The present study deals with the exact solutions of the Einstein’s field equations with variable gravitational and cosmological “constants” for a spatially homogeneous and anisotropic Bianchi type-I space-time. We assume that the conservation law for the matter is fulfilled. Hence giving rise to separate equations one for the perfect fluid and other connecting gravitational and cosmological constants. Assuming that G be a function of volume scale V, the metric functions, Λ-term, energy density and pressure are found to be functions of V. The equation for V is found through Einstein’s field equations and solved both analytically and numerically. The present study also allows a time dependent deceleration parameter (DP). It is found that for empty universe, the derived model is accelerating whereas for radiating dominated and stiff fluid universes, we obtain models that depict a transition of the universe from the early decelerated phase to the recent accelerating phase. The cosmological constant Λ is obtained as a decreasing function of time and approaching a small positive value at present epoch which is corroborated by consequences from recent supernovae Ia observations. The physical significances of the cosmological models have also been discussed.

The Gowdy spacetime metric splits the vacuum Einstein field equations into evolution equations, known as Gowdy equations. In this paper, Lie classical method is applied to investigate symmetries of the Gowdy equations, that is a coupled system of nonlinear second order partial differential equations. Symmetries which are obtained in this paper, are further helpful for reducing the coupled system of partial differential equations into ordinary differential equations. Moreover, some new solutions of Gowdy equations are derived from reduced differential equations.

In this paper, we introduce the local fractional Christoffel index symbols of the first and second kind. The divergence of a local fractional contravariant vector and the curl of local fractional covariant vector are defined. The fractional intrinsic derivative is given. The local fractional Riemann-Christoffel and Ricci tensors are obtained. Finally, the Einstein tensor and Einstein field are generalized by involving the fractional derivatives. Illustrative examples are presented.

In this paper, we have studied the FRW metric for variable $G$ and Λ in $f (R, T )$ gravity with the modified Chaplygin gas equation of state, i.e., $p = A\rho - \frac{B}{\rho^n}$ . We have
used the hybrid exponential law (HEL) for scale factor to obtain the solution of the field equations. Here also we have discussed some physical behaviour of the model.

In the present study, we discuss a non-equilibrium picture of thermodynamics at the apparent horizon of flat Friedmann-Roberton-Walker universe in $f (T, θ)$ theory of gravity, where $T$ is the torsion scalar and $\theta$ is the trace of the energy-momentum tensor. Mainly, we investigate the validity of the first and second laws of thermodynamics in this scenario. We consider two descriptions of the energy-momentum tensor of dark energy density and pressure and discuss that an equilibrium picture of gravitational thermodynamics can not be given in both cases. Furthermore, we also conclude that the second law of gravitational thermodynamics can be achieved both in phantom and quintessence phases of the universe.

We present a reliable study for the linear and the nonlinear Schlömilch’s integral equation and its generalized forms. We also introduce Schlömilch-type integral equations and study it as well. The Schlömilch’s integral equation has been used for many ionospheric problems, atmospheric and terrestrial physics. We use the regularization method combined with the Adomian decomposition method to handle all forms of Schlömilch’s integral equations. The combined regularization-Adomian method can be used in many applied physics, applied mathematics and engineering applications. We justify the reliability of the regularization-Adomian method through illustrative examples.

This paper studies the long-wave short-wave interaction equation that produces soliton solutions as well as other exact solutions. Exact 1-soliton solutions are obtained for this equation, with time-dependent coefficients, by the aid of ansatz method. Subsequently, the simplest equation approach also gives soliton solutions as well as other solutions such as singular periodic solutions and plane waves. There are several constraints that naturally emerge for the solutions to exist.

This work is devoted to studying the oscillator fractional differential equations in the vibration research field. To this end, the Bagley-Torvik, Rayleigh, and Van der Pol equations with fractional damping are considered as certain types of oscillator fractional equations. Operational matrix of fractional integration, based upon block-pulse functions and the second kind Chebyshev polynomials, is applied to reduce the fractional equations into an algebraic system that can be solved by an appropriate method. It is shown that by increasing the number of iterations, the accuracy of the approximate solutions can be improved. The numerical results are included to demonstrate the validity and applicability of the operational matrix for solving oscillator fractional differential equations.

In this paper, Sumudu decomposition method is developed to solve general form of fractional partial differential equation. The proposed method is based on the application of Sumudu transform to nonlinear fractional partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivatives are described in the Caputo sense. The Sumudu method is found to be fast and accurate. Illustrative examples are given to demonstrate the validity and applicability of the proposed technique.

