a+ dpZp = {x ∈ X | x ≡ a (mod dp N )}, where a ∈ Z lies in 0 ≤ a < dp , see [1-21]. The p-adic absolute value in Cp is normalized so that |p|p = 1/p. When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C or a p-adic number q ∈ Cp. If q ∈ Cp, then we assume |q − 1|p < p − 1 p−1 , so that q = exp(x log q) for |x|p ≤ 1. We use the notation [x]q = [x :...

we study connected orientable spacelike hypersurfaces $x:m^{n}rightarrowm_q^{n+1}(c)$, isometrically immersed into the riemannian or lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~l_kx=ax+b$,~ where $l_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $h_{k+1}$ of the hypersurface for a fixed integer $0leq k

$P_c$ resonances are studied in the approach of quark model and group theory. It is found that there totally 17 possible pentaquark states with contents $q^3Q \bar Q$ ($q$ $u$ $d$ quarks; $Q$ $c$ quark) compact picture, where hidden heavy may take color singlet-singlet ($[111]_{{qqq}}\otimes [111]_{{c c}}$) octet-octet ($[21]_{{qqq}}\otimes [21]_{{c configurations. The partial decay widths calc...

We consider elliptic equations with operators $L=a^{ij}D_{ij}+b^{i}D_{i}-c$ $a$ being almost in VMO, $b\in L_{d}$ and $c\in L_{q}$, $c\geq 0$, $d>q\geq d/2$. prove the solvability of $Lu=f\in L_{p}$ bounded $C^{1,1}$-domains, $10$. Weak uniqueness martingale problem associated such is also obtained.

Part 1: In this problem we will examine randomized classifiers. Define, for any point x, a probabilty distribution q(c|x) over the class labels c. We define a randomized decision rule given by h r (x; q) = c r , for c r ∼ q(c|x). The risk R(h r ; q) for this classifier is given by the expectation over all possible outcomes such that R(h r ; q) = x C c=1 C c =1 L(c , c)q(c r = c |x)p(x, y = c)dx...

We prove versions of various standard inequalities in which the dependence of the constant on the metric is explicit. 1 Technical results Definition. Let (M, g) be a smooth Riemannian n-manifold and let x ∈ M . Given Q > 1, k ∈ N, and p > n, the (Q, k, p)-harmonic radius at x, rH(Q, k, p)(x), is the supremum of reals r such that, on the geodesic ball Bx(r) of center x and radius r, there is a h...

In the \((1+{\varepsilon },r)\)-approximate near-neighbor problem for curves (ANNC) under some similarity measure \(\delta \), goal is to construct a data structure given set \(\mathcal {C}\) of that supports approximate queries: Given query curve Q, if there exists \(C\in \mathcal such (Q,C)\le r\), then return \(C'\in with (Q,C')\le (1+{\varepsilon })r\). There an efficient reduction from })\...

Given an odd prime q and integer m ≤ q, a binary mq × q2 quasi-cyclic parity-check matrix H(m, q) can be constructed for array low-density (LDPC) code C(m, q). In this letter, we investigate the first separating redundancy of We prove that is 1-separating any pair (m, q), from which conclude upper bounded by mq. Then show our bound on tighter than general deterministic constructive bounds in li...