Malmquist-type indices in the presence of negative data:an application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Mathematics Subject Classification: 26A16, 26A33, 46E15.

A circular Malmquist-type index for measuring productivity

This paper develops two new indices for measuring productivity in multi-input multi-output situations. One index enables the measure of productivity change of a unit over time while the second index makes it possible to compare two units on productivity at the same or different points in time. Productivity in a single input single output context is defined as the ratio of output to input. In multi-input multi-output contexts this ratio is not defined. Instead, one of the methods traditionally used is the Malmquist Index of productivity change over time. This is computed by reference to the distances of the input-output bundles of a production unit at two different points in time from the efficient boundaries corresponding to those two points in time. The indices developed in this paper depart form the use of two different reference boundaries and instead they use a single reference boundary which in a sense is the most efficient boundary observed over two or more successive time periods. We discuss the assumptions which make possible the definition of such a single reference boundary and proceed to develop the two Malmquist-type indices for measuring productivity. One key advantage of using a single reference boundary is that the resulting index values are circular. That is it is possible to use the index values of successive time periods to derive an index value of productivity change over a time period of any length covered by successive index values or vice versa. Further, the use of a single reference boundary makes it possible to construct an index for comparing the productivities of two units either at the same or at two different points in time. This was not possible with the traditional Malmquist Index. We decompose both new indices into components which isolate production unit from industry or comparator unit effects. The components themselves like the indices developed are also circular. The components of the indices drill down to reveal more clearly the performance of each unit over time relative either to itself or to other units. The indices developed and their components are aimed at managers of production units to enable them to diagnose the performance of their units with a view to guiding them to improved performance.

Representation of the Weddell Sea deep water masses in the ocean component of the NCAR-CCSM model

We examine Weddell Sea deep water mass distributions with respect to the results from three different model runs using the oceanic component of the National Center for Atmospheric Research Community Climate System Model (NCAR-CCSM). One run is inter-annually forced by corrected NCAR/NCEP fluxes, while the other two are forced with the annual cycle obtained from the same climatology. One of the latter runs includes an interactive sea-ice model. Optimum Multiparameter analysis is applied to separate the deep water masses in the Greenwich Meridian section (into the Weddell Sea only) to measure the degree of realism obtained in the simulations. First, we describe the distribution of the simulated deep water masses using observed water type indices. Since the observed indices do not provide an acceptable representation of the Weddell Sea deep water masses as expected, they are specifically adjusted for each simulation. Differences among the water masses` representations in the three simulations are quantified through their root-mean-square differences. Results point out the need for better representation (and inclusion) of ice-related processes in order to improve the oceanic characteristics and variability of dense Southern Ocean water masses in the outputs of the NCAR-CCSM model, and probably in other ocean and climate models.

Evaluation of strain energy based damage indices for flexural crack detection of RC beams

Vibration Based Damage Identification Techniques which use modal data or their functions, have received significant research interest in recent years due to their ability to detect damage in structures and hence contribute towards the safety of the structures. In this context, Strain Energy Based Damage Indices (SEDIs), based on modal strain energy, have been successful in localising damage in structuers made of homogeneous materials such as steel. However, their application to reinforced concrete (RC) structures needs further investigation due to the significant difference in the prominent damage type, the flexural crack. The work reported in this paper is an integral part of a comprehensive research program to develop and apply effective strain energy based damage indices to assess damage in reinforced concrete flexural members. This research program established (i) a suitable flexural crack simulation technique, (ii) four improved SEDI's and (iii) programmable sequentional steps to minimise effects of noise. This paper evaluates and ranks the four newly developed SEDIs and existing seven SEDIs for their ability to detect and localise flexural cracks in RC beams. Based on the results of the evaluations, it recommends the SEDIs for use with single and multiple vibration modes.

