Q0 is an elegant version of Church’s type theory formulated and extensively studied by Peter B. Andrews. Like other traditional logics, Q0 does not admit undefined terms. The traditional approach to undefinedness in mathematical practice is to treat undefined terms as legitimate, nondenoting terms that can be components of meaningful statements. Qu0 is a modification of Andrews’ type theory Q0 ...

in many seismological applications, the earth is considered as a perfectly elastic, homogeneous, and isotropic body. although this assumption is approximately valid, it is known that seismic waves pass through the real earth that is anelastic, inhomogeneous and anisotropic.  we consider four processes that can reduce wave amplitude, i.e.: geometrical spreading, scattering, multi-pathing, and an...

Let R = ⊕ n≥0 Rn be a Noetherian homogeneous ring with onedimensional local base ring (R0,m0). Let q0 ⊆ R0 be an m0-primary ideal, let M be a finitely generated graded R-module and let i ∈ N0. Let Hi R+ (M) denote the i-th local cohomology module of M with respect to the irrelevant ideal R+ := ⊕ n>0 Rn of R. We show that the first Hilbert-Samuel coefficient e1 ( q0, Hi R+ (M)n ) of the n-th gra...

Deficiencies of early components of the classical complement pathway are known to be associated with systemic lupus erythematosus (SLE). C4 null alleles, C4A Q0 and C4B Q0, are prime candidates for the major histocompatibility complex associated factor which determines susceptibility to SLE. There is poor correlation, however, between the presence of low concentrations of C4 and possession of C...

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation f ′′ +Q ( e ) f ′ + (A1e a1z +A2e 2) f = 0, where n > 2 is an integer, Aj (z) ( 6≡ 0) (j = 1, 2) are entire functions with max {σ (Aj) : j = 1, 2} < 1, Q (z) = qmz + · · · + q1z + q0 is a nonconstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove tha...

Let $R$ be a commutative ring. An $R$-module $M$ is called semi-regular $w$-flat module if $\Tor_1^R(R/I,M)$ $\GV$-torsion for any finitely generated ideal $I$. In this article, we show that the class of modules covering class. Moreover, introduce dimensions $R$-modules and $sr$-$w$-weak global ring $R$. Utilizing these notions, give some homological characterizations $\WQ$-rings $Q_0$-\PvMR s.

In order to make better use of converter dust achieve effective pre-dephosphorization molten iron, the influence addition ratio dedusting ash and oxide scale on dephosphorization iron was compared, so as reveal reasons for decrease rate caused by dust. Through theoretical analysis, XRD, SEM-EDS, Raman infrared spectroscopy, mineral phase structure, polymerization degree phosphorus structure fin...

Introduced by Peter Andrews in the 1960’s, Q0 is a classical higher-order logic based on simply-typed lambda calculus. This paper presents our work in progress on the formalizing of Q0 in a programming language, Rogue-Sigma-Pi (RSP), with the aim of validating its meta-theory. The main challenge of this project arises from the fact that while all logical derivations are carried out in much deta...

We improved the approximation of the model of the wormhole generated physical universe constructed by Choudhury and Pendharkar. We show here that the negative pressure of the unphysical wormhole can generate the right physical condition to explain the correct sign of the deacceleration parameter q0. The negative sign of q0 implies an accelerating universe.