In this work, we study the volume ratio of the projective tensor products `p ⊗π `q ⊗π `r with 1 ≤ p ≤ q ≤ r ≤ ∞. We obtain asymptotic formulas that are sharp in almost all cases. As a consequence of our estimates, these spaces allow for a nearly Euclidean decomposition of Kašin type whenever 1 ≤ p ≤ q ≤ r ≤ 2 or 1 ≤ p ≤ 2 ≤ r ≤ ∞ and q = 2. Also, from the Bourgain-Milman bound on the volume rat...

Present bias is an old idea. The notion that people are susceptible to the over-pursuit of immediate gratification dates (at least) to the ancient Greeks. In academic research, psychologists working with animals in the 1960s and 1970s proposed “hyperbolic discounting”—a functional form of discounting that generates present bias—as a natural way to represent how animals respond to time delays, a...

Although the Box–Cox transformation provides a flexible functional form for regression models, its applicability is often hampered by the difficulty of choosing an appropriate value for the Box–Cox parameter. This paper presents an explicit variance formula for the Box–Cox estimator of the functional form, from which the analytical behavior of the estimator and its precision can be assessed.  ...

This paper considers the evaluation of the average treatment effect of a binary endogenous regressor on a binary outcome when one imposes a threshold crossing model on both the endogenous regressor and the outcome variable but without imposing parametric functional form or distributional assumptions. Without parametric restrictions, the average effect of the binary endogenous variable is not ge...

Regular consumer demand systems almost invariably employ specifications that involve common functional forms in all equations. When applications involve crosssectional data it is often the case that demographic effects are important. However it is plausible that demographic effects are commodity-specific. In this case, there may be a loss of efficiency if a common functional form across commodi...

Small regulatory RNAs are a class of non-coding RNAs that function primarily as negative regulators of other RNA transcripts. The principal members of this class are microRNAs and siRNAs, which are involved in post-transcriptional gene silencing. These small RNAs, which in their functional form are singlestranded and ~22 nucleotides in length, guide a gene silencing complex to an mRNA by comple...

This paper reviews critiques of the Human Development Report over the last twenty years. The critiques are mostly related to the choice of indicators, to high correlation of HDI components, functional form of the HDI including normalization of component indicators, aggregation vs. multiplication, and issues related to weighting. A thorough analysis of the critiques leads us to a proposal for mo...

Correspondence: gaoyingimu@163. com Department of Mathematics, Chongqing Normal University, Chongqing 400047, China Abstract In this paper, a pair of nondifferentiable multiobjective fractional programming problems is formulated. For a differentiable function, we introduce the definition of higher-order (F, a, r, d)-convexity, which extends some kinds of generalized convexity, such as second or...

State-of-the-art first-order automated theorem proving systems have reached considerable strength over recent years. However, in many areas of mathematics they are still a long way from reliably proving theorems that would be considered relatively simple by humans. For example, when reasoning about sets, relations, or functions, first-order systems still exhibit serious weaknesses. While it has...