Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Affine Hall-Littlewood Functions for A(1)((1)) And Some Constant Term Identities of Cherednik-Macdonald-Mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A(1)((1)). We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher level generalizations of Cherednik's Macdonald and Macdonald-Mehta constant term identities.

Ethnobotany of the Monpa ethnic group at Arunachal Pradesh, India

Background: The present paper documents the uses of plants in traditional herbal medicine for human and veterinary ailments, and those used for dietary supplements, religious purpose, local beverage, and plants used to poison fish and wild animals. Traditional botanical medicine is the primary mode of healthcare for most of the rural population in Arunachal Pradesh. Materials and methods: Field research was conducted between April 2006 and March 2009 with randomly selected 124 key informants using semi-structured questionnaire. The data obtained was analyzed through informant consensus factor (F(IC)) to determine the homogeneity of informant's knowledge on medicinal plants. Results: We documented 50 plants species belonging to 29 families used for treating 22 human and 4 veterinary ailments. Of the medicinal plants reported, the most common growth form was herbs (40%) followed by shrubs, trees, and climbers. Leaves were most frequently used plant parts. The consensus analysis revealed that the dermatological ailments have the highest F(IC) (0.56) and the gastro-intestinal diseases have F(IC) (0.43). F(IC) values indicated that there was high agreement in the use of plants in dermatological and gastro-intestinal ailments category among the users. Gymnocladus assamicus is a critically rare and endangered species used as disinfectant for cleaning wounds and parasites like leeches and lice on livestocks. Two plant species (Illicium griffithii and Rubia cordifolia) are commonly used for traditional dyeing of clothes and food items. Some of the edible plants recorded in this study were known for their treatment against high blood pressure (Clerodendron colebrookianum), diabetes mellitus (Momordica charantia), and intestinal parasitic worms like round and tape worms (Lindera neesiana, Solanum etiopicum, and Solanum indicum). The Monpas of Arunachal Pradesh have traditionally been using Daphne papyracea for preparing hand-made paper for painting and writing religious scripts in Buddhist monasteries. Three plant species (Derris scandens, Aesculus assamica, and Polygonum hydropiper) were frequently used to poison fish during the month of June-July every year and the underground tuber of Aconitum ferrox is widely used in arrow poisoning to kill ferocious animals like bear, wild pigs, gaur and deer. The most frequently cited plant species; Buddleja asiatica and Hedyotis scandens were used as common growth supplements during the preparation of fermentation starter cultures. Conclusion: The traditional pharmacopoeia of the Monpa ethnic group incorporates a myriad of diverse botanical flora. Traditional knowledge of the remedies is passed down through oral traditions without any written document. This traditional knowledge is however, currently threatened mainly due to acculturation and deforestation due to continuing traditional shifting cultivation. This study reveals that the rural populations in Arunachal Pradesh have a rich knowledge of forest-based natural resources and consumption of wild edible plants is still an integral part of their socio-cultural life. Findings of this documentation study can be used as an ethnopharmacological basis for selecting plants for future phytochemical and pharmaceutical studies.

SOME INFINITE SUMS IDENTITIES

We find the sum of series of the form Sigma(infinity)(i=1) f(i)/i(r) for some special functions f. The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mezo's paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of pi.