Bilinear equation for the cylinder with overlap and the Pomeron residue

A bilinear integral equation for the cylinder is derived within the meson sector of the theory of dual topological unitarization. The equation is more general than conventional linear cylinder equations since it includes regions of phase space in which produced particles overlap in rapidity. The equation also permits a simple treatment of phase space which corresponds to that of the planar bootstrap problem. Two classes of solutions are found, only one of which results in the Pomero\u27n-f identity. This treatment also indicates that the residue of the Pomeron may be twice as large as that suggested by earlier calculations but in agreement with a more recent calculation

Bilinear equation for the cylinder with overlap and the Pomeron residue

A bilinear integral equation for the cylinder is derived within the meson sector of the theory of dual topological unitarization. The equation is more general than conventional linear cylinder equations since it includes regions of phase space in which produced particles overlap in rapidity. The equation also permits a simple treatment of phase space which corresponds to that of the planar bootstrap problem. Two classes of solutions are found, only one of which results in the Pomero\u27n-f identity. This treatment also indicates that the residue of the Pomeron may be twice as large as that suggested by earlier calculations but in agreement with a more recent calculation

Construction of a quasiconserved quantity in the Henon-Heiles problem using a single set of variables

The problem of finding the coefficients of a simple series expansion for a quasiconserved quantity K for the Henon-Heiles Hamiltonian H using a single set of variables is solved. In the past, this type of approach has been problematic because the solution to the equations determining the coefficients in the expansion is not unique. As a result, the existence of a consistent expression for K to all orders had not previously been established. We show how to deal with this arbitrariness in the expansion coefficients for K in a consistent way. Due to this arbitrariness, we find a class of expansions for K, in contrast to the single unique expansion for K generated by the normal-form approach of Gustavson [Astron. J. 71, 670 (1966)]. It may be possible to devise a criterion for deciding which one of our expansions is optimally convergent, although we do not deal with this question here. We proceed by introducing a single set of dynamic variables that have simple symmetry properties and that also diagonalize the problem of finding the coefficients of K. No canonical transformations are required. A straightforward constructive procedure is given for generating the power series to any order for quantities having the symmetry of the Hamiltonian that -are formally conserved. This leads to a very practical method for calculating a quasiconserved quantity in the Henon-Heiles problem. A comparison is made through several orders of the terms generated by this approach and those generated in the original Gustavson expansion in normal form

Results of the 2016 Indianapolis Biodiversity Survey, Marion County, Indiana

Surprising biodiversity can be found in cities, but urban habitats are understudied. We report on a bioblitz conducted primarily within a 24-hr period on September 16 and 17, 2016 in Indianapolis, Indiana, USA. The event focused on stretches of three waterways and their associated riparian habitat: Fall Creek (20.6 ha; 51 acres), Pleasant Run (23.5 ha; 58 acres), and Pogue’s Run (27.1 ha; 67 acres). Over 75 scientists, naturalists, students, and citizen volunteers comprised 14 different taxonomic teams. Five hundred ninety taxa were documented despite the rainy conditions. A brief summary of the methods and findings are presented here. Detailed maps of survey locations and inventory results are available on the Indiana Academy of Science website (https://www.indianaacademyofscience.org/)

Poplar GTL1 Is a Ca2+/Calmodulin-Binding Transcription Factor that Functions in Plant Water Use Efficiency and Drought Tolerance

