Universal relationship between the penetration depth and the normal-state conductivity in YBaCuO. Abstract The absolute values of the conductivity in the normal state σ n and of the low temperature penetration depths λ(0) were measured for a number of different samples of the YBaCuO family. We found a striking correlation between σ n and λ −2 regardless of doping, oxygen reduction or defects, t...

Let XdB be a normal random variable (RV) with mean mXdB and variance σ 2 XdB and let X = 10XdB/10 be the corresponding log-normal RV. (a) Express the mean of X in terms of mXdB and σ 2 XdB . (b) Express the variance of X in terms of mXdB and σ 2 XdB . (c) Express the median of X in terms of mXdB . Based on that, can you now explain why the area mean is sometimes referred to as the median link g...

Assuming that the common-spectrum process in NANOGrav 12.5-year dataset has an origin of scalar-induced gravitational waves, we study enhancement primordial curvature perturbations and mass function black holes, by performing Bayesian parameter inference for first time. We obtain lower limits on spectral amplitude, i.e., A≳10−2 at 95% confidence level, when assuming power spectrum to follow a l...

Here, μ represents the overall mean, βi is the deviation of respondent i from the overall mean, and εij is the deviation of i-th respondent’s reported value from his true value, μ+ βi, on occasion j. βi and εij are independent normal with mean 0 and variance σ β and σ , respectively. The intraclass correlation coefficient (ICC) ρ is calculated as share of between-class variability σ β in total ...

The linear case of context-free, conjunctive and Boolean grammars. Trellis automata. Examples. Equivalence of grammars and automata. 1 Linear Boolean grammars Definition 1. A Boolean grammar G = (Σ, N, P, S) is said to be linear if every rule A→ α1& . . .&αm&¬β1& . . .&¬βn, has αi, βj ∈ Σ∗ ∪ (Σ ∪N)∗. If a linear Boolean grammar is conjunctive (context-free), it is called a linear conjunctive (l...

If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.

Unfortunately, there’s no simple formula for this integral. Instead, tables or numerical approximation routines are used to evaluate it. The normal distribution has a characteristic bell shaped pdf. The center of the bell is at x = μ, and the parameter σ controls the width of the bell. The particular case in which μ = 0, and σ = 1 is referred to as the standard normal random variable. The lette...

Let V be a real vector space of dimension d and V ∗ its dual space. By a cone in V ∗ we will always mean a closed polyhedral cone σ with apex 0 such that σ ∩ −σ = {0}. Let Σ be a fan in V ∗, i.e., a collection of cones such that (1) if σ ∈ Σ then any face of σ belongs to Σ, (2) if σ1, σ2 ∈ Σ then σ1 ∩ σ2 is a face in both. We will assume that Σ is complete, that is ∪Σ = V ∗. The elements of Σ a...

Bayesian testing of a point null hypothesis is considered. The null hypothesis is that an observation, x, is distributed according to the normal distribution with a mean of zero and known variance σ. The alternative hypothesis is that x is distributed according to a normal distribution with an unknown nonzero mean, μ, and variance σ. The testing problem is formulated as a prediction problem. Ba...

1. The multivariate normal distribution Let X := (X1 � � � � �X�) be a random vector. We say that X is a Gaussian random vector if we can write X = μ + AZ� where μ ∈ R, A is an � × � matrix and Z := (Z1 � � � � �Z�) is a �-vector of i.i.d. standard normal random variables. Proposition 1. Let X be a Gaussian random vector, as above. Then, EX = μ� Var(X) := Σ = AA� and MX(�) = e � μ+ 1 2 �A���2 =...