Given a velocity field u(x,t), we consider the evolution of passive tracer θ governed by ∂tθ+u⋅∇θ=Δθ+g with time-independent source g(x). When u is small in some sense, Batchelor, Howells and Townsend (Batchelor et al., 1959) predicted that spectrum scales as |θk|2∝|k|−4|uk|2. Following our recent work for two-dimensional case, this paper prove BHT59 scaling does hold probabilistically, asympto...

This work contains a constructive example of a class of Jacobi operators with an arbitrary finite number of gaps in its unbounded essential spectrum. The construction of this class is based on elementary ideas of gluing finite-dimensional Jacobi matrices whose sizes grow to infinity. The precise analysis of the finite-dimensional pieces leads to a new “finite essential spectrum” besides the nat...

We review the BRST analysis of the system of a (super)conformal matter coupled to 2D (super)gravity. The spectrum and its operator realization are reported. In particular, the operators associated with the states of nonzero ghost number are given. We also discuss the ground ring structure of the super-Liouville coupled to ĉ = 1 matter. In appendices, hermiticities, states for c < 1 conformal ma...

We consider a bound state problem for a family of supersymmetric gauge theories with fundamental matter. These theories can be obtained by a dimensional reduction of supersymmetric QCD from three dimensions to 1+1 and subsequent truncation of some of the fields. We find that the models without adjoint scalar converge to well-defined continuum limits and calculate the resulting spectra of these ...

We have constructed general dimensional hyperdiamond lattices which are analogues of the three dimensional diamond lattice. Each site has the minimal number of bonds as possible in that dimension and the structure of the bond vectors is similar to that of the Clifford algebra. Furthermore, the spectrum zeros of the tight-binding hopping model on the hyperdiamond lattice are also investigated. T...

We study the discreteness of the spectrum of Schrödinger operators which are defined on N -dimensional rooted trees of a finite or infinite volume, and are subject to a certain mixed boundary condition. We present a method to estimate their eigenvalues using operators on a one-dimensional tree. These operators are called width-weighted operators, since their coefficients depend on the section w...

Abstract: Accurate channel estimation is necessary for coherent detection and adaptive control techniques, e.g., adaptive modulation and demodulation, of multicarrier signals. In this paper, we study one-dimensional channel estimation in frequencyor time-domain and 2-dimensional channel estimation in time-frequency domain. It is shown that the frequency (time)-domain interpolation channel estim...