Periodic points of algebraic functions and Deuring’s class number formula

The Ramanujan Journal - In this paper, transformation formulas for the function $$\begin{aligned} A_{1}\left( z,s:\chi \right) =\sum \limits _{n=1}^{\infty }\sum \limits _{m=1} ^{\infty }\chi...     

Micromixing models for turbulent flows

In transported probability density function and filtered density function methods, micromixing models are required to close the molecular mixing term. The accuracy and computational efficiency of improved versions of the parameterized scalar profile (PSP) model are assessed and compared with commonly used mixing models such as Curl, modified Curl, interaction by exchange with the mean and Euclidean minimum spanning tree. Different generalizations of the PSP mixing model for spatially inhomogeneous flow configurations are presented. The selected test cases focus on molecular mixing and avoid interference with other models. Simulation results for a three-stream problem, involving two inert scalars, and a multi-scalar test case with mean-scalar-gradients are presented.     

An economic¯X-chart approach to the joint control of the means of independent quality characteristics

Summary In controlling the mean of a multivariate normally distributed quality characteristic the main disadvantage of the globalT ²-control charts is that they don't indicate the component of the quality characteristic which gives rise to an alarm. To avoid this disadvantage the joint use of¯x-charts is proposed in this paper, where — for the sake of simplicity — the investigations are restricted to the case of independent components and to one-sided¯x-charts. On the basis of an economic objective function an approximation to the optimal design of the¯x-charts procedure is derived and discussed. It turns out that at least in the bivariate case the nearly optimal economic design is very close to the exact solution.Supported by the Deutsche Forschungsgemeinschaft (DFG).     

Computing transitive closure of bipolar weighted digraphs

We define a bipolar weighted digraph as a weighted digraph together with the sign function on the arcs such that the weight of each arc lies between 0 and 1, and no two parallel arcs have the same sign. Bipolar weighted digraphs are utilized to model so-called fuzzy cognitive maps, which are used in science, engineering, and the social sciences to represent the causal structure of a body of knowledge. It has been noted in the literature that a transitive closure of a bipolar weighted digraph contains useful new information for the fuzzy cognitive map it models.In this paper we ask two questions: what is a sensible and useful definition of transitive closure of a bipolar weighted digraph, and how do we compute it? We give two answers to each of these questions, that is, we present two distinct models. First, we give a review of the fuzzy digraph model, which has been, in a different form and less rigorously, studied previously in the fuzzy systems literature. Second, we carefully develop a probabilistic model, which is related to the notion of network reliability.This paper is intended for a mathematical audience.     

On Dedekind Modules

In this article the authors give the relation between a finitely-generated torsionfree Dedekind module M over a domain R and prime submodules of the 𝒪(M)-module M and the ring 𝒪(M). They also prove that M is a finitely-generated torsionfree Dedekind module over a domain R if and only if every semi-maximal submodule of R-module M is invertible.     

Measurement and characterization of the human spinal cord SEEP response using event-related spinal fMRI

Although event-related fMRI is able to reliably detect brief changes in brain activity and is now widely used throughout systems and cognitive neuroscience, there have been no previous reports of event-related spinal cord fMRI. This is likely attributable to the various technical challenges associated with spinal fMRI (e.g., imaging a suitable length of the cord, reducing image artifacts from the vertebrae and intervertebral discs, and dealing with physiological noise from spinal cord motion). However, with many of these issues now resolved, the largest remaining impediment for event-related spinal fMRI is a deprived understanding of the spinal cord fMRI signal time course. Therefore, in this study, we used a proton density-weighted HASTE sequence, with functional contrast based on signal enhancement by extravascular water protons (SEEP), and a motion-compensating GLM analysis to (i) characterize the SEEP response function in the human cervical spinal cord and (ii) demonstrate the feasibility of event-related spinal fMRI. This was achieved by applying very brief (1 s) epochs of 22°C thermal stimulation to the palm of the hand and measuring the impulse response function. Our results suggest that the spinal cord SEEP response (time to peak ≈8 s; FWHM ≈4 s; and probably lacking pre- and poststimulus undershoots) is slower than previous estimates of SEEP or BOLD responses in the brain, but faster than previously reported spinal cord BOLD responses. Finally, by detecting and mapping consistent signal-intensity changes within and across subjects, and validating these regions with a block-designed experiment, this study represents the first successful demonstration of event-related spinal fMRI.     

