New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Effective nonlinear model of resonant tunneling nanostructures

We introduce a model of a nonlinear double-barrier structure to describe in a simple way the effects of electron-electron scattering while remaining analytically tractable. The model is based on a generalized effective-mass equation where a nonlinear local field interaction is introduced to account for those inelastic scattering phenomena. Resonance peaks seen in the transmission coefficient spectra for the linear case appear shifted to higher energies depending on the magnitude of the nonlinear coupling. Our results are in good agreement with self-consistent solutions of the Schrodinger and Poisson equations. The calculation procedure is seen to be very fast, which makes our technique a good candidate for a rapid approximate analysis of these structures.

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

Comparison of estimates and calculations of risk of coronary heart disease by doctors and nurses using different calculation tools in general practice: cross sectional study

OBJECTIVE: To assess the effect of using different risk calculation tools on how general practitioners and practice nurses evaluate the risk of coronary heart disease with clinical data routinely available in patients' records. DESIGN: Subjective estimates of the risk of coronary heart disease and results of four different methods of calculation of risk were compared with each other and a reference standard that had been calculated with the Framingham equation; calculations were based on a sample of patients' records, randomly selected from groups at risk of coronary heart disease. SETTING: General practices in central England. PARTICIPANTS: 18 general practitioners and 18 practice nurses. MAIN OUTCOME MEASURES: Agreement of results of risk estimation and risk calculation with reference calculation; agreement of general practitioners with practice nurses; sensitivity and specificity of the different methods of risk calculation to detect patients at high or low risk of coronary heart disease. RESULTS: Only a minority of patients' records contained all of the risk factors required for the formal calculation of the risk of coronary heart disease (concentrations of high density lipoprotein (HDL) cholesterol were present in only 21%). Agreement of risk calculations with the reference standard was moderate (kappa=0.33-0.65 for practice nurses and 0.33 to 0.65 for general practitioners, depending on calculation tool), showing a trend for underestimation of risk. Moderate agreement was seen between the risks calculated by general practitioners and practice nurses for the same patients (kappa=0.47 to 0.58). The British charts gave the most sensitive results for risk of coronary heart disease (practice nurses 79%, general practitioners 80%), and it also gave the most specific results for practice nurses (100%), whereas the Sheffield table was the most specific method for general practitioners (89%). CONCLUSIONS: Routine calculation of the risk of coronary heart disease in primary care is hampered by poor availability of data on risk factors. General practitioners and practice nurses are able to evaluate the risk of coronary heart disease with only moderate accuracy. Data about risk factors need to be collected systematically, to allow the use of the most appropriate calculation tools.

Dynamic behaviour of rotary mechanical seals

This thesis covers both experimental and computer investigations into the dynamic behaviour of mechanical seals. The literature survey shows no investigations on the effect of vibration on mechanical seals of the type common in the various process industries. Typical seal designs are discussed. A form of Reynolds' equation has been developed that permits the calculation of stiffnesses and damping coefficients for the fluid film. The dynamics of the mechanical seal floating ring have been investigated using approximate formulae, and it has been shown that the floating ring will behave as a rigid body. Some elements, such as the radial damping due to the fluid film, are small and may be neglected. The equations of motion of the floating ring have been developed utilising the significant elements, and a solution technique described. The stiffness and damping coefficients of nitrile rubber o-rings have been obtained. These show a wide variation, with a constant stiffness up to 60 Hz. The importance of the effect of temperature on the properties is discussed. An unsuccessful test rig is described in the appendices. The dynamic behaviour of a mechanical seal has been investigated experimentally, including the effect of changes of speed, sealed pressure and seal geometry. The results, as expected, show that high vibration levels result in both high leakage and seal temperatures. Computer programs have been developed to solve Reynolds' Equation and the equations of motion. Two solution techniques for this latter program were developed, the unsuccesful technique is described in the appendices. Some stability problems were encountered, but despite these the solution shows good agreement with some of the experimental conditions. Possible reasons for the discrepancies are discussed. Various suggestions for future work in this field are given. These include the combining of the programs and more extensive experimental and computer modelling.

The Methodology of the Subsistence Minimum Calculation for Developing Countries and its Computation on the Georgian Example

This article shows the social importance of subsistence minimum in Georgia. The methodology of its calculation is also shown. We propose ways of improving the calculation of subsistence minimum in Georgia and how to extend it for other developing countries. The weights of food and non-food expenditures in the subsistence minimum baskets are essential in these calculations. Daily consumption value of the minimum food basket has been calculated too. The average consumer expenditures on food supply and the other expenditures to the share are considered in dynamics. Our methodology of the subsistence minimum calculation is applied for the case of Georgia. However, it can be used for similar purposes based on data from other developing countries, where social stability is achieved, and social inequalities are to be actualized. ACM Computing Classification System (1998): H.5.3, J.1, J.4, G.3.

