Let D be an unbounded domain in R with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1D(x)m(x)dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r...

let $e$ be an elliptic curve over $bbb{q}$ with the given weierstrass equation $ y^2=x^3+ax+b$. if $d$ is a squarefree integer, then let $e^{(d)}$ denote the $d$-quadratic twist of $e$ that is given by $e^{(d)}: y^2=x^3+ad^2x+bd^3$. let $e^{(d)}(bbb{q})$ be the group of $bbb{q}$-rational points of $e^{(d)}$. it is conjectured by j. silverman that there are infinitely many primes $p$ for which $...

We study (approximate) null-controllability of parabolic equations in $L_p(\mathbb{R}^d)$ and provide explicit bounds on the control cost. In particular we consider systems form $\dot{x}(t) = -A_p x(t) + \mathbf{1}_E u(t)$, $x(0) x_0\in L_p (\mathbb{R}^d)$, with interior a so-called thick set $E \subset \mathbb{R}^d$, where $p\in [1,\infty)$, $A$ is an elliptic operator order $m \in \mathbb{N}$...

We provide a complete picture of the upper quantization dimension in terms Rényi by proving that order r &gt; 0 r&gt;0</mml:annotatio...

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

pyrazoles and isoxazoles are well-known important heterocyclic compounds that due to their participation in the structure of many drugs are very important. pyrazoles and isoxzaloes can be prepared by oxidation of pyrazolines and isoxazolines respectively. in this work, trans-3,5-dihydroperoxy-3,5-dimethyl-1,2-dioxalane (dhpdmdo)/nh4i has been used as a new, powerful, nearly green, effective and...

Let D be an unbounded domain in R with d ≥ 3. We show that if D contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on D is transient. Next assume that RBM X on D is transient and let Y be its time change by Revuz measure 1D(x)m(x)dx for a strictly positive continuous integrable function m on D. We further show that if there is some r > 0 so that D \ B(0, r...

Ex = Ax + Bu (1.1) where x e 3C ~ R" e % ~ R, (E, A, B)e R x R x R. Note that E and A are non square. We can always assume without loss of generality that B is monic. In the sequel, (1.1) will be referred to by the triple (E, A, B). Now, let I denote the set of all such (E, A, B)'s. Define T P D = {(W, V, G, FP, FD)eR qXq x R x x R x R x R with W, F a n d G non singular}. The action of this gro...

and Applied Analysis 3 Here are some useful examples of regularized quasi-semigroups. Example 2.2. Let {Tt}t≥0 be an exponentially bounded strongly continuous C-semigroup on Banach space X, with the generator A. Then K s, t : Tt, s, t ≥ 0, 2.5 defines a C-quasi-semigroup with the generator A s A, s ≥ 0, and so D D A . Example 2.3. Let X BUC R , the space of all bounded uniformly continuous func...