In this paper we prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let A(X) be a standard operator algebra on X and let L(X) be an algebra of all bounded linear operators on X. Suppose we have a linear mapping D : A(X) → L(X) satisfying the relation D(Am+n) = D(Am)An + AmD(An) for all A ∈ A(X) and some fixed integers m ≥ 1, ...

Given a complex manifold X, a normal crossing divisor D ⊂ X whose irreducible components D 1 ,. .. , D s are smooth, and a choice of natural numbers r = (r 1 ,. .. , r s), we construct a manifold X(D, r) with an action of a torus Γ and we prove that some full subcategory of the category of Γ-equivariant vector bundles on X(D, r) is equivalent to the category of parabolic vector bundles on (X, D...

t h e s p e c i a l c o n c e n t r i c a l l y b r a c e d f r a m e (s c b f) i s a c o m m o n t y p e o f s t e e l s t r u c t u r a l s y s t e m f o r r e s i s t i n g l a t e r a l l o a d i n g. t h i s t y p e o f s y s t e m p r o v i d e s t h e r e q u i r e d s t i f f n e s s a n d s t r e n g t h a t r e l a t i v e l y l o w c o s t. d e s i g n c o d e s, b a s e d o n p a s ...

urinary 1-hydroxypuren (1-ohp) is commonly used as a major metabolite and biological indicator of the overall exposure to polycyclic aromatic hydrocarbons (pahs). for evaluation of human exposure to such compounds, biological monitoring is an essential process, in which, preparation of samples is one of the most time-consuming and error-prone aspects prior to chromatographic techniques. in this...

Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x), x], [d(y), y]] = 0, for all x, y ∈ I. We prove that if [I, I]I ≠ 0, then d(I)I = 0. 1. Introduction. Let R be a prime ring and d a nonzero derivation of R. Define [x, y] 1 = [x, y] = xy − yx, then an Engel condition is a polynomial [x, y] k = [[x, y] k−1 ,y]

Throughout this paper, R is an associative ring; andN ,C,C(R), and J denote, respectively, the set of nilpotent elements, the center, the commutator ideal, and the Jacobson radical. An element x of R is called potent if xn = x for some positive integer n= n(x) > 1. A ring R is called periodic if for every x in R, xm = xn for some distinct positive integersm=m(x), n = n(x). A ring R is called we...

We consider Itô’s stochastic differential equation (SDE). First, we would review a standard theory under standard assumptions. Then we would see how such a standard theory should be modified under different and more general assumptions and how and what new notions need be introduced to discuss such modifications. Consider the following SDE on R dX (t) = σ k(X(t))dB (t) + b(X(t))dt, X(0) = x (1)...

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that usH(u)ut = 0 for all u ∈ L, where s ≥ 0, t ≥ 0 are fixed integers. Then H(x) = 0 for all x ∈ R unless char R = 2 and R satisfies S4, the standard identity in four variables. Let R be an associative ring with center Z(R). For x, y ∈ R, the commutator xy− yx will be denoted by [x, y]. An add...

In this note, we establish $L^p$-bounds for the semigroup $e^{-tq^w(x,D)}$, $t \ge 0$, generated by a quadratic differential operator $q^w(x,D)$ on $\mathbb{R}^n$ that is Weyl quantization of complex-valued form $q$ defined phase space $\mathbb{R}^{2n}$ with non-negative real part $\operatorname{Re} q 0$ and trivial singular space. Specifically, show $e^{-tq^w(x,D)}$ bounded from $L^p(\mathbb{R...

Consider the first exit time τ D of a (d + 1)-dimensional Brownian motion from an unbounded open domain D = {(x, y) ∈ R d+1 : y > f (x), x ∈ R d } starting at (x 0 , f (x 0) + 1) ∈ R d+1 for some x 0 ∈ R d , where the function f (x) on R d is convex and f (x) → ∞ as the Euclidean norm |x| → ∞. Very general estimates for the asymptotics of log P(τ D > t) are given by using Gaussian techniques. I...