An m×(n+1) multiplicity matrix is a M=(μi,j) with rows enumerated by i∈{1,2,…,m} and columns j∈{0,1,…,n} whose coordinates are nonnegative integers satisfying the following two properties: (1) If μi,j≥1, then j≤n−1 μi,j+1=μi,j−1, (2) colsumj(M)=∑i=1mμi,j≤n−j for all j. Let K be field of characteristic 0 let f(x) polynomial degree n coefficients in K. f(j)(x) jth derivative f(x). Λ=(λ1,…,λm) seq...

We simulate lattice QCD at a finite chemical potential μI for isospin (I3) at zero and finite temperatures. At some μI = μc QCD has a second order transition with mean-field critical exponents to a state where (I3) is broken spontaneously by a charged pion condensate. Heating the system with μI > μc we find there is some temperature at which this condensate evaporates. This transition appears t...

Suppose we have, after possible rescaling to obtain unit variance, observed a sequence X = (Xi)i∈I satisfying Xi = μi + i, for i ∈ I, where μ = (μi)i∈I is a possibly sparse signal (i.e. some/most of the μi are believed to be zero), the i are independentN(0, 1) noise, and I is a possibly multidimensional index domain. Being a generalisation of the EbayesThresh method, the TreeThresh method is ba...

Consider s + 1 univariate normal populations with common variance σ2 and means μi, i = 0, 1, . . . , s, constrained by the tree-order restrictions μ0 ≤ μi, i = 1, 2, . . . , s. For certain sequences μ0, μ1, . . . the maximum likelihood-based estimator (MLBE) of μ0 diverges to −∞ as s → ∞ and its bias is unbounded. By contrast, the bias of an alternative estimator of μ0 proposed by Cohen and Sac...

We report on high-resolution laser spectroscopy studies Cf249–253 with spectral linewidths in the order of 100 MHz carried out at RISIKO mass separator Mainz University. In total three atomic ground-state transitions were investigated and hyperfine parameters for odd-A isotopes isotope shift all examined have been determined from measured spectra. The measurements allowed tracking changes mean-...

i=1 (∆− μiI)vk = h(x), x ∈ <+, μi > 0, ( ∂vi ∂xn + snvi)xn=0 = φi(x ′ ), x ′ = (x1, ...xn−1) ∈ a; and we obtain for h(x)≡ 0 a relation between the inverse Laplace transforms v k,2m(x ′ , sn) and solutions of a similar problem to (1) in x ′ ∈ 0 instead of μi, and then using inverse tabular t...

Let F be a nearly holomorphic vector-valued Siegel modular form of weight ρ with respect to some congruence subgroup of Sp2n(Q). In this note, we prove that the function on Sp2n(R) obtained by lifting F has the moderate growth (or “slowly increasing”) property. This is a consequence of the following bound that we prove: ‖ρ(Y )F (Z)‖ ∏n i=1(μi(Y ) λ1/2 + μi(Y ) −λ1/2) where λ1 ≥ . . . ≥ λn is th...

In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof of his result. Our approach allows us to give an explicit bound for this kind of fair division. Furthermore, we also give a theoretical answer to an open problem posed by Barbanel in 1996. Roughly speaking, this ques...

We consider a discrete-time probabilistic inference system where the conclusions and inputs are probability measures on measurable spaces X,X and Y,Y respectively. We are given a kernel N from X to Y (N : X × Y → [0, 1]), which represents the way information about states of affairs (represented by X) is transmitted to a receptor (represented by Y ). Suppose that at time t = i the conclusion is ...