A random n-permutation may be generated by sequentially removing random cards C1, ..., Cn from an n card deck D = {1, ..., n}. The permutation σ is simply the sequence of cards in the order they are removed. This permutation is itself uniformly random, as long as each random card Ct is drawn uniformly from the remaining set at time t. We consider, here, a variant of this simple procedure in whi...

We give a complete characterization of integral functionals which are Lipschitzian on a Lebesgue space Lp with p finite. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces Lp. In every cases, the Lipchitzian properties of the integral functional are described by Lipschitzian properties of the integrand. Mathematics Subje...

begin{abstract} In this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable Banach space. end{abstract}

Abstract Within the framework of a renormalizable SU(5)L × U(1)Y electro-weak gauge model with no exotic electric charges, we obtain all neutral weak charge operators and their quantization, once diagonalization boson mass matrix is properly performed. Our results open up path to rich promising phenomenological outcome. All Standard Model phenomenology recovered by simply decoupling latter’s sc...

We prove that a sequence of, possibly branched, weak immersions of the two-sphere S into an arbitrary compact riemannian manifold (M, h) with uniformly bounded area and uniformly bounded L−norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a subsequence, to a Lipschitz mapping of S and whose image is made of a connected union of f...

Abstract Let $f:\mathbb {C}^2\to \mathbb {C}^2$ be a polynomial skew product that leaves invariant an attracting vertical line $ L $. Assume moreover $f$ restricted to $L$ is non-uniformly hyperbolic, in the sense satisfies one of following conditions: (1) $f|_L$ topological Collet–Eckmann and weak regularity conditions. (2) The Lyapunov exponent at every critical value point lying Julia set $f...

It is proved that L(`p, `q) has the KK property if and only if it has the UKK property if and only if 1 < q < 2 < p < ∞. It is also proved that L(c0, `1) has the UKK property and that L(c0, `q) can be renormed to have the weak-star UKK property if (and only if) 1 ≤ q < 2. In all other cases L(`p, `q) has no equivalent UKK norm. Finally, it is proved that none of these spaces is either strictly ...

Letting $A \subset \mathbb{R}^n$ be Borel measurable and $W_0 : A \to \mathbb{G}(n,m)$ Lipschitzian, we establish that \begin{equation*} \limsup_{r 0^+} \frac{\mathcal{H}^m \left[ \cap B(x,r) (x+ W_0(x))\right]}{\alpha(m)r^m} \geq \frac{1}{2^n}, \end{equation*} for $\mathcal{L}^n$-almost every $x \in A$. In particular, it follows $A$ is $\mathcal{L}^n$-negligible if only $\mathcal{H}^m(A (x+W_0...

We prove an L subsequence ergodic theorem for sequences chosen by independent random selector variables, thereby showing the existence of universally L-good sequences nearly as sparse as the set of squares. In the process, we prove that a certain deterministic condition implies a weak maximal inequality for a sequence of l convolution operators (Prop. 3.1).