Tables of complex hyperbolic and circular functions,

Bibliography: p. 209-212.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

Insight into the fractional calculus via a spreadsheet

Many students of calculus are not aware that the calculus they have learned is a special case (integer order) of fractional calculus. Fractional calculus is the study of arbitrary order derivatives and integrals and their applications. The article begins by stating a naive question from a student in a paper by Larson (1974) and establishes, for polynomials and exponential functions, that they can be deformed into their derivative using the μ-th order fractional derivatives for 0<μ<1. Through the power of Excel we illustrate the continuous deformations dynamically through conditional formatting. Some applications are discussed and a connection made to mathematics education.

Brownian dynamics simulation of dense binary colloidal mixtures. II. Translational and bond-orientational order

We report the Brownian dynamics simulation results on the translational and bond-angle-orientational correlations for charged colloidal binary suspensions as the interparticle interactions are increased to form a crystalline (for a volume fraction phi = 0.2) or a glassy (phi = 0.3) state. The translational order is quantified in terms of the two- and four-point density autocorrelation functions whose comparisons show that there is no growing correlation length near the glass transition. The nearest-neighbor orientational order is determined in terms of the quadratic rotational invariant Q(l) and the bond-orientational correlation functions g(l)(t). The l dependence of Q(l) indicates that icosahedral (l = 6) order predominates at the cost of the cubic order (l = 4) near the glass as well as the crystal transition. The density and orientational correlation functions for a supercooled liquid freezing towards a glass fit well to the streched-exponential form exp[-(t/tau)(beta)]. The average relaxation times extracted from the fitted stretched-exponential functions as a function of effective temperatures T* obey the Arrhenius law for liquids freezing to a crystal whereas these obey the Vogel-Tamman-Fulcher law exp[AT(0)*/(T* - T-0*)] for supercooled Liquids tending towards a glassy state. The value of the parameter A suggests that the colloidal suspensions are ''fragile'' glass formers like the organic and molecular liquids.

Dynamics of spontaneous emission from SiN with two-dimensional photonic crystals

We investigated the dynamics of spontaneous emission from a photonic crystal etched into a SiN slab. After fitting the decay curves of the emission to double exponential functions, we divided the dynamic process of the spontaneous emission into a fast process and a slow process. It was observed that the presence of the photonic crystal increased the proportion of the fast decay component, and consequently, the emission rate and time-integrated emission intensity were also enhanced. These enhancements were a result of the coupling of the guide modes to the leaky modes of the photonic crystal slab waveguide. (C) 2008 Optical Society of America.

A laboratory study of rheological properties of mudflows in Hangzhou Bay, China

A laboratory study of the rheology of mudflows in Hangzhou Bay, China, is reported in this paper. Both the steady and oscillatory (dynamic) rheological properties are studied using RMS-605 rheometer. A Dual-Bingham model is proposed for analyzing flow curves and compared with Worrall-Tuliani model. It is found that Dual-Bingham plastic rheological model is easier to implement than Worrall-Tuliani model and can provide satisfactory representations of the steady mudflows in Hangzhou Bay and other published data. The dependence of the yield stress and viscosity on sediment concentration is discussed based on the data from Hangzhou Bay mud and other published data. For the dynamic rheological properties of Hangzhou Bay mud, empirical expressions for elastic modulus and dynamic viscosity are provided in the form of exponential functions of sediment volume concentration, and comparisons with other published data also discussed.

Effects of temperature, glucose and inorganic nitrogen inputs on carbon mineralization in a Tibetan alpine meadow soil

High levels of available nitrogen (N) and carbon (C) have the potential to increase soil N and C mineralization We hypothesized that with an external labile C or N supply alpine meadow soil will have a significantly higher C mineralization potential and that temperature sensitivity of C mineralization will increase To test the hypotheses an incubation experiment was conducted with two doses of N or C supply at temperature of 5 15 and 25 C Results showed external N supply had no significant effect on CO2 emission However external C supply increased CO2 emission Temperature coefficient (Q(10)) ranged from 113 to 1 29 Significantly higher values were measured with C than with N addition and control treatment Temperature dependence of C mineralization was well-represented by exponential functions Under the control CO2 efflux rate was 425 g CO2-Cm-2 year(-1) comparable to the in situ measurement of 422 g CO2-Cm-2 year(-1) We demonstrated if N is disregarded microbial decomposition is primarily limited by lack of labile C It is predicted that labile C supply would further increase CO2 efflux from the alpine meadow soil (C) 2010 Elsevier Masson SAS All rights reserved

