Existence and uniqueness of Q-processes with a given finite μ-invariant measure

Let Q be a stable and conservative Q-matrix over a countable state space S consisting of an irreducible class C and a single absorbing state 0 that is accessible from C. Suppose that Q admits a finite mu-subinvariant measure in on C. We derive necessary and sufficient conditions for there to exist a Q-process for which m is mu-invariant on C, as well as a necessary condition for the uniqueness of such a process.

Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.

Existence and multiplicity results for quasilinear elliptic equations

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f (x, s), we show the following problem: -Delta(p)u = lambda f(x,u) in Omega, u/(partial derivative Omega) = 0, where Omega is a bounded open subset of R-N, N >= 2, with smooth boundary, lambda is a positive parameter and Delta(p) is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large lambda.

Neutron-mapping polymer flow: Scattering, flow visualization, and molecular theory

Flows of complex fluids need to be understood at both macroscopic and molecular scales, because it is the macroscopic response that controls the fluid behavior, but the molecular scale that ultimately gives rise to rheological and solid-state properties. Here the flow field of an entangled polymer melt through an extended contraction, typical of many polymer processes, is imaged optically and by small-angle neutron scattering. The dual-probe technique samples both the macroscopic stress field in the flow and the microscopic configuration of the polymer molecules at selected points. The results are compared with a recent tube model molecular theory of entangled melt flow that is able to calculate both the stress and the single-chain structure factor from first principles. The combined action of the three fundamental entangled processes of reptation, contour length fluctuation, and convective constraint release is essential to account quantitatively for the rich rheological behavior. The multiscale approach unearths a new feature: Orientation at the length scale of the entire chain decays considerably more slowly than at the smaller entanglement length.

Genetic resource impacts of habitat loss and degradation; reconciling empirical evidence and predicted theory for neotropical trees

The theoretical impacts of anthropogenic habitat degradation on genetic resources have been well articulated. Here we use a simulation approach to assess the magnitude of expected genetic change, and review 31 studies of 23 neotropical tree species to assess whether empirical case studies conform to theory. Major differences in the sensitivity of measures to detect the genetic health of degraded populations were obvious. Most studies employing genetic diversity (nine out of 13) found no significant consequences, yet most that assessed progeny inbreeding (six out of eight), reproductive output (seven out of 10) and fitness (all six) highlighted significant impacts. These observations are in line with theory, where inbreeding is observed immediately following impact, but genetic diversity is lost slowly over subsequent generations, which for trees may take decades. Studies also highlight the ecological, not just genetic, consequences of habitat degradation that can cause reduced seed set and progeny fitness. Unexpectedly, two studies examining pollen flow using paternity analysis highlight an extensive network of gene flow at smaller spatial scales (less than 10 km). Gene flow can thus mitigate against loss of genetic diversity and assist in long-term population viability, even in degraded landscapes. Unfortunately, the surveyed studies were too few and heterogeneous to examine concepts of population size thresholds and genetic resilience in relation to life history. Future suggested research priorities include undertaking integrated studies on a range of species in the same landscapes; better documentation of the extent and duration of impact; and most importantly, combining neutral marker, pollination dynamics, ecological consequences, and progeny fitness assessment within single studies.

Myths and Truths: The "Law and Finance Theory" Revisited

The law and finance theory identifies two dominating legal traditions, a common law tradition inherited from England, and a civil law tradition that is going back to 19th century codifications in France, Germany and Scandinavia. Another key notion of the theory is the distinction between insiders (stakeholders, "the State") and outsiders (shareholders as well as creditors). The micro foundation of this approach is the willingness to invest. The innovative addition of the law and finance theory to these ideas lies in the way it combines them with its peculiar view on legal history. The innovative addition of the law and finance theory to these ideas lies in the way it combines them with its peculiar view on legal history. The major conclusion of this theory is that the common law system provides the best basis for financial development and economic growth, followed by Scandinavian and German origin civil law and finally French origin civil law.

A new system of variational inclusions with (H,eta)-monotone operators in Hilbert spaces

In this paper, we introduce and study a new system of variational inclusions involving (H, eta)-monotone operators in Hilbert space. Using the resolvent operator associated with (H, eta)monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (c) 2005 Elsevier Ltd. All rights reserved.

Theory of mind and relational complexity

Cognitive complexity and control theory and relational complexity theory attribute developmental changes in theory of mind (TOM) to complexity. In 3 studies, 3-, 4-, and 5-year-olds performed TOM tasks (false belief, appearance-reality), less complex connections (Level 1 perspective-taking) tasks, and transformations tasks (understanding the effects of location changes and colored filters) with content similar to TOM. There were also predictor tasks at binary-relational and ternary-relational complexity levels, with different content. Consistent with complexity theories: (a) connections and transformations were easier and mastered earlier than TOM; (b) predictor tasks accounted for more than 80% of age-related variance in TOM; and (c) ternary-relational items accounted for TOM variance, before and after controlling for age and binary-relational items. Prediction did not require hierarchically structured predictor tasks.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).