We show that there exist knots K ⊂ S with g(E(K)) = 2 and g(E(K#K#K)) = 6. Together with [5, Theorem 1.5], this proves existence of counterexamples to Morimoto’s Conjecture [10]. This is a special case of [6]. Let Ki (i = 1, 2) be knots in the 3-sphere S, and let K1#K2 be their connected sum. We use the notation t(·), E(·), and g(·) to denote tunnel number, exterior, and Heegaard genus respecti...

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let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

3. Dolovich M, Vanzielegham M, Hidinger K-G, Newhouse MT. Influence of inspiratory flow rate on the response to terbutaline sulphate inhaled via the Turbuhaler. Am Rev Respir Dis, 1988, 137, A433. 4. Engel T, Heinig JH, Madsen F, Weeke B, Nikander K. Peak inspiratory flow rate and inspiratory vital capacity of patients with asthma, measured with and wilhout Turbuhaler. Proceedings of European A...

In this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (K, ?) are equivalent. For a normal subgroup H of K, we define a weight function ?? on KIH and obtain connection between left amenability of (K, ?) and (K|H, ??). Let H be a compact subhypergroup of K. We define the weight function on K||H and obtain connection...

Single-bubble sonoluminescence (SBSL) spectra in H2O show featureless continuum emission. From an acoustically driven, moving bubble in phosphoric acid (H3PO4), we observe very strong molecular emission from excited OH radicals (∼310  nm), which can be used as a spectroscopic thermometer by fitting the experimental SBSL spectra to the OH A 2Σ+ - X 2Π rovibronic transitions. The observed emissio...