In this article, we consider the following modified quasilinear critical Kirchhoff-Schrödinger problem involving Stein-Weiss type nonlinearity: $$ \mathcal K(u)= \lambda f(x) |u(x)|^{q-2} u(x)+ \Big ( \int_{\mathbb R^N}\frac{|u(y)|^{2p_{\beta,\mu}^{*}}} {|x-y|^{\mu}|y|^{\beta}}dy ) \frac {|u(x)|^{2p_{\beta,\mu}^{*}-2} u(x)}{|x|^\beta} \; \text{ in }\; \mathbb R^N, where $\lambda > 0$ is a param...

Impaired functioning of pancreatic beta cells is a key hallmark of type 2 diabetes. beta cell function is modulated by the actions of different classes of heterotrimeric G proteins. The functional consequences of activating specific beta cell G protein signaling pathways in vivo are not well understood at present, primarily due to the fact that beta cell G protein-coupled receptors (GPCRs) are ...

The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant rho and assumes that [formula: see text] where g: rho(s) = log(rho-1(s-rho - 1)) for rho > 0, g0(s) = log(-logs), S(t[symbol: see text]Z) is the survival function of the time to event for an individual with q x 1 covariate vector Z, beta is a q x 1 vector of unknown regression param...

There are two objects naturally associated with a braid $\beta\in B_n$ of pseudo-Anosov type: (relative) homeomorphism $\varphi_\beta\colon S^2\to S^2$; and the finite volume complete hyperbolic structure on 3-manifold $M_\beta$ obtained by excising closure $\beta$, together its axis, from $S^3$. We show disconnect between these objects, exhibiting family braids $\{\beta_q:q\in{\mathbb{Q}}\cap(...

Let $p$ be a prime number greater than three. In this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(S)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm Ext}_A^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ up to nonzero scalar in the Adams spectral sequence, where $ngeq m+2>5$, $0leq sExt}_A^{s+2,q[(s+2)p...

Charge movement was measured in frog cut twitch fibers with the double Vaseline-gap technique. Steady-state inactivation of charge movement was studied by changing the holding potential from -90 mV to a level ranging from -70 to -30 mV. Q beta and Q gamma at each holding potential were separated by fitting the Q-V plot with a sum of two Boltzmann distribution functions. At -70 mV Q beta and Q g...

For a family of random-cluster models with cluster weights $q\geq 1$, we prove that the probability $0$ is connected to $x$ asymptotically equal $\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$. The method developed in this article can be applied any spin model for which there exists representation one-monotonic.

In this paper, some recursive relations of the derivatives of the gamma function Γ(α) and incomplete gamma function Γ(α, z) are obtained for complex number α ̸= 0,−1,−2, · · ·. Moreover, the recurrence relation of the derivative of the k−gamma function Γk(x) are also given. Thus, the partial derivative ∂ p+q ∂νp∂μq B(ν, μ) of the Beta function B(ν, μ) can also be represented for p, q = 0, 1, 2, ...