Serum vitamin D levels are lower in Australian children and adolescents with type 1 diabetes than in children without diabetes

Vitamin D is synthesised in the skin through the action of UVB radiation (sunlight), and 25-hydroxy vitamin D (25OHD) measured in serum as a marker of vitamin D status. Several studies, mostly conducted in high latitudes, have shown an association between type 1 diabetes mellitus (T1DM) and low serum 25OHD. We conducted a case-control study to determine whether, in a sub-tropical environment with abundant sunlight (latitude 27.5°S), children with T1DM have lower serum vitamin D than children without diabetes. Fifty-six children with T1DM (14 newly diagnosed) and 46 unrelated control children participated in the study. Serum 25OHD, 1,25-dihydroxy vitamin D (1,25(OH)2D) and selected biochemical indices were measured. Vitamin D receptor (VDR) polymorphisms Taq1, Fok1, and Apa1 were genotyped. Fitzpatrick skin classification, self-reported daily hours of outdoor exposure, and mean UV index over the 35d prior to blood collection were recorded. Serum 25OHD was lower in children with T1DM (n=56) than in controls (n=46) [mean (95%CI)=78.7 (71.8-85.6) nmol/L vs. 91.4 (83.5-98.7) nmol/L, p=0.02]. T1DM children had lower self-reported outdoor exposure and mean UV exposure, but no significant difference in distribution of VDR polymorphisms. 25OHD remained lower in children with T1DM after covariate adjustment. Children newly diagnosed with T1DM had lower 1,25(OH)2D [median (IQR)=89 (68-122) pmol/L] than controls [121 (108-159) pmol/L, p=0.03], or children with established diabetes [137 (113-153) pmol/L, p=0.01]. Children with T1DM have lower 25OHD than controls, even in an environment of abundant sunlight. Whether low vitamin D is a risk factor or consequence of T1DM is unknown. © 2012 John Wiley & Sons A/S.

Lens shape and refractive index distribution in type 1 diabetes

Purpose: To compare lens dimensions and refractive index distributions in type 1 diabetes and age-matched control groups. Methods: There were 17 participants with type 1 diabetes, consisting of two subgroups (7 young [23 ± 4 years] and 10 older [54 ± 4 years] participants), with 23 controls (13 young, 24 ± 4 years; 10 older, 55 ± 4 years). For each participant, one eye was tested with relaxed accommodation. A 3T clinical magnetic resonance imaging scanner was used to image the eye, employing a multiple spin echo (MSE) sequence to determine lens dimensions and refractive index profiles along the equatorial and axial directions. Results: The diabetes group had significantly smaller lens equatorial diameters and larger lens axial thicknesses than the control group (diameter mean ± 95% confidence interval [CI]: diabetes group 8.65 ± 0.26 mm, control group 9.42 ± 0.18 mm; axial thickness: diabetes group 4.33 ± 0.30 mm, control group 3.80 ± 0.14 mm). These differences were also significant within each age group. The older group had significantly greater axial thickness than the young group (older group 4.35 ± 0.26 mm, young group 3.70 ± 0.25 mm). Center refractive indices of diabetes and control groups were not significantly different. There were some statistically significant differences between the refractive index fitting parameters of young and older groups, but not between diabetes and control groups of the same age. Conclusions: Smaller lens diameters occurred in the diabetes groups than in the age-matched control groups. Differences in refractive index distribution between persons with and without diabetes are too small to have important effects on instruments measuring axial thickness.

On Orlicz-Sobolev capacities

This thesis consists of three articles on Orlicz-Sobolev capacities. Capacity is a set function which gives information of the size of sets. Capacity is useful concept in the study of partial differential equations, and generalizations of exponential-type inequalities and Lebesgue point theory, and other topics related to weakly differentiable functions such as functions belonging to some Sobolev space or Orlicz-Sobolev space. In this thesis it is assumed that the defining function of the Orlicz-Sobolev space, the Young function, satisfies certain growth conditions. In the first article, the null sets of two different versions of Orlicz-Sobolev capacity are studied. Sufficient conditions are given so that these two versions of capacity have the same null sets. The importance of having information about null sets lies in the fact that the sets of capacity zero play similar role in the Orlicz-Sobolev space setting as the sets of measure zero do in the Lebesgue space and Orlicz space setting. The second article continues the work of the first article. In this article, it is shown that if a Young function satisfies certain conditions, then two versions of Orlicz-Sobolev capacity have the same null sets for its complementary Young function. In the third article the metric properties of Orlicz-Sobolev capacities are studied. It is usually difficult or impossible to calculate a capacity of a set. In applications it is often useful to have estimates for the Orlicz-Sobolev capacities of balls. Such estimates are obtained in this paper, when the Young function satisfies some growth conditions.

