A refinement of the gauss-lucas theorem

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.

Dynamics, rheology and critical properties of colloidal fluid mixtures

Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.

Optimization of the AZO dyes decoloration process through neural networks: Determination of the H2O2 addition critical point

The concentration of hydrogen peroxide is an important parameter in the azo dyes decoloration process through the utilization of advanced oxidizing processes, particularly by oxidizing via UV/H2O2. It is pointed out that, from a specific concentration, the hydrogen peroxide works as a hydroxyl radical self-consumer and thus a decrease of the system`s oxidizing power happens. The determination of the process critical point (maximum amount of hydrogen peroxide to be added) was performed through a ""thorough mapping"" or discretization of the target region, founded on the maximization of an objective function objective (constant of reaction kinetics of pseudo-first order). The discretization of the operational region occurred through a feedforward backpropagation neural model. The neural model obtained presented remarkable coefficient of correlation between real and predicted values for the absorbance variable, above 0.98. In the present work, the neural model had, as phenomenological basis the Acid Brown 75 dye decoloration process. The hydrogen peroxide addition critical point, represented by a value of mass relation (F) between the hydrogen peroxide mass and the dye mass, was established in the interval 50 < F < 60. (C) 2007 Elsevier B.V. All rights reserved.

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization.

The liquid-liquid critical point scenario of water hypothesizes the existence of two metastable liq- uid phases low-density liquid (LDL) and high-density liquid (HDL) deep within the supercooled region. The hypothesis originates from computer simulations of the ST2 water model, but the stabil- ity of the LDL phase with respect to the crystal is still being debated. We simulate supercooled ST2 water at constant pressure, constant temperature, and constant number of molecules N for N ≤ 729 and times up to 1 μs. We observe clear differences between the two liquids, both structural and dynamical. Using several methods, including finite-size scaling, we confirm the presence of a liquid-liquid phase transition ending in a critical point. We find that the LDL is stable with respect to the crystal in 98% of our runs (we perform 372 runs for LDL or LDL-like states), and in 100% of our runs for the two largest system sizes (N = 512 and 729, for which we perform 136 runs for LDL or LDL-like states). In all these runs, tiny crystallites grow and then melt within 1 μs. Only for N ≤ 343 we observe six events (over 236 runs for LDL or LDL-like states) of spontaneous crystal- lization after crystallites reach an estimated critical size of about 70 ± 10 molecules.

Vendor Managed Inventory: the Critical Success Factors from the Manufacturer Point of View

Yritykset ovat pakotettuja erilaisiin yhteistyömuotoihin pärjätäkseen kiristyvässä kilpailussa. Yhteistyösuhteet kulkevat eri nimillä riippuen teollisuuden alasta ja siitä, missä kohtaa toimitusketjua ne toteutuvat, mutta periaatteessa kaikki pohjautuvat samaan ideaan kuin Vendor Managed Inventory (VMI); varastoon jakysyntään liittyvä tieto jaetaan toimitusketjun eri osapuolien kesken, jotta tuotanto, jakelu ja varastonhallinta olisi mahdollista optimoida. Vendor Managed Inventory on ideana yksinkertainen, mutta vaatii onnistuakseen paljon. Perusolettamus on, että toimittajan on kyettävä hallinnoimaan asiakkaan varastoa paremmin kuin asiakas itse. Tämä ei kuitenkaan ole mahdollista ilman riittävää yhteistyötä, oikeanlaista informaatiota tai sopivia tuoteominaisuuksia. Tämän työn tarkoitus on esitellä kriittiset menestystekijät valmistajan kannalta, kun näkyvyys todelliseen kysyntään on heikko ja kyseessäolevat tuotteet ovat ominaisuuksiltaan toimintamalliin huonosti soveltuvia. VMItoimintamallin soveltuvuus matkapuhelimia valmistavan yrityksen liiketoimintaan, sekä sen vaikutus asiakasyhteistyöhön, kannattavuuteen ja toiminnan tehostamiseen on myös tutkittu.

