Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there finite different WSFs, $s_1,\ldots,s_K$, so that WSF jumps one another suddenly, WSFs and encode useful information. We present an iterative warping clustering algorithm estimate $s_1,\ldots,s_K$ nonstationary sig...

A set of polynomials is called a submodule $\mathbb C [x_1 ,\ldots , x_n ]$ if it translation invariant linear subspace ]$. We present description the submodules [x,y]$ in terms

We present an explicit construction of infinite sequences points $$(x_{0}, x_{1}, x_{2}, \ldots)$$ in the d-dimensional unit-cube whose periodic L2-discrepancy satisfies $$L_{2,N}^{{\rm per}}(\{x_{0},x_{1},\ldots, x_{N-1}\}) \le C_d N^{-1} (\log N)^{d/2} \quad \text{for all } N \ge 2,$$ where factor $$C_d > 0$$ depends only on dimension d. The is based higher order digital as introduced by J. D...

For a Brownian directed polymer in Gaussian random environment, with $q(t,\cdot)$ denoting the quenched endpoint density and \[ Q_n(t,x_1,\ldots,x_n)=\mathbf{E}[q(t,x_1)\ldots q(t,x_n)], \] we derive hierarchical PDE system satisfied by $\{Q_n\}_{n\geq1}$. We present two applications of system: (i) compute generator $\{\mu_t(dx)=q(t,x)dx\}_{t\geq0}$ for some special functionals, where $\{\mu_t(...

Abstract There has been recent interest in a hybrid form of the celebrated conjectures Hardy–Littlewood and Chowla. We prove that for any $k,\ell \ge 1$ distinct integers $h_2,\ldots ,h_k,a_1,\ldots ,a_\ell $ , we have: $$ \begin{align*}\sum_{n\leq X}\mu(n+h_1)\cdots \mu(n+h_k)\Lambda(n+a_1)\cdots\Lambda(n+a_{\ell})=o(X)\end{align*} all except $o(H)$ values $h_1\leq H$ so long as $H\geq (\log X...

In the paper we study equiaffine immersions $f\colon (M^n,\nabla) \rightarrow {\mathbb{R}}^{n+2}$ with flat connection $\nabla$ and one-dimensional Weingarten mapping. For such there are two types of transversal distribution frame.We give a parametrization submanifold given properties for both frame. The main result is contained in Theorems 1, 2 Corollary 1: Let ({M}^n,\nabla)\rightarrow({\math...

Abstract For a graph G , two dominating sets D and $$D'$$ D ′ in non-negative integer k the set is said to -transform if there sequence $$D_0,\ldots ,D_\ell $$ 0 , … ℓ ...

Abstract This paper studies the joint tail asymptotics of extrema multi-dimensional Gaussian process over random intervals defined as $P(u)\;:\!=\; \mathbb{P}\{\cap_{i=1}^n (\sup_{t\in[0,\mathcal{T}_i]} ( X_{i}(t) +c_i t )>a_i u )\}$ , $u\rightarrow\infty$ where $X_i(t)$ $t\ge0$ $i=1,2,\ldots,n$ are independent centered processes with stationary increments, $\boldsymbol{\mathcal{T}}=(\mathca...

Let $$S=K[x_1,\ldots ,x_n]$$ , where K is a field, and $$t_i$$ denotes the maximal shift in minimal graded free S-resolution of algebra S/I at degree i. In this paper, we prove:

we study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by devroye et. al (2011). in a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor ix_i floor$ where $x_0$, $ldots$ , $x_n$ is a sequence of i.i.d. random variables, with support in [0,...