Green Formula Research Articles

Performance Evaluation of Green Cushion Gum Composite Formulated Based on Hybrid Filler and Curing System

Cushion gum is a type of rubber composite material used as adhesive in the manufacture of retread tires. Therefore, cushion gum should have good processability and mechanical characteristics, particularly tensile property, and adhesion strength. The effect of hybrid filler and curing system on the performance of green cushion gum composite was investigated to determine the appropriate green cushion gum formula designed at a laboratory scale. The content of CB N330/lignin in hybrid filler was arranged at 40/10 phr and 50/10 phr. Meanwhile, the curing system was performed semi-efficient (CBS/S 1.6/1.6 phr) and conventional (CBS/S 1.6/2.2 phr). Green cushion gum composite was also formulated using pine tar oil as a bio plasticizer. Referred to the curing characteristic and mechanical property test result, it showed that green cushion gum composite formula coded by RF1 which composed of CB N330/lignin as 50/10 phr and applied conventional curing system which ratio of CBS/S as 1.6/2.2 phr was regarded as the acceptable combination in designing green cushion gum composite formula. Higher CB N330 loading in hybrid filler composition and conventional curing system attributed to the relatively high crosslink density indicated by MH-ML value. Consequently, green cushion gum composite was obtained using the RF1 formula that has a better optimum curing time accompanied by good tensile property and adhesion strength. The composite was also comparable to conventional commercial cushion gum.

The Neumann and Dirichlet problems for the total variation flow in metric measure spaces

Abstract We study the Neumann and Dirichlet problems for the total variation flow in doubling metric measure spaces supporting a weak Poincaré inequality. We prove existence and uniqueness of weak solutions and study their asymptotic behavior. Furthermore, in the Neumann problem we provide a notion of solutions which is valid for L 1 {L^{1}} initial data, as well as prove their existence and uniqueness. Our main tools are the first-order linear differential structure due to Gigli and a version of the Gauss–Green formula.

Leibniz rules and Gauss–Green formulas in distributional fractional spaces

We apply the results established in [12] to prove some new fractional Leibniz rules involving BVα,p and Sα,p functions, following the distributional approach adopted in the previous works [8,13,14]. In order to achieve our main results, we revise the elementary properties of the fractional operators involved in the framework of Besov spaces and we rephraze the Kenig–Ponce–Vega Leibniz-type rule in our fractional context. We apply our results to prove the well-posedness of the boundary-value problem for a general 2α-order fractional elliptic operator in divergence form.

Effect of field pea (Pisum sativum subsp. arvense (L.) Asch.) and pea-oat (Avena sativa L.) biculture cover crops on high tunnel vegetable under organic production system

In general, adaptation of cover cropping in crop rotation practices to organic tunnels by methods supporting soil health and quality has not yet been fully optimized. Effect of field pea and pea-oat cover crops to soil physicochemical properties and cash crop quality was assessed in an organic high tunnel in southern Poland in 2016–2017, with the following planting sequence: spring cover crops/tomato/romaine lettuce/green bean/iceberg lettuce. The sole pea produced a lower aboveground biomass (3.06 t ha−1) than the pea-oat mixture (4.17 t ha−1), and the N content in their biomass was 155 kg N ha−1 and 136 kg N ha−1, respectively. The results indicated that a high residue input from cover crops was important for soil organic carbon stock, for retaining plant-available N in organic matter, and for improving soil physical properties, especially wet aggregate stability. We observed an increase in soil pH and the availability of some mineral nutrients in the soil under cover crop treatments, especially Ca, Mg, K, and P. N uptake by the subsequent cash crop significantly (p ≤ 0.05) increased with pea than with pea-oat biculture, and in the green manure formula than with the mulch treatment. Early spring cover cropping depressed the subsequent tomato yield, but enhanced green bean yield in the second year of cropping.

