The Catalyst Effect of Historic Preservation: A Spatial Analysis of the Impact of Historic District Designation on Housing Renovations in New York City

The constraints on property use along with the economic merits of historic districts are critical points in the debate over preservation policies. Improving the existing housing stock is a substantial economic activity and a significant part of the nation’s overall construction industry. The purpose of this study is to present an empirical analysis of the relationship between historic district designation and renovation decisions. The results of the analysis found that historic preservation does not inhibit the renovation activity of single-family homeowners. However, contrary to the claims made by proponents, it does not give a powerful incentive for owners in undesignated neighborhoods

Maximal codeword lengths in Huffman codes

The following question about Huffman coding, which is an important technique for compressing data from a discrete source, is considered. If p is the smallest source probability, how long, in terms of p, can the longest Huffman codeword be? It is shown that if p is in the range 0 less than p less than or equal to 1/2, and if K is the unique index such that 1/F(sub K+3) less than p less than or equal to 1/F(sub K+2), where F(sub K) denotes the Kth Fibonacci number, then the longest Huffman codeword for a source whose least probability is p is at most K, and no better bound is possible. Asymptotically, this implies the surprising fact that for small values of p, a Huffman code's longest codeword can be as much as 44 percent larger than that of the corresponding Shannon code

On the H\'enon-Lane-Emden conjecture

We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden system \hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when $pq>1$, $p,q,a,b\ge0$. The main conjecture states that there is no non-trivial non-negative solution whenever $(p,q)$ is under the critical Sobolev hyperbola, i.e. $\frac{N+a}{p+1}+\frac{N+b}{q+1}>{N-2}$. We show that this is indeed the case in dimension N=3 provided the solution is also assumed to be bounded, extending a result established recently by Phan-Souplet in the scalar case. Assuming stability of the solutions, we could then prove Liouville-type theorems in higher dimensions. For the scalar cases, albeit of second order ($a=b$ and $p=q$) or of fourth order ($a\ge 0=b$ and $p>1=q$), we show that for all dimensions $N\ge 3$ in the first case (resp., $N\ge 5$ in the second case), there is no positive solution with a finite Morse index, whenever $p$ is below the corresponding critical exponent, i.e $1<p<\frac{N+2+2a}{N-2}$ (resp., $1<p<\frac{N+4+2a}{N-4}$). Finally, we show that non-negative stable solutions of the full H\'{e}non-Lane-Emden system are trivial provided \label{sysdim00} N<2+2(\frac{p(b+2)+a+2}{pq-1}) (\sqrt{\frac{pq(q+1)}{p+1}}+ \sqrt{\frac{pq(q+1)}{p+1}-\sqrt\frac{pq(q+1)}{p+1}}).Comment: Theorem 4 has been added in the new version. 23 pages, Comments are welcome. Updated version - if any - can be downloaded at http://www.birs.ca/~nassif/ or http://www.math.ubc.ca/~fazly/research.htm

Optimization of feeding and growth performance of African catfish (Clarias gariepinus Burchell, 1822) fingerlings.

The present studies were undertaken because feeding remains the single most important determinant of the economic viability of fish culture The research identified the factors pertinent to feeding strategies and growth performance of African catfish Clarias gariepinus (Burchell, 1822) fingerlings. Existing literature relating to the feeding and growth of African catfish is reviewed and the key factors highlighted. A preliminary experiment investigated the effect of the three most important factors - density, light and shelter - on the growth and survival of C. gariepinus. Low density, low light intensity and shelter enhanced growth rates, although not the rates of survival of C. gariepinus fingerlings. The second preliminary experiment was conducted in order to establish an appropriate methodology for measuring feed intake and gastric evacuation. The X-ray method using radio opaque Ballotinis proved successful for accurate estimation of feed intake and gastric evacuation of C. gariepinus. These two studies provided information on environmental parameters in catfish rearing and the appropriate techniques for monitoring feed consumption and evacuation rate. Using feed marker and X-ray technology, based on gastric evacuation and return of appetite, maximum daily feed intake was estimated and a feeding schedule for fingerlings of this species proposed. The effects of particle size and energy level of food on gastric evacuation are evaluated and optimum feed particle sizes and energy levels were determined. Fingerling C. gariepinus grow best on diets of intermediate pellet size (1.5 and 2 mm) and intermediate dietary energy level (22.84 kJ g'1), resulting in high feed intake and feed utilization and low food conversion. Although this species is believed to have a nocturnal feeding habit, to date no research has established a diel rhythm. Using infrared video technology and continuous recording of feeding activities a precise diel rhythm was identified. Predominantly a nocturnal feeder, C. gariepinus shows two distinct feeding peaks given access to feed for 24 h - one immediately after the onset of dark phase and the second just prior to the onset of the light phase. In order to maximize growth performance and feed intake, fish were fed with diets of intermediate pellet size and energy level in three different modes - following their feeding rhythm, only in light phase and in light and dark phase continuously. Fish fed in response to their rhythmic feeding peak had highest weight gain, feed intake and feed utilization and lowest feed conversion. On this basis, a comprehensive feeding guide for fmgerling C. gariepinus was established