Thus Tf(x) can be viewed as averaging the function f over the curve t → γ(x, t) with respect to the fractional integral kernel k(t). The condition γ(x, 0) = x is a way of saying the curve at x is ”centered at x”, and the condition that ∂γ ∂t (x, t) 6= 0 ensures that the averaging is smooth. In fact, the arguments of this paper will go through with k(t) replaced by k(x, t) satisfying appropriate...

Analyzing the effective conformal field theory for the parafermionic Hall states, corresponding to filling fractions νk = 2 + k/(kM + 2), k = 2, 3, . . ., M odd, we show that the even k plateaux are expected to be more stable than their odd k neighbors. The reason is that the parafermion chiral algebra can be locally extended for k even. This reconciles the theoretical implication, that the big...

Two types of light polypeptide chain (kappa and lambda) are present in guinea pig immunoglobulins. The ratios of K/L molecules in anti-hapten antibodies differ sometimes markedly from that found in normal serum. Anti-DNP antibodies and anti-pipsyl antibodies have, respectively, a higher and a lower than normal K/L ratio. The possibility that the L chain type affects the range of configurations ...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

A fractional [a, b]-factor of a graph G is function h from E(G) to [0, 1] satisfying \(a \le d_G^h(v) b\) for every vertex v G, where \(d_G^h(v) = \sum\limits_{e \in E(v)} {h(e)} \) and E(v) {e uv : u ? V (G)}. called b]-covered if contains with h(e) 1 any edge e G. (a, b, k)-critical covered — Q ? V(G) ?Q? k. In this article, we demonstrate neighborhood condition be covered. Furthermore, claim...

In this paper, we prove the existence of at least three solutions to the following Kirchhoff nonlocal fractional equation:  M (∫ Rn×Rn |u(x)− u(y)| K(x− y)dxdy − ∫ Ω |u(x)|dx ) ((−∆)u− λu) ∈ θ(∂j(x, u(x)) + μ∂k(x, u(x))), in Ω, u = 0, in R \ Ω, where (−∆) is the fractional Laplace operator, s ∈ (0, 1) is a fix, λ, θ, μ are real parameters and Ω is an open bounded subset of R, n > 2s, with L...

We prove nonexistence of nontrivial bounded solutions to some nonlinear problems involving nonlocal operators of the form Lu(x) = − ∑ aij∂iju+ PV ∫ Rn (u(x)− u(x+ y))K(y)dy. These operators are infinitesimal generators of symmetric Lévy processes. Our results apply to even kernels K satisfying that K(y)|y| is nondecreasing along rays from the origin, for some σ ∈ (0, 2) in case aij ≡ 0 and for ...