Ray helicity: a geometric invariant for multi-dimensional resonant wave conversion

For a multicomponent wave field propagating into a multidimensional conversion region, the rays are shown to be helical, in general. For a ray-based quantity to have a fundamental physical meaning it must be invariant under two groups of transformations: congruence transformations (which shuffle components of the multi-component wave field) and canonical transformations (which act on the ray phase space). It is shown that for conversion between two waves there is a new invariant not previously discussed: the intrinsic helicity of the ray

Classification of Standard Model Particles in E6E_6 Orbifold Grand Unified Theories

We classify the standard model fermions, which originate from bulk fields of the $\bf{27}$ or $\bar{\bf{27}}$ representation after orbifold breaking, in $E_6$ grand unified theories on 5 or 6-dimensional space-time, under the condition that $q$, $e^c$ and $u^c$ survive as zero modes.Comment: 24 pages, typos corrected, to appear in IJMP

A q-analog of the ADHMN construction and axisymmetric multi-instantons

In the preceding paper (Phys. Lett. B463 (1999) 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.Comment: 11pages, Latex2e, to appear in Journal of Physics A: Mathematical and General as a `Special Issue/Difference Equations

Исследование закономерностей развития структурно-химической неоднородности в разнородном сварном соединении трубопроводного переходника

Данная работа посвящена исследованию структурно-химической неоднородности (СХН) трубопроводного переходника из разнородных сталей, выполненного аргонодуговой сваркой (АрДС). При помощи оптического микроскопа получены фотографии СХН и ее размеры. СХН выражается в появлении прослоек (карбидной и ферритной) с разным химическим составом. Приведены графики роста ширин прослоек от времени выдержки и температуры.This paper is devoted to the comparison of the structural and chemical inhomogeneity (SCI) of adapters made of dissimilar steels, made by tungsten insert gas (TIG). By means of optical microscope, photographs of the SCI and its dimensions were obtained. SCI is expressed in the appearance of interlayers (carbide and ferritic) with different chemical composition. Graphs of the growth of the widths of the interlayers from the time of exposure and temperature are given

The Nambu sum rule and the relation between the masses of composite Higgs bosons

We review the known results on the bosonic spectrum in various NJL models both in the condensed matter physics and in relativistic quantum field theory including $^3$He-B, $^3$He-A, the thin films of superfluid He-3, and QCD (Hadronic phase and the Color Flavor Locking phase). Next, we calculate bosonic spectrum in the relativistic model of top quark condensation suggested in \cite{Miransky}. In all considered cases the sum rule appears that relates the masses (energy gaps) $M_{boson}$ of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion $M_f$ as $\sum M_{boson}^2 = 4 M_f^2$. Previously this relation was established by Nambu in \cite{Nambu} for $^3$He-B and for the s - wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases this rule allows to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.Comment: Latex, 15 page

Stable bundles on hypercomplex surfaces

A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin's and Gualtieri's generalized complex geometry, (4,4)-manifolds are called ``generalized hyperkaehler manifolds''. We show that the moduli space of anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a (4,4)-structure.Comment: 17 pages. Version 3.0: reference adde

Phylogenetic Study of Plant Q-type C2H2 Zinc Finger Proteins and Expression Analysis of Poplar Genes in Response to Osmotic, Cold and Mechanical Stresses

Plant Q-type C2H2 zinc finger transcription factors play an important role in plant tolerance to various environmental stresses such as drought, cold, osmotic stress, wounding and mechanical loading. To carry out an improved analysis of the specific role of each member of this subfamily in response to mechanical loading in poplar, we identified 16 two-fingered Q-type C2H2-predicted proteins from the poplar Phytozome database and compared their phylogenetic relationships with 152 two-fingered Q-type C2H2 protein sequences belonging to more than 50 species isolated from the NR protein database of NCBI. Phylogenetic analyses of these Q-type C2H2 proteins sequences classified them into two groups G1 and G2, and conserved motif distributions of interest were established. These two groups differed essentially in their signatures at the C-terminus of their two QALGGH DNA-binding domains. Two additional conserved motifs, MALEAL and LVDCHY, were found only in sequences from Group G1 or from Group G2, respectively. Functional significance of these phylogenetic divergences was assessed by studying transcript accumulation of six poplar C2H2 Q-type genes in responses to abiotic stresses; but no group specificity was found in any organ. Further expression analyses focused on PtaZFP1 and PtaZFP2, the two genes strongly induced by mechanical loading in poplars. The results revealed that these two genes were regulated by several signalling molecules including hydrogen peroxide and the phytohormone jasmonate

D0-D4 brane tachyon condensation to a BPS state and its excitation spectrum in noncommutative super Yang-Mills theory

We investigate the D0-D4-brane system for different B-field backgrounds including the small instanton singularity in noncommutative SYM theory. We discuss the excitation spectrum of the unstable state as well as for the BPS D0-D4 bound state. We compute the tachyon potential which reproduces the complete mass defect. The relevant degrees of freedom are the massless (4,4) strings. Both results are in contrast with existing string field theory calculations. The excitation spectrum of the small instanton is found to be equal to the excitation spectrum of the fluxon solution on R^2_theta x R which we trace back to T-duality. For the effective theory of the (0,0) string excitations we obtain a BFSS matrix model. The number of states in the instanton background changes significantly when the B-field becomes self-dual. This leads us to the proposal of the existence of a phase transition or cross over at self-dual B-field.Comment: a4 11pt Latex2e 40 pages; v2: typos fixed, refined comments on renormalisation, refs added, v3: ref added, version publishe