − X t ⟩ + 1 2 · (1 + δ 2k...

A metathesis reaction between unsolvated NaB(3)H(8) and NH(4)Cl provides a simple and high-yield synthesis of NH(4)B(3)H(8). Structure determination through X-ray single crystal diffraction analysis reveals weak N-H(δ+)---H(δ-)-B interaction in NH(4)B(3)H(8) and strong N-H(δ+)---H(δ-)-B interaction in NH(4)B(3)H(8)·18-crown-6·THF adduct. Pyrolysis of NH(4)B(3)H(8) leads to the formation of hydr...

Let Δ be an n-dimensional simplex in Euclidean space E contained in an n-dimensional closed ball B. The following question is considered. Given any point x ∈ Δ, does there exist a reflection r : E → E in one of the facets of Δ such that r(x) ∈ B? Mathematics Subject Classification (2000). 51M04, 51M16, 51B11.

A “coaxial” transmission line has inner conductor of radius a and outer conductor of radius b, but the axes of these two cylinders are offset by a small distance δ ¿ b. Deduce the capacitance and inductance per unit length, and the impedance Z, accurate to order δ/b. The (relative) dielectric constant and permeability of the medium between the two conductors both unity. The relevant frequencies...

Time-dependence in B(t) → ππ and B0(t) → ππ is utilized to obtain a maximal set of information on strong and weak phases. One can thereby check theoretical predictions of a small strong phase δ between penguin and tree amplitudes. A discrete ambiguity between δ ≃ 0 and δ ≃ π may be resolved by comparing the observed charge-averaged branching ratio predicted for the tree amplitude alone, using m...