in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

Coherence plays a very important role in Grover search algorithm (GSA). In this paper, we define the normalization coherence N(C), where C is measurement. virtue of constraint large N and Shannon's maximum entropy principle, surprising complementary relationship between success probability GSA obtained. Namely, P_s(t)+N(C(t))\simeq 1, terms relative l_1 norm coherence, t number iterations GSA. ...

Let $p$ be an odd prime, $q=p^e$, $e \geq 1$, and $\mathbb{F} = \mathbb{F}_q$ denote the finite field of $q$ elements. $f: \mathbb{F}^2\to \mathbb{F}$ $g: \mathbb{F}^3\to functions, let $P$ $L$ two copies 3-dimensional vector space $\mathbb{F}^3$. Consider a bipartite graph $\Gamma_\mathbb{F} (f, g)$ with vertex partitions edges defined as follows: for every $(p)=(p_1,p_2,p_3)\in P$ $[l]= [l_1,...

Simple bilevel problems are optimization in which we want to find an optimal solution inner problem that minimizes outer objective function. Such appear many machine learning and signal processing applications as a way eliminate undesirable solutions. In our work, suggest new approach is designed for with simple functions, such the \(l_1\) norm, not required be either smooth or strongly convex....

Permutations of the form \(F(x)=L_1(x^{-1})+L_2(x)\) with linear functions \(L_1,L_2\) are closely related to several interesting questions regarding CCZ-equivalence and EA-equivalence inverse function. In this paper, we show that F cannot be a permutation on binary fields if kernel \(L_1\) or \(L_2\) is large. A key step our proof an observation maximal size subspace V \(\mathbb {F}_{2^n}\) co...

In extreme learning machine (ELM) framework, the hidden layer setting determines its generalization ability; and in presence of outliers training set, weights between output based on least squares would be overly estimated. To address these two problems ELM implementation, we extend robust penalized statistical framework propose a general ELM, which consists components (robust loss function reg...