The first integral method is applied to get the different types of solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and Hirota equations. We obtain envelope, bell shaped, trigonometric, and kink soliton solutions of these nonlinear evolution equations. The applied method is an effective one to obtain different types of solutions of nonlinear partial differential equations.

We show that the Wei-Norman method applied to describe the evolution on the Siegel-Jacobi disk $\mathcal{D}_{1}^{J} = \mathcal{D}_1 \times \mathbb{C}^1$, where $\mathcal{D}_1$ denotes the Siegel disk, determined by a hermitian Hamiltonian linear in the generators of the Jacobi group $G^{J}_{1}$ and Berezin’s scheme using coherent states give the same equations of quantum and classical motion when are expressed in the coordinates in which the Kähler two-form $\omega_{\mathcal{D}_{1}^{J}}$ can be written as $\omega_{\mathcal{D}_{1}^{J}}=\omega_{\mathcal{D}_1}+\omega_{\mathbb{C}^1}$. The Wei-Norman equations on $\mathcal{D}_{1}^{J}$ are a particular case of equations of motion on the Siegel-Jacobi ball $\mathcal{D}_{n}^{J}$ generated by a hermitian Hamiltonian linear in the generators of the Jacobi group $G_{n}^{J}$ obtained in Berezin’s approach based on coherent states on $\mathcal{D}_{n}^{J}$.

Investigations of the fragmentation potential energy surface is realized in the frame of the macroscopic-microscopic model in order to emphasize the importance of the shell effects in the synthesis and the stability of superheavy nuclei. The shell effects and the macroscopic potential are reported separately. The origin of several minima that are responsible for metastable states is discussed.

The momentum of inertia is calculated for the ²⁴⁰Pu alpha decay process within the cranking model. The alpha decay is treated as a superasymmetric fission process within the macroscopic-microscopic model. The microscopic part is based on the Woods-Saxon two center shell model. The moment of inertia exhibits a rapid variation in the vicinity of the ground state of the parent configuration.

The even-even isotopes of the ^180-196Pt chain are analyzed in the framework of two solvable approaches for the quadrupole intrinsic variables, called the Davidson and Spheroidal Approach (DSA) and Davidson and Mathieu Approach (DMA), respectively. The energy spectra of the ground and first β and γ bands, E2 transition probabilities between states belonging to these bands and shapes of the ground and some excited states are determined for each isotope. The numerical results are compared with the corresponding experimental data as well as with those obtained with two recently proposed models, namely, the Sextic and Spheroidal Approach (SSA) and Sextic and Mathieu Approach (SMA).

In this paper we are concerning with the integro-differential equation of 1-dimensional neutron transport problem in the stationary case by means of a vectorial variant of the decomposition method. The numerical test proves excellent agreement between the approximate solution and exact solution.

The average of event shape variables is studied in $e^+ e^-$ annihilation within the context of next to leading order (NLO) perturbative QCD prediction. We measure the strong coupling constant $\alpha_S (M_{(Z^0)})$ by fitting the NLO model with the variance distribution. Then, the parameters of non-perturbative part of theory are measured. These parameters are extracted from the dispersive model for ($\alpha_0$) and also from the shape function model for ($\lambda$). We explain all these features in this article.

The pressure evolutions of cobalt moments in rare-earth compounds are studied by using band structure calculations. The computed magnetic moments are compared with those experimentally determined. The peculiar features of the magnetic-nonmagnetic transitions are analysed. The magneto-volume effects are discussed in correlation with the localization degree of transition metal moments.

Energy-based surgery has greatly expanded in recent years because of the many areas that can be applied in the field of human medicine. These procedures are known to produce a toxic smoke in operating room that can pose a health risk both for surgeons and patients. Compared to abundant studies on the qualitative composition on surgical smoke, the quantitative data on personnel exposure are incomplete. More information regarding smoke concentrations are required to discuss the potential health impact of the resulting exposures. Therefore, the quantitative composition of surgical smoke is of great interest. Using Laser Photoacoustic Spectroscopy (LPAS), smoke samples produced in vitro by CO₂ laser vaporization of fresh animal tissues were investigated. Traces of acetonitrile, acrolein, ammonia, benzene, ethylene, and toluene were detected in surgical smoke in the ppb to ppm range. Half of the identified gases were found exceeding in quantities the occupational exposure limit. The measured concentrations of these compounds indicated a strong relation of the potential hazards with irradiation conditions (laser power and exposure time). The sensitive CO₂ laser photoacoustic spectroscopy measurements are well suited to provide quantitative information on gas products emitted during laser-tissue interaction.

