Series representations of the form f(f)-IE 2 a,,kv(t-n)e2n'k' for bounded signals f(t) are studied, as are conditions on the unit function v(r), such that the coefficients a,, k reveal the energy content of f(t) in the time interval n-(l/2) < t I n +(1/2) and frequency interval 2m(k-(l/2)) I w I 2n(k +(1/2)). These conditions turn out to he 1) orthogonal&y, i.e., if n=k=O otherwise and 2) integ...

A full scale swine (300 pigs) waste treatment system, including a solid/liquid separation unit (3 m) with a solids holding tank (1.2 m) and a liquid holding tank (20 m), two anaerobic reactors (10 m each) in series, an intermittent aeration unit (20 m), a sedimentation/polishing unit (20 m) and a sludge dewatering bed (17 m), was used to investigate the impact of integrating an intermittent aer...

This is an updated guideline prepared for the British Association of Dermatologists’ (BAD) Clinical Standards Unit, made up of the Therapy & Guidelines (T&G) subcommittee. Members of the Clinical Standards Unit are: J. Hughes (Chairman T&G), J. McLelland, S. Punjabi, D.A. Buckley, I. Nasr, V.J. Swale, C.E. Duarte Williamson, P.M. McHenry, S. Wagle (British National Formulary), S. Amin (British ...

Let T(X) be the full transformation semigroup on a set X, and let L(V) under composition of all linear transformations vector space V over field. For subset Y X subspace W V, consider semigroups $${\overline{T}}(X, Y) = \{f\in T(X):Yf \subseteq Y\}$$ $${\overline{L}}(V, W) L(V):Wf W\}$$ composition. We describe unit-regular elements in Y)$$ W)$$ . Using these, we determine when are unit-regular...

It is shown that every unit-cost random-access machine (RAM) that runs in time T can be simulated by a concurrent-read exclusive-write parallel random-access machine (CREW PRAM) in time O(T 1/2 log T ). The proof is constructive; thus it gives a mechanical way to translate any sequential algorithm designed to run on a unit-cost RAM into a parallel algorithm that runs on a CREW PRAM and obtain a...

A “dyadic rectangle” is a set of the form R = [a2−s, (a+1)2−s]×[b2−t, (b+1)2−t], where s and t are non-negative integers. A dyadic tiling is a tiling of the unit square with dyadic rectangles. In this paper we study n-tilings which consist of 2 nonoverlapping dyadic rectangles, each of area 2−n, whose union is the unit square. We discuss some of the underlying combinatorial structures, provide ...

Suppose that ϕ(z) is an analytic self-map of the unit disk ∆. We consider the boundedness of the composition operator C ϕ from Bloch space Ꮾ into the spaces Q T (Q T ,0) defined by a nonnegative, nondecreasing function T (r) on 0 ≤ r < ∞. 1. Introduction. Let ∆ = {z : |z| < 1} be the unit disk of complex plane C and let H(∆) be the space of all analytic functions in ∆. For a ∈ ∆, Green's functi...

The strongest and the weakest t-norms that coincide with the given t-norm on a subregion of the unit interval are discussed. The question whether such a t-norm can be obtained as a limit of the sequence of continuous t-norms that coincide with the original t-norm on the given subregion is investigated.

We study the structure of a $3-$Leibniz algebra $T$ graded by an arbitrary abelian group $G,$ which is considered dimension and over base field $\bbbf.$ show that form $T=\uu\oplus\sum_jI_j,$ with $\uu$ linear subspace $T_1,$ homogeneous component associated to unit element $1$ in any $I_j$ well described ideal $T,$ satisfying $$ [I_j, T, I_k] = I_k, T] [T, I_j, 0, if $j\neq k.$ In case being m...

in the complex z = e -2H plane, where H is the reduced external magnetic field. At infinite temperature (T = m) the spins are noninteracting and the partition function reduces to (z 1í2 + z-ìë)~, where N is the total number of spins. The zeros are therefore N-fold degenerate at 8 = a. As the temperature is lowered, the zeros spread into an arc segment of the unit circle centered about 8 = 7r an...