The principal transmission condition

<abstract><p>The paper treats pseudodifferential operators $ P = \operatorname{Op}(p(\xi)) $ with homogeneous complex symbol $ p(\xi) $ of order $ 2a > 0 $, generalizing the fractional Laplacian $ (-\Delta)^a $ but lacking its symmetries, and taken to act on the halfspace ${\mathbb R}^n_+$. The operators are seen to satisfy a principal $ \mu $-transmission condition relative to ${\mathbb R}^n_+$, but generally not the full $ \mu $-transmission condition satisfied by $ (-\Delta)^a $ and related operators (with $ \mu = a $). However, $ P $ acts well on the so-called $ \mu $-transmission spaces over ${\mathbb R}^n_+$ (defined in earlier works), and when $ P $ moreover is strongly elliptic, these spaces are the solution spaces for the homogeneous Dirichlet problem for $ P $, leading to regularity results with a factor $ x_n^\mu $ (in a limited range of Sobolev spaces). The information is then shown to be sufficient to establish an integration by parts formula over ${\mathbb R}^n_+$ for $ P $ acting on such functions. The formulation in Sobolev spaces, and the results on strongly elliptic operators going beyond certain operators with real kernels, are new. Furthermore, large solutions with nonzero Dirichlet traces are described, and a halfways Green's formula is established, as new results for these operators. Since the principal $ \mu $-transmission condition has weaker requirements than the full $ \mu $-transmission condition assumed in earlier papers, new arguments were needed, relying on work of Vishik and Eskin instead of the Boutet de Monvel theory. The results cover the case of nonsymmetric operators with real kernel that were only partially treated in a preceding paper.</p></abstract>

Thermodynamically consistent generalized hydrodynamic theory of thermal conduction and integral equations of thermal conductivity of simple fluids in electromagnetic fields

We have reviewed thermodynamically consistent evolution equations of fluids in an invited review article in the McGill University bicentennial memorial issue [B. C. Eu, Can. J. Chem. (in press) (2021)]. In this article, we apply the generalized hydrodynamic evolution equations of heat fluxes to derive integral equations for thermal conductivity coefficients of fluids in electromagnetic fields, which generalize the linear response theory formula of Green and Kubo to nonlinear heat conduction phenomena. The constitutive equation for the temperature field derived is compared with the temperature evolution equation obtained by Guo et al. [Physica D 342, 24 (2017)] on the basis of extended irreversible thermodynamics. They are considerably different.

Connections between finite difference and finite element approximations

We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one dimension coincides with the finite element approximation of the solution. This result can be viewed as an extension of the Green function formula for the solution at the continuous level. We write the finite difference and the finite element systems such that the two corresponding linear systems have the same stiffness matrices and compare the right hand side load vectors for the two methods. Using evaluation of the Green function, a formula for the inverse of the stiffness matrix is extended to the case of non-uniformly distributed mesh points. We provide an error analysis based on the connection between the two methods and estimate the energy norm of the difference of the two solutions. Interesting extensions to the 2D case are provided.

New Flory‐Huggins interaction parameter between SBR and p‐phenylenediamine antioxidants and the predictive power in molecular structure and rubber formula design

AbstractThe software package was employed to calculate the three‐dimensional solubility parameters (HSP) of SBR and antioxidants. The HSP values of antioxidants are higher than SBR, meaning that the antioxidants have higher polarity compared with SBR. The solubility measurements of antioxidants in both sulfur and peroxide cured SBR vulcanizates were performed at elevated temperatures from 80 to 130°C. The maximum solubilities (∆S) of antioxidants were correlated with the temperature and also with the new Flory‐Huggins interaction parameters (χN) calculated by the HSP values. The results turn out to be that ∆S increases with increasing temperature as expected and 4020 shows higher ∆S value. Furthermore, ∆S increases with decreasing χN, and by quantitatively mathematical fitting, one functional relationship between ∆S and χN was achieved, regardless of what the crosslinking type of SBR was and what the temperature was involved. Through prediction with χN, one can get that SBR grades with higher styrene content and butadiene/vinyl ratio result in lower χN and accordingly better compatibility with N3100. One of the possible applications of χN is to select suitable SBR and antioxidant structures to design the ever‐increasing SBR‐based green tire tread formula.

Development of three-dimensional integral-type reconstruction formula for magnetic resonance elastography.

