Solubility of high molecular weight n-paraffins in supercritical carbon dioxide has been a matter of interest to many researchers. However, not sufficient solubility experimental data are available although the methods by which the experimental data are obtained have many varieties. Utilizing cubic equations of state is an effective method for solubility prediction of n-paraffins in supercr...

Renormalization group methods are well-established tools for the (numerical) investigation of low-energy properties correlated quantum many-body systems, allowing us to capture their scale-dependent nature. The functional renormalization (FRG) allows continuously evolve a microscopic model action an effective as function decreasing energy scales via exact flow equation, which is then approximat...

Two super cubic convergence methods to solve systems of nonlinear equations are presented. The first method is based on the Adomian decomposition method. We state and prove a theorem which shows the cubic convergence for this method. But numerical examples show super cubic convergence. The second method is based on a quadrature formulae to obtain the inverse of Jacobian matrix. Numerical exampl...

1 The theory of equations 3 1.1 Primitive question . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Quadratic equations . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 The remainder theorem . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Relation between coefficients and roots . . . . . . . . . . . . . 5 1.5 Complex roots of 1 . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Cub...

In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.

this paper presents a mathematical model for the vibration analysis of a three-component piezoelectric force sensor. the cubic theory of weakly nonlinear electroelasticity is applied to the model for describing the electromechanical coupling effect in the piezoelectric sensing elements which operate in thickness-shear and thickness-stretch vibration modes. hamilton's principle is used to d...

In this paper a, b are complex numbers. The following propositions are true: (1) a · a = a2. (2) a · a · a = a3. (3) a · a · a · a = a4. (4) (a− b) = (a2 − 2 · a · b) + b2. (5) (a− b) = ((a3 − 3 · a2 · b) + 3 · b2 · a)− b3. (6) (a− b) = (((a4 − 4 · a3 · b) + 6 · a2 · b2)− 4 · b3 · a) + b4. Let n be a natural number and let r be a real number. We introduce r1/n as a synonym of n √ r. Let n be a ...

A semilinear elliptic equation with generalized cubic nonlinearity is studied. Global bifurcation diagrams and the existence of multiple solutions are obtained and in certain cases, exact multiplicity is proved.

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...