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...

The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use this to address Bass’ question, whether Kn(R) = Kn(R[t]) implies Kn(R) = Kn(R[t1, t2]). The answer to this question is affirmative when R is essential...

We investigate the persistence probability in the Voter model for dimensions d ≥ 2. This is achieved by mapping the Voter model onto a continuum reaction–diffusion system. Using path integral methods , we compute the persistence probability r(q, t), where q is the number of " opinions " in the original Voter model. We find r(q, t) ∼ exp[−f 2 (q)(ln t) 2 ] in d = 2; r(q, t) ∼ exp[−f d (q)t (d−2)...

and Applied Analysis 3 (1) V is continuous in ((n − 1)T, (n + τ − 1)T] × R + , ((n + τ − 1)T, nT] × R + and for each x ∈ R + , n ∈ N, lim (t,y)→ ((n+τ−1)T + ,x) V(t, y) = V((n + τ − 1)T + , x) and lim (t,y)→ (nT + ,x) V(t, y) = V(nT, x) exist. (2) V is locally Lipschitzian x. Definition 1. Letting V ∈ V 0 , one defines the upper right derivative of V with respect to the impulsive differential s...

In this paper we study the transport equation in $\mathbb{R}^{n} \times (0,T)$, $T >0$, $n\ge 2$, $$ \partial \_t f + v\cdot \nabla = g, \quad f(\cdot,0)= f\_0 \text{in }\mathbb{R}^{n}, generalized Campanato spaces $\mathscr{L}^{s}{{q(p, N)}}(\mathbb{R}^{n})$. The critical case is particularly interesting, and applied to local well-posedness problem for incompressible Euler equations a space cl...

An i n f l u e n c e o f d e p a r t u r e f r o m r o t a t i o n a l e q u i l i b r i u m on t h e f l o w s t r u c t u r e n e a r a s p h e r e o f r a d i u s R = 0 . 3 m c a n be e x p e c t e d f o r f l i g h t a t a l t i t u d e s 9 0 1 2 0 km [ 1 ] . I n t h e e x p e r i m e n t a l s i m u l a t i o n o f t h e s e f l o w r e g i m e s i n w i n d t u n n e l s , t h e n o n e q...

We present symmetric Rogers--Hölder's inequalities on time scales when $frac{1}{p}+frac{1}{q}+frac{1}{r}=0$ and $frac{r}{p}+frac{r}{q}$ is not necessarily equal to $1$ where $p,$ $q$ and $r$ are nonzero real numbers.

Evaluation of the cardiovascular system of canine pediatrics requires awareness of the anatomical and physiological changes occurring from birth to six months of age. The aim of this study was to report electrocardiographic changes in the littermate mongrel dogs from birth tosix months. Serial six-lead electrocardiograms were recorded from ten normal littermate mongrel dogs kept on right latera...

Consider in a real Hilbert space H the differential equation (E) : p(t)u′′(t) + q(t)u′(t) ∈ Au(t) + f(t), for a.a. t ∈ R+ = [0,∞), with the condition u(0) = x ∈ D(A), where A : D(A) ⊂ H → H is a maximal monotone operator, with [0, 0] ∈ A (or, more generally, 0 ∈ R(A)); p, q ∈ L∞(R+), with ess inf p > 0 and either ess inf q > 0 or ess sup q < 0; and f : R+ → H is a given function. Recall that eq...