Iron complex compounds synthesized by Pseudomonas aeruginosa could be of interest as bactericidal agents against other pathogen germs. A possible biotechnological application was studied in an experimental design using magnetite nanoparticles coated with citric acid and dispersed in deionized water. The magnetite concentrations supplied in the culture medium of Pseudomonas aeruginosa were equal to: 0.25-0.290.34-0.44-0.66-1.1-1.9-3.6-7.0 μg/ml. Stimulatory effect of relative low concentrations of magnetite on the siderophore synthesis was evidenced through fluorescence measurements. The antimicrobial effect of Pseudomonas thermolysate against several strains of Sarcina lutea and Staphylococcus aureus (clinical isolates from hospital patients) was revealed with higher amplitude in the case of Pseudomonas strain supplied with some concentrations of nanosized magnetite–although no specific correlation could be emphasized between size of growth inhibition areas and magnetic nanoparticle concentration.

The aim of this study was to determine the concentrations of toxic elements Cu, Cr, Ni, Pb, Cd, Zn, Hg, As and Cr(VI) employing spectroscopic techniques ICP–AES, ETAAS and CVAAS, and to assess the possibility of using the sludge for application on agricultural land. Sewage sludge (n=21 samples) was collected in different seasons in the period 2007–2011 from three municipal wastewater treatment plants (WWTPs) in Northern Greece (Kavala, Drama and Palio). Due to the low concentration values (mg/kg dry matter) found for all the metals (Cd: 0.8–7.3, mean 2.13±1.61; Cr: 13.2–355, mean 103.8±100.8; Cr(VI): 0.28–4.30, mean 1.56±1.32; Cu: 51–198, mean 136.5±45.5; Hg: <0.2; Ni: 8.8–64, mean 29.2±15.5; Pb: 12–102, mean 62.0±23.1, Zn: 810–1880, mean 1256.1±334.3 and Cr(VI): 0.28–4.3, mean 1.56±1.32), the sewage sludge produced in the WWTPs of all three cities may be used as fertilizer for agricultural soil according to the European Council Directive 86/278/EEC and Greek legislation 80568/4225/91. Although the As content of sludge is not regulated in Greece, the concentrations found in selected sludge samples (6.3–9.2 mg/kg dry matter) must be corroborated with the As concentration in background soil in case that agricultural disposal of sludge is the chosen route.

The purpose of this study was to determine heavy metals content including Pb, Cd, Cr, Ni, Mn, Zn and Fe, in surface water, depth water and mud samples collected from six salt lakes from Prahova and Dambovita counties, Romania. The concentrations of these elements were determined by atomic absorption spectrometry. The results indicate that concentrations were highest in mud samples from all six salt lakes compared with the surface water and depth water samples. In general, metal content in mud is indicative of the degree of pollution and serve as source of solubilization into water depending on the physicochemical properties (pH, salinity, conductivity, temperature etc.) and the uptake by benthic organisms.

A series of laboratory tests have been conducted to evaluate the quantitative retention of ²²⁶Ra by three different strong cation exchange resins under varying conditions. The influence of the maximum flow rate, which could be obtained with the extraction chromatography columns, was tested. The Radium Selective Complexer (RSC) showed a relatively higher adsorption capacity for radium with an average ²²⁶Ra recovery of 96.4%. The effect of increasing the amounts of the competing Ca and Mg ions on the uptake of ²²⁶Ra by the three types of resins has been evaluated. The Purolite resin showed a relatively higher adsorption capacity for radium in water samples that have Ca and Mg ions as high as 3000 mg/L. The average radium recovery achieved by the Purolite resin was 90.7%. The influence of Iron (III) on the recovery of radium using the three types of resins was significant. The maximum ²²⁶Ra recovery obtained was 89.9% using the Purolite resin. A groundwater sample was analyzed for ²²⁶Ra and measured by gamma spectrometry using the three types of resins, and also analyzed by alpha spectrometry and a radon detector (RAD-7) for comparison. The recoveries of ²²⁶Ra achieved by the three types of resins were comparable, and the results of comparison with the different techniques were very encouraging for the use of such water softener resins in the extraction of radium isotopes from large number of groundwater samples, when rapid and inexpensive method is needed.