We define a rank function rk, mapping modal μ-formulae on ordinals below ω such that rk(μx.φ) > rk(φ(x)) for n ∈ N, with φ(x) ≡ x and φ(x) ≡ φ[x/φ(x)], and rk(φ) > rk(ψ) for all proper subformulae ψ of φ. The corresponding induction on formulae is thus justified by transfinite induction on ω. We then show that ω is the least such ordinal. Further, we give an algorithm to compute rk(φ) by primit...

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.

We have studied the decay of the φ meson in nuclear matter by taking into account the renormalization of the K and K̄ mesons in the medium. We separate the contribution of the total width into different reaction channels, KK̄ and KY h , the latter ones associated with the φN → K+Y reactions. We find a total width at normal nuclear matter density of about 22 MeV, considerably larger than the free ...

Traveling waves play a key role in mathematical models since they characterize observable fundamental phenomena in nature. A typical traveling wave corresponds to a state which is time independent (in some cases time periodic) in a moving coordinates. In a one space dimensional setting, it depends only on z := x − ct where c is the wave speed and x and t are respectively space and time variable...

Proof. First note that the map φ is uniquely determined by its components φ11, φ12, φ21, φ22. Indeed, by the universal property of the coproduct M1 ⊕ M2 we see that φ is uniquely determined by the maps φ∗1 := φ◦ι1 and φ∗2 := φ◦ι2. Then from the universal property of the product N1⊕N2 we see that the map φ∗1 is uniquely determined by the maps φ11 = π1 ◦φ∗1 and φ21 = π2 ◦ φ∗1. Similarly, φ∗2 is u...

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

this study proposed a new discharge estimation method using a mean velocity formula derived from chiu’s 2d velocity formula of probabilistic entropy concept and the river bed shear stress of channel. in particular, we could calculate the mean velocity, which is hardly measurable in flooding natural rivers, in consideration of several factors reflecting basic hydraulic characteristics such as ri...

We present the calculations of the incidence rates used in [1]. I. GENERAL CASE With respect to the main text, here we assume that χ ∈ [θ, θ + 2π] instead of χ ∈ [−π, π]. This is adopted for reasons of mathematical convenience, as we show later on. As all incidence rates are periodic, with a period 2π, with respect to χ, this assumption is not in any way restrictive. We expand the description o...

A (2k+1)-dimensional Lie algebra is called contact if it admits a one-form φ such that φ∧(dφ)k≠0. Here, we extend recent work to describe combinatorial procedure for generating contact, type-A poset algebras whose associated posets have chains of arbitrary cardinality, and conjecture our construction leads complete characterization.