We define the differential operator ∂ ∂z on infinitely differentiable functions (also called smooth or C∞ functions) on some open set in C by ∂ ∂z = 1 2 ( ∂ ∂x + i ∂ ∂y ). A quick calculation shows that ∂ ∂z obeys the product rule. Recall that a function f is holomorphic if and only if ∂ ∂z (f) = 0. A function is biholomorphic, or an analytic isomorphism, if it is holomorphic and has holomorphi...

The evidence for the impact of saturated fat intake on cardiovascular disease remains inconsistent. One reason for this inconsistency may be the large difference in the distribution of saturated fat intake between the East and West. In this review, we focus on the published literature on this topic among Japanese population. Three studies have examined the link between saturated fat intake and ...

In this article, only connected bipartite graphs G with a unique perfect matching M are considered. Let Gw denote the weighted graph obtained from G by giving weights to its edges using the positive weight function w : E(G)→ (0,∞) such that w(e) = 1 for each e ∈ M. An unweighted graph G may be viewed as a weighted graph with the weight function w ≡ 1 (all ones vector). A weighted graph Gw is no...

In this paper we generalize to groups of Galois type some results of P. Hall on finite solvable groups [l; 2; 3]. We need, in a modified form, some results of van Dantzig: the definition of supernatural numbers (which are related to van Dantzig's universal numbers) and Theorem 5, which he proved for ordinary ¿>-Sylow subgroups [6]. Lemmas 1 and 4 and the method of proof in Theorem 5 are due to ...

In this paper we show that an inverse limit is 1-dimensional whenever the bonding functions are upper semi-continuous from [0, 1] into C([0, 1]) and dim(G(fi ◦ fi+1 ◦ · · · ◦ fj)) = 1 for all integers i and j, 1 ≤ i ≤ j. We apply this result to show that such an inverse limit is treelike and also to show that unions of certain finite collections of interval-valued upper semi-continuous function...

We present new generalized Jacobson?s lemma for Drazin inverses. This extends the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear & Multilinear Algebra, 68(2020), 81-93).

Let G = (V, E), V {v1, v2,..., vn}, be a simple graph without isolated vertices, with the sequence of vertex degrees d1 ? d2 ?...? dn > 0, di d(vi). If vertices vi and vj are adjacent in G, we write i ~ j, otherwise ~/ j. The inverse degree topological index is defined to ID(G) ?ni=1 1/di i~j (1/d2i + 1/d2j), coindex ?ID(G) i~/j(1/d2i 1/d2j). We obtain number inequalities which determine bou...

Cortical spreading depolarization causes a breakdown of electrochemical gradients following acute brain injury, and also elicits dynamic changes in regional cerebral blood flow that range from physiological neurovascular coupling (hyperaemia) to pathological inverse coupling (hypoperfusion). In this study, we determined whether pathological inverse neurovascular coupling occurred as a mechanism...

Consider the Schrödinger equation in R with the compactly supported potential q (x) , x ∈ R. The problem of the reconstruction of the function q (x) from measurements of the solution of that equation on a certain set is called “inverse scattering problem”. In this paper we prove uniqueness theorems for some 3-d inverse scattering problems in the case when only the modulus of the complex valued ...

To understand how structurally distinct ligands regulate CB(1) receptor interactions with Gi1, Gi2, and Gi3, we quantified the Galphai and betagamma proteins that coimmunoprecipitate with the CB(1) receptor from a detergent extract of N18TG2 membranes in the presence of ligands. A mixture of A, R, G(GDP) (or G_), and ARG(GDP) (or ARG_) complexes was observed in the presence of aminoalkylindole ...