The aim of this paper is to establish some a priori bounds for solutions of Landesman-Lazer problem. We show the application for the solution structure of the nonlinear diierential equation of the fourth order 1. The general theory Let X be a real Banach space with the norm k k and let D(L) X be the domain of the closed Fredholm operator L : D(L) ! X with index zero. We shall suppose that 0 is ...

We have isolated the gene encoding the Schwann cell glycoprotein P0, the major structural protein of the peripheral myelin sheath. In rats and mice, this gene is split into six exons distributed over 7 kb of DNA. The segregation of these exons is consistent with the functional segregation of the P0 protein into extracellular, membrane-spanning, and cytoplasmic domains. We find that the P0 extra...

The chaotic order A B among positive invertible operators A,B > 0 on a Hilbert space is introduced by logA≥ logB. Using Uchiyama’s method and Furuta’s Kantorovich-type inequality, we will point out that A B if and only if ‖BpA−p/2B−p/2‖Ap ≥ Bp holds for any 0 < p < p0, where p0 is any fixed positive number. On the other hand, for any fixed p0 > 0, we also show that there exist positive invertib...

1. Note that Y1 is independent of {Xn}n=1. Now, observe that H0 is a composite hypothesis, and we are in a Bayesian situation with the rv θ (= the rv P0) taking values in Θ0 = {1/4, 3/4} with P0[θ = 1 4 ] = 14 = 1 − P0[θ = 34 ], where P0 denotes the conditional pmf of θ given H = H0. H1 is a simple hypothesis. Under H0: For each t ∈ Θ0 = { 1 4 , 4}, {Yn}n=1 is a 1st order Markov process with tr...

P0 protein, the dominant protein in peripheral nervous system myelin, was studied immunocytochemically in both developing and mature Schwann cells. Trigeminal and sciatic nerves from newborn, 7-d, and adult rats were processed for transmission electron microscopy. Alternating 1-micrometer-thick Epon sections were stained with paraphenylenediamine (PD) or with P0 antiserum according to the perox...

Expression of myelin proteins has been shown to be altered in transgenic mice that express papovaviral large tumor (T) antigens. This paper analyzes the effect on P0 gene expression in secondary Schwann cells transfected with the SV40 T antigen gene and in Schwann cells immortalized by T antigen. In secondary Schwann cells, both T antigen and c-Jun are required for significant inhibition of the...

A three-dimensional polynomial algebra of order m is defined by the commutation relations [P0, P±] = ±P±, [P+, P−] = φ (P0) where φ(P0) is an m-th order polynomial in P0 with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders l and m can be combined to give two distinct (l + m + 1)-th order polynomial ...

where z = (x, t) ∈ RN×R and 1 ≤ p0 ≤ N. By convenience, hereafter the term “Kolmogorov equation” will be shortened to KE. We assume the following hypotheses: (H.1) the matrix A0 = (aij)i,j=1,...,p0 is symmetric and uniformly positive definite in R p0 : there exists a positive constant μ such that |η| μ ≤ p0 ∑ i,j=1 aij(z)ηiηj ≤ μ|η|, ∀η ∈ R0 , z ∈ R; (1.2) (H.2) the matrix B ≡ (bij) has constan...

We have analyzed the effects of cAMP-elevating drugs (dibutyryl cAMP, forskolin, and isobutyl methylxanthine) on growth properties and myelin-specific gene expression in the peripheral neurinoma cell line D6P2T. The steady-state levels of RNA and polypeptide for the two major PNS myelin proteins, P0 glycoprotein (P0) and myelin basic protein (MBP), were measured by Northern blotting and immunob...