With the help of a commercial bank in China, we studied consumer credit card debt behavior in correlation with demographics, attitude, personality, and credit card features factors. The study was conducted by using mail-in questionnaires, which were sent to credit card holders who was using or had used either revolving credit or petty installment plans. According to regression functions, we fou...

As Schneider [50] observes, the classical Brunn-Minkowski theory had its origin at the turn of the 19th into the 20th century, when Minkowski joined a method of combining convex bodies (which became known as Minkowski addition) with that of ordinary volume. One of the core concepts that Minkowski introduced within the Brunn-Minkowski theory is that of projection body (precise definitions to fol...

"Petty corruption and honesty in all health care systems" is the original title of one of the bioethics networks within the worldwide study projects of the International Association of Bioethics. As the coordinator of this network, it still puzzles me why the word "petty" is in the title when in the past few years-through interviews and questionnaires involving 18 countries-it has become eviden...

Projection and intersection bodies define continuous and GL(n) contravariant valuations. They played a critical role in the solution of the Shephard problem for projections of convex bodies and its dual version for sections, the Busemann– Petty problem. We consider the question whether ΦK ⊆ ΦL implies V (K) ≤ V (L), where Φ is a homogeneous, continuous operator on convex or star bodies which is...

We would like to thank T.L. Petty for his interesting comments regarding our trial of ambulatory oxygen (AO) in chronic obstructive pulmonary disease (COPD) [1]. The question raised by T.L. Petty was the following: when is the best time to initiate AO in oxygen-dependent COPD? He suggested AO should be provided as early as possible after the introduction of long-term oxygen therapy (LTOT) to av...

The lower dimensional Busemann-Petty problem asks whether origin symmetric convex bodies in R with smaller volume of all k-dimensional sections necessarily have smaller volume. As proved by Bourgain and Zhang, the answer to this question is negative if k > 3. The problem is still open for k = 2, 3. In this article we formulate and completely solve the lower dimensional Busemann-Petty problem in...

The generalized Busemann–Petty problem asks: If K and L are origin-symmetric convex bodies in Rn, and the volume of K ∩H is smaller than the volume of L ∩H for every i-dimensional subspace H, 1 < i < n, does it follow that the volume of K is smaller than the volume of L? The hyperplane case i = n−1 is known as the Busemann–Petty problem. It has a negative answer when n > 4, and has a positive a...

YI-CHENG TSAI, CHIN-LAUNG LEI, JAN-MING HO, MING-YANG KAO AND SZU-LANG LIAO Electrical Engineering and Computer Science National Taiwan University Taipei, 116 Taiwan Institute of Information Science Academia Sinica Taipei, 115 Taiwan Electrical Engineering and Computer Science Northwestern University Evanston, IL 60201, USA Department of Money and Banking National Chung-Cheng University Taipei,...