The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find that the spinodal is associated with the zeros of the partition function in four-dimensional complex temperature/magnetic field space. The zeros approach the real temperature/magnetic field plane as the range of interaction increases.

The Sturm comparison theorems for second order ODEs are classical results from which information on the properties of the zeros of special functions can be obtained. Sturm separation and comparison theorems are also available for difference-differential systems under oscillatory conditions. The separation theorem provides interlacing information for zeros of some special functions and the compa...

This paper studies the Schrödinger operator with Morse potential Vk(u) = 1 4e 2u + keu on a right half-line [u0,∞), and determines the Weyl asymptotics of eigenvalues for constant boundary conditions at the endpoint u0. In consequence it obtains information on the location of zeros of the Whittaker function Wκ,μ(x), for fixed real parameters κ, x with x > 0, viewed as an entire function in the ...

H.264 video standard is used to achieve high quality video and high data compression when compared to other existing video standards. H.264 uses context-based adaptive variable length coding (CAVLC) to code residual data in Baseline profile.The H.264 bitstream consist of zeros and ones.At one of the decoding stages of contextbased adptive variable length decoder (CAVLD), Total Zeros decoder is ...

We examine the behaviour of the zeros of the real and imaginary parts of ξ(s) on the vertical line Rs = 1/2 + λ, for λ 6= 0. This can be rephrased in terms of studying the zeros of families of entire functions A(s) = 1 2 (ξ(s+λ)+ξ(s−λ)) and B(s) = 1 2i (ξ(s+λ)−ξ(s−λ)). We will prove some unconditional analogues of results appearing in [3], specifically that the normalized spacings of the zeros ...

We study the distribution of zeros of holomorphic Hecke cusp forms in several “thin” sets as the weight, k, tends to infinity. We obtain unconditional results for slowly shrinking (with k) hyperbolic balls. This relies on a new, effective, proof of Rudnick’s theorem and on an effective version of Quantum Unique Ergodicity for holomorphic forms, which we obtain in this paper. In addition, assumi...

The zeros of semi-orthogonal functions with respect to a probability measure µ supported on the unit circle can be applied to obtain Szeg˝ o quadrature formulas. The discrete measures generated by these formulas weakly converge to the orthogonality measure µ. In this paper we construct families of semi-orthogonal functions with interlacing zeros, and give a representation of the support of µ in...

We give a definition of the zeros of an infinite-dimensional system with bounded control and observation operators B and C respectively. The zeros are defined in terms of the spectrum of an operator on an invariant subspace. These zeros are shown to be exactly the invariant zeros of the system. For the case of SISO systems, where also the range of B is not in the kernel of C, we show that this ...

An important problem in number theory is to study the distribution of the non-trivial zeros of the Riemann zeta-function which, if one is willing to assume the Riemann Hypothesis, all lie on a vertical line. It is relatively easy to count how many of these zeros lie in a large interval, so the average spacing between consecutive zeros is easy to compute. However, it is a difficult and interesti...

The densities of Yang-Lee zeros for the Ising ferromagnet on the L x L square lattice are evaluated from the exact grand partition functions (L=3 approximately 16). The properties of the density of Yang-Lee zeros are discussed as a function of temperature T and system size L. The three different classes of phase transitions for the Ising ferromagnet--first-order phase transition, second-order p...