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...

In this paper, we propose a new numerical method for determining a moving boundary from Cauchy data in one dimensional heat equation. The numerical scheme is based on the use of fundamental solutions of the heat equation as basis functions. In order to regularize the ill-conditioned linear system of equations resulted by collocating boundary data, we apply successfully the Tikhonov regularizati...

1 Schrödinger Equation and Time Development Operators 1 1.1 Schrödinger’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Time-dependent kets and operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Solutions to Schrödinger’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Time developme...

This paper presents two views of stepwise enhancement, one a pragmatic syntax-based approach and the other a semantic approach based on higher-order functions and relating to shape and polytypism. The approaches are outlined, and the perhaps surprisingly close relationship between the two described. By combining the advantages of both approaches, it is shown how more code in both functional and...

In Quantum Mechanics the transition from a deterministic description to a probabilistic one is done using a simple rule termed the Born rule. This rule states that the probability of an outcome (a) given a state (Ψ) is the square of their inner products ((a>Ψ)2). In this paper, we unravel a new probabilistic justification for popular algebraic algorithms, based on the Born rule. These algorithm...