Classical Affine {\mathcal{W}}-Algebras for {\mathfrak{gl}_N} and Associated Integrable Hamiltonian Hierarchies

We apply the new method for constructing integrable Hamiltonian hierarchies of Lax type equations developed in our previous paper to show that all \({\mathcal{W}}\)-algebras \({\mathcal{W}(\mathfrak{gl}N, f)}\) carry such a hierarchy. As an application, we show that all vector constrained KP hierarchies and their matrix generalizations are obtained from these hierarchies by Dirac reduction, which provides the former with a bi-Poisson structure.     

Paths for $${\mathcal{Z}}_k$$ Parafermionic Models

We present a simple bijection between restricted Bressoud lattice paths and paths in regime II of the Andrews–Baxter–Forrester restricted solid–on–solid model. Both types of paths describe states in parafermionic irreducible modules. The bijection implies a direct correspondence between a RSOS path and a parafermionic state in a quasi-particle basis.      

{\mathcal {PT}}-symmetric dimers with time-periodic gain/loss function

\({\mathcal {PT}}\) -symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schrödinger dimer representing the coupling of field amplitudes, each system representing a wide class of physical models. Through a thorough analysis of their stability behavior, we find that turning on the coupling parameter in the classical dimer system leads initially to decreased stability but then to re-entrant transitions from the exact to the broken \({\mathcal {PT}}\) -phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schrödinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behavior of the two dimer systems coincides and/or reduces to that of a single oscillator.     

Classical {\mathcal{W}} -Algebras and Generalized Drinfeld-Sokolov Bi-Hamiltonian Systems Within the Theory of Poisson Vertex Algebras

We describe of the generalized Drinfeld-Sokolov Hamiltonian reduction for the construction of classical ${\mathcal{W}}$ W -algebras within the framework of Poisson vertex algebras. In this context, the gauge group action on the phase space is translated in terms of (the exponential of) a Lie conformal algebra action on the space of functions. Following the ideas of Drinfeld and Sokolov, we then establish under certain sufficient conditions the applicability of the Lenard-Magri scheme of integrability and the existence of the corresponding integrable hierarchy of bi-Hamiltonian equations.     

Stability of {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} and {\text{SrZr}}_{{0.2}} {\text{Ce}}_{{0.7}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} under H2 atmospheres

Previous H₂ permeation tests showed a degradation of H₂ permeation flux with time. To understand the cause of degradation and develop a solution, the stability of $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ and $ {\text{SrZr}}_{{0.2}} {\text{Ce}}_{{0.7}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ samples were studied under dry and wet H₂ atmospheres. Total conductivity of $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ increased with time in dry H₂. The X-ray diffraction pattern of $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ after dry hydrogen atmosphere heat treatments show CeO₂ peaks indicating that $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ decomposes under dry H₂ atmospheres; scanning electron microscopy and energy dispersive X-ray spectroscopy analyses prove that decomposition proceeded along the grain boundaries. $ {\text{SrZr}}_{{0.2}} {\text{Ce}}_{{0.7}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ was investigated and demonstrated greater stability under dry hydrogen atmospheres. However, Zr substitution results in a tradeoff with electrical properties.     

Fast proton conduction path in {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{2.9 - \delta }} membrane

The effect of metal-to-oxide grain boundary layer in $ {\text{Ni}} - {\text{BaCe}}_{{0.8}} {\text{Y}}_{{0.2}} {\text{O}}_{{3 - \delta }} $ (BCY) cermet membrane on hydrogen permeation was studied by applying the different size of oxide grain on Ni-BCY membranes. Two types of cermet membranes having different grain size of oxide were prepared by using different starting particle size of oxide powder. The hydrogen flux of coarse-oxide-grain membrane showed higher flux than that of small-oxide-grain membrane. It was understood that the negative potential at metal-to-oxide grain boundary, reference to the bulk oxide ( $ \phi _{0} < \phi _{\infty } = 0 $ ), was developed, and the accumulation of the effectively positively charged protons may occur at the grain boundary layer (space charge layer), which may result in providing highly conductive proton path by shifting the charge neutrality condition from $ {\left[ {OH^{ \bullet }_{O} } \right]} = {\left[ {Y^{/}_{{Ce}} } \right]} $ to $ {\left[ {OH^{ \bullet }_{O} } \right]} = n $ .     

${\mathcal{PT}}$-Symmetric Square Well-Perturbations and the Existence of Metric Operator

We consider PT{\mathcal{PT}}-symmetric square well in more general setting: we impose PT{\mathcal{PT}}-symmetric boundary conditions instead of Dirichlet ones. We investigate the existence and properties of a metric operator.     

