In this note, we prove that H is a g-closed subgroup of the compact group K if and only if every sequentially continuous character of the dual of H is continuous-in other words, if the dual of H is a so-called sk-group. We conclude that every countable subgroup of a compact group is g-closed, and thus give a positive answer to a problem of Dikranjan, Milan and Tonolo. We also show that the rela...

We give a lower bound on the speed at which Newton’s method (as defined in [5, 6]) converges over arbitrary ω-continuous commutative semirings. From this result, we deduce that Newton’s method converges within a finite number of iterations over any semiring which is “collapsed at some k ∈ N” (i.e. k = k + 1 holds) in the sense of [1]. We apply these results to (1) obtain a generalization of Par...

For a metric space X let Cvc(X) (that is, the set of all graphs of real-valued continuous functions with a compact domain in X) be equipped with the Hausdorff metric induced by the hyperspace of nonempty closed subsets of X×R. It is shown that there exists a continuous mapping Φ : Cvc(X) → Cb(X) satisfying the following conditions: (i) Φ(f)| dom f = f for all partial functions f. (ii) For every...

The present experiment examined changes in the ability of the selective 5-HT3 receptor agonist, 1(m-chlorophenyl)-biguanide (mCPBG), to facilitate K-induced dopamine (DA) release during withdrawal from continuous cocaine administration. Rats were withdrawn from continuous cocaine administration (40 mg/kg per day cocaine for 14 days) for 7 days, and then slices from the nucleus accumbens obtaine...

Let n be any positive integer and p any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with abutment π∗(LK(n)(X)) and E2-term equal to the continuous cohomology of Gn, the extended Morava stabilizer group, with coefficients in a certain discrete Gn-module that is built from various homotopy fixed point spect...

Let 1 p 1 and W : R ! (0;1) be continuous. Does W admit a Jackson Theorem in Lp? That is, does there exist a sequence f ng 1 n=1 of positive numbers with limit 0 such that inf deg(P ) n k (f P )W kLp(R) n k f W kLp(R) for all absolutely continuous f with k f 0W kLp(R) …nite? We show that such a theorem is true i¤ lim x!1 W 1 Lq [0;x] kWkLp[x;1) = 0; where q is the conjugate parameter of p. In a...

We give a simple criterion for a stochastic process Z := H+K ·W , where H and K are respectively continuous and left-continuous processes independent of the driving Brownian motion W , which ensures that Z has the conditional full support property, introduced by Guasoni, Rásonyi, and Schachermayer, in connection to pricing models with transaction costs. As an application of this result, we show...

and Applied Analysis 3 A2 there exist g x , h x , and k t 0, such that 0 ≤ f t, x ≤ k t g x h x , ∀x ∈ 0,∞ , a.e. t ∈ 0, 1 , 1.6 here g : 0,∞ → 0,∞ is continuous and nonincreasing, h : 0,∞ → 0,∞ is continuous, and h/g is nondecreasing; A3 There exist two positive constants R > r > 0 such that R > ΦR1 γ∗ ≥ r > 0, ∫1 0 k s g ( rsα−1 ) ds < ∞, R ≥ ( 1 h R g R )∫1 0 1 − s α−β−1 Γ α ( 1 − aξα−β−1 s ...

k-nearest neighbour algorithm is a non-parametric machine learning algorithm generally used for classification. It is also known as instance based learning or lazy learning. K-NN algorithm can also be adapted for regression that is for estimating continuous variables. In this research paper the researcher endow with a generalized K-nearest algorithm used for predicting a continuous value. In or...