A stereoselective synthesis of (25S)-Δ(1)-, (25S)-Δ(1,4)-, (25S)-Δ(1,7)-, (25S)-Δ(8(14))-, (25S)-Δ(4,6,8(14))-dafachronic acid, methyl (25S)-Δ(1,4)-dafachronate and (25S)-5α-hydroxy-3,6-dioxocholest-7-en-26-oic acid is described. (25S)-Δ(1,4)-Dafachronic acid and its methyl ester are natural products isolated from corals and have been obtained by synthesis for the first time. (25S)-5α-Hydroxy-3...

The measurement of stable carbon ( 13 δ C) and nitrogen ( 15 δ N) isotopes in tissues of organisms has formed the foundation of isotopic food web reconstructions, as these values directly reflect assimilated diet. In contrast, stable hydrogen ( 2 δ H) and oxygen ( 18 δ O) isotope measurements have typically been reserved for studies of migratory origin and paleoclimate reconstruction based on s...

We consider a real analytic map-germ (f, g) : (R, 0) → (R, 0). Under some conditions, we establish degree formulas for the following quantities : χ({f = α} ∩ {g = δ} ∩B ε ), χ({f = α} ∩ {g ≥ δ} ∩B ε )− χ({f = α} ∩ {g ≤ δ} ∩B ε ), where (α, δ) is a regular value of (f, g) and 0 < |(α, δ)| ¿ ε ¿ 1.

We have previously shown that peroxisome proliferator activating receptor ß/δ (PPAR β/δ is overexpressed in psoriasis. PPAR β/δ is not present in adult epidermis of mice. Targeted expression of PPAR β/δ and activation by a selective synthetic agonist is sufficient to induce an inflammatory skin disease resembling psoriasis. Several signalling pathways dysregulated in psoriasis are replicated in...

Suppose that κ is indestructibly supercompact and there is a measurable cardinal λ > κ. It then follows that A1 = {δ < κ | δ is measurable, δ is not a limit of measurable cardinals, and δ is not δ+ supercompact} is unbounded in κ. If in addition λ is 2λ supercompact, then A2 = {δ < κ | δ is measurable, δ is not a limit of measurable cardinals, and δ is δ+ supercompact} is unbounded in κ as well...

and Applied Analysis 3 Lemma 4. For λ > 0, one has 󵄩󵄩󵄩󵄩󵄩 K δ,l,j λ f (x) 󵄩󵄩󵄩󵄩󵄩 2 2 ≤ C2 −2M(j+l) δ 2M󵄩󵄩󵄩󵄩f 󵄩󵄩󵄩󵄩 2 2 , (19) where the constant C is independent of λ and δ. Proof. With the method similar to the proof of Lemma 4 in [9], we write h(t) = φ(t) − φ(2t) and expandm into a Taylor series around λt. Then, ?̂? δ,l,j λ (t) = ∫m δ (λ(t − 2 −(j+l) δ 2 r λ )) ĥ (r) dr = ∫m δ (λt − 2 −(j+l) δ 2 ...

Let δ(P) = (δ0, δ1, . . . , δd) be the δ-vector of an integral convex polytope P of dimension d. First, by using two well-known inequalities on δ-vectors, we classify the possible δ-vectors with ∑d i=0 δi ≤ 3. Moreover, by means of Hermite normal forms of square matrices, we also classify the possible δ-vectors with ∑d i=0 δi = 4. In addition, for ∑d i=0 δi ≥ 5, we characterize the δ-vectors of...

Galvin showed that for all fixed δ and sufficiently large n, the n-vertex graph with minimum degree δ that admits the most independent sets is the complete bipartite graph Kδ,n−δ. He conjectured that except perhaps for some small values of t, the same graph yields the maximum count of independent sets of size t for each possible t. Evidence for this conjecture was recently provided by Alexander...

Pulmonary edema is a major cause of mortality due to acute lung injury (ALI). The involvement of protein kinase C-δ (PKC-δ) in ALI has been a controversial topic. Here we investigated PKC-δ function in ALI using PKC-δ knockout (KO) mice and PKC inhibitors. Our results indicated that although the ability to produce proinflammatory mediators in response to LPS injury in PKC-δ KO mice was similar ...

Let u(x) x ∈ Rq be a symmetric non-negative definite function which is bounded away from zero but which may have u(0) = ∞. Let px,δ(·) be the density of an Rq valued canonical normal random variable with mean x and variance δ and let {Gx,δ; (x, δ) ∈ Rq× [0, 1]} be the mean zero Gaussian process with covariance EGx,δGy,δ′ = ∫ ∫ u(s− t)px,δ(s)py,δ′(t) ds dt. A finite positive measure μ on Rq is s...