Abstract Two new species of Bulbophyllum, namely, B. gurungianum (sect. Biseta) and B. punakhaense (sect. Brachyrantha) are described and illustrated. Bulbophyllum gurungianum is similar to B. brevispicatum and B. sonii but differs strikingly by having pseudobulbs placed distantly on the rhizome, a shorter peduncle, and oblong petals with a ciliated margin. Bulbophyllum punakhaense is morphologically similar to B. farreri,B. thaiorum, and B. mamillatum, but can be easily distinguished by its larger leaves, pseudobulbs distantly placed on the rhizome, longer peduncle, and oblong-lanceolate petals with shortly papillate margin towards the apex. We provide a detailed description of each species, and information on their distribution, ecology, and conservation status.

Resumen Consideramos un grupo de Lie compacto con métrica bi-invariante, que proviene de la forma de Killing. En este artículo estudiamos espacios productos alabeados de Einstein, M = M1 × f 1 M2 para los casos (i) M1 es un grupo de Lie (ii) M2 es un grupo de Lie y (iii) ambos M1 y M2 son grupos de Lie. Más aún, obtenemos condiciones para que un producto alabeado de Einstein de grupos de Lie sea una variedad producto simple. Luego, caracterizamos la función de alabeo para el espacio-tiempo generalizado de Robertson-Walker, (M = I ×f 1 G2, −dt 2 + f 1 2 g2 cuya fibra G2 es un grupo de Lie compacto semi-simple de dim G2 > 2 con una métrica bi-invariante, que proviene de la forma de Killing.

Abstract We consider a compact Lie group with bi-invariant metric, coming from the Killing form. In this paper, we study Einstein warped product space, M = M1× f1 M2 for the cases, (i) M1 is a Lie group (ii) M2 is a Lie group and (iii) both M1 and M2 are Lie groups. Moreover, we obtain the conditions for an Einstein warped product of Lie groups to become a simple product manifold. Then, we characterize the warping function for generalized Robertson-Walker spacetime, (M = I ×f 1 G2, −dt 2 + f 1 2 g2 whose fiber G2, being semi-simple compact Lie group of dim G2 > 2, having bi-invariant metric, coming from the Killing form.

Abstract. An overview of the orchid genus Corybas in Vietnam is presented. It was known to be represented by a single species, C. annamensis. In this article, we report two new records, C. himalaicus, and C. geminigibbus. Detailed descriptions, synonyms, type data, information on ecology and phenology, distribution and color plates are provided for all three species along with the key to their identification.

Abstract The cable-suspended bridges differ from the elastic structures because of the inherent nonlinearity of the suspension cables. The primary focus of the available theories is to investigate the effect of nonlinearities associated with the distributed self-weight of the cable and its finite elastic displacements. The main point of departure of this paper is to study the effect of the configurational nonlinearity of the weightless linear elastic suspension cables undergoing small elastic displacements. Based upon authors’ theory of weightless elasto-flexible planar sagging cables, a new Beam with Elasto-Flexible Support (BEFS) model of the cable-deck interaction is proposed here. Rate-type constitutive equations and third order differential equations of motion are derived for a simple four-node cable-suspended beam structure undergoing small elastic vertical displacements. Static and dynamic analysis of the cable-suspended structures is carried out to reveal their characteristic configurational response. The proposed theory is critically evaluated in the context of existing theories of suspension bridges.

Abstract In this Paper, a theory of single sagging planer weightless elasto-flexible cables is proposed. In reference to the instantaneous natural state, hypoelastic rate- type constitutive equations and third-order nonlinear differential equations of planer motion for massless cables with nodal masses are derived. New concepts like configurational complementary potential and contra-gradient principles are proposed. Typical dynamic response of these elastic cables with different sustained loads, axial rigidity and sag/span ratios is determined. Modal, subharmonic and internal resonances, jump and beat phenomena, etc., a re predicted. A new mode of damping of 'free' vibration of the system perturbed from its equilibrium state is identified. Significance of the proposed theory of weightless sagging elasto-flexible cables is discussed.