1.1 Basic Definitions Throughout these notes, V will be a finite dimensional Q-vector space. By a lattice in V we mean a finitely generated sybmodule that generates V as a Q-vector space. A subset X ⊆ V is said to be bounded if X is contained in a lattice. For a given function f on V and a vector ` ∈ V we say ` is a period of f if f(x + `) = f(x) for all x ∈ V . The set of all periods of f will...

OBJECTIVE To examine whether frontal lobe abnormalities on magnetic resonance spectroscopy (MRS) in amyotrophic lateral sclerosis (ALS) correlate with poor letter fluency (LF). METHODS Twenty-five patients with ALS (20 with definite, probable, or possible ALS and 5 with progressive muscular atrophy) performed an LF task, involving F word generation in 1 minute, and underwent MRS. Comparisons ...

We investigated the change in activity of the sympathetic nervous system (SNS) in high-sucrose diet (HSD)-induced obese rats compared with controls. Power spectral analyses of R-R interval variability were performed to obtain the low frequency (LF, 0.04-0.699 Hz) and high frequency (HF, 0.7-3.0 Hz) powers. The percents of fat mass to body weight (%F/BW) and fat to muscle ratios (F/M) were signi...

review and classification of electric load forecasting (lf) techniques based on artificial neuralnetworks (ann) is presented. a basic anns architectures used in lf reviewed. a wide range of annoriented applications for forecasting are given in the literature. these are classified into five groups:(1) anns in short-term lf, (2) anns in mid-term lf, (3) anns in long-term lf, (4) hybrid anns inlf,...

Consider the Parzen-Rosenblatt kernel estimate f. = (l/n) ~ Kh (x-Xi), where h > 0 is a constant, K is an absolutely integrable i=1 function with integral one, Kh(X)=(1/ha)K(x/h), and X1 ..... X. are iid random variables with common density f on R d. We show that for all e > 0, n8 2 2 sup P(lSlf.-fl-E~lf.-fll>e)<Ze 32~1KI. whenever liminfl~E~lf,-f]=oo. We also study what happens when h is allow...

Let G be a stratified Lie group and L be the sub-Laplacian on G. Let 0 6= f ∈ S(R). We show that Lf(L)δ, the distribution kernel of the operator Lf(L), is an admissible function on G. We also show that, if ξf(ξ) satisfies Daubechies’ criterion, then Lf(L)δ generates a frame for any sufficiently fine lattice subgroup of G.

ion (X, Qlfl ),Store) "-raise_comparative (Qlf0, Q1 fl, Store ) . raise_comparative (quant (Det0, Cn item), quant (Detl, Cn_it era),Store) --ralse_ccmparative (Det 0, Detl, Store) . raise cc~paratlve (quant (Det, cn (Head, [Mod0] ) ), quant (Det, cn (Head, [Modl] ) ),Store) "-raise_comparative (Mod0,Modl, Store). raise_cc~paratlve (role (Role, Quant0 ),role (Role...