Development and validation of an ultra‐high‐performance liquid chromatography–tandem mass spectrometry method to determine the bioavailability of warfarin and its major metabolite 7‐hydroxy warfarin in rats dosed with oral formulations containing different polymorphic forms

A simple, sensitive and rapid ultra‐high‐performance liquid chromatography–electrospray ionization–tandem mass spectrometry method was developed and validated for the quantification of warfarin and 7‐hydroxy warfarin in Sprague Dawley (SD) rats. Animals were administered a single dose of warfarin sodium formulations (crystalline and amorphous) at 12 mg/kg via oral gavage and blood was drawn over a 96‐h time course. Sample process recoveries, matrix effect and analyte stability were determined. The linearity for warfarin and 7‐hydroxy warfarin was from 5 to 2000 ng/mL in blank SD rat plasma. Correlation coefficients (r²) for standard calibration curves were >.98 and analytes quantified within ±15% of target at all calibrator concentrations. The average percent accuracy and precision for intra‐ and inter‐day were 93.7%–113.8% and ≤12.1%, respectively, for warfarin and 7‐hydroxy warfarin, across the quality control standards (5, 10, 500, 1800 and 2000 ng/mL). Acceptable analytical recovery (>55%) was achieved with process efficiencies >41.5% and matrix effects <139.9% over the analytical range. Both analytes were stable in stock solution, autosampler, benchtop and three cycles of freeze–thaw with percent accuracy ≥90.2% and precision (percent relative standard deviation) ≤14%. The validated method was successfully applied to a pre‐clinical bioavailability study of crystalline and amorphous warfarin sodium formulations in SD rats.     

Cooperative Effect of Noncovalent Interactions on Tetrel Bonding in Halogenated Silanes

Tetrel bond, a weak noncovalent interaction between the σ-hole of a Group IV element (silicon in our case) and the cloud of an electronegative element (oxygen in our case) is the focus of this work. The percentage strengthening of tetrel bond has been investigated by optimizing 16 binary complexes of halogenated silane and water of general formula SiX_nH_4−n−H₂O and 16 ternary complexes, of general formula NaX−SiX_nH_4−n−H₂O, where X=F, Cl, Br and I and n=1, 2, 3 and 4 at various levels of theory defined within the formalism of density functional theory (DFT). With the addition of NaX, tetrel bond between Si and O in SiX_nH_4−n−H₂O gets strengthened up to 49 %, owing to cooperativity effect exerted by hydrogen bonding between X and H in the ternary complex NaX−SiX_nH_4−n−H₂O. In the series of complexes studied here, overall stabilization due to cooperativity lies between 10 kJ/mol to 170 kJ/mol. This large extent of reinforcement due to cooperativity has never been showcased before. The exceptional stabilization and reinforcement owe its genesis to the transformation of the ternary complex into a cluster orchestrated by the H-bonding in most of the cases and covalent bonding in few of the cases.     

A Chimeric DNA/RNA Antiparallel Quadruplex with Improved Stability

Nucleic acid quadruplexes are proposed to play a role in the regulation of gene expression, are often present in aptamers selected for specific binding functions and have potential applications in medicine and biotechnology. Therefore, understanding their structure and thermodynamic properties and designing highly stable quadruplexes is desirable for a variety of applications. Here, we evaluate DNA→RNA substitutions in the context of a monomolecular, antiparallel quadruplex, the thrombin-binding aptamer (TBA, GGTTGGTGTGGTTGG) in the presence of either K⁺ or Sr²⁺. TBA predominantly folds into a chair-type configuration containing two G-tetrads, with G residues in both syn and anti conformation. All chimeras with DNA→RNA substitutions (G→g) at G residues requiring the syn conformation demonstrated strong destabilization. In contrast, G→g substitutions at Gs with anti conformation increased stability without affecting the monomolecular chair-type topology. None of the DNA→RNA substitutions in loop positions affected the quadruplex topology; however, these substitutions varied widely in their stabilizing or destabilizing effects in an unpredictable manner. This analysis allowed us to design a chimeric DNA/RNA TBA construct that demonstrated substantially improved stability relative to the all-DNA construct. These results have implications for a variety of quadruplex-based applications including for the design of dynamic nanomachines.