Diminishing global fresh water availability has focused research to elucidate mechanisms of water use in poplar, an economically important species. A GT-2 family trihelix transcription factor that is a determinant of water use efficiency (WUE), PtaGTL1 (GT-2 like 1), was identified in Populus tremula × P. alba (clone 717-IB4). Like other GT-2 family members, PtaGTL1 contains both N- and C-terminal trihelix DNA binding domains. PtaGTL1 expression, driven by the Arabidopsis thaliana AtGTL1 promoter, suppressed the higher WUE and drought tolerance phenotypes of an Arabidopsis GTL1 loss-of-function mutation (gtl1-4). Genetic suppression of gtl1-4 was associated with increased stomatal density due to repression of Arabidopsis STOMATAL DENSITY AND DISTRIBUTION1 (AtSDD1), a negative regulator of stomatal development. Electrophoretic mobility shift assays (EMSA) indicated that a PtaGTL1 C-terminal DNA trihelix binding fragment (PtaGTL1-C) interacted with an AtSDD1 promoter fragment containing the GT3 box (GGTAAA), and this GT3 box was necessary for binding. PtaGTL1-C also interacted with a PtaSDD1 promoter fragment via the GT2 box (GGTAAT). PtaSDD1 encodes a protein with 60% primary sequence identity with AtSDD1. In vitro molecular interaction assays were used to determine that Ca2+-loaded calmodulin (CaM) binds to PtaGTL1-C, which was predicted to have a CaM-interaction domain in the first helix of the C-terminal trihelix DNA binding domain. These results indicate that, in Arabidopsis and poplar, GTL1 and SDD1 are fundamental components of stomatal lineage. In addition, PtaGTL1 is a Ca2+-CaM binding protein, which infers a mechanism by which environmental stimuli can induce Ca2+ signatures that would modulate stomatal development and regulate plant water use

Relativistic momentum

Introductory treatments of relativistic dynamics rely on the invariance of momentum conservation (i.e., on the assumption that momentum is conserved in all inertial frames if it is conserved in one) to establish the relationship for the momentum of a particle in terms of its mass and velocity. By contrast, more advanced treatments rely on the transformation properties of the four-velocity and/or proper time to obtain the same result and then show that momentum conservation is invariant. Here, we will outline a derivation of that relationship that, in the spirit of the more advanced treatments, relies on an elemental feature of the transformation of momentum rather than on its conservation but does not have as a prerequisite the introduction of four-vectors and invariants. The steps in the derivation are no more involved than in the usual introductory treatments; indeed, the arithmetic is almost identical

An Extension of the Rishon Model

We present an extension of the Rishon Model of Harari, et. al. [1] [2] [3] In that model, the first generation leptons and quarks are each made from three rishons of two varieties, T and V as follows: ve = V V V , e+ = T T T , d = T V V , and u = T T V . In addition to the original rishons and their anti-rishons T and V , we introduce the dark rishon X and its anti-rishon X; all have spin 1/2. An exciting possibility that emerges from this idea is the possiblity of ‘beams’ of dark matter coming from the decays of higher generation fermions – much in the same way as ‘beams’ of neutrinos are made. The result of such collisions could produce known particles via color/hypercolor interactions or another - as yet unknown - interaction of dark rishons

Existence of Fixed Poles and Their Role in Conspiracy

It is shown that unitarity allows fixed poles at certain nonsense points of either right or wrong signature. The conditions for the existence of these poles are found. These conditions are then used to locate the poles allowed in hadronic reactions. Possible mechanisms for the poles are considered. It is then argued that fixed poles provide the most natural explanation of the conspiracy phenomenon

Limited Resurrection of the Born Approximation

It is shown that the ordinary Born approximation for pn and pp̅ charge-exchange scattering correctly accounts for (1) the shape of the forward peak for 0 ≤ (-t) ≤ µ2/2 at PL = 8 GeV/c, and (2) the energy dependence of the cross sections at t=0 in the energy range PL,=2—8 GeV/c. This result is analogous to the well-known success of the electric Born approximation in Π+ photoproduction. It is then shown that the simplest interpretation of this surprising result within the framework of Regge-pole theory is in terms of the fixed poles which are allowed by unitarity in hadronic amplitudes at certain nonsense points of right signature. Finally, it is shown how such a Axed pole at a nonsense point of one helicity amplitude aGects another amplitude for which the corresponding point is sense