Synthesis, Characterization, and Electronic Structure of New Type of Heterometallic Boride Clusters

The reaction of [Cp*TaCl(4)], 1 (Cp* = eta(5)-C(5)Me(5)), with [LiBH(4)center dot THF] at -78 degrees C, followed by thermolysis in the presence of excess [BH(3)center dot THF], results in the formation of the oxatantalaborane cluster [(Cp*Ta)(2)B(4)H(10)O], 2 in moderate yield. Compound 2 is a notable example of an oxatantalaborane cluster where oxygen is contiguously bound to both the metal and boron. Upon availability of 2, a room temperature reaction was performed with [Fe(2)(CO)(9)], which led to the isolation of [(Cp*Ta)(2)B(2)H(4)O{H(2)Fe(2)(CO)(6)BH} ] 3. Compound 3 is an unusual heterometallic boride cluster in which the [Ta(2)Fe(2)] atoms define a butterfly framework with one boron atom lying in a semi-interstitial position. Likewise, the diselenamolybdaborane, [(Cp*Mo)(2)B(4)H(4)Se(2)], 4 was treated with an excess of [Fe(2)(CO)(9)] to afford the heterometallic boride cluster [(Cp*MoSe)(2)Fe(6)(CO)(13)B(2)(BH)(2)], 5. The cluster core of 5 consists of a cubane [Mo(2)Se(2)Fe(2)B(2)] and a tricapped trigonal prism [Fe(6)B(3)] fused together with four atoms held in common between the two subclusters. In the tricapped trigonal prism subunit, one of the boron atoms is completely encapsulated and bonded to six iron and two boron atoms. Compounds 2, 3, and 5 have been characterized by mass spectrometry, IR, (1)H, (11)B, (13)C NMR spectroscopy, and the geometric structures were unequivocally established by crystallographic analysis. The density functional theory calculations yielded geometries that are in close agreement with the observed structures. Furthermore, the calculated (11)B NMR chemical shifts also support the structural characterization of the compounds. Natural bond order analysis and Wiberg bond indices are used to gain insight into the bonding patterns of the observed geometries of 2, 3, and 5.

Staging ovaries of Haddock (Melanogrammus aeglefinus): implications for maturity indices and field sampling practices

We build on recent efforts to standardize maturation staging methods through the development of a field-proof macroscopic ovarian maturity index for Haddock (Melanogrammus aeglefinus) for studies on diel spawning periodicity. A comparison of field and histological observations helped us to improve the field index and methods, and provided useful insight into the reproductive biology of Haddock and other boreal determinate fecundity species. We found reasonable agreement between field and histological methods, except for the regressing and regenerating stages (however, differentiation of these 2 stages is the least important distinction for determination of maturity or reproductive dynamics). The staging of developing ovaries was problematic for both methods partly because of asynchronous oocyte hydration during the early stage of oocyte maturation. Although staging on the basis of histology in a laboratory is generally more accurate than macroscopic staging methods in the field, we found that field observations can uncover errors in laboratory staging that result from bias in sampling unrepresentative portions of ovaries. For 2 specimens, immature ovaries observed during histological examination were incorrectly assigned as regenerating during macroscopic staging. This type of error can lead to miscalculation of length at maturity and of spawning stock biomass, metrics that are used to characterize the state of a fish population. The revised field index includes 3 new macroscopic stages that represent final oocyte maturation in a batch of oocytes and were found to be reliable for staging spawning readiness in the field. The index was found to be suitable for studies of diel spawning periodicity and conforms to recent standardization guidelines.