The viscoelasticity (storage modulus and loss modulus) of living tissues is known to be related to diseases. Magnetic resonance elastography (MRE) is a quantitative method for non-invasive measuring viscoelasticity. The viscoelasticity is calculated from the elastic wave images using an inversion algorithm. The estimation accuracy of the inversion algorithm is degraded by background noise. This study aims to propose novel inversion algorithms that are applicable for noisy elastic wave images. The proposed algorithms are based on the Voigt-type viscoelastic equation. The algorithms are designed to improve the noise robustness by avoiding direct differentiation of measurement data by virtue of Green's formula. Similarly, stabilization is introduced to the curl-operator which works to eliminate the compression waves in measurement data. To clarify the characteristics of the algorithms, the proposed algorithms were compared with the conventional algorithms using isotropic and anisotropic voxel numerical simulations and phantom experimental data. From the results of the numerical simulations, normalized errors of stiffness of proposed algorithms were 3% or less. The proposed algorithms mostly showed better results than the conventional algorithms despite noisy elastic wave images. From the gel phantom experiment, we confirmed the same tendency as the characteristics of the algorithms observed in the numerical simulation results. We have developed a novel inversion algorithm and evaluated it quantitatively. The results confirm that the proposed algorithms are highly quantitative and noise-robust methods for estimating storage and loss modulus regardless of noise, voxel anisotropy, and propagation direction. Therefore, the proposed algorithms will appropriate to various three-dimensional MRE systems.

On BV functions and essentially bounded divergence-measure fields in metric spaces

By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation (BV) in terms of suitable vector fields on a complete and separable metric measure space (\mathbb{X},d,\mu) equipped with a non-negative Radon measure \mu finite on bounded sets. Then, we extend the concept of divergence-measure vector fields \mathcal{DM}^p(\mathbb{X}) for any p\in[1,\infty] and, by simply requiring in addition that the metric space is locally compact, we determine an appropriate class of domains for which it is possible to obtain a Gauss–Green formula in terms of the normal trace of a \mathcal{DM}^\infty(\mathbb{X}) vector field. This differential machinery is also the natural framework to specialize our analysis for \mathsf{RCD}(K,\infty) spaces, where we exploit the underlying geometry to determine the Leibniz rules for \mathcal{DM}^\infty(\mathbb{X}) and ultimately to extend our discussion on the Gauss–Green formulas.

Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains

The method of the fundamental solutions (MFS) is used to construct an approximate solution for a partial differential equation in a bounded domain. It is demonstrated by combining the fundamental solutions shifted to the points outside the domain and determining the coefficients of the linear sum to satisfy the boundary condition on the finite points of the boundary. In this paper, the existence of the approximate solution by the MFS for the Neumann problems of the modified Helmholtz equation in disk domains is rigorously demonstrated. We reveal the sufficient condition of the existence of the approximate solution. Applying the Green formula to the Neumann problem of the modified Helmholtz equation, we bound the error between the approximate solution and exact solution into the difference of the function of the boundary condition and the normal derivative of the approximate solution by boundary integrations. Using this estimate of the error, we show the convergence of the approximate solution by the MFS to the exact solution with exponential order, that is, N2aN order, where a is a positive constant less than one and N is the number of collocation points. Furthermore, it is demonstrated that the error tends to 0 in exponential order in the numerical simulations with increasing number of collocation points N.

ОКТ-менискометрия как метод количественной оценки баланса слезной системы

All diseases of the lacrimal apparatus of the eye disrupt the balance of the lacrimal system either due to changes in the production of tears, or due to the insufficiency of its removal, so the study of the quantity and quality of tears on the eye surface allows us to reliably assess the effectiveness of methods of treating the pathology of the lacrimal organs. OCT-meniscometry is the only non-contact, non-invasive, accurate method of examining the lacrimal apparatus, which is reflected in the publications of many authors. The aim of our study was to improve the accuracy and automate the process of calculating the area of the lacrimal meniscus, as well as to evaluate the correlation between the indicators of OCT-meniscometry and functional tests. Materials and methods. The study included 50 patients with dacryostenosis (group 1), who were examined before and 1 month after surgical treatment (recanalization of SOP), as well as 30 patients without pathology of the lacrimal organs, who did not complain of lacrimation and dry eyes (group 2). All patients underwent a Schirmer and Norn test according to the generally accepted method, and OCT-meniscometry was performed using an optical coherence tomograph. The resulting OCT-meniscogram was transferred to a special mathematical program. Green's formula was used to calculate the area. Results. Meniscometry data had a strong correlation with functional tests (p<0.05) and high diagnostic sensitivity and specificity. Conclusion. The method of OCT-meniscometry has a higher sensitivity and specificity compared to routine tests, is less invasive, highly informative, which, of course, increases the reliability of the analysis of treatment results. Key words: meniscometry, TMA, lacrimal meniscus area, lacrimal system balance, dacryology.