Glycogen synthase kinase 3 (GSK3) in the heart: a point of integration in hypertrophic signalling and a therapeutic target? A critical analysis

Glycogen synthase kinase 3 (GSK3, of which there are two isoforms, GSK3alpha and GSK3beta) was originally characterized in the context of regulation of glycogen metabolism, though it is now known to regulate many other cellular processes. Phosphorylation of GSK3alpha(Ser21) and GSK3beta(Ser9) inhibits their activity. In the heart, emphasis has been placed particularly on GSK3beta, rather than GSK3alpha. Importantly, catalytically-active GSK3 generally restrains gene expression and, in the heart, catalytically-active GSK3 has been implicated in anti-hypertrophic signalling. Inhibition of GSK3 results in changes in the activities of transcription and translation factors in the heart and promotes hypertrophic responses, and it is generally assumed that signal transduction from hypertrophic stimuli to GSK3 passes primarily through protein kinase B/Akt (PKB/Akt). However, recent data suggest that the situation is far more complex. We review evidence pertaining to the role of GSK3 in the myocardium and discuss effects of genetic manipulation of GSK3 activity in vivo. We also discuss the signalling pathways potentially regulating GSK3 activity and propose that, depending on the stimulus, phosphorylation of GSK3 is independent of PKB/Akt. Potential GSK3 substrates studied in relation to myocardial hypertrophy include nuclear factors of activated T cells, beta-catenin, GATA4, myocardin, CREB, and eukaryotic initiation factor 2Bvarepsilon. These and other transcription factor substrates putatively important in the heart are considered. We discuss whether cardiac pathologies could be treated by therapeutic intervention at the GSK3 level but conclude that any intervention would be premature without greater understanding of the precise role of GSK3 in cardiac processes.

Influence of super-ohmic dissipation on a disordered quantum critical point

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

Parameterized fast decoupled power flow methods for obtaining the maximum loading point of power systems. Part I. Mathematical modeling

The conventional Newton and fast decoupled power flow (FDPF) methods have been considered inadequate to obtain the maximum loading point of power systems due to ill-conditioning problems at and near this critical point. It is well known that the PV and Q-theta decoupling assumptions of the fast decoupled power flow formulation no longer hold in the vicinity of the critical point. Moreover, the Jacobian matrix of the Newton method becomes singular at this point. However, the maximum loading point can be efficiently computed through parameterization techniques of continuation methods. In this paper it is shown that by using either theta or V as a parameter, the new fast decoupled power flow versions (XB and BX) become adequate for the computation of the maximum loading point only with a few small modifications. The possible use of reactive power injection in a selected PV bus (Q(PV)) as continuation parameter (mu) for the computation of the maximum loading point is also shown. A trivial secant predictor, the modified zero-order polynomial which uses the current solution and a fixed increment in the parameter (V, theta, or mu) as an estimate for the next solution, is used in predictor step. These new versions are compared to each other with the purpose of pointing out their features, as well as the influence of reactive power and transformer tap limits. The results obtained with the new approach for the IEEE test systems (14, 30, 57 and 118 buses) are presented and discussed in the companion paper. The results show that the characteristics of the conventional method are enhanced and the region of convergence around the singular solution is enlarged. In addition, it is shown that parameters can be switched during the tracing process in order to efficiently determine all the PV curve points with few iterations. (C) 2003 Elsevier B.V. All rights reserved.

NONLINEAR DIFFUSION PROCESS IN A BENARD SYSTEM AT THE CRITICAL-POINT FOR THE ONSET OF CONVECTION

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts.

Comparison of hexamethyidisilazane and critical point drying treatments for SEM analysis of anaerobic biofilms and granular sludge

We present a fast procedure for scanning electron microscopy (SEM) analysis in which hexamethyldisilazane (HMDS) solvent, instead of the critical point drying, is used to remove liquids from a microbiological specimen. The results indicate that the HMDS solvent is suitable for drying samples of anaerobic cells for examination by SEM and does not cause cell structure disruption.

On the number of critical periods for planar polynomial systems

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree l with at least 2[(l - 2)/2] critical periods as well as study concrete families of potential, reversible and Lienard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not. increases with the order of the perturbation. (C) 2007 Elsevier Ltd. All rights reserved.

Rounding of a first-order quantum phase transition to a strong-coupling critical point

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the N-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong-coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail and find stronger thermodynamic singularities than in the random transverse field Ising chain. We also discuss the implications for higher spatial dimensions as well as unusual aspects of our renormalization-group scheme. DOI: 10.1103/PhysRevB.86.214204

Tirosh lo Yayin : or, The wine question considered in an entirely novel point of view ; with a scheme of Hebrew wines, and illustrations (philosophical and critical) of the principle passages of the Bible connected with the subject.

Includes index.