Cycle-preserving extension of demand functions to new commodities

New commodities, new consumers

Because current literature on globalization largely neglects racism, it fails to explain the experiences of contemporary African American youth within the new racialized social class formations of globalization. I suggest that because African American youth live within the borders of the sole remaining world superpower, their experiences might shed light on social class relations of advanced ca...

Behavior Preserving Extension of Univariate and Bivariate Functions

Given function values on a domain D0 , possibly with noise, we examine the possibility of extending the function to a larger domain D,D0 ⊂ D. In addition to smoothness at the boundary of D0 , the extension to D \ D0 should also inherit behavioral trends of the function on D0 , such as growth and decay or even oscillations. The approach chosen here is based upon the framework of linear models, u...

Linear Functions Preserving Multivariate and Directional Majorization

Let V and W be two real vector spaces and let &sim be a relation on both V and W. A linear function T : V → W is said to be a linear preserver (respectively strong linear preserver) of &sim if Tx &sim Ty whenever x &sim y (respectively Tx &sim Ty if and only if x &sim y). In this paper we characterize all linear functions T : M_{n,m} → M_{n,k} which preserve or strongly preserve multivariate an...

Linear Functions Preserving Sut-Majorization on RN

Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if t...

Introduction to Metric-preserving Functions