Let $ A$ be a $ n\times n$ real matrix. Is there a vector $ \vec x \in \mathbb{R}^n$ with exactly $ 0 \le k < n$ zero entries such that $ A \vec x = 0$ ? Is there an efficient algorithm to tackle this question?Read more
Let $ A$ be a $ n\times n$ real matrix. Is there a vector $ \vec x \in \mathbb{R}^n$ with exactly $ 0 \le k < n$ zero entries such that $ A \vec x = 0$ ? Is there an efficient algorithm to tackle this question?Read more
Let $ \mathcal{K}$ be a $ \lambda$ -accessible category and $ \hat{\mathcal{K}}$ its free completion under connected limits. Is $ \hat{\mathcal{K}}$ still accessible? $ \mathcal{K}$ can be identified with a subcategory of $ \text{Set}^{\text{Pres}_{\lambda}(\mathcal{K}) ^{\text{op}}}$ , is it true that $ \hat{\mathcal{K}}$ is just the closure under connected limits of this subcategory? It looks likeRead more
Consider the diophantine equation $ $ x_1y_1^3 + \dots + x_s y_s^3 = 0. $ $ For fixed $ \mathbf{y}$ with coprime coordinates this is a $ s-1$ dimensional lattice $ \Lambda(\mathbf{y})$ . Let $ N(X)$ denote the number of integer points in this lattice with $ \max |x_i| \leq X$ . Then we shouldRead more
Given any $ g \in L^\infty(\mathbb{R})$ , define the associated multiplier operator $ T_g \colon L^2(\mathbb{R}) \to L^2(\mathbb{R})$ by $ $ \mathcal{F}(T_g f) \ = \ g.\mathcal{F}f $ $ where $ \mathcal{F}$ denotes the Fourier transform. Definition. We will say that a function $ f \in L^\infty(\mathbb{R})$ is nice if for every bounded $ gRead more
Modern solutions implemented to the online store can increase your profits. I recommend to get acquainted here: https://www.growcode.com/blog/6-tactics-optimize-mobile-ecommerce-conversion-rate Very useful tools that can be used in your own store. I personally recommend.Read more
Suppose $ A$ is a $ k$ -algebra, with $ k$ a field, and let $ \ell$ be a field extension of $ k$ . Is there an easy way to see/recover $ \mathrm{Spec}(A)$ in/from $ \mathrm{Spec}(A \otimes_k \ell)$ , using the action of $ \mathrm{Gal}(\ell/k)$ ? Important special case: $ \ell$ is an algebraicRead more
I have a travel blog and want to optimize the images in my blog posts. Please suggest the ways and methods to do so.Read more
Let $ G(t,\omega)$ be a stochastic process with a.s. continuous paths defined on a probability space $ \Omega$ with $ \omega \in \Omega$ and over a time period $ t\in[0,T]$ . $ T$ here is a constant, not a random variable. Suppose that the distribution of the process at every time point is known. IRead more
i can understand why the VC-dimension of arithmetic progression, will be bounded, but i am not success to prove it. Let (X , F) be the range space where X = Z and each range in F is an arithmetic progression {a, a + b, a + 2b, . . . , a + ib,Read more
Trilixton ;-It advances the breakdown and union of estrogen inside the body. It helps our body in decreasing its levels of "terrible" exogenous estrogen and expanding "great" endogenous estrogenFenugreek Seed Extract: It can support the muscle quality And cause metabolic-endocrine changes in the bodyHow to Use Trilixton?Each container of Trilixton accompanies 60 cases. http://www.wellness4healthy.com/trilixton/Read more