The Index and Spectrum of Lie Poset Algebras of Types B, C, and D

We define posets of types B, C, and D. These posets encode the matrix forms of certain Lie algebras which lie between the algebras of upper-triangular and diagonal matrices. Our primary concern is the index and spectral theories of such type-B, C, and D Lie poset algebras. For an important restricted class, we develop combinatorial index formulas and, in particular, characterize posets corresponding to Frobenius Lie algebras. In this latter case we show that the spectrum is binary; that is, consists of an equal number of 0's and 1's. Interestingly, type-B, C, and D Lie poset algebras can be related to Reiner's notion of a parset.

Elementary Index Bias: Evidence for the Euro Area from a Large Scanner Dataset

We provide evidence on the effect of elementary index choice on inflation measurement in the euro area. Using scanner data for 15,844 individual items from 42 product categories and 10 euro area countries, we compute product category level elementary price indexes using eight different elementary index formulas. Measured inflation outcomes of the different index formulas are compared with the Fisher ideal index to quantify elementary index bias. We have three main findings. First, elementary index bias is quite variable across product categories, countries and index formulas. Second, a comparison of elementary index formulas with and without expenditure weights shows that a shift from price only indexes to expenditure weighted indexes would entail at the product level multiple percentage points differences in measured price changes. And finally, we show that elementary index bias is quantitatively more important than upper level substitution bias.

The Mysterious Cross-Country Dispersion in Mobile Phone Price Trends

Mobile phones have been central to ICT innovation since the introduction of the smartphone and constant-quality prices are a barometer of their economic impact. Official consumer price indices (CPIs) indicate that impact differs wildly across countries: for the 2008–18 period, average annual rates of mobile phone inflation range from no change to a 25 per cent decline among 12 key countries examined in this paper. Although evidence indicates certain fundamental factors are at play, mis-measurement may lead the spread in rates to be overstated. Examination of methods employed in CPI calculation, including quality adjustment and index formulas, illuminates but does not resolve the mystery.

Remarks on Geo-Logarithmic Price Indices

As is known, all geo-logarithmic indices enjoy the axiomatic properties of being proportional, commensurable and homogeneous, together with their cofactors (Martini 1992a). Geologarithmic price indices satisfying the axioms of monotonicity, basis reversibility and factor reversibility have been investigated by Marco Fattore (2010), who has shown that the superlative Fisher price index does not belong to this family of indices. In this article, we discuss geo-logarithmic price indices with reference to the Laspeyres-Paasche bounding test and we propose a modification of the considered index family that satisfies this test. We also modify the structure of geo-logarithmic indices by using an additional parameter and, following the economic approach, we list superlative price index formulas that are members of the considered price index family. We obtain a special subfamily that approximates superlative price indices and includes the Fisher, Walsh and Sato-Vartia price indices.

Running Safety and Comfort Analysis of Railway Vehicles Moving on Curved Tracks

Using a heuristic linear creep model, this study derives the governing differential equations of motion for the railway vehicle traveling on curved tracks. The railway vehicle is modeled as a car system with 27 degrees-of-freedom (DOFs), taking into account the lateral and vertical displacements, roll and yaw angles of the wheelsets and truck frames, as well as the lateral displacement, roll and yaw angles of the car body. The effects of railway vehicle speeds on the derailment quotients and offload factors related to running safety are evaluated by both the linear and nonlinear creep models for various radii of curved tracks. Using the Sperling and modified Sperling index formulas, the effects of railway vehicle speeds on lateral riding quality and comfort are illustrated for the two models with various radii of curved tracks. Furthermore, the effects of railway vehicle speeds on the lateral Sperling comfort index of the 27-DOF car model are presented and compared for various suspension parameters. Finally, the acceptable region for riding quality and comfort are drawn.