When joined to a stipulated neighborhood digraph, an objective function deÞned on the solution space of a real combinatorial optimization problem forms a landscape. Grover shows that landscapes satisfying a certain difference equation have properties favorable to local search. Studying only symmetric and regular neighborhood digraphs, Stadler deÞnes elementary landscapes as those which can be r...

The decomposition of Spinc(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation ∆Aμ = −λAμ has been discovered. Here λ is the vacuum expectation value of the spinor field, λ = ‖Φ‖, and Aμ the twisting U(1) potential. It is found that when λ takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian o...

In this work we are concerned about a singular boundary value problem involving the p-laplacian which arises in mathematical models of fluid mechanics. We analyze the asymptotic behavior of the solutions of the considered ordinary differential equation near the singularities and introduce a computational method which takes this behavior into account. Key–Words: Singular boundary value problem, ...

for a simple connected graph $g$ with $n$-vertices having laplacian eigenvalues‎ ‎$mu_1$‎, ‎$mu_2$‎, ‎$dots$‎, ‎$mu_{n-1}$‎, ‎$mu_n=0$‎, ‎and signless laplacian eigenvalues $q_1‎, ‎q_2,dots‎, ‎q_n$‎, ‎the laplacian-energy-like invariant($lel$) and the incidence energy ($ie$) of a graph $g$ are respectively defined as $lel(g)=sum_{i=1}^{n-1}sqrt{mu_i}$ and $ie(g)=sum_{i=1}^{n}sqrt{q_i}$‎. ‎in th...

We investigate the interface dynamics in Laplacian growth model, using the conformal mapping technique. Starting from the governing equation obtained by B.Shraiman and D.Bensimon, we derive intergro-differential evolution equation of interphase dynamics. It is shown that such representation of the conformal mapping technique is convenient for computer simulations of the quasi-stationary Stefan ...

In this work, we investigate the following p-Laplacian Liénard equation: (φp(x (t))) + f(x(t))x(t) + g(x(t)) = e(t). Under some assumption, a necessary and sufficient condition for the existence and uniqueness of periodic solutions of this equation is given by using Manásevich–Mawhin continuation theorem. Our results improve and extend some known results.

We study the ground state solutions for following p&q‐Laplacian equation where is a parameter large enough, with denotes ‐Laplacian operator, and . Under some assumptions periodic potential , weight function nonlinearity without Ambrosetti–Rabinowitz condition, we show above has solution.

In this paper we derive in a coordinate-free manner the field equations for a lagrangean consisting of Yang-Mills kinetical term plus Chern-Simons self-coupling term. This equation turns out to be an eigenvalue equation for the covariant laplacian. ∗This work is supported by a grant from CNPQ-Brazil

In this paper, we study the nonlinear heat equation ∂ ∂t △u(x, t) − c♦u(x, t) = f(x, t, u(x, t)), where△k is the Laplacian operator iterated k− times and is defined by (1.4)and ♦k is the Diamond operator iterated k− times and is defined by (1.2). We obtain an interesting kernel related to the nonlinear heat equation.

We deal with symmetry properties for solutions of nonlocal equations of the type (−∆) s v = f (v) in R n , where s ∈ (0, 1) and the operator (−∆) s is the so-called fractional Laplacian. The study of this nonlocal equation is made via a careful analysis of the following degenerate elliptic equation −div (x α ∇u) = 0 on R