A stable and easily sintering {\text{BaCe}}_{0.7} {\text{Sn}}_{0.1} {\text{Gd}}_{0.2} {\text{O}}_{3 - \delta } electrolyte for solid oxide fuel cells

${\text{BaCe}}_{0.7} {\text{Sn}}_{0.1} {\text{Gd}}_{0.2} {\text{O}}_{3 - \sigma } $ (BCSG) and ${\text{BaCe}}_{0.8} {\text{Gd}}_{0.2} {\text{O}}_{3 - \sigma } $ (BCG) powders were prepared by solid-state reaction method. After exposure in 5% CO₂?+?5% H₂O?+?90% N₂ at 500 °C for 5 h, the BCSG powders were hardly affected while the BCG powders decomposed into CeO₂ and BaCO₃ phases. Moreover, the relative density of BCSG reaches 97%, while the BCG just displays 91% after sintering at 1,400 °C. The BCSG displays a conductivity of 0.01 S/cm at 700 °C in humid hydrogen, which is quite close to 0.012 S/cm for BCG. A fuel cell with BCSG exhibits 1.02 V for open circuit voltage, 420 mW/cm² for peak performance and 0.23 Ω cm² for interfacial resistance at 700 °C, respectively.     

Cosmological analysis of reconstructed $${\mathcal {F}}(T,T_{\mathcal {G}})$$ models

In this paper, we analyze cosmological consequences of the reconstructed generalized ghost pilgrim dark energy \({\mathcal {F}}(T,T_{\mathcal {G}})\) models in terms of redshift parameter z. For this purpose, we consider power-law scale factor, scale factor for two unified phases and intermediate scale factor. We discuss graphical behavior of the reconstructed models and examine their stability analysis. Also, we explore the behavior of equation of state as well as deceleration parameters and \(\omega _{\Lambda }-\omega _{\Lambda }^{'}\) as well as \(r-s\) planes. It is found that all models are stable for pilgrim dark energy parameter 2. The equation of state parameter satisfies the necessary condition for pilgrim dark energy phenomenon for all scale factors. All other cosmological parameters show great consistency with the current behavior of the universe.     

Elliptic Genera of 2d $${\mathcal{N}}$$ N = 2 Gauge Theories

We consider the spectrum of discrete Schrödinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency.     

Cohomology of {\mathcal {K}(2)} Acting on Linear Differential Operators on the Superspace {\mathbb{R}^{1|2}}

We compute the first differential cohomology of the Lie superalgebra ${\mathcal{K}(2)}$ of contact vector fields on the (1, 2)-dimensional real superspace with coefficients in the superspace of linear differential operators between the superspaces of weighted densities—a superisation of a result by Feigin and Fuchs. We give explicit expressions of 1-cocycles generating these spaces.     

Investigation of atmospheric {\text{O}}_{2}{\text{X}}{^{ 3}}{ \sum_{\text{g}}^{ - }} \,{\text{to}}\, {\text{b}}{^{ 1}}{ \sum_{\text{g}}^{ + }} using open-path tunable diode laser absorption spectroscopy

A tunable diode laser absorption spectroscopy (TDLAS) device fiber coupled to a pair of 12.5 in. telescopes was used to study atmospheric propagation for open path lengths of 100–1,000 meters. More than 50 rotational lines in the molecular oxygen A-band O₂ $ {\text{X}}{^{ 3}}{ \sum_{\text{g}}^{ - }} \,{\text{to}}\, {\text{b}}{^{ 1}}{ \sum_{\text{g}}^{ + }} $ transition near 760 nm were observed. Temperatures were determined from the Boltzmann rotational distribution to within 1.3 % (less than ±2 K). Oxygen concentration was obtained from the integrated spectral area of the absorption features to within 1.6 % (less than ±0.04 × 10¹⁸ molecules/cm³). Pressure was determined independently from the pressure-broadened Voigt lineshapes to within 10 %. A fourier transform interferometer (FTIR) was also used to observe the absorption spectra at 1 cm^?1 resolution. The TDLAS approach achieves a minimum observable absorbance of 0.2 %, whereas the FTIR instrument is almost 20 times less sensitive. Applications include atmospheric characterization for high energy laser propagation and validation of monocular passive raging.     

Hidden Symmetries and Integrable Hierarchy of the $${\mathcal{N}}$$ = 4 Supersymmetric Yang-Mills Equations

We describe an infinite-dimensional algebra of hidden symmetries of supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solving the equations of the hierarchy. We embed the SYM equations in the infinite system of the hierarchy equations and show that this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations. Presumably, the existence of such nonlocal symmetries underlies the observed integrable structures in quantum SYM theory. On leave from Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russia. Address after October 1st, 2006: Theoretical Physics Group, The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom.     

Regular Strongly Typical Blocks of $${\mathcal{O}^{\mathfrak {q}}}$$

We use the technique of Harish-Chandra bimodules to prove that regular strongly typical blocks of the category for the queer Lie superalgebra are equivalent to the corresponding blocks of the category for the Lie algebra .