Superconvergence analysis of a MFEM for BBM equation with a stable scheme

In this paper, superconvergence properties are presented for the nonlinear Benjamin-Bona-Mahony (BBM) equation with a mixed finite element method (MFEM). We propose an Euler scheme combined with the artificial Douglas-Dupont regularization terms, which guarantee the stability of the numerical scheme. Splitting technique is utilized to get rid of the ratio between the time step τ and the subdivision parameter h. Temporal error estimates and unconditional spatial error estimates are gained through some techniques, such as the function's monotonicity and the Green formula and so on. In turn, the regularities of the solutions about the time-discrete equations and the boundedness of the numerical solution are derived. Based on the above achievements, the unconditional superconvergent results of un in H1-norm and q→n in L2-norm with order O(h2+τ) are obtained through the trigonometric inequality. The global superconvergent results are deduced by use of the interpolated postprocessing operators. Numerical example shows the validity of the theoretical analysis.

Further developments on boundary-field equation methods for nonlinear transmission problems

This paper is concerned with new insights on the application of the boundary-field equation approach, which refers basically to the combined use of finite element and boundary integral equation methods, to numerically solve nonlinear exterior transmission problems in 2D and 3D. As a model, we consider a nonlinear second-order elliptic equation in divergence form holding in an annular domain coupled with the Laplace equation in the corresponding unbounded exterior region, together with transmission conditions on the interface and a suitable radiation condition at infinity. We first extend the classical Johnson & Nédélec coupling procedure, which makes use of only one boundary integral equation, to our nonlinear model without assuming any restrictive smoothness requirement on the boundary but only Lipschitz-continuity. Next, we extend the applicability of a recently introduced modification of the Costabel & Han coupling method, which employs the two boundary integral equations arising from the Green representation formula, to our nonlinear model as well. This new boundary-field equation method is based on the introduction of both Cauchy data on the boundary as independent unknowns. Primal and dual-mixed variational formulations are analyzed for each extension described above, and suitable hypotheses on the nonlinear coefficient of the elliptic equation allow to establish well-posedness of the corresponding continuous and discrete schemes by using monotone operator and nonlinear Babuška-Brezzi theories. Finally, a priori error estimates are established.

A short proof of Green's formula

We give a short proof of Green's formula on Hall numbers. By using rotation of triangles, we find that Green's formula is just the associativity of derived Hall numbers.

Integration by parts for nonsymmetric fractional-order operators on a halfspace

For a strongly elliptic pseudodifferential operator L of order 2a (0<a<1) with real kernel, we show an integration-by-parts formula for solutions of the homogeneous Dirichlet problem, in the model case where the operator is x-independent with homogeneous symbol, considered on the halfspace R+n. The new aspect compared to (−Δ)a is that L is nonsymmetric, having both an even and an odd part. Hence it satisfies a μ-transmission condition where generally μ≠a.We present a complex method, relying on a factorization in factors holomorphic in ξn in the lower or upper complex halfplane, using order-reducing operators combined with a decomposition principle originating from Wiener and Hopf. This is in contrast to a real, computational method presented very recently by Dipierro, Ros-Oton, Serra and Valdinoci. Our method allows μ in a larger range than they consider.Another new contribution is the (model) study of “large” solutions of nonhomogeneous Dirichlet problems when μ>0. Here we deduce a “halfways Green's formula” for L:∫R+nLuv¯dx−∫R+nuL⁎v‾dx=c∫Rn−1γ0(u/xnμ−1)γ0(v¯/xnμ⁎)dx′, when u solves a nonhomogeneous Dirichlet problem for L, and v solves a homogeneous Dirichlet problem for L⁎; μ⁎=2a−μ. Finally, we show a full Green's formula, when both u and v solve nonhomogeneous Dirichlet problems; here both Dirichlet and Neumann traces of u and v enter, as well as a first-order pseudodifferential operator over the boundary.

