Holomorphic Hermitian vector bundles over the Riemann sphere

We give a complete classification of isomorphism classes of all SU(2)-equivariant holomorphic Hermitian vector bundles on CP¹. We construct a canonical bijective correspondence between the isomorphism classes of SU(2)-equivariant holomorphic Hermitian vector bundles on CP¹ and the isomorphism classes of pairs ({Hn}_n∈Z,T), where each Hn is a finite dimensional Hilbert space with Hn=0 for all but finitely many n, and T is a linear operator on the direct sum _⊕n∈ZHn such that T(Hn)⊂Hn+2 for all n.     

The layer disorders defect in coir fiber under thermal and chemical treatment

Natural coir fibers, subjectd to thermal treatments in the range of 0°C to 200°C and alkali treatment with 5% to 30% concentration w/w, have been used in the present investigation to determine the interlayer variability of the cellulose planes (020), (110) and (1$ \bar 1 $ \bar 1 0). Among the equatorial reflections (110), (1$ \bar 1 $ \bar 1 0) and (020), the extent of variability is found to be more with the proportion of such affected planes less for (020) reflection in the native cellulose at lower temperature while at higher temperature (110) and (1$ \bar 1 $ \bar 1 0) become more affected by variability defect. (110) and (1$ \bar 1 $ \bar 1 0) planes are more affected also with alkali treatment.     

Torsionfree sheaves over a nodal curve of arithmetic genus one

We classify all isomorphism classes of stable torsionfree sheaves on an irreducible nodal curve of arithmetic genus one defined over ℂ. Let X be a nodal curve of arithmetic genus one defined over ℝ, with exactly one node, such that X does not have any real points apart from the node. We classify all isomorphism classes of stable real algebraic torsionfree sheaves over X of even rank. We also classify all isomorphism classes of real algebraic torsionfree sheaves over X of rank one.     

Calorimetric investigation of the magnetic transition in quasi-one-dimensional molecule-based ferrimagnets: [Mn(OC14H29)4TPP][TCNE]·MeOH and [MnF4TPP][TCNE]·0.5MeOH

Heat capacity study was performed, for the first time, for [MnF₄TPP][TCNE]·0.5MeOH and [Mn(OC₁₄H₂₉)₄TPP][TCNE]·MeOH complexes in the 1.8-100 K temperature range under the 0-9 T magnetic field and disclosed new aspects inherent in such strongly coupled charge-transfer Mn-porphyrin-TCNE linear chain systems, where TPP=5,10,15,20-tetraphenylporphyrinato, TCNE=tetracyanoethylene and MeOH=methanol. Any heat capacity anomaly due to the onset of the magnetic long-range-order was not detected, whereas the magnetic phase transition has clearly been observed around 20 K by previous magnetic studies. As these materials are well approximated by quasi-one-dimensional ferrimagnetic Heisenberg chains with very large intrachain spin-spin interactions, the most part of the magnetic entropy is retained above the phase transition temperature as the dominant short-range order. This is the reason why no magnetic phase transition was detected by calorimetry. On the other hand, the big effect observed in the magnetic susceptibility is well accounted for if the formation of magnetic domains is assumed in the crystal.     

On theta characteristics of a compact Riemann surface

Let σ be a nontrivial automorphism of a compact connected Riemann surface X of genus at least two. Assume that σ fixes each of the theta characteristics of X. We prove that X is hyperelliptic, and σ is the unique hyperelliptic involution of X.     

Simplicity of stable principal sheaves

Let M be a compact connected Kähler manifold, and let Gbe a connected complex reductive linear algebraic group. Weprove that a principal G-sheaf on M admits an admissible Einstein–Hermitianconnection if and only if the principal G-sheaf is polystable.Using this it is shown that the holomorphic sections of theadjoint vector bundle of a stable principal G-sheaf on M aregiven by the center of the Lie algebra of G. The Bogomolov inequalityis shown to be valid for polystable principal G-sheaves.     

Efimov Effect in 2-Neutron Halo Nuclei

We provide a brief overview of our theoretical investigations, carried out in recent years, to study Efimov effect in 2-n halo nuclei. The calculations provide the evidence for the occurrence of at least two Efimov states in ²⁰C. These states disappear one by one as the two-body binding energy is increased and show up as asymmetric resonances in the elastic scattering cross section of n–¹⁹C system. The asymmetric nature of the resonances is explained by invoking the mechanism of Fano resonance.     

Two-Neutron Alignment in <Superscript>127</Superscript>Xe

High spin states in ¹²⁷Xe have been investigated via ⁹Be induced fusion-evaporation reaction at 48 MeV. Spin and parity of excited states up to \( \sim \frac {47}{2} \hbar \) have been confirmed from angular correlation and linear polarization results. Rotational alignment of the second pair of h _11/2 neutrons has been observed at \(\hbar \omega \sim \) 0.44 MeV; beyond that, the band is associated with ν[h _11/2]³ configuration. The alignment phenomena has been discussed in comparison with the neighboring ^125,129Xe.     

Non-isothermal analysis of extrusion film casting using multi-mode Phan-Thien Tanner constitutive equation and comparison with experiments

Extrusion film casting (EFC) is an industrially important process which produces thousands of tons of polymer films, sheets, and coating used for various industrial as well as household applications. In this paper, we focus on an instability which occurs during certain polymer processing operations operating under predominantly elongational flow, such as extrusion film casting and fiber spinning. This instability, called the draw resonance, occurs in the form of sustained periodic fluctuations in the film dimensions. It appears when the process goes beyond the critical line speed of the EFC process. In this work, a conventional linear stability analysis is carried out for nonisothermal EFC process to determine the onset of the draw resonance. The polymer rheology is modeled by the Phan-Thien Tanner (PTT) multi-mode constitutive equation. For the implementation, a conventional shooting method approach is used. Extrusion film casting experiments were also carried out using a conventional linear low-density polyethylene (LLDPE) by varying process parameters such as draw ratio and aspect ratio, to observe the effect on the stability of the process. Linear stability analysis results under non-isothermal conditions are compared and validated with existing results from literature and with our own experimental data. This work displays the effect of multiple relaxation modes as well as the temperature influence on the stability of EFC process. Finally, results also indicate that the temperature highly affects the stability of the EFC process and cannot be ignored from modeling of EFC process.