In the previous article (J. Geom. Phys. 43 (2002) 146), we show the hyperelliptic solutions of a loop soliton as a study of a quantized elastica. This article gives some functional relations in a loop soliton as a quantized elastica. 2000 MSC: 37K20, 35Q53, 14H45, 14H70

BACKGROUND Venous invasion by tumour is an independent prognostic indicator of both prognosis and risk of development of distant metastases in colorectal carcinoma. The use of special stains to aid its detection in pathology specimens is not currently universally recommended. AIMS To determine whether an elastica stain significantly increases the incidence of detection of vascular invasion co...

Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain ...

A new object segmentation method based on second-order energy minimisation is proposed. It is called pseudoelastica as it relates to the classic Euler’s elastica but resulting contours cannot be expected to converge towards continuous elastica if the resolution is increased. Comparing to prior works, our segmentation technique can be easily applied to both closed contours and open contours with...

Closed loop solitons in a plane, whose curvatures obey the modified Korteweg-de Vries equation, were investigated. It was shown that their tangential vectors are expressed by ratio of Weierstrass sigma functions for genus one case and ratio of Baker’s sigma functions for the genus two case. This study is closely related to classical and quantized elastica problems. 2000 MSC: 35Q53, 53A04, 14H45...

The solutions of the dual bending energy functional on unit sphere S2 ? D3 are investigated. Dual spherical elastica is characterized by Euler-Lagrange equation using techniques calculus variation. real and parts differential solved different methods. shown to correspond elastic strip constituted planar in R3.

Natural products are an important source of antioxidant molecules like tannins, phenolic compounds, flavonoids, etc., Helicanthus elastica (Desr.) Danser (Loranthaceae) is one such plant belonging to the category of mistletoe, and grows commonly on the mango trees in India. In the present study, an attempt has been made to assess the antioxidant properties of the plant. Ethanol extract of H. el...

The Eringen’s nonlocal elastica equation does not possess a Lagrangian formulation. In this article, we find variational integrating factor which enables us to provide and Hamiltonian structure associated equation. Explicit expressions of the solutions in terms elliptic integrals first kind are then deduced. We derive discrete version preserving compare it with Challamel’s co-worker definition ...

Quantization needs evaluation of all of states of a quantized object rather than its stationary states with respect to its energy. In this paper, we have investigated moduli Melas of a quantized elastica, a quantized loop on with an energy functional associated with the Schwarz derivative, on a Riemannian sphere P. Then we proved that its moduli is decomposed to equivalent classes determined by...

Inspired by experiments on the instability of confined interfacial cracks, we construct a minimal mathematical model based on symmetry arguments that can reproduce the form of the crack front in a confined domain. We show that the model can be interpreted in terms of the buckling and post-buckling response of a compressed elastica with a nonuniform bending stiffness that is adhered to a linearl...