Let G be a finite group and H a subgroup. Denote by D(G;H) (or D(G)) the crossed product of C(G) and \mathbb{C}H (or \mathbb{C}G) with respect to the adjoint action of the latter on the former. Consider the algebra \left \langle D(G), e\right \rangle generated by D(G) and e, where we regard E as an idempotent operator e on D(G) for a certain conditional expectation E of D(G) onto D(G; H). Let us call \left \langle D(G), e\right \rangle the basic construction from the conditional expectation E: D(G) → D(G; H). The paper constructs a crossed product algebra C(G/H ×G) \rtimes \mathbb{C}G, and proves that there is an algebra isomorphism between \left \langle D(G), e\right \rangle and C(G/H×G) \rtimes \mathbb{C} G., Qiaoling Xin, Lining Jiang, Zhenhua Ma., and Obsahuje seznam literatury
The basis number of a graph $G$ was defined by Schmeichel to be the least integer $h$ such that $G$ has an $h$-fold basis for its cycle space. He proved that for $m,n\ge 5$, the basis number $b(K_{m,n})$ of the complete bipartite graph $K_{m,n}$ is