We sharpen Hájek’s Completeness Theorem for theories extending predicate product logic, Π∀. By relating provability in this system to embedding properties of ordered abelian groups we construct a universal BL-chain L in the sense that a sentence is provable from Π∀ if and only if it is an L-tautology. As well we characterize the class of lexicographic sums that have this universality property.

This paper presents the application of Buckingham’s π theorem to scale the powertrain of a High Mobility Multipurpose Wheeled Vehicle (HMMWV) by deriving non dimensional ratios called π parameters. A Hardware In the Loop (HIL) setup is constructed and the resulting longitudinal dynamics of the scaled vehicle are validated against those of a full scale vehicle model. This is performed with the u...

For given a graphH , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. Let Km −H be the graph obtained from Km by removing the edges set E(H) where H is a subgraph of Km. In this paper, we characterize the potentially K2,5-graphic sequences. This characterization implies a theorem due to Yin et al. [15].

Let ΩX be the space of Moore loops on a finite, qconnected, n-dimensional CW complex X , and let p be an odd prime. We prove the theorem: If p ≥ n/q, then the Hurewicz homomorphism induces isomorphisms U(Fπ∗(ΩX(p))) = −→ FH∗(ΩX(p)) and UE ∞ π (ΩX) = −→ E∞ H (ΩX) of Hopf algebras, where E ∞ π and E ∞ H are the limit terms of the homotopy and homology Bockstein spectral sequences, respectively, a...

The most precise value for the \pi^0 π0 mass was obtained from measurement of difference m_{\pi^-}-m_{\pi^0} = 4.593\,64(48) display="inline">mπ−−...

For given a graphH , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. Let Km −H be the graph obtained from Km by removing the edges set E(H) where H is a subgraph of Km. In this paper, we characterize the potentially K6 − C4-graphic sequences. This characterization implies a theorem due to Hu and Lai [7].

For given a graphH , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. In this paper, we characterize the potentially Hgraphic sequences where H denotes 3-regular graph with 6 vertices. In other words, we characterize the potentially K3,3 and K6 − C6graphic sequences where Kr,r is an r × r complete bipa...

For given a graphH , a graphic sequence π = (d1, d2, · · · , dn) is said to be potentially H-graphic if there exists a realization of π containing H as a subgraph. Let Km − H be the graph obtained from Km by removing the edges set E(H) where H is a subgraph of Km. In this paper, we characterize potentially K2,5-graphic sequences. This characterization implies a special case of a theorem due to ...

Ramanujan proved that the inequality π(x) < ex log x π (x e ) holds for all sufficiently large values of x. Using an explicit estimate for the error in the prime number theorem, we show unconditionally that it holds if x ≥ exp(9658). Furthermore, we solve the inequality completely on the Riemann Hypothesis, and show that x = 38, 358, 837, 682 is the largest integer counterexample.

We use the interactive theorem prover Isabelle to prove that the algebraic axiomatization of bisimulation equivalence in the pi-calculus is sound and complete. This is the first proof of its kind to be wholly machine checked. Although the result has been known for some time the proof had parts which needed careful attention to detail to become completely formal. It is not that the result was ev...