Study on the internal reflection of the multimode-interference-type device

The internal reflection of the multimode-interference (MMI)-type device is calculated with the bidirectional beam propagation method. The calculated results indicate that the difference of the effective refractive indices between the core region and the surrounding region has a determining effect on the internal reflection of the MMI-type device. The output taper for the MMI-type combiner and splitter has a more evident effect on the internal reflection than the input taper. The internal reflection decreases with increasing the end width of the taper. For the MMI-type device with appropriate tapers, the internal reflection does not show evident degradation with the deviation of the length of the MMI region from its optimal value. (C) 2004 Society of Photo-Optical Instrumentation Engineers.

Determination of fractional energy loss of waves in nearshore waters using an improved high-order Boussinesq-type model

Fractional energy losses of waves due to wave breaking when passing over a submerged bar are studied systematically using a modified numerical code that is based on the high-order Boussinesq-type equations. The model is first tested by the additional experimental data, and the model's capability of simulating the wave transformation over both gentle slope and steep slope is demonstrated. Then, the model's breaking index is replaced and tested. The new breaking index, which is optimized from the several breaking indices, is not sensitive to the spatial grid length and includes the bottom slopes. Numerical tests show that the modified model with the new breaking index is more stable and efficient for the shallow-water wave breaking. Finally, the modified model is used to study the fractional energy losses for the regular waves propagating and breaking over a submerged bar. Our results have revealed that how the nonlinearity and the dispersion of the incident waves as well as the dimensionless bar height (normalized by water depth) dominate the fractional energy losses. It is also found that the bar slope (limited to gentle slopes that less than 1:10) and the dimensionless bar length (normalized by incident wave length) have negligible effects on the fractional energy losses.

Glycosylation of low density lipoprotein in patients with type 1 (insulin-dependent) diabetes:correlations with other parameters of glycaemic control

Glycosylation of low density lipoproteins obtained from 16 patients with Type 1 (insulin-dependent) diabetes and from 16 age-, sex-, and race-matched controls, was determined. The diabetic patients were normolipaemic and were in good or fair glycaemic control. Eleven patients performed home blood glucose monitoring. Glycosylation of low density lipoproteins in the diabetic patients was significantly higher (p less than 0.001) than in the control subjects, and was significantly correlated with haemoglobin A1c, (p less than 0.01), glycosylation of plasma proteins, (p less than 0.001), and mean home blood glucose, (p less than 0.01). This study confirms that, in diabetic patients, increased glycosylation of low density lipoprotein occurs to an extent which correlates closely with other commonly used indices of glycaemic control.

Clinical correlates of serum pigment epithelium-derived factor in type 2 diabetes patients

Aim: To determine if serum pigment epithelium-derived factor (PEDF) levels in Type 2 diabetes are related to vascular risk factors and renal function. Methods: PEDF was quantified by ELISA in a cross-sectional study of 857 male Veterans Affairs Diabetes Trial (VADT) subjects, and associations with cardiovascular risk factors and renal function were determined. In a subset (n = 246) in whom serum was obtained early in the VADT (2.0 ± 0.3 years post-randomization), PEDF was related to longitudinal changes in renal function over 3.1 years. Results: Cross-sectional study: In multivariate regression models, PEDF was positively associated with serum triglycerides, waist-to-hip ratio, serum creatinine, use of ACE inhibitors or angiotensin receptor blockers, and use of lipid-lowering agents; it was negatively associated with HDL-C (all p < 0.05). Longitudinal study: PEDF was not associated with changes in renal function over 3.1 years (p > 0.09). Conclusions: Serum PEDF in Type 2 diabetic men was cross-sectionally associated with dyslipidemia, body habitus, use of common drugs for blood pressure and dyslipidemia, and indices of renal function; however, PEDF was not associated with renal decline over 3.1 years.