The set of lagrange and routh formulations for non-linear networks

Formulations of systems of Lagrange and Routh equations for arbitrary non-linear electrical circuits are given. the use of Routh equations for this purpose is new. It is proved that these formulations are equivalent to the complete system of Kirchhoff equations (instead of only a part of it as in prior works). the vector of generalized coordinates for the system of Lagrange equations consists of four subvectors (loop charges for fundamental loops, cut-set fluxes for fundamental cut-sets, branch fluxes for voltage and flux controlled elements and branch charges for current and charge controlled elements). For the defined set of Lagrange formulations, the uniqueness of a parametric representation is proved. the structure of the Lagrange (Hamilton, Routh) formulation set is then studied and it is proved that this set is an Abelian group. A duality of Lagrange triples for electrically and topologically dual circuits is established and it is proved that this relation between the sets of Lagrange triples is an isomorphism. It is also shown that the Brayton-Moser equations and the anti-Lagrangian equations similar to those of M. Mili? and L. Novak represent partial cases of the formulated set.     

Analysis of the classical pseudo-3D model for hydraulic fracture with equilibrium height growth across stress barriers

This paper deals with the so-called “pseudo three-dimensional” (P3D) model for a hydraulic fracture with equilibrium height growth across two symmetric stress barriers. The key simplifying assumptions behind the P3D model are that (i) each cross section perpendicular to the main propagation direction is in a condition of plane-strain, and (ii) the local fracture height is determined by a balance between the effect of the stress jump across the barriers and that of the rock toughness. Furthermore, in the equilibrium height growth P3D models, the pressure is assumed to be uniform in each vertical cross-section. We revisit this particular model by first formulating the non-linear differential equations governing the evolution of the length, height, and aperture of the hydraulic fracture, in contrast to the numerical formulations adopted in many previous studies. Scaling of these equations shows that the solution depends, besides the dimensionless space and time coordinates, on only two numbers representing a scaled toughness and a scaled leak-off coefficient. Analysis of the governing equations enables us to determine explicitly the conditions under which breakthrough takes place (i.e., the onset of growth into the bounding layers), as well as the conditions of unstable height growth (i.e., the conditions of “runaway height” when the main assumptions of the equilibrium height model become invalid). The mathematical model is solved numerically using a novel implicit fourth order collocation scheme on a moving mesh, which makes explicit use of the fracture tip asymptotics. We then report the results of several numerical simulations conducted for different values of the dimensionless toughness and the dimensionless leak-off coefficients, as well as a comparison with closed-form small and large time similarity solutions that are valid under conditions where the fracture remains contained within the reservoir layer.     

Gender stereotypes and superior conformity of the self in a sample of cyclists

In the field of driving, people tend to think they are more competent and more cautious than others. This is the superior conformity of the self (SCS). Our main hypothesis was that, among cyclists, women would show a higher SCS on cautiousness, though men would show a higher SCS concerning competence. 1799 cyclists provided a self-assessment of their own cautiousness and of other people's cautiousness. The same procedure was used for competence. Consistent with the hypothesis, the SCS was gender-specific: it was more prominent for women concerning cautiousness and more prominent for men concerning competence. These results could explain why people tend to ignore the safety campaigns. They also indicate the importance of adapting messages concerning safety measures to gender.     

Adaptive controller design and disturbance attenuation for SISO linear systems with zero relative degree under noisy output measurements

In this paper, we present robust adaptive controller design for SISO linear systems with zero relative degree under noisy output measurements. We formulate the robust adaptive control problem as a nonlinear H^∞‐optimal control problem under imperfect state measurements, and then solve it using game theory. By using the a priori knowledge of the parameter vector, we apply a soft projection algorithm, which guarantees the robustness property of the closed‐loop system without any persistency of excitation assumption of the reference signal. Owing to our formulation in state space, we allow the true system to be uncontrollable, as long as the uncontrollable part is stable in the sense of Lyapunov, and the uncontrollable modes on the jω‐axis are uncontrollable from the exogenous disturbance input. This assumption allows the adaptive controller to asymptotically cancel out, at the output, the effect of exogenous sinusoidal disturbance inputs with unknown magnitude, phase, and frequency. These strong robustness properties are illustrated by a numerical example. Copyright © 2009 John Wiley & Sons, Ltd.     

Determination of absorption coefficients for chlorophyll a,phycocyanin, mineral matter and CDOM from three central Indiana reservoirs

Absorption coefficients are used in semi-empirical and bio-optical models to estimate various optically active constituents in water. This study determines the mass-specific absorption coefficients of chlorophyll a (a*_chl), phycocyanin (a*_pc), minerals (a*_m), and chromophoric dissolved organic matter (CDOM; a*_CDOM) and the absorption coefficient for CDOM (a_CDOM) for three central Indiana reservoirs. Absorption spectra were collected using a Shimadzu spectrophotometer equipped with a Spectralon coated integrating sphere. Quantitative measurements from either fluorometric (chlorophyll a, phycocyanin, CDOM) or weight-based (mineral) measurements were used to determine the mass-specific absorption coefficients tested in this study and an exponential function was used to estimate a_CDOM. While a*_chl showed minimum variability between reservoirs, a*_pc, a*_m, a*_CDOM, and a_CDOM showed statistically significant differences between reservoirs; however, for a*_m, there was greater variation within each reservoir. Variability in a*_CDOM and a_CDOM between reservoirs was likely due to different inflows. All absorption coefficients fell within previously published ranges for each constituent examined, with the exception of a*_pc. Differences in a*_pc were likely due to different techniques used in extracting and estimating phycocyanin.     

Quantitative Insight into the Design of Compounds Recognized by the L‐Type Amino Acid Transporter 1 (LAT1)

L ‐Type amino acid transporter 1 (LAT1) is a transmembrane protein expressed abundantly at the blood–brain barrier (BBB), where it ensures the transport of hydrophobic acids from the blood to the brain. Due to its unique substrate specificity and high expression at the BBB, LAT1 is an intriguing target for carrier‐mediated transport of drugs into the brain. In this study, a comparative molecular field analysis (CoMFA) model with considerable statistical quality (Q²=0.53, R²=0.75, Q² SE=0.77, R² SE=0.57) and good external predictivity (CCC=0.91) was generated. The model was used to guide the synthesis of eight new prodrugs whose affinity for LAT1 was tested by using an in situ rat brain perfusion technique. This resulted in the creation of a novel LAT1 prodrug with L ‐tryptophan as the promoiety; it also provided a better understanding of the molecular features of LAT1‐targeted high‐affinity prodrugs, as well as their promoiety and parent drug. The results obtained will be beneficial in the rational design of novel LAT1‐binding prodrugs and other compounds that bind to LAT1.     

Discovery of a Cell-Active SuTEx Ligand of Prostaglandin Reductase 2

Sulfonyl-triazoles have emerged as a new reactive group for covalent modification of tyrosine sites on proteins through sulfur-triazole exchange (SuTEx) chemistry. The extent to which this sulfur electrophile can be tuned for developing ligands with cellular activity remains largely underexplored. Here, we performed fragment-based ligand discovery in live cells to identify SuTEx compounds capable of liganding tyrosine sites on diverse protein targets. We verified our quantitative chemical proteomic findings by demonstrating concentration-dependent activity of SuTEx ligands, but not inactive counterparts, against recombinant protein targets directly in live cells. Our structure-activity relationship studies identified the SuTEx ligand HHS-0701 as a cell-active inhibitor capable of blocking prostaglandin reductase 2 (PTGR2) biochemical activity.