Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?

A new, coercive formulation of the Helmholtz equation was introduced in [Moiola, Spence, SIAM Rev. 2014]. In this paper we investigate $h$-version Galerkin discretisations of this formulation, and the iterative solution of the resulting linear systems. We find that the coercive formulation behaves similarly to the standard formulation in terms of the pollution effect (i.e. to maintain accuracy as $k\to\infty$, $h$ must decrease with $k$ at the same rate as for the standard formulation). We prove $k$-explicit bounds on the number of GMRES iterations required to solve the linear system of the new formulation when it is preconditioned with a prescribed symmetric positive-definite matrix. Even though the number of iterations grows with $k$, these are the first such rigorous bounds on the number of GMRES iterations for a preconditioned formulation of the Helmholtz equation, where the preconditioner is a symmetric positive-definite matrix.Comment: 27 pages, 7 figure

Neuroendocrine mechanisms in relation to control of maturation in cultivable teleost fishes

Reproductive processes are by no means fully impaired in captivity. The progressive development of the gonads -remains, in general, inhibited upto the final stages of gamete maturation, and it is only at the point of gamete release that the sequence is arrested. Both-gonadal maturation and spawning behaviour have long been known in responses to environmental stimuli viz., temperature, light and rainfall etc

Physiological and Endocrinological approaches in captive breeding of marine finfish

Reproductive processes are by no means fully impaired in captivity. The gradual and progressive development of the gonads remains, in general, uninhibited upto the final stage of gamete maturation, and it is only at the point of gamete release that the sequence is arrested. Both gonadal maturation and breeding behaviour have long been known in responses to environmental stimuli viz., temperature, light, rainfall etc. Our fishery scientists have made a timely breakthrough by inventing the technique of induced breeding through hormonal manipulation. Though the induced breeding technique has now been successfully used for carps many brackishwater and marine fishes have either responded to this technique with partial success or no response. This is because of the lack of understanding the mechanisms involved in the environmental complexities and their impact on neuroendocrine mechanisms in control of reproduction

Physiology of digestion in fishes and shellfishes

Some fish feed on plants, some on animals and a third group derives ijs protein, carbohydrate, fats, vijamins and minerals from both plant and animal sources. Some fishes live on blood and tissue fluid of other fishes (eg. Petromyzon). Some fishes feed on plankton during part of their life and some throughou1 life. Others feed on weeds. Many other feed on zooplankton and also on other larger animals like annelid worms, snail. mussel, clams, crustaceans, insect, birds, mammals, reptiles and amphibians. Even human beings are found in the stomach

Neurological endocrinology: the coordinating mechanism

The nervous and endocrine systems are integrative in nature for they provide th'e organism with sophisticated external and internal sensing devices which feed information into the central nervous system for appropriate responses of the target system

Subdural Hematoma in Grave’s Disease Induced Thrombocytopenia.

Subdural hematoma (SDH) usually occurs secondary to trauma, in bleeding disorders it may occur spontaneously. It is a rare complication of immune thrombocytopenia. Here we report a case of 45 years female presenting with presenting with complaints of headache, palpitation and menorrhagia and later diagnosed to be a case of Grave's disease with thrombocytopenia with sub dural hematoma. No such case reports are available in literature