Reliability of Different RBC Indices and Formulas in the Discrimination of ?-Thalassemia Minor and Iron Deficiency Anemia in Surabaya, Indonesia

In this study, we evaluated the RBC indices in differentiating ?-thalassemia minor and iron deficiencyanemia in a healthcare center. This was an observational analytic study with a cross-sectional design usingblood specimens of children aged 3 years to 17 years with microcytic hypochromic anemia based onthe results of complete blood counts and evaluation of peripheral blood smears. Calculation of the RBCindices was performed as an initial screening to differentiate ?-thalassemia minor and iron deficiencyanemia. Iron profile examination and hemoglobin electrophoresis were performed to confirm the diagnosisof ?-thalassemia minor and iron deficiency anemia. The results of the independent samples t-test showedsignificant differences in Hb, MCV, MCH, and MCHC between ?-thalassemia minor and iron deficiencyanemia (p <0.05). The results of the Mann Whitney test showed a significant difference in the MentzerIndex to distinguish between ?-thalassemia minor and iron deficiency anemia (p <0.05). Also, the resultsof the independent samples t-test showed significant differences in the Green & King formula, Sirdah etal. formula, and the Maltos and Carvalho Index (p <0.05). The Green and King formula has a diagnosticsensitivity of 78.6% and a specificity of 76.6% and an accuracy of 78.03%. Various formulas based on theresults of complete blood count parameters have been developed to detect ?-thalassemia minor in areas witha high prevalence of ?-thalassemia with different sensitivity and specificity. In this study, it showed that theGreen and King formula has a diagnostic sensitivity of 78.6% and a specificity of 76.6%, and an accuracyof 78.03%. Green and King’s formula can be applied as an initial screening to differentiate ?-thalassemiaminor and iron deficiency anemia

The matrix of the Green function and the Green representation formula of the Stokes equations for a half space

In this paper, we consider the matrix of the Green function of the Stokes equations for a half space. To the best of author’s knowledge, the matrix of the Green function has been obtained for a half space in [Formula: see text]. But the matrix of the Green function for a half space in [Formula: see text] has not been obtained. Moreover, the author considers that the form of the matrix of the Green function in [Formula: see text] is irregular. In this paper, we obtain the regular form of the matrix of the Green function of the Stokes equations for a half space in [Formula: see text]. Moreover we obtain the Green representation formula of the Stokes equations for a half space in [Formula: see text].

Green's formulas and Poisson's equation for bosonic Laplacians

A bosonic Laplacian is a conformally invariant second‐order differential operator acting on smooth functions defined on domains in Euclidean space and taking values in higher‐order irreducible representations of the special orthogonal group. In this paper, we firstly introduce the motivation for study of the generalized Maxwell operators and bosonic Laplacians (also known as the higher spin Laplace operators). Then, with the help of connections between Rarita–Schwinger type operators and bosonic Laplacians, we solve Poisson's equation for bosonic Laplacians. A representation formula for bounded solutions to Poisson's equation in Euclidean space is also provided. In the end, we provide Green's formulas for bosonic Laplacians in scalar‐valued and Clifford‐valued cases, respectively. These formulas reveal that bosonic Laplacians are self‐adjoint with respect to a given L2 inner product on certain compact supported function spaces.

Harmonic Green and Neumann functions for domains bounded by two intersecting circular arcs

ABSTRACT The parqueting-reflection principle is shown to work for constructing the harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two intersecting circular arcs in with a particular angle . With the explicit expressions of the harmonic Green and Neumann functions, we solve the Dirichlet and Neumann boundary problems to the Poisson equation in these domains by applying the Green and Neumann representation formulas.