We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein-Maxwell fiel...

Thermodynamics drive the spontaneous dissolution of a graphite intercalation compound (GIC) KC(8) in NMP to form stable solutions. Reduction potential of graphene is measured at +22 mV vs. SCE. Single layer graphene flakes (ca. 1 μm(2)) have been unambiguously identified by electron diffraction.

Lu = aij(x)Diju for u ∈ C(Ω). Suppose u ∈ C(Ω) is a supersolution in Ω, i.e. Lu ≤ 0. Then if φ ∈ C(Ω) satisfies Lφ > 0, we get L(u− φ) < 0 in Ω, hence by the maximum principle, u− φ does not have interior local minima in Ω. Put differently, if φ ∈ C(Ω) is such that u− φ has a local minimum at x0 ∈ Ω, then necessarily Lφ(x0) ≤ 0. Geometrically, u− φ having a local minimum at x0 means that the gr...

No problem is ever permanently closed. The editor is always pleased to consider for publication new solutions or new insights o n p a s t p r oblems. (1) Determine the set of all c > 0 such that whenever (1) holds, then we have x + y + z xy + yz+ zx. The positive r eals c asked for are those satisfying c 4. From (1), we have xy < c and z = c ; xy x + y + xy. Substituting this value of z into th...

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

sueyoshi and sekitani in 2007 presented a paper that explores the measurement of returns to scale under a possible occurrence of multiple solution in a reference set and a supporting hyperplane. the occurrence ofmultiple solutions is classified into type i and type ii. type i is an occurrence of multiple solutions in a reference set. type ii is an occurrence of multiple solutions on a supportin...

‎we mainly discuss the existence of meromorphic (entire) solutions of‎ ‎certain type of non-linear difference equation of the form‎: ‎$f(z)^m+p(z)f(z+c)^n=q(z)$‎, ‎which is a supplement of previous‎ ‎results in [k‎. ‎liu‎, ‎l. z‎. ‎yang and x‎. ‎l‎. ‎liu‎, ‎existence of entire solutions of nonlinear difference‎ ‎equations‎, ‎czechoslovak math. j. 61 (2011)‎, no. 2, ‎565--576‎, and x‎. ‎g‎. ‎qi‎...

this paper uses integrated data envelopment analysis (dea) models to rank all extreme and non-extreme efficient decision making units (dmus) and then applies integrated dea ranking method as a criterion to modify genetic algorithm (ga) for finding pareto optimal solutions of a multi objective programming (mop) problem. the researchers have used ranking method as a shortcut way to modify ga to d...