We study boundary value problems of the form −∆u = f on Ω and Bu = g on the boundary ∂Ω, with either Dirichlet or Neumann boundary conditions, where Ω is a smooth bounded domain in Rn and the data f, g are distributions. This problem has to be first properly reformulated and, for practical applications, it is of crucial importance is to obtain the continuity of the solution u in terms of f and ...

This article offers a reformulation of the negative reinforcement model of drug addiction and proposes that the escape and avoidance of negative affect is the prepotent motive for addictive drug use. The authors posit that negative affect is the motivational core of the withdrawal syndrome and argue that, through repeated cycles of drug use and withdrawal, addicted organisms learn to detect int...

Any vertex labeling f : V → {0, 1} of the graph G = (V,E) induces a partial edge labeling f ∗ : E → {0, 1} defined by f ∗(uv) = f(u) if and only if f(u) = f(v). The balance index set of G is defined as {|f ∗−1(0)− f ∗−1(1)| ∣∣ |f−1(0) − f−1(1)| ≤ 1}. In this paper, we propose a new and easier approach to find the balance index set of a graph. This new method makes it possible to determine the b...

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, scalar product, orthogonality, linear functional are derivable from statistical description micro-events Hilbertian sum squares $|\mathfrak{a}_1|^2+|\mathfrak{a}_2|^2+\cdots$. latter leads (non-axiomatically) to standard writing Born formula $\mathtt{f} = |\langle\psi|\varphi\rangle...

The Valsalva maneuver was performed during cardiac catheterization in 9 patients who had undergone a Fontan operation (Fontan group) and in 10 control subjects. The Fontan group had higher right atrial (RA) pressure (16 f 1 vs 4 f 0.5 mm Hg, p <O.OOi), lower cardiac index (2.5 f 0.1 vs 3.7 f 0.2 liters/min/m*, p <0.05), lower stroke index (32 f 2 vs 44 f 2 ml/beat/m*, p <0.05), and higher syste...

In a Fog Radio Access Network (F-RAN), fog access points (F-APs) are equipped with caches that can store popular files during off-peak hours. Besides, they densely deployed to have overlapping radio coverage so requested be delivered cooperatively using beamforming. The bottleneck of the network is typically in bandwidth-limited wireless fronthaul, which connects cloud server F-APs. This work s...