Let $A_{1},\dots ,A_{m}$ be $n\times n$ real matrices such that for each $1\leq i\leq m,$ $A_{i}$ is invertible and $A_{i}-A_{j}$ is invertible for $i\neq j$. In this paper we study integral operators of the form $$ Tf( x) =\int k_{1}( x-A_{1}y) k_{2}( x-A_{2}y) \dots k_{m}( x-A_{m}y) f( y) {\rm d} y, $$ $k_{i}( y) =\sum _{j\in \mathbb Z}2^{jn/{q_{i}}}\varphi _{i,j}( 2^{j}y) $, $1\leq q_{i}<\infty,$ $1/{q_{1}}+1/{q_{2}}+\dots +1/{q_{m}}=1-r,$ $0\leq r<1,$ and $\varphi _{i,j}$ satisfying suitable regularity conditions. We obtain the boundedness of $T\colon H^{p}( \mathbb {R} ^{n}) \rightarrow L^{q}
(\mathbb {R}^{n}) $ for $ 0<p<1/{r}$ and $1/{q}=1/{p}-r.$ We also show that we can not expect the $H^{p}$-$H^{q}$ boundedness of this kind of operators.
The paper deals with a flow validation study performed using our in-house 3D-computer-code which implements mathematical and numerical model capable to simulate the atmospheric boundary layer flow in general. The validation study is related to a neutrally stratified boundary layer 2D-flow over an isolated hill with a rough wall including pollution dspersion according to Castro [1].
Our mathematical model is based on the system of RANS equations closed by two-equation high-Reynolds number k-ε turbulence model together with wall functions. The finite volume method and the explicit Runge-Kutta time integration method are utilized for the numerics. and Obsahuje seznam literatury
The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.
The possibility to study quantitatively the diet of the Antarctic shag Phalacrocorax bransfieldensis by the analysis of pellets, applying correction factors to compensate for the digestion and loss through the gastrointestinal tract of fish otoliths represented in pellets, was evaluated at two localities of the South Shetland Islands. For such purpose, the results from the analysis of 566 pellets (= regurgitated casts) collected at Harmony Point, and 296 at Duthoit Point, throughout the 1995/96 and 1996/97 breeding seasons, were corrected with the mentioned factors and the shag daily consumption rate was estimated. The estimations indicated that, except for Duthoit Point in 1996/97, the daily food intake increased from November to January (pre-laying to late-rearing) and slightly decreased in February when chicks start to fledge, thus reflecting the energy requirements at the nest. These estimations, in general, are in line with those previously obtained for other colonies and/or shag species by different methods, which suggests that after correction the use of pellets is an acceptable method to quantify the diet of the Antarctic Shag.
For a domain Ω ⊂ n let H(Ω) be the holomorphic functions on Ω and for any k ∈ N let A k (Ω) = H(Ω) ∩ C k (Ω). Denote by A k D(Ω) the set of functions f : Ω → [0, ∞) with the property that there exists a sequence of functions fj ∈ A k (Ω) such that {|fj |} is a nonincreasing sequence and such that f(z) = lim j→∞ |fj (z)|. By A k I (Ω) denote the set of functions f : Ω → (0, ∞) with the property that there exists a sequence of functions fj ∈ A k (Ω) such that {|fj |} is a nondecreasing sequence and such that f(z) = lim j→∞ |fj (z)|. Let k ∈ N and let Ω1 and Ω2 be bounded A k -domains of holomorphy in m1 and m2 respectively. Let g1 ∈ A k D(Ω1), g2 ∈ A k I (Ω1) and h ∈ A k D(Ω2)∩A k I (Ω2). We prove that the domains Ω = {(z, w) ∈ Ω1 × Ω2 : g1(z) < h(w) < g2(z)} are A k -domains of holomorphy if int Ω = Ω. We also prove that under certain assumptions they have a Stein neighbourhood basis and are convex with respect to the class of A k -functions. If these domains in addition have C 1 -boundary, then we prove that the A k -corona problem can be solved. Furthermore we prove two general theorems concerning the projection on n of the spectrum of the algebra Ak.
In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented and tested using the so-called \emph{generalized Lorenz system} (GLS) family making advantage of its special parametrization. Such an implementation relies on the parameter dependent synchronization of several identical copies of the GLS obtained through the observer-based design for nonlinear systems. The purpose of this paper is to study and compare two different methods for the anti-synchronization detection, including further underlying theoretical study of the GLS. Resulting encryption schemes are also compared and analyzed with respect to both the encryption redundancy and the encryption security. Numerical experiments illustrate the results.
Let <span class="tex">ε</span>-Argmin<span class="tex">(Z)</span> be the collection of all <span class="tex">ε</span>-optimal solutions for a stochastic process <span class="tex">Z</span> with locally bounded trajectories defined on a topological space. For sequences <span class="tex">(Z<sub>n</sub>)</span> of such stochastic processes and <span class="tex">(ε<sub>n</sub>)</span> of nonnegative random variables we give sufficient conditions for the (closed) random sets <span class="tex">ε<sub>n</sub></span>-Argmin<span class="tex">(Z<sub>n</sub>)</span> to converge in distribution with respect to the Fell-topology and to the coarser Missing-topology.