A connected graph G is optimal-κ if the connectivity κ(G) = δ(G), where δ(G) is the minimum degree of G. It is super-κ if every minimum vertex cut isolates a vertex. An optimal-κ graph G is moptimal-κ if for any vertex set S ⊆ V (G) with |S| ≤ m, G−S is still optimal-κ. The maximum integer of such m, denoted by Oκ(G), is the vertex fault tolerance of G with respect to the property of optimal-κ....

k x[k]δ[n − k] : convolution of x[n] and δ[n] = · · · + x[−2]δ[n + 2] + x[−1]δ[n + 1] + x[0]δ[n] + x[1]δ[n − 1] + · · · : any sequence can be decomposed as a sum of scaled and shifted impulses. (a) Scale (by x[k]) and shift (from δ[n] to δ[n− k]) imply linearity and time-invariance, respectively. (b) Envision x[n] : {..., x[−1], x[0], x[1], ...} as a signal vector, and δ[n − k] : {..., 0, δ[n −...

Peroxisome proliferator-activated receptor β/δ (PPARβ/δ) is a nuclear receptor involved in regulation of lipid and glucose metabolism, wound healing and inflammation. PPARβ/δ has been associated also with cancer. Here we investigated the expression of PPARβ/δ and components of the prostaglandin biosynthetic pathway in non-small cell lung cancer (NSCLC). We found increased expression of PPARβ/δ,...

Let R be a ring and S a nonempty subset of R. Suppose that θ and φ are endomorphisms of R. An additive mapping δ : R → R is called a left (θ,φ)-derivation (resp., Jordan left (θ,φ)derivation) on S if δ(xy) = θ(x)δ(y)+φ(y)δ(x) (resp., δ(x2) = θ(x)δ(x)+φ(x)δ(x)) holds for all x,y ∈ S. Suppose that J is a Jordan ideal and a subring of a 2-torsion-free prime ring R. In the present paper, it is show...

The Gilbert–Varshamov bound guarantees the existence of families of codes over the finite field F` with good asymptotic parameters. We show that this bound can be improved for all non-prime fields F` with ` ≥ 49, except possibly ` = 125. We observe that the same improvement even holds within the class of transitive codes and within the class of self-orthogonal codes. The Gilbert–Varshamov bound...

Analytic curves are classified w.r.t. their symmetry under a given regular and separately analytic Lie group action G×M→M on an manifold. We show that non-constant curve γ:D→M is either free or exponential – i.e., up to reparametrization of the form t↦exp⁡(t⋅g→)⋅x. The vector g→∈g additionally proven be unique (non-zero scalation and) addition elements in algebra stabilizer Gγ≡{g∈G|g⋅γ=γ} γ. fu...

Delta-sarcoglycan is a component of the sarcoglycan subcomplex within the dystrophin-glycoprotein complex located at the plasma membrane of muscle cells. While recessive mutations in δ-sarcoglycan cause limb girdle muscular dystrophy 2F, dominant mutations in δ-sarcoglycan have been linked to inherited dilated cardiomyopathy (DCM). The purpose of this study was to investigate functional cellula...

The assessment of provenance of heparin is becoming a major concern for the pharmaceutical industry and its regulatory bodies. Batch-specific [carbon (δ(13) C), nitrogen (δ(15) N), oxygen (δ(18) O), sulfur (δ(34) S), and hydrogen (δD)] stable isotopic compositions of five different animal-derived heparins were performed. Measurements readily allowed their differentiation into groups and/or subg...