The three invariants of C are key to expressing this tensor and its inverse as a polynomial in C. Simple and symmetric expressions are presented connecting the two sets of invariants {I1, I2, I3} and {i1, i2, i3} of C and C, respectively. The first result is a bivariate function relating I1, I2 to i1, i2. The functional form of i1 is the same as that of i2 when the roles of the C-invariants are...

We prove the following theorems: 1) The Laurent expansions in ε of the Gauss hypergeometric functions 2F1(I1 + aε, I2 + bε; I3 + p q + cε; z), 2F1(I1 + p q + aε, I2 + p q + bε; I3+ p q + cε; z) and 2F1(I1+ p q +aε, I2+ bε; I3 + p q + cε; z), where I1, I2, I3, p, q are arbitrary integers, a, b, c are arbitrary numbers and ε is an infinitesimal parameter, are expressible in terms of multiple poly...

Let i1 ≥ i2 ≥ i3 ≥ 1 be integers. An L(i1, i2, i3)-labelling of a graph G = (V, E) is a mapping φ : V → {0, 1, 2, . . .} such that |φ(u)− φ(v)| ≥ it for any u, v ∈ V with d(u, v) = t, t = 1, 2, 3, where d(u, v) is the distance in G between u and v. The integer φ(v) is called the label assigned to v under φ, and the difference between the largest and the smallest labels is called the span of φ. ...

BACKGROUND Two pertussis toxin sensitive G(i) proteins, G(i2) and G(i3), are expressed in cardiomyocytes and upregulated in heart failure. It has been proposed that the highly homologous G(i) isoforms are functionally distinct. To test for isoform-specific functions of G(i) proteins, we examined their role in the regulation of cardiac L-type voltage-dependent calcium channels (L-VDCC). METHOD...

Let p be a large prime number, K,L, M, λ be integers with 1 ≤ M ≤ p and gcd(λ, p) = 1. The aim of our paper is to obtain sharp upper bound estimates for the number I2(M ; K, L) of solutions of the congruence xy ≡ λ (mod p), K + 1 ≤ x ≤ K + M, L + 1 ≤ y ≤ L + M and for the number I3(M ; L) of solutions of the congruence xyz ≡ λ (mod p), L + 1 ≤ x, y, z ≤ L + M. Using the idea of Heath-Brown from...

Heterotrimeric G proteins of the Gα(i) family have been implicated in signaling pathways regulating cell migration in immune diseases. The Gα(i)-protein-coupled C5a receptor is a critical regulator of IgG FcR function in experimental models of immune complex (IC)-induced inflammation. By using mice deficient for Gα(i2) or Gα(i3), we show that Gα(i2) is necessary for neutrophil influx in skin an...

Various heterotrimeric G(i) proteins are considered to be involved in cell migration and effector function of immune cells. The underlying mechanisms, how they control the activation of myeloid effector cells, are not well understood. To elucidate isoform-redundant and -specific roles for Gα(i) proteins in these processes, we analyzed mice genetically deficient in Gα(i2) or Gα(i3). First, we sh...

A range of ligands displayed agonism at the long isoform of the human dopamine D(2) receptor, whether using receptor-G protein fusions or membranes of cells in which pertussis toxin-resistant mutants of individual Galpha(i)-family G proteins could be expressed in an inducible fashion. Varying degrees of efficacy were observed for individual ligands as monitored by their capacity to load [(35)S]...

Heterotrimeric G proteins of the G(i) class have been implicated in signaling pathways regulating growth and metabolism under physiological and pathophysiological conditions. Knockout mice carrying inactivating mutations in both of the widely expressed Galpha(i) class genes, Galpha(i2) and Galpha(i3), demonstrate shared as well as gene-specific functions. The presence of a single active allele ...