A Survey in Mean Value Theorems

A variety of new mean value theorems are presented along with interesting proofs and generalizations of the standard theorems. Three proofs are given for the ordinary Mean Value Theorem for derivatives, the third of which is interesting in that it is independent of of Rolle\u27s Theorem. The Second Mean Value Theorem for derivatives is generalized, with the use of determinants, to three functions and also generalized in terms of nth order derivatives. Observing that under certain conditions the tangent line to the curve of a differentiable function passes through the initial point, we find a new type of mean value theorem for derivatives. This theorem is extended to two functions and later in the paper an integral analog is given together with integral mean value theorems. Many new mean value theorems are presented in their respective settings including theorems for the total variation of a function, the arc length of the graph of a function, and for vector-valued functions. A mean value theorem in the complex plane is given in which the difference quotient is equal to a linear combination of the values of the derivative. Using a regular derivative, the ordinary Mean Value Theorem for derivatives is extended into Rn, n\u3e1

On the information content of incubation studies

The measurement of the production of CO2 from soils in incubation studies has been used for many years to gain information about the influence of different soils types, changing temperatures and water contents, as well as the addition of amendments on the soil respiration. While in the early years the kinetic modelling (or fitting) was restricted to the single or one pool model due to the possibility of solving the problem by log-transforming the observed data an using a linear regression for the estimation of the rate constant (by doing so an analytical solution can be applied), more recent publications chose multi-pool models (2, 3, and even 4-pools), which can will be fitted iteratively using appropriate computer software. In general, there are different methods used in literature to estimate the kinetic parameters resulting in different kinetic parameter values even for the same data set. Additionally, screening of existing literature revealed that the 2-pool model (or even higher pool models) were sometimes obviously wrong fitted or over fitted. In our presentation, we will show how different constrains in the fitting process will influence the results of the kinetic parameter values, how obviously wrong fitting and overfitting can be easily detected, and how the information content of the incubation data can be easily judged prior any fitting. Finally, we will provide recommendations how to extract information from incubation experiments

Challenges in using mid-infrared spectroscopy for the determination of soil physical, chemical, and biochemical properties on undisturbed soil samples

Diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy in the mid-infrared range (MIR) has become an established analytical tool for quantitative and qualitative analysis of soil samples. The heterogeneity of soil requires sample preparation procedures to optimize the reproducibility and accuracy of the spectroscopic measurement. These procedures have not been standardized. Generally, soil is dried and ground before measurement to avoid reflections of surface water films and minimize the intra- and inter-particle variability, respectively. Additionally, the sample surface is levelled to a plain surface for an ideal reflection. These sample preparation techniques are limited to disturbed samples only. Thus, a potential DRIFT mapping of undisturbed soil samples requires an adjusted calibration to allow for an accurate prediction of soil properties. In this study, we developed a method for calibrating the prediction of DRIFT spectra collected from undisturbed soil samples. In a first step, differences of spectral information measured from undisturbed and ground soil samples have been evaluated. Therefore, we record the DRIFT spectra of 120 German and 120 West-African chemically well characterized soils. DRIFT spectra of both, ground and sieved only soil samples are recorded and both calibrated against different physio-chemical soil properties, such as texture, CEC, organic carbon, pH, or iron oxides. In preliminary experiments, we found that spectra of sieved and ground samples significantly differed in specific spectral regions representing clay minerals, as well as organic matter. It can be assumed that the prediction of surface related soil parameters could be superior using sieved soil spectra, as grounding alters the surface structure of the soil. In a further step, microtopgraphy effects on spectra quality from disturbed and undisturbed soil samples have been evaluated. Therefore, spectral information has been taken from two dimensional disturbed and undisturbed soil samples at a high spatial resolution. The spectra quality was significantly higher in the disturbed soils since microtopography was absent in these samples. Thus, a digital elevation model (DEM) will be constructed using close-range digital photogrammetry to correct these topography effects. With this new method, there is a potential of imaging soil parameters on a microscale that can help considerably in locating and understanding soil processes on a small scale

Riociguat for the treatment of chronic thromboembolic pulmonary hypertension.

