Counting Real Connected Components of Trinomial Curve Intersections and m-nomial Hypersurfaces

We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees were much larger, e.g., 248832 (for just the non-degenerate roots) via a famous general result of Khovanski. Our bound is sharp, allows real exponents, allows degeneracies, and extends to certain systems of n-variate fewnomials, giving improvements over earlier bounds by a factor exponential in the number of monomials. We also derive analogous sharpened bounds on the number of connected components of the real zero set of a single n-variate m-nomial.Comment: 27 pages, 2 figures. Extensive revision of math.CO/0008069. To appear in Discrete and Computational Geometry. Technique from main theorem (Theorem 1) now pushed as far as it will go. In particular, Theorem 1 now covers certain fewnomial systems of type (n+1,...,n+1,m) and certain non-sparse fewnomial systems. Also, a new result on counting non-compact connected components of fewnomial hypersurfaces (Theorem 3) has been adde

Combustor flame flashback

A stainless steel, two-dimensional (rectangular), center-dump, premixed-prevaporized combustor with quartz window sidewalls for visual access was designed, built, and used to study flashback. A parametric study revealed that the flashback equivalence ratio decreased slightly as the inlet air temperature increased. It also indicated that the average premixer velocity and premixer wall temperature were not governing parameters of flashback. The steady-state velocity balance concept as the flashback mechanism was not supported. From visual observation several stages of burning were identified. High speed photography verified upstream flame propagation with the leading edge of the flame front near the premixer wall. Combustion instabilities (spontaneous pressure oscillations) were discovered during combustion at the dump plane and during flashback. The pressure oscillation frequency ranged from 40 to 80 Hz. The peak-to-peak amplitude (up to 1.4 psi) increased as the fuel/air equivalence ratio was increased attaining a maximum value just before flashback. The amplitude suddenly decreased when the flame stabilized in the premixer. The pressure oscillations were large enough to cause a local flow reversal. A simple test using ceramic fiber tufts indicated flow reversals existed at the premixer exit during flickering. It is suspected that flashback occurs through the premixer wall boundary layer flow reversal caused by combustion instability. A theoretical analysis of periodic flow in the premixing channel has been made. The theory supports the flow reversal mechanism

Effects of cobalt in nickel-base superalloys

The role of cobalt in a representative wrought nickel-base superalloy was determined. The results show cobalt affecting the solubility of elements in the gamma matrix, resulting in enhanced gamma' volume fraction, in the stabilization of MC-type carbides, and in the stabilization of sigma phase. In the particular alloy studied, these microstructural and microchemistry changes are insufficient in extent to impact on tensile strength, yield strength, and in the ductilities. Depending on the heat treatment, creep and stress rupture resistance can be cobalt sensitive. In the coarse grain, fully solutioned and aged condition, all of the alloy's 17% cobalt can be replaced by nickel without deleteriously affecting this resistance. In the fine grain, partially solutioned and aged condition, this resistance is deleteriously affected only when one-half or more of the initial cobalt content is removed. The structure and property results are discussed with respect to existing theories and with respect to other recent and earlier findings on the impact of cobalt, if any, on the performance of nickel-base superalloys

Folk moral relativism

It has often been suggested that people’s ordinary folk understanding of morality involves a rejection of moral relativism and a belief in objective moral truths. The results of six studies call this claim into question. Participants did offer apparently objectivist intuitions when confronted with questions about individuals from their own culture, but they offered increasingly relativist intuitions as they were confronted with questions about individuals from increasingly different cultures or ways of life. In light of these data, the authors hypothesize that people do not have a fixed commitment to moral objectivism but instead tend to adopt different views depending on the degree to which they consider radically different perspectives on moral questions. [NOTE: This is a reprint of Sarkissian et al 2011

On direction of spontaneous magnetization in a "cubic" ferromagnet

The magnetic properties of anisotropic films have been studied using 3D-neutron polarization analysis. The experimental facts refer to essential distinction of the sample states, magnetized in opposite directions. For an explanation of asymmetrical effects the model is offered, in which the fundamental theoretical principles of structural phase transitions are used.Comment: 4 pages LaTeX (phbauth) and 4 figures (epsfig

Structure of the saxiphilin:saxitoxin (STX) complex reveals a convergent molecular recognition strategy for paralytic toxins.

Dinoflagelates and cyanobacteria produce saxitoxin (STX), a lethal bis-guanidinium neurotoxin causing paralytic shellfish poisoning. A number of metazoans have soluble STX-binding proteins that may prevent STX intoxication. However, their STX molecular recognition mechanisms remain unknown. Here, we present structures of saxiphilin (Sxph), a bullfrog high-affinity STX-binding protein, alone and bound to STX. The structures reveal a novel high-affinity STX-binding site built from a "proto-pocket" on a transferrin scaffold that also bears thyroglobulin domain protease inhibitor repeats. Comparison of Sxph and voltage-gated sodium channel STX-binding sites reveals a convergent toxin recognition strategy comprising a largely rigid binding site where acidic side chains and a cation-π interaction engage STX. These studies reveal molecular rules for STX recognition, outline how a toxin-binding site can be built on a naïve scaffold, and open a path to developing protein sensors for environmental STX monitoring and new biologics for STX intoxication mitigation

Taking a Razor to Dark Matter Parameter Space at the LHC

Dark matter (DM) has been searched for at colliders in a largely model independent fashion by looking for an excess number of events involving a single jet, or photon, and missing energy. We investigate the possibility of looking for excesses in more inclusive jet channels. Events with multiple jets contain more information and thus more handles to increase the signal to background ratio. In particular, we adapt the recent CMS "razor" analysis from a search for supersymmetry to a search for DM. We consider simplified models where DM is a Dirac fermion that couples to the quarks of the Standard Model (SM) through exchange of vector or axial-vector mediators or to gluons through scalar exchange. We consider both light and heavy (leading to effective contact interactions) mediators. Since the razor analysis requires multiple jets in the final state, the data set is complementary to that used for the monojet search and thus the bounds can be combined.Comment: 25 pages, 10 figures; v2 published version; v3 removes duplication of manuscript in pd

Traffic jams and intermittent flows in microfluidic networks

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle density even in the dilute limit where no particle collision occurs. We demonstrate that this non-linear behavior stems from long range hydrodynamic interactions. Importantly, we also establish that there exists a maximal current above which no stationary particle flow can be sustained. For higher current values, intermittent traffic jams form thereby inducing the ejection of the particles from the initial path and the subsequent invasion of the network. Eventually, we put our findings in the broader context of the transport proccesses of driven particles in low dimension