Families of orthogonal Laurent polynomials,hyperelliptic lie algebras and elliptic integrals

We describe a family of polynomials discovered via a particular recursion relation, which have connections to Chebyshev polynomials of the first and the second kind, and the polynomial version of Pell's equation. Many of their properties are listed in Section 3. We show that these families of polynomials in the variable t satisfy certain second-order linear differential equations that may be of interest to mathematicians in conformal field theory and number theory. We also prove that these families of polynomials in the setting of Date–Jimbo–Kashiwara–Miwa algebras when multiplied by a suitable power of t are orthogonal with respect to explicitly described kernels. Particular cases lead to new identities of elliptic integrals (see Section 5).     

Necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators

Fibrators help detect approximate fibrations. A closed, connected -manifold is called a codimension-2 fibrator if each map defined on an -manifold such that all fibre , are shape equivalent to is an approximate fibration. The most natural objects to study are s-Hopfian manifolds. In this note we give some necessary and sufficient conditions for s-Hopfian manifolds to be codimension-2 fibrators.

     

K-loops and quasidirect products in 2-dlmensional Linear Groups over a Pythagorean Field

For a group G = (G, ·), we define the (internal) quasidirect product f · U = F × U of a certain K-loop (F,+) with F ? G and a suitable subgroup il of G (cf. (3.1)). Let K be a commutative pythagorean field and let L = K(i) be the quadratic extension of K with i2 = ～-1. Then the future cone H:= A ∈ GL(2,L) ¦ A = A*, det A ∈ K⁺, Tr A ∈ K⁺ is a K-loop with respect to the binary operation $A?ggsquaredplus B:=sqrt{AB^{2}A},{? where}sqrt{A}=({? Tr}A+2sqrt {{? det}A})^{1?er 2}(sqrt {? det}AE+A)$} (cf. (2.4)), and the (internal) quasidirect product $H^{}</Emphasis>{\mathop \times\limits_{Q}}Q_{1}$ of the K-loop (H},+) and the group Q₁:= {X ∈ GL(2,L) ¦ X*X = E) is a subgroup of GL(2,L) (cf. (3.2)). Moreover, S L(2,1) = $H^{1+}{\mathop \times\limits_{Q}}Q^{1}$ , where H¹+ = SL(2,L)∩ H ≤} (H},+), Q¹ = S L(2, L) ∩ Q₁ (cf. (3.4)), and if K is euclidean, then (cf. (3.6)).     

A computational analysis of strained laminar flame propagation in a stratified CH4/H2/air mixture

Propagation of a H₂-added strained laminar CH₄/air flame in a rich-to-lean stratified mixture is numerically studied. The back-support effect, which is known to enhance the consumption speed of a flame propagating into a leaner mixture compared to that into a homogeneous mixture, is evaluated. A new method is devised to characterize unsteady reactant-to-reactant counterflow flames under transiently decreasing equivalence ratio, in order to elucidate the influence of flow strain on the back-support effect. In contrast to the conventional reactant-to-product configurations, the current configuration is more relevant to unsteady stratified flames back-supported by their own combustion products. Moreover, since H₂ distribution downstream of the flame is known to play a crucial role in back-supported CH₄/air flames, the influence of H₂ addition in the upstream mixture is examined. The results suggest that a larger strain rate leads to a larger equivalence ratio gradient at the reaction zone through increased flow divergence, which amplifies the back-support. Meanwhile, since H₂ addition in the upstream mixture does not affect the downstream H₂ content, the relative increase in the consumption speed, i.e. the back-support, is suppressed with larger H₂ addition. Especially, when the upstream H₂ content decreases with the equivalence ratio, the H₂ preferentially diffuses toward the unburned gas, which mitigates H₂ accumulation in the preheat zone and further weakens the back-support.     

Flame dynamics under various backpressures in a model scramjet with and without a cavity flameholder

Flame dynamics under various backpressure conditions were experimentally investigated using direct flame visualization, high-speed CH* chemiluminescence imaging, and wall pressure measurements. The stagnation pressure and temperature used in the present study were 100 kPa and 2500 K, respectively, with a freestream Mach number of 4.5. Rectangular scramjet models with and without a cavity were used to explore the effects of the cavity on flame dynamics when operating in scramjet mode, ramjet mode, and unstart. The flow rate of the ethylene jet was varied to impose backpressures corresponding to each operation mode. For both models, reverse flame propagation was observed for ramjet mode and unstart. For ramjet mode, flame fluctuation occurred within the isolator due to the coupling of fluid dynamics and combustion. The presence of a cavity enhanced combustion and reduced flame fluctuation in both scram and ramjet mode. The cavity promoted unstart because of the greater heat release from combustion. Further research using spatially resolved diagnostic techniques is needed to identify the flame locations for ramjet mode and unstart.     

Neutral Higgs bosons in the MNMSSM with explicit CP violation

Within the framework of the minimal non-minimal supersymmetric standard model (MNMSSM) with tadpole terms, CP violation effects in the Higgs sector are investigated at the one-loop level, where the radiative corrections from the loops of the quark and squarks of the third generation are taken into account. Assuming that the squark masses are not degenerate, the radiative corrections due to the stop and sbottom quarks give rise to CP phases which trigger the CP violation explicitly in the Higgs sector of the MNMSSM. The masses, the branching ratios for dominant decay channels, and the total decay widths of the five neutral Higgs bosons in the MNMSSM are calculated in the presence of explicit CP violation. The dependence of these quantities on the CP phases is quite recognizable, for given parameter values.     

Nanomanipulator-assisted fabrication and characterization of carbon nanotubes inside scanning electron microscope

We have installed two nanomanipulators, which can travel about 20mm with a minimum increment of 1 nm, for manipulation of nanostructured materials inside field-emission scanning electron microscope (FE-SEM). Both manipulators render motions in x, y, and z directions, providing various manipulation freedoms such as moving, bending, cutting, and biasing. In addition, we have conducted in situ characterization of the electrical breakdown of multi-walled carbon nanotubes (MWCNTs). Our results demonstrate the possibility that MWCNTs can be used as a gas sensor.