A scaling vector = (1 ; ; r) T is a compactly supported and vector-valued distribution vector that satisses a matrix reenement equation (x) = P P k (2x ? k); where (P k) is a nite matrix sequence. We call P (z) = 1 2 P P k z k the symbol of. A symbol P (z) is said two-scale similar to a polynomial matrix Q(z) if there is an invertible polynomial matrix T (z) that satisses P (z) = T (z 2)Q(z)T ?...

and Applied Analysis 3 F2 F t, xn, . . . , x0 W t, x0 − H t, xn, . . . , x0 , for every t ∈ Z, W,H are continuously differentiable in x0 and xn, . . . , x0, respectively. Moreover, there is a bounded set J ⊂ Z such that H t, xn, . . . , x0 ≥ 0; 2.2 F3 There is a constant μ > p such that 0 < μW t, x0 ≤ W ′ 2 t, x0 x0, ∀ t, x0 ∈ Z × R \ {0} ; 2.3 F4 H t, 0, . . . , 0 ≡ 0, and there is a constant ...

F u z z y D C F : a c o n t r a d i c t i o n i n t e r m s , o r a w a y t o b e t t e r F u z z y D C F : a c o n t r a d i c t i o n i n t e r m s , o r a w a y t o b e t t e r F u z z y D C F : a c o n t r a d i c t i o n i n t e r m s , o r a w a y t o b e t t e r F u z z y D C F : a c o n t r a d i c t i o n i n t e r m s , o r a w a y t o b e t t e r F u z z y D C F : a c o n t r a d i c...

We present a novel framework for representation learning that builds a lowdimensional latent dynamical model from high-dimensional sequential raw data, e.g., video. The framework builds upon recent advances in the amortized inference that constructs a fully-differentiable network, and takes advantage of the duality between control and inference to solve the intractable inference problem using t...

In this note we extend a Theorem of Kwong and Zettl concerning the inequality Z 1 0 t ju 0 j p K Z 1 0 t juj p 1=2 Z 1 0 t ju 00 j p 1=2 to all ; ; such that = (+)=2 except for the triple: = p ?1, = ?1, = ?1?p. In this case the inequality is false; however u satisses the inequality Z 1 0 t ju 0 j p K 1 (Z 1 0 t juj p 1=2 Z 1 0 t ju 00 j p 1=2 + Z 1 0 t juj p) : 1. Notation. Let I = (a; b), ?1 a...

For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.

Here, T is the time of an event and Z a p-dimensional vector of covariates, φ a square integrable function, and F(t | z) = P (T ≤ t | Z = z) and H( dz) = P (Z ∈ dz) denote the conditional survival distribution and the marginal law of Z , respectively. For example, θ(I {t > t∗}) is the marginal survival probability at time t∗, θ(I {t > t∗, z1 > z∗ 1}) the bivariate distribution at (t∗, z∗ 1) (Ak...

It is proved analogues of the classical Wiman's inequality} for class $\mathcal{D}$ absolutely convergents in whole complex plane $\mathbb{C}^p$ (entire) Dirichlet series form $\displaystyle F(z)=\sum\limits_{\|n\|=0}^{+\infty} a_ne^{(z,\lambda_n)}$ with such a sequence exponents $(\lambda_n)$ that $\{\lambda_n\colon n\in\mathbb{Z}^p\}\subset \mathbb{C}^p$ and $\lambda_n\not=\lambda_m$ all $n\n...