BACKGROUND: Riociguat, a member of a new class of compounds (soluble guanylate cyclase stimulators), has been shown in previous clinical studies to be beneficial in the treatment of chronic thromboembolic pulmonary hypertension. METHODS: In this phase 3, multicenter, randomized, double-blind, placebo-controlled study, we randomly assigned 261 patients with inoperable chronic thromboembolic pulmonary hypertension or persistent or recurrent pulmonary hypertension after pulmonary endarterectomy to receive placebo or riociguat. The primary end point was the change from baseline to the end of week 16 in the distance walked in 6 minutes. Secondary end points included changes from baseline in pulmonary vascular resistance, N-terminal pro-brain natriuretic peptide (NT-proBNP) level, World Health Organization (WHO) functional class, time to clinical worsening, Borg dyspnea score, quality-of-life variables, and safety. RESULTS: By week 16, the 6-minute walk distance had increased by a mean of 39 m in the riociguat group, as compared with a mean decrease of 6 m in the placebo group (least-squares mean difference, 46 m; 95% confidence interval [CI], 25 to 67; P<0.001). Pulmonary vascular resistance decreased by 226 dyn · sec · cm-5in the riociguat group and increased by 23 dyn · sec · cm-5in the placebo group (least-squares mean difference, -246 dyn · sec · cm-5; 95% CI, -303 to -190; P<0.001). Riociguat was also associated with significant improvements in the NT-proBNP level (P<0.001) and WHO functional class (P = 0.003). The most common serious adverse events were right ventricular failure (in 3% of patients in each group) and syncope (in 2% of the riociguat group and in 3% of the placebo group). CONCLUSIONS: Riociguat significantly improved exercise capacity and pulmonary vascular resistance in patients with chronic thromboembolic pulmonary hypertension. (Funded by Bayer HealthCare; CHEST-1 and CHEST-2 ClinicalTrials.gov numbers, NCT00855465 and NCT00910429, respectively.) Copyright © 2013 Massachusetts Medical Society

Micromechanical properties and structural characterization of modern inarticulated brachiopod shells

[1] We investigated micromechanical properties and ultrastructure ofthe shells of the modern brachiopod species Lingula anatina, Disciniscalaevis, and Discradisca stella with scanning electron microscopy (SEM,EDX), transmission electron microscopy (TEM) and Vickers microhardnessindentation analyses. The shells are composed of two distinct layers, anouter primary layer and an inner secondary layer. Except for the primarylayer in Lingula anatina, which is composed entirely of organic matter,all other shell layers are laminated organic/inorganic composites. Theorganic matter is built of chitin fibers, which provide the matrix forthe incorporation of calcium phosphate. Amorphous calcium phosphate inthe outer, primary layer and crystalline apatite is deposited into theinner, secondary layer of the shell. Apatite crystallite sizes in theumbonal region of the shell are about 50 x 50 nm, while within thevalves crystallite sizes are significantly smaller, averanging 10 x 25nm. There is great variation in hardness values between shell layers andbetween the investigated brachiopod species. The microhardness of theinvestigated shells is significantly lower than that of inorganichydroxyapatite. This is caused by the predominantly organic materialcomponent that in these shells is either developed as purely organiclayers or as an organic fibrous matrix reinforced by crystallites. Ourresults show that this particular fiber composite material is veryefficient for the protection and the support of the soft animal tissue.It lowers the probability of crack formation and effectively impedescrack propagation perpendicular to the shell by crack-deviationmechanisms. The high degree of mechanical stability and toughness isachieved by two design features. First, there is the fiber compositematerial which overcomes some detrimental and enhances some advantageousproperties of the single constituents, that is the softness andflexibility of chitin and the hardness and brittleness of apatite.Second, there is a hierarchical structuring from the nanometer to amicrometer level. We could identify at least seven levels of hierarchywithin the shells

In cis TP53 and RAD51C pathogenic variants may predispose to sebaceous gland carcinomas