Achievable rates and outage probability of cognitive radio with dynamic frequency hopping under imperfect spectrum sensing

In this study, the authors propose simple methods to evaluate the achievable rates and outage probability of a cognitive radio (CR) link that takes into account the imperfectness of spectrum sensing. In the considered system, the CR transmitter and receiver correlatively sense and dynamically exploit the spectrum pool via dynamic frequency hopping. Under imperfect spectrum sensing, false-alarm and miss-detection occur which cause impulsive interference emerged from collisions due to the simultaneous spectrum access of primary and cognitive users. That makes it very challenging to evaluate the achievable rates. By first examining the static link where the channel is assumed to be constant over time, they show that the achievable rate using a Gaussian input can be calculated accurately through a simple series representation. In the second part of this study, they extend the calculation of the achievable rate to wireless fading environments. To take into account the effect of fading, they introduce a piece-wise linear curve fitting-based method to approximate the instantaneous achievable rate curve as a combination of linear segments. It is then demonstrated that the ergodic achievable rate in fast fading and the outage probability in slow fading can be calculated to achieve any given accuracy level.

Spectral properties of resonant Bose-Fermi mixtures

The object of study of the present work are Bose-Fermi mixtures in three dimensions at zero temperature. The system is characterized by a great tunability of physical parameters that is achieved by means of a Fano-Feshbach resonance. As a result, there are mainly two regimes: we move from a situation in which bosons and fermions are weakly interacting to a context in which bosons are coupled to fermions so as to form molecules that are composite fermions, as the coupling between the two types of particles is increased. In the former case, we can describe the mixture as a weakly attractive Bose-Fermi one, while in the latter the same is described in terms of molecules and excess atoms or particles which are unpaired. The main aim of the thesis is to analyze the spectral weight functions which represent the single-particle excitation spectra of the system and are relevant to recent radio-frequency spectroscopy experiments of the system. In order to pursue this objective, diagrammatic methods are used. The formalism is developed within the T-matrix approach: it consists of an approximate calculation whichselects exclusively the class of Feynman’s diagrams that collects all possible repeated boson-fermion interaction.

The Crystal-t Algorithm: A New Approach To Calculate The Sle Of Lipidic Mixtures Presenting Solid Solutions.

Lipidic mixtures present a particular phase change profile highly affected by their unique crystalline structure. However, classical solid-liquid equilibrium (SLE) thermodynamic modeling approaches, which assume the solid phase to be a pure component, sometimes fail in the correct description of the phase behavior. In addition, their inability increases with the complexity of the system. To overcome some of these problems, this study describes a new procedure to depict the SLE of fatty binary mixtures presenting solid solutions, namely the Crystal-T algorithm. Considering the non-ideality of both liquid and solid phases, this algorithm is aimed at the determination of the temperature in which the first and last crystal of the mixture melts. The evaluation is focused on experimental data measured and reported in this work for systems composed of triacylglycerols and fatty alcohols. The liquidus and solidus lines of the SLE phase diagrams were described by using excess Gibbs energy based equations, and the group contribution UNIFAC model for the calculation of the activity coefficients of both liquid and solid phases. Very low deviations of theoretical and experimental data evidenced the strength of the algorithm, contributing to the enlargement of the scope of the SLE modeling.

Effect Of Roux-en-y Gastric Bypass On Nonalcoholic Fatty Liver Disease Evaluated Through Nafld Fibrosis Score: A Prospective Study.

Nonalcoholic fatty liver disease (NAFLD) is common among subjects who undergo bariatric surgery and its postsurgical improvement has been reported. This study aimed to determine the evolution of liver disease evaluated through NAFLD fibrosis score 12 months after surgery. It is a prospective cohort study which evaluated patients immediately before and 12 months following Roux-en-Y gastric bypass (RYGB). Mean score decreased from 1.142 to 0.066; surgery led to a resolution rate of advanced fibrosis of 55 %. Resolution was statistically associated with female gender, percentage of excess weight loss, postsurgical body mass index, postsurgical platelet count, and diabetes resolution. As previously reported by studies in which postsurgical biopsies were performed, RYGB leads to a great resolution rate of liver fibrosis. Since postsurgical biopsy is not widely available and has a significant risk, calculation of NAFLD fibrosis score is a simple tool to evaluate this evolution through a noninvasive approach.

