Ozsváth and Szabó defined an analog of the Frøyshov invariant in the form of a correction term for the grading in Heegaard Floer homology. Applying this to the double cover of the 3-sphere branched over a knot K, we obtain an invariant δ of knot concordance. We show that δ is determined by the signature for alternating knots and knots with up to nine crossings, and conjecture a similar relation...

where the second equality holds because of the change of measure with dP̃ dP |Ft = e Xt−rt. Because St has a continuous distribution under both P and P̃ , then f1(k) and f2(k) are in C. Besides, P̃ ( St ≥ e−k ) and P ( St ≥ e−k ) are both increasing in k. Therefore, applying Lemma 3.1 yields that both f1(k) and f2(k) satisfy Assumption 1. Note that for any σ ∈ (−1,−σl − 1), ∫ +∞ −∞ ef2(k)dk =e −rt...

Let us consider an algebraic function field defined over a finite Galois extension K of a perfect field k. We give some conditions allowing the descent of the definition field of the algebraic function field from K to k. We apply these results to the descent of the definition field of a tower of function fields. We give explicitly the equations of the intermediate steps of an Artin-Schreier typ...

Let G be a split connected semisimple group over a field. We give a conjectural formula for the motive of the stack of G-bundles over a curve C, in terms of special values of the motivic zeta function of C. The formula is true if C = P or G = SLn. If k = C, upon applying the Poincaré or Serre characteristic, the formula reduces to results of Teleman and Atiyah-Bott on the gauge group. If k = Fq...

We enhance real-time search algorithms with bounded propagation of heuristic changes. When the heuristic of the current state is updated, this change is propagated consistently up to k states. Applying this idea to HLRTA*, we have developed the new HLRTA*(k) algorithm, which shows a clear performance improvement over HLRTA*. Experimentally, HLRTA*(k) converges in less trials than LRTA*(k), whil...

. . . , s k are positive integers with s 1 > 1. For k ≤ n, let E(2n, k) be the sum of all multiple zeta values with even arguments whose weight is 2n and whose depth is k. The well-known result E(2n, 2) = 3ζ(2n)/4was extended to E(2n, 3) and E(2n, 4) by Z. Shen and T. Cai. Applying the theory of symmetric functions, Hoffman gave an explicit generating function for the numbers E(2n, k) and then ...

Let C be a smooth projective absolutely irreducible curve of genus g ≥ 2 over a number field K of degree d, and denote its Jacobian by J . Denote the Mordell–Weil rank of J(K) by r. We give an explicit and practical Chabauty-style criterion for showing that a given subset K ⊆ C(K) is in fact equal to C(K). This criterion is likely to be successful if r ≤ d(g − 1). We also show that the only sol...

In this paper, two suboptimum detectors are proposed for coherent radar signal detection in K-distributed clutter. Assuming certain values for several initial moments of clutter amplitude, the characteristic function of the clutter amplitude is approximated by a limited series. Using the Pade approximation, it is then converted to a rational fraction. Thus, the pdf of the clutter amplitude is o...

This paper expresses the prominent features of the fuzzy expert system by applying the algorithm Fuzzy Assessment Methodology using K ratio. To diagnosis the diabetes Fuzzy Assessment Methodology using k ratio is developed. Fuzzy Expert System consists of following elements such as Fuzzification interface, Fuzzy Assessment Methodology using K ratio and Defuzzification interface. The crisp value...