In this short article, I build an idea-based growth model with perfect competition in a representative household economy. obtain significant findings that confirm Boitier (2019). First, competitive equilibrium, increasing returns to scale, and innovations can be tenable. For that, firms must raise capital from shareholders, the production function show decreasing scale stock of ideas labor. Sec...

Garoufalidis and Levine introduced the homology cobordism group of homology cylinders over a surface. This group can be regarded as a generalization of the mapping class group. Using torsion invariants, we show that the abelianization of this group is infinitely generated provided that the first Betti number of the surface is positive. In particular, this shows that the group is not perfect. Th...

We apply recursive methods to obtain a finite dimensional and recursive representation of an equilibrium of one of Townsend’s models of ‘forecasting the forecasts of others’. The equilibrium has the property that decision makers make common forecasts of the hidden state variable whose presence motivates them to pay attention to prices in other markets. Thus, the model has too few sources of ran...

In this paper, we have dened and studied a generalized form of topological vector spaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of Levine. Along with other results, it is proved that every s-topological vector space is generalized homogeneous space. Every open subspace of an s-topological vector space is...

Neovascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In two previous papers, [Levine, H.A. and Sleeman, B.D. (1997) "A system of reaction diffusion equations arising in the theory of reinforced random walks" SIAM J. AppL Math. 683-730; Levine, H.A., Sleema...

Gene expression is stochastic and displays variation ("noise") both within and between cells. Intracellular (intrinsic) variance can be distinguished from extracellular (extrinsic) variance by applying the law of total variance to data from two-reporter assays that probe expression of identically regulated gene pairs in single cells. We examine established formulas [Elowitz, M. B., A. J. Levine...

Levine, Wigod, Backer, and Ponder (1949) and Levine, Kuhmichel, and Wigod (1952) have described two examples of an antibody, " antiCellano," which reacts with all blood samples except those from individuals belonging to the rare genotype KK. The first example was found in a woman whose infant had mild haemolytic disease of the newborn; the second was found in a patient who had received several ...