Behaviour of albino and melanic variants of Biomphalaria glabrata Say, 1818 (Mollusca: Planorbidae) following infection by Schistosoma mansoni Sambon, 1907

The behaviour of the albino and melanic variants of Biomphalaria glabrata of Belo Horizonte (MG. Brazil) was studied comparatively, in terms of their respective susceptibilities to infection by Schistosoma mansoni of the same origin, through observation of the elimination of cercariae for a three-month period and the calculation of mortality and infection rates, in control and in infected snails. The number of amoebocytes, granulocytes and hyalinocytes in the circulating hemolymph during different periods of infection was analyzed. The evolution of the infection in the tissues was observed by means of histological cross-sections. The melanic variant showed greater susceptibility to infection and a higher mortality rate. The albino variant showed a higher number of circulating amoebocytes, both granulocytes and hyalinocytes. A higher number of degenerated sporocysts were seen in the histological cross-sections of the albino variant. The results suggest that the melanic variant of B. glabrata was more susceptible to infection by S. mansoni than was the albino variant.

Análise do desempenho muscular do quadríceps e dos isquiotibiais em função da série temporal e da amplitude de movimento de atletas amadoras de futsal feminino = : Analysis of muscle performance of the quadriceps and hamstrings as a function of the times series and range of motion of amateurfemale futsal athletes

Universidade Estadual de Campinas . Faculdade de Educação Física

Screening process for activity determination of conductive oxide electrodes for organic oxidation

A modified method for the calculation of the normalized faradaic charge (q fN) is proposed. The method involves the simulation of an oxidation process, by cyclic voltammetry, by employing potentials in the oxygen evolution reaction region. The method is applicable to organic species whose oxidation is not manifested by a defined oxidation peak at conductive oxide electrodes. The variation of q fN for electrodes of nominal composition Ti/RuX Sn1-X O2 (x = 0.3, 0.2 and 0.1), Ti/Ir0.3Ti0.7O2 and Ti/Ru0.3Ti0.7O2 in the presence of various concentrations of formaldehyde was analyzed. It was observed that electrodes containing SnO2 are the most active for formaldehyde oxidation. Subsequently, in order to test the validity of the proposed model, galvanostatic electrolyses (40 mA cm-2) of two different formaldehyde concentrations (0.10 and 0.01 mol dm-3) were performed. The results are in agreement with the proposed model and indicate that this new method can be used to determine the relative activity of conductive oxide electrodes. In agreement with previous studies, it can be concluded that not only the nature of the electrode material, but also the organic species in solution and its concentration are important factors to be considered in the oxidation of organic compounds.

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic-plastic materials

In this work, the effects of indenter tip roundness oil the load-depth indentation curves were analyzed using finite element modeling. The tip roundness level was Studied based on the ratio between tip radius and maximum penetration depth (R/h(max)), which varied from 0.02 to 1. The proportional Curvature constant (C), the exponent of depth during loading (alpha), the initial unloading slope (S), the correction factor (beta), the level of piling-up or sinking-in (h(c)/h(max)), and the ratio h(max)/h(f) are shown to be strongly influenced by the ratio R/h(max). The hardness (H) was found to be independent of R/h(max) in the range studied. The Oliver and Pharr method was successful in following the variation of h(c)/h(max) with the ratio R/h(max) through the variation of S with the ratio R/h(max). However, this work confirmed the differences between the hardness values calculated using the Oliver-Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that Occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (W(p)/W(t)) was found to be independent of the ratio R/h(max), which demonstrates that the methods for the Calculation of mechanical properties based on the *indentation energy are potentially not Susceptible to errors caused by tip roundness.

Analysis of the effects of conical indentation variables on the indentation response of elastic-plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load-depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 2(6) was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/h(max), n, theta, E, and h(max). The dimensional variables E and h(max) were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/h(max) was obtained with two different h(max) values. A set of dimensionless functions was defined to analyze the effect of the input variables: Pi(1) = P(1)/Eh(2), Pi(2) = h(c)/h, Pi(3) = H/Y, Pi(4) = S/Eh(max), Pi(6) = h(max)/h(f) and Pi(7) = W(P)/W(T). These six functions were found to depend only on the dimensionless variables studied (Y/E, R/h(max), n, theta). Another dimension less function, Pi(5) = beta, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on beta was theta. However, beta showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that beta is especially Susceptible to the error in the Calculation of the initial unloading slope.