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. [2] Morita , S. 2001 Geometry of Differential Forms AMS Translations of Mathematical Monographs 209 Providence, RI. [3

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The general relativistic and covariant differential form of Helmholtz's first vorticity theorem is presented. We prove in relation with it an invariant kinematic identity which is the generalisation of the Helmholtz theorem for general continua.

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, R. and Tu, L. W. , Differential forms in algebraic topology , Graduate Texts in Mathematics 82, Springer-Verlag, Berlin, 1982. MR 83i :57016 Tu L. W

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Abstract  

A new method of the multiple rate iso-temperature was used to define the most probable mechanism g(α) of a reaction; the iterative iso-conversional procedure has been employed to estimate apparent activation energy E a, the pre-exponential factor A was obtained on the basis of E a and g(α). In this new method, the thermal analysis kinetics triplet of dehydration of calcium oxalate monohydrate is determined, which apparent activation energy E a is 82.83 kJ mol-1, pre-exponential factor A is 1.142105-1.235105 s-1, the most probable mechanism belongs to phase boundary reaction Rn with integral form g(α)=1-(1-α)n and differential form f(α)=n(1-α)1-(1/n), where accommodation factor n=2.40-1.40.

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Abstract

3,3-Dinitroazetidinium (DNAZ) salt of perchloric acid (DNAZ·HClO4) was prepared, it was characterized by the elemental analysis, IR, NMR, and a X-ray diffractometer. The thermal behavior and decomposition reaction kinetics of DNAZ·HClO4 were investigated under a non-isothermal condition by DSC and TG/DTG techniques. The results show that the thermal decomposition process of DNAZ·HClO4 has two mass loss stages. The kinetic model function in differential form, the value of apparent activation energy (E a) and pre-exponential factor (A) of the exothermic decomposition reaction of DNAZ·HClO4 are f(α) = (1 − α)−1/2, 156.47 kJ mol−1, and 1015.12 s−1, respectively. The critical temperature of thermal explosion is 188.5 °C. The values of ΔS , ΔH , and ΔG of this reaction are 42.26 J mol−1 K−1, 154.44 kJ mol−1, and 135.42 kJ mol−1, respectively. The specific heat capacity of DNAZ·HClO4 was determined with a continuous C p mode of microcalorimeter. Using the relationship between C p and T and the thermal decomposition parameters, the time of the thermal decomposition from initiation to thermal explosion (adiabatic time-to-explosion) was evaluated as 14.2 s.

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Abstract  

The title compound 3,3-dinitroazetidinium (DNAZ) 3,5-dinitrosalicylate (3,5-DNSA) was prepared and the crystal structure has been determined by a four-circle X-ray diffractometer. The thermal behavior of the title compound was studied under a non-isothermal condition by DSC and TG/DTG techniques. The kinetic parameters were obtained from analysis of the TG curves by Kissinger method, Ozawa method, the differential method and the integral method. The kinetic model function in differential form and the value of E a and A of the decomposition reaction of the title compound are f(α)=4α3/4, 130.83 kJ mol−1 and 1013.80s−1, respectively. The critical temperature of thermal explosion of the title compound is 147.55 °C. The values of ΔS , ΔH and ΔG of this reaction are −1.35 J mol−1 K−1, 122.42 and 122.97 kJ mol−1, respectively. The specific heat capacity of the title compound was determined with a continuous C p mode of mircocalorimeter. Using the relationship between C p and T and the thermal decomposition parameters, the time of the thermal decomposition from initiation to thermal explosion (adiabatic time-to-explosion) was obtained.

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construction of logarithmic differential forms, Adv. Math. , 76 (1989), no. 1, 116–154. MR 90j :32016 Ziegler G. Combinatorial construction of logarithmic differential forms

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The dynamics of predator-prey systems relate strongly to the density (in)dependent attributes of the predator’s feeding rate, i.e., its functional response. The outcome of functional response models is often used in theoretical or applied ecology in order to extract information about the mechanisms associated with the feeding behavior of predators. The focus of this study centres upon Holling’s type II functional response model, commonly known as the disc equation, which describes an inverse-density dependent mortality caused by a single predator to its prey. A common method to provide inference on functional response data involves nonlinear least squares optimization, assuming independent Gaussian errors, an assumption often violated in practice due to the heteroscedasticity which is typically present in the data. Moreover, as prey depletion is common in functional response experiments, the differential form of disc equation ought to be used in principle. We introduce a related statistical model and adopt a Bayesian approach for estimating parameters in ordinary differential equation models. In addition, we explore model uncertainty via Bayes factors. Our approach is illustrated via the analysis of several data sets concerning the functional response of a widespread ladybird beetle (Propylea quatuordecimpunctata) to its prey (Aphis fabae), predicting the efficiency of this predator on a common and important aphid species. The results showed that the approach developed in this study is towards a direction for accurate estimation of the parameters that determine the shape of the functional response of a predator without having to make unnecessary assumptions. The R (www.r-project.org) code for fitting the proposed model to experimental data is made freely available.

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. [2] Agrebaoui , B. Ben Fraj , N. Ben Ammar , M. Ovsienko , V. 2003 Deformation of modules of differential forms

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In defense of thermodynamics

Comment on “Concepts against mathematics: self-inconsistency in thermodynamic evaluations”

Journal of Thermal Analysis and Calorimetry
Author: Robert H. Swendsen

]. From the differential form of the fundamental relation in the energy representation, we see that Because the energy of the classical ideal gas is where k B is Boltzmann's constant, we have Using the ideal gas law, PV = Nk B T , the energy

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