Entire matrix-valued functions of a complex argument (entire matrix pencils) are considered. Bounds for spectral variations of pencils are derived. In particular, approximations of entire pencils by polynomial pencils are investigated. Our results are new even for polynomial pencils. © 2005 Elsevier Inc. All rights reserved.

Recent developments in cosmology indicate that every history having a nonzero probability is realized in infinitely many distinct regions of spacetime. Thus, it appears that the universe contains infinitely many civilizations exactly like our own, as well as infinitely many civilizations that differ from our own in any way permitted by physical laws. We explore the implications of this conclusi...

In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunctions of generalized Laplacians, i.e., symmetric matrices with non-positive off-diagonal entries. this paper, we establish arbitrary by exploring the induced signed graph structure. Our concepts domains any function on a are switching invariant. When is balanced, our definitions upper bound estima...

Penrose et al. investigated the physical incoherence of spacetime with negative mass via bending light. Precise estimates time-delay null geodesics were needed and played a pivotal role in their proof. In this paper, we construct an intermediate diagonal metric make reduction problem to causality comparison compactified spacetimes regarding timelike connectedness near conformal infinities. This...

Anselm’s Ontological Argument fails, but not for any of the various reasons commonly adduced. In particular, its failure has nothing to do with violating deep Kantian principles by treating ‘exists’ as a predicate or making reference to ‘Meinongian’ entities. Its one fatal flaw, so far from being metaphysically deep, is in fact logically shallow, deriving from a subtle scope ambiguity in Anselm...

We investigate which represented spaces enjoy the fixed-point property, is property that every continuous multi-valued function has a fixed-point. study basic theory of this notion and its uniform version. provide complete characterization countable-based T0-spaces with showing they are exactly pointed ω-continuous dcpos. prove whose lattice open sets enjoys countably-based spaces. While role p...

We provide a rigorous treatment of continuous limits for various generalizations the pentagram map on polygons in RPd by means quantum calculus. Describing this limit detail case short-diagonal map, we verify that construction yields (2,d+1)-KdV equation, and moreover, Lax form is proved to become representation corresponding KdV system. More generally, introduce χ-pentagram geometric defining ...

We have implemented a translator that translates Carneades Argument Graphs as specified in the LKIF files of the Carneades editor to a database specification of the Argument Interchange Format and vice versa. In this paper the algorithms for this translation are presented.

An explicit construction of a geodesic flow-invariant distribution lying in the discrete series of weight 2k isotopic component is found, using techniques from representation theory of SL2(R). It is found that the distribution represents an AC measure on the unit tangent bundle of the hyperbolic plane minus an explicit singular set. Finally, via an averaging argument, a geodesic flow-invariant ...