Denote the joint numerical radius of an m-tuple of bounded operators A = (A1, . . . , Am) by w(A). We give a complete description of maps f satisfying w(A − B) = w(f(A) − f(B)) for any two m-tuples of operators A = (A1, . . . , Am) and B = (B1, . . . , Bm). We also characterize linear isometries for the joint numerical radius, and maps preserving the joint numerical range of A. AMS Classificati...

a) Zeigen Sie, dass B := (v1, v2, v3, v4) eine Basis von W := Lin(v1, v2, v3, v4) ist. b) Für f ∈ W definiere D(f) := f ′. Begründen Sie, dass D von W nach W abbildet, und zeigen Sie, dass die Abbildung D : W → W, f 7→ f ′, linear ist. c) Geben Sie die Darstellungsmatrix von D : W → W und D : W → W bezüglich der Basis B von W an. (Dabei ist D(f) := D(D(f)) für f ∈ W .) d) Sei g : (−π, π)→ R, x ...

Abstract In this paper we provide non-smooth atomic decompositions of 2-microlocal Besov-type and Triebel–Lizorkin-type spaces with variable exponents $$B^{\varvec{w}, \phi }_{p(\cdot ),q(\cdot )}({\mathbb {R}}^n)$$ B p ( · ) <mm...

The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...

We provide a new characterization of the Bivariate normal-Wishart distribution. Let ~ x = fx 1 x 2 g have a non-singular Bivariate normal pdf f(~ x) = N(~ W) with unknown mean vector ~ and unknown precision matrix W. L e t f(~ x) = f(x 1)f(x 2 jx 1) where f(x 1) = N(m 1 1=v 1) and f(x 2 jx 1) = N(m 2j1 +b 12 x 1 1=v 2j1). Similarly, deene fv 2 v 1j2 b 21 m 2 m 1j2 g using the factorization f(~ ...

Certain gastric disorders affect spatiotemporal parameters of the gastric slow wave. Whereas the electrogastrogram (EGG) evaluates electric potentials to determine primarily temporal parameters, fundamental physical limitations imposed by the volume conduction properties of the abdomen suggest the evaluation of gastric magnetic fields. We used a multichannel superconducting quantum interference...

In the present study, the effect of seaweed liquid fertilizer (SLF) of Ulva fasciata, Nizimuddinia zunardini and Gracilaria corticata without chemical fertilizer on seed germination, growth parameter, pigment and carbohydrate content of Wheat var. (Chamran) was investigated. The seeds soaked with aqueous extract of seaweeds performed better when compared to the water soaked controls. The 10% co...

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

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...