In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

The ground charge density distributions (CDD), elastic charge form factors and proton, charge, neutron, and matter root mean square (rms) radii for stable 40Ca and 48Ca have been calculated using single-particle radial wave functions of Woods-Saxon (WS) and harmonic-oscillator (HO) potentials. Different central potential depths are used for each subshell which is adjusted so as to reproduce the experimental single-nucleon binding energies. An excellent agreement between the calculated rms charge radii and experimental data are found for both nuclei using WS and HO potentials. The calculated proton rms radii for 40Ca are found to be in good agreement with experiment data using both WS and HO potentials while the results for 48Ca showed an ov

International relations scholars have increasingly debated the evolving landscape of actors that challenge the traditional state-centric world order. A key element of this transformation is the rise of sub-state actors, which engages in alternative diplomacy parallel to the state, transcending traditional state-centric frameworks. This paper explores the significant shifts in international actorness over the late 20th century, focusing on the emergence and implications of sub-state diplomacy, or "paradiplomacy." First, the study introduces sub-state actors and their role in challenging the dominant state-centric discourse. It then examines the dynamic evolution of paradiplomacy, highlighting how sub-states have expanded their global

This deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values

In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

This research aims to develop new spectrophotometric analytical method to determine drug compound Salbutamol by reaction it with ferric chloride in presence potassium ferricyanide in acid median to formation of Prussian blue complex to determine it by uv-vis spectrophotmetric at wavelengths rang(700-750)nm . Study the optimal experimental condition for determination drug and found the follows: 1- Volume of(10M) H2SO4 to determine of drug is 1.5 ml . 2- Volume and concentration of K3Fe(CN)6 is 1.5 ml ,0.2% . 3- Volume and concentration of FeCl3 is 2.5ml , 0.2%. 4- Temperature has been found 80 . 5- Reaction time is 15 minute . 6- Order of addition is (drug + K3Fe(CN)6+ FeCl3 + acid) . Concentration rang (0.025-5 ppm) , limit detecti

We describe the synthesis and characterization of a novel 2D-MnOx material using a combination of HR-TEM, XAS, XRD, and reactivity measurements. The ease with which the 2D material can be made and the conditions under which it can be made implies that water oxidation catalysts previously described as “birnessite-like” (3D) may be better thought of as 2D materials with very limited layer stacking. The distinction between the materials as being “birnessite-like” and “2D” is important because it impacts on our understanding of the function of these materials in the environment and as catalysts. The 2D-MnOx material is noted to be a substantially stronger chemical oxidant than previously noted for other birnessite-like manganese oxi

This contribution reports a comprehensive investigation into the structural, electronic and thermal properties of bulk and surface terbium dioxide (TbO2); a material that enjoys wide spectra of catalytic and optical applications. Our calculated lattice dimension of 5.36 Å agrees well with the corresponding experimental value at 5.22 Å. Density of states configuration of the bulk structure exhibits a semiconducting nature. Thermo-mechanical properties of bulk TbO2 were obtained based on the quasi-harmonic approximation formalism. Heat capacities, thermal expansions and bulk modulus of the bulk TbO2 were obtained under a wide range of temperatures and pressures. The dependency of these properties on operational pressure is very evident. Cle