Given a sequence X=(X1,X2,…) of random observations, Bayesian forecaster aims to predict Xn+1 based on (X1,…,Xn) for each n≥0. To this end, in principle, she only needs select collection σ=(σ0,σ1,…), called “strategy” what follows, where σ0(·)=P(X1∈·) is the marginal distribution X1 and σn(·)=P(Xn+1∈·|X1,…,Xn) nth predictive distribution. Because Ionescu–Tulcea theorem, σ can be assigned direct...

Using a sum-product result due to Bourgain, Katz, and Tao, we show that for every 0 < 2 ≤ 1, and every integer k ≥ 1, there exists an integer N = N(2, k), such that for every prime p and every residue class a (mod p), there exist positive integers x1, ..., xN ≤ p satisfying a ≡ 1 x1 + · · ·+ 1 xN (mod p).

Let pm be any prime power and Kn(a, pm) be the Kloosterman sum Kn(a, pm) = ∑pm x1=1 · · · ∑pm xn=1 epm (x1 + · · ·+ xn + ax1x2 . . . xn), where the xi are restricted to values not divisible by p. Let m, n be positive integers with m ≥ 2 and suppose that pγ‖(n + 1). We obtain the upper bound |Kn(a, pm)| ≤ (n + 1, p − 1)p 1 2 min(γ,m−2)pmn/2, for odd p. For p = 2 we obtain the same bound, with an...

We consider homogeneous varieties of linear algebras over an associative-commutative ring K with 1, i.e., the varieties in which free algebras are graded. Let F = F (x1, ..., xn) be a free algebra of some variety Θ of linear algebras over K freely generated by a set X = {x1, ..., xn}, EndF be the semigroup of endomorphisms of F , and Aut EndF be the group of automorphisms of the semigroup EndF ...

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

We characterized the molecular species of human macrophage colony-stimulating factor (hM-CSF) found in serum and urine, using immunoblot analysis after partial purification on an antibody-bound affinity column. Although antibodies were prepared using the recombinant product of the large form of hM-CSF with a molecular weight (MW) of 85 Kd as the antigen, this immunoblot system was also capable ...

Housaku Monogatari (HM) is a plant activator prepared from a yeast cell wall extract. We examined the efficacy of HM application and observed that HM treatment increased the resistance of Arabidopsis thaliana and Brassica rapa leaves to bacterial and fungal infections. HM reduced the severity of bacterial leaf spot and anthracnose on A. thaliana and Brassica crop leaves with protective effects....

The effects of HM-1 killer toxin (HM-1) on yeast spheroplasts of Saccharomyces cerevisiae were examined under osmotically stabilized conditions. Prolonged incubation of spheroplasts in nutrient-rich media resulted in an increase in volume, accompanied by aberrant morphological changes. By contrast, spheroplasts were enlarged, maintaining a round shape, when incubated in HM-1 media. The required...

This paper concerns rigidity results to Serrin’s overdetermined problem in an epigraph  ∆u + f(u) = 0, in Ω = {(x′, xn) : xn > φ(x′)}, u > 0, in Ω, u = 0, on ∂Ω, |∇u| = const., on ∂Ω. We prove that up to isometry the epigraph must be an half space and that the solution u must be one-dimensional, provided that one of the following assumptions are satisfied: either n = 2; or φ is globally ...

DNA strands containing a 5-hydroxymethylcytosine ((hm)C), which have recently been found in neuron cells and embryonic stem cells, were synthesized through a facile synthetic technique. The (hm)C-containing strands were efficiently oxidized at (hm)C using an osmium oxidation assay. The (hm)C was oxidized as easily as 5-methylcytosine, which can be distinguished from unmethylated cytosine.