Pathogenic variants in TP53 have been classically thought to cause Li-Fraumeni syndrome (LFS), a cancer predisposition with high risks for various childhood- and adult-onset malignancies. However, increased genetic testing has lately revealed, that pathogenic variant carriers exhibit a broader range of phenotypes and that penetrance may be dependent both on variant type and modifiers. Using next generation sequencing and short tandem repeat analysis, we identified germline pathogenic variants in TP53 and RAD51C located in cis on chromosome 17 in a 43-year-old male, who has developed a rare sebaceous gland carcinoma (SGC) but so far no tumors of the LFS spectrum. This course mirrors a Trp53-Rad51c-double-mutant cis mouse-model, which similarly develops SGC, while the characteristic Trp53-associated tumor spectrum occurs with significantly lower frequency. Therefore, we propose that co-occurent pathogenic variants in RAD51C and TP53 may predispose to SGC, reminiscent of Muir-Torre syndrome. Further, this report supports the diversity of clinical presentations associated with germline TP53 alterations, and thus, the proposed expansion of LFS to heritable TP53-related cancer syndrome

A unique coral biomineralization pattern has resisted 40 million years of major ocean chemistry change

Today coral reefs are threatened by changes to seawater conditions associated with rapid anthropogenic global climate change. Yet, since the Cenozoic, these organisms have experienced major fluctuations in atmospheric CO2 levels (from greenhouse conditions of high pCO2 in the Eocene to low pCO2 ice-house conditions in the Oligocene-Miocene) and a dramatically changing ocean Mg/Ca ratio. Here we show that the most diverse, widespread, and abundant reef-building coral genus Acropora (20 morphological groups and 150 living species) has not only survived these environmental changes, but has maintained its distinct skeletal biomineralization pattern for at least 40 My: Well-preserved fossil Acropora skeletons from the Eocene, Oligocene, and Miocene show ultra-structures indistinguishable from those of extant representatives of the genus and their aragonitic skeleton Mg/Ca ratios trace the inferred ocean Mg/Ca ratio precisely since the Eocene. Therefore, among marine biogenic carbonate fossils, well-preserved acroporid skeletons represent material with very high potential for reconstruction of ancient ocean chemistry

Testing the preservation potential of early diagenetic dolomites as geochemical archives

Early marine diagenetic dolomite is a rather thermodynamically‐stable carbonate phase and has potential to act as an archive of marine porewater properties. However, the variety of early to late diagenetic dolomite phases that can coexist within a single sample can result in extensive complexity. Here, the archive potential of early marine dolomites exposed to extreme post‐depositional processes is tested using various types of analyses, including: petrography, fluid inclusion data, stable δ13C and δ18O isotopes, 87Sr/86Sr ratios, and U‐Pb age dating of various dolomite phases. In this example, a Triassic carbonate platform was dissected and overprinted (diagenetic temperatures of 50 to 430°C) in a strike‐slip zone in Southern Spain. Eight episodes of dolomitization, a dolostone cataclasite and late stage meteoric/vadose cementation were recognized. The following processes were found to be diagenetically relevant: (i) protolith deposition and fabric‐preservation, and marine dolomitization of precursor aragonite and calcite during the Middle–Late Triassic; (ii) intermediate burial and formation of zebra saddle dolomite and precipitation of various dolomite cements in a Proto‐Atlantic opening stress regime (T ca 250°C) during the Early–Middle Jurassic; (iii) dolomite cement precipitation during early Alpine tectonism, rapid burial to ca 15 km, and high‐grade anchizone overprint during Alpine tectonic evolution in the Early Eocene to Early Miocene; (iv) brecciation of dolostones to cataclasite during the onset of the Carboneras Fault Zone activity during the Middle Miocene; and (v) late‐stage regression and subsequent meteoric overprint. Data shown here document that, under favourable conditions, early diagenetic marine dolomites and their archive data may resist petrographic and geochemical resetting over time intervals of 108 or more years. Evidence for this preservation includes preserved Late Triassic seawater δ13CDIC values and primary fluid inclusion data. Data also indicate that oversimplified statements based on bulk data from other petrographically‐complex dolomite archives must be considered with caution