45,020 research outputs found
On a conjecture of Wilf about the Frobenius number
Given coprime positive integers , the Frobenius number is
the largest integer which is not representable as a non-negative integer
combination of the . Let denote the number of all non-representable
positive integers: Wilf conjectured that . We prove
that for every fixed value of the conjecture
holds for all values of which are sufficiently large and are not
divisible by a finite set of primes. We also propose a generalization in the
context of one-dimensional local rings and a question on the equality
Oscillating solutions for prescribed mean curvature equations: Euclidean and Lorentz-Minkowski cases
This paper deals with the prescribed mean curvature equations both in the
Euclidean case and in the Lorentz-Minkowski case in presence of a nonlinearity
such that . We show the existence of oscillating solutions, namely
with an unbounded sequence of zeros. We show the existence of oscillating
solutions, namely with an unbounded sequence of zeros. Moreover these solutions
are periodic, if , while they are radial symmetric and decay to zero at
infinity with their derivatives, if .Comment: 11 page
The structural transformation between manufacturing and services and the deline in the U.S. GDP volatility
For a single firm with a given volatility of total factor productivity at the gross output
level (GTFP), the volatility of total factor productivity at the value added level (YTFP)
increases with the share of intermediate goods in gross output. For a Cobb-Douglas
production function in capital, labor and intermediate goods, YTFP volatility is equal to
GTFP volatility divided by one minus the share of intermediate goods in gross output.
In the U.S., this share is steadily around 0.6 for manufacturing and 0.38 for services
during the 1960-2005 period. Thus, the same level of GTFP volatility in the two sectors
implies a 55% larger YTFP volatility in manufacturing. This fact contributes to the
higher measured YTFP volatility in manufacturing with respect to services. It follows
that, as the services share in GDP increases from 0.53 in 1960 to 0.71 in 2005 in the
U.S., GDP volatility is reduced. I construct a two-sector dynamic general equilibrium
input-output model to quantify the role of the structural transformation between
manufacturing and services in reducing the U.S. GDP volatility. Numerical results for
the calibrated model economy suggest that the structural transformation can account
for 32% of the GDP volatility reduction between the 1960-1983 and the 1984-2005
periods
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