a pair of degenerate primers, gmpf1 and gmpr1, was designed on the basis of alignment of previously reported grapevine fanleaf virus (gflv) movement protein (mp) nucleotide sequences from iran and other parts of the world. cdna was synthesized by the use of oligo d(t)18 from total rna extraction from each diseased grapevine leaf sample and subjected to polymerase chain reaction (pcr) with the d...

We study the degenerate Kolmogorov equations (also known as kinetic Fokker–Planck equations) in nondivergence form. The leading coefficients $$a^{ij}$$ are merely measurable t and satisfy vanishing mean oscillation condition x, v with respect to some quasi-metric. also assume boundedness uniform nondegeneracy of v. prove global a priori estimates weighted mixed-norm Lebesgue spaces solvability ...

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...

This paper considers the least mean-squared error linear estimation problems, using covariance information, in linear discrete-time stochastic systems with uncertain observations for the case of white plus coloured observation noises. The different kinds of estimation problems treated include one-stage prediction, filtering, and fixed-point smoothing. The recursive algorithms are derived by emp...

We consider an abstract equation F (λ, u) = 0 with one parameter λ, where F ∈ C(R × X,Y ), p ≥ 2 is a nonlinear differentiable mapping, and X,Y are Banach spaces. We apply Lyapunov-Schmidt procedure and Morse Lemma to obtain a “double” saddle-node bifurcation theorem near a degenerate point with a two-dimensional kernel. It is shown that the solution set of the equation is the union of two para...

We study radially symmetric finite time blow-up dynamics for the aggregation equation with degenerate diffusion ut = ∆u m − ∇ · (u ∗ ∇(K ∗ u)) in R, where the kernel K(x) is of power-law form |x|−γ . Depending on m, d, γ and the initial data, the solution exhibits three kinds of blow-up behavior: self-similar with no mass concentrated at the core, imploding shock solution and near-self-similar ...

This work establishes nonlinear orbital asymptotic stability of scalar radiative shock profiles, namely, traveling wave solutions to the simplified model system of radiating gas [8], consisting of a scalar conservation law coupled with an elliptic equation for the radiation flux. The method is based on the derivation of pointwise Green function bounds and description of the linearized solution ...

Many discrepancy principles are known for choosing the parameter in the regularized operator equation (T T + I)x = T y , ky ?y k , in order to approximate the minimal norm least-squares solution of the operator equation Tx = y. In this paper we consider a class of discrepancy principles for choosing the regularization parameter when T T and T y are approximated by A n and z n respectively with ...

We introduce a new notion of linear stability for standing waves of the nonlinear Schrödinger equation (NLS) which requires not only that the spectrum of the linearization be real, but also that the generalized kernel be not degenerate and that the signature of all the positive eigenvalues be positive. We prove that excited states of the NLS are not linearly stable in this more restrictive sens...