Earliness penalties on a single machine subject to precedence constraints: SLK due date assignment

The paper considers the single machine due date assignment and scheduling problems with n jobs in which the due dates are to be obtained from the processing times by adding a positive slack q. A schedule is feasible if there are no tardy jobs and the job sequence respects given precedence constraints. The value of q is chosen so as to minimize a function ϕ(F,q) which is non-decreasing in each of its arguments, where F is a certain non-decreasing earliness penalty function. Once q is chosen or fixed, the corresponding scheduling problem is to find a feasible schedule with the minimum value of function F. In the case of arbitrary precedence constraints the problems under consideration are shown to be NP-hard in the strong sense even for F being total earliness. If the precedence constraints are defined by a series-parallel graph, both scheduling and due date assignment problems are proved solvable in time, provided that F is either the sum of linear functions or the sum of exponential functions. The running time of the algorithms can be reduced to if the jobs are independent. Scope and purpose We consider the single machine due date assignment and scheduling problems and design fast algorithms for their solution under a wide range of assumptions. The problems under consideration arise in production planning when the management is faced with a problem of setting the realistic due dates for a number of orders. The due dates of the orders are determined by increasing the time needed for their fulfillment by a common positive slack. If the slack is set to be large enough, the due dates can be easily maintained, thereby producing a good image of the firm. This, however, may result in the substantial holding cost of the finished products before they are brought to the customer. The objective is to explore the trade-off between the size of the slack and the arising holding costs for the early orders.

Observação e controlo da segurança estrutural de barragens de betão: utilização integrada de modelos numéricos e de modelos de separação de efeitos

Dissertação de Natureza Científica elabora da no âmbito do protocolo de cooperação entre o ISEL e o LNEC para obtenção do grau de Mestre em Engenharia Civil

The effects of moisture, cation concentration, temperature, density and composition of soils on their electrical resistivity

The effects. of moisture, cation concentration, dens ity , temper~ t ure and grai n si ze on the electrical resistivity of so il s are examined using laboratory prepared soils. An i nexpen si ve method for preparing soils of different compositions was developed by mixing various size fractions i n the laboratory. Moisture and cation c oncentration are related to soil resistivity by powe r functions, whereas soil resistiv ity and temperature, density, Yo gravel, sand , sil t, and clay are related by exponential functions . A total of 1066 cases (8528 data) from all the experiments were used in a step-wise multiple linear r egression to determine the effect of each variable on soil resistivity. Six variables out of the eight variables studied account for 92.57/. of the total variance in so il resistivity with a correlation coefficient of 0.96. The other two variables (silt and gravel) did not increase the · variance. Moisture content was found to be - the most important Yo clay. variable- affecting s oil res istivi ty followed by These two variables account for 90.81Yo of the total variance in soil resistivity with a correlation ~oefficient ·.of 0 . 95. Based on these results an equation to ' ~~ed{ ct soil r esist ivi ty using moisture and Yo clay is developed . To t est the predicted equation, resistivity measurements were made on natural soils both in s i tu a nd i n the laboratory. The data show that field and laboratory measurements are comparable. The predicted regression line c losely coinciqes with resistivity data from area A and area B soils ~clayey and silty~clayey sands). Resistivity data and the predicted regression line in the case of c layey soils (clays> 40%) do not coincide, especially a t l ess than 15% moisture. The regression equation overestimates the resistivity of so i l s from area C and underestimates for area D soils. Laboratory prepared high clay soils give similar trends. The deviations are probably caused by heterogeneous distribution of mo i sture and difference in the type o f cl ays present in these soils.

Semi-dwarfing (Rht-B1b) improves nitrogen-use efficiency in wheat, but not at economically optimal levels of nitrogen availability

A UK field experiment compared a complete factorial combination of three backgrounds (cvs Mercia, Maris Huntsman and Maris Widgeon), three alleles at the Rht-B1 locus as Near Isogenic Lines (NILs: rht-B1a (tall), Rht-B1b (semi-dwarf), Rht-B1c (severe dwarf)) and four nitrogen (N) fertilizer application rates (0, 100, 200 and 350 kg N/ha). Linear+exponential functions were fitted to grain yield (GY) and nitrogen-use efficiency (NUE; GY/available N) responses to N rate. Averaged over N rate and background Rht-B1b conferred significantly (P<0.05) greater GY, NUE, N uptake efficiency (NUpE; N in above ground crop / available N) and N utilization efficiency (NUtEg; GY / N in above ground crop) compared with rht-B1a and Rht-B1c. However the economically optimal N rate (Nopt) for N:grain price ratios of 3.5:1 to 10:1 were also greater for Rht-B1b, and because NUE, NUpE and NUtE all declined with N rate, Rht-Blb failed to increase NUE or its components at Nopt. The adoption of semi-dwarf lines in temperate and humid regions, and the greater N rates that such adoption justifies economically, greatly increases land-use efficiency, but not necessarily, NUE.

Uma proposta alternativa para o ensino progressões relacionadas a funções

Generally, arithmetic and geometric progressions are taught separately from ane and exponential functions, only by the use of memorized formulas and without any concern of showing students how these contents are related. This paper aims at presenting a way of teaching such contents in an integrated way, starting with the definition of ane and exponential functions relating them to situations from the daily life of the students. Then, characteristics and graphics of those functions are presented and, subsequently, arithmetic and geometric progression are shown as a restriction of the ane and exponential functions. Thus, the study of the progressions is introduced based on the functions mentioned above using situations from students daily lives as examples

Temperature dependence of photoinduced birefringence in mixed Langmuir-Blodgett (LB) films of azobenzene-containing polymers

The temperature dependence of photoinduced birefringence was investigated for mixed Langmuir-Blodgett (LB) films from the homopolymer poly[4'-[[2-(methacryloyloxy)ethyl]ethyl-amino]-2-chloro-4-nitroazobenzene] (HPDR13) and cadmium stearate (Cdst) and from the copolymer 4-[N-ethyl-N-(2-hydroxyethyl)]amino-2'-chloro-4'-nitroazobenzene (MMA-DR13) and CdSt. Birefringence was achieved by impinging a linearly polarized light on the LB films. The maximum birefringence achieved decreased with temperature as thermal relaxation of the chromophores was facilitated. The buildup curves for birefringence were fitted with biexponential functions representing distinctly different mechanisms with time constants. The first, fast process is thermally activated and may be represented by an Arrhenius process. The decay of birefringence after switching off the laser source was described by a Kohlraush-Williams-Watts (KWW) function, consistent with a distribution of relaxation times for the polymer system. Activation energies were obtained from Arrhenius plots of the rate constant of the exponential functions and KWW function, which showed that the buildup of birefringence was very similar for the two polymer systems. The decay, however, was slower for the LB film from MMA-DR13/CdSt. (C) 2002 Published by Elsevier B.V. Ltd.

Kinetics of photoinduced birefringence in the guest-host system of poly(methyl methacrylate) doped with azobenzene-containing crown ethers

The kinetics of the buildup and decay of photoinduced birefringence was examined in a series of host-guest systems: azobenzene-containing crown ethers, differing in the size of the crowns, dissolved in a poly (methyl methacrylate) matrix. In all samples, the kinetics of the buildup of the birefringence was reasonably described by a sum of two exponential functions, the time constants being inversely proportional to the intensity of the pumping light and the magnitudes of the signals at the saturation level depending on the pumping light intensity and sample thickness. The dark decays were best described by the stretched exponential function, with the characteristic parameters (time constant and stretch coefficient) being practically independent of the type of crown ether. The time constants of the signal decay were orders of magnitude shorter than the respective constants of the dark isomerization of the azo crown ethers, thus indicating that the process controlling the decay was a relaxation of the polymer matrix and/or a rearrangement of the flexible parts of the crowns. (C) 2007 Wiley Periodicals, Inc.