Reflexivity

Thus we obtain the imbedding of the space V into the second dual one y. The imbedding operator is denoted by tt. If Try = V, the space y is called reflexive (Kantorovich, Akilov, 1984). The simplest example of reflexive spaces are LP fl) for 1 < p < 00 since... 

The compactness properties are closely connected with the reflexivity of spaces. On that score we formulate two theorems widely used in this book (Vainberg, 1972). 

Theorem 1.5. A bounded set of reflexive Banach spaces is weakly compact. 

Theorem 1.10. A closed convex set of a reflexive Banach space is weakly closed. 

Theorem 1.11. Let V be a reflexive Banach space, and K c V be a closed convex set. Assume that J V R is a coercive and weakly lower semicontinuous functional. Then the problem... 

Theorem 1.14. Let V be a reflexive separable Banach space. Assume that an operator A E —> E possesses the following properties ... 

Let K c V he a convex closed set. We assume that y is a strictly convex reflexive Banach space. For given u G V an element Pu G K is called a projection of u onto the set K if... 

Let K cV he a. convex closed subset of a reflexive Banach space V, I he a duality mapping, and P be a projection operator of V onto K. We are in a position to give a definition of a penalty operator. An operator (5 V V is called a penalty operator connected with the set K if the following conditions are fulfilled. Firstly, / is a monotonous bounded semicontinuous operator. Secondly, a kernel of / coincides with K, i.e. 

Let K he a closed convex subset in a reflexive Banach space V let an operator A act from V into V and let f G V he given. Consider the variational inequality... 

Allergic Seasonal or Perennial Rhinoconjunctivitis. Histamine can cause all pathologic features of allergic rhinitis (35—37), with the exception of late-phase inflammatory reactions. Pmritus is caused by stimulation of receptors on sensory nerve endings prostaglandins (qv) may also contribute. Sneering, like pmritus, is an H -mediated neural reflex and can also be mediated by eicosanoids. Mucosal edema, which manifests as nasal... 

Fig. 1. Sight glass gauges (a) tubular, (b) reflex. Courtesy of John C. Ernst Co.

OT receptors are localized ia the brain hypothalamus, limbic system, cortex, striatum, olfactory system, and brain stem. In the periphery, OT is best known for its stimulation of uterine smooth muscle and the milk ejection reflex. Thr , Om ]oxytocin(l—8),... 

Morphine has certain undesirable side effects. Among these are respiratory depression, nausea, and vomiting, depression of the cough reflex, cardiovascular depression and hypotension, smooth muscle contraction (constipation), and histamine release (93). Morphine s onset of action, duration, and low therapeutic indices have prompted a search for a more effective opiate iv anesthetic. Extreme simplification of the complex morphine molecule has resulted in anilido —piperidines, the fentanyl class of extremely potent opiate iv anesthetics (118,119). 

Neurological symptoms result from demyelination of the spinal cord and are potentially irreversible. The symptoms and signs characteristic of a vitamin B 2 deficiency include paresthesis of the hands and feet, decreased deep-tendon reflexes, unsteadiness, and potential psychiatric problems such as moodiness, hallucinations, delusions, and psychosis. Neuropsychiatric disorders sometimes develop independently of the anemia, particularly in elderly patients. Visual loss may develop as a result of optic atrophy. 

The cardiovascular adverse effects associated with quinidine therapy are hypotension and tachycardia, both of which are related to its a-adrenoceptor blocking actions. The tachycardia may be a reflex adjustment to the fall in blood pressure or may also be a direct action of the dmg on sympathetic nerve terminals leading to an increased release of NE. Quinidine also produces ringing in the ears (cinchonism) (1,2). 

Phenylephrine. Phenylephrine hydrochloride is an a -adrenoceptor agonist. Phenylephrine produces powerful vasoconstrictor and hypertensive responses. This results in baroreceptor activation of a reflex bradycardia and thus is useful in the treatment of supraventricular tachyarrhythmias. Unlike epinephrine [51-43-4] the actions of which are relatively transient, phenylephrine responses are more sustained (20 min after iv dosing and 50 min after subcutaneous dosing) (86). 

The cardiac effects of the calcium antagonists, ie, slowed rate (negative chronotropy) and decreased contractile force (negative inotropy), are prominent in isolated cardiac preparations. However, in the intact circulation, these effects may be masked by reflex compensatory adjustments to the hypotension that these agents produce. The negative inotropic activity of the calcium antagonists may be a problem in patients having heart failure, where contractility is already depressed, or in patients on concomitant -adrenoceptor blockers where reflex compensatory mechanisms are reduced. 

Prazosin, a selective a -adrenoceptor antagonist, exerts its antihypertensive effect by blocking the vasoconstrictor action of adrenergic neurotransmitter, norepinephrine, at a -adrenoceptors in the vasculature (200,227,228). Prazosin lowers blood pressure without producing a marked reflex tachycardia. It causes arteriolar and venular vasodilation, but a significant side effect is fluid retention. Prazosin increases HDL cholesterol, decreases LDL cholesterol, and does not cause glucose intolerance. 

Nifedipine, verapamil, and diltiazem are all efficacious in the treatment of mild and moderate hypertension, but nifedipine is more efficacious than diltiazem and verapamil in the control of severe hypertension. Nifedipine does not cause significant reflex tachycardia or orthostatic hypotension. Nifedipine benefits the older and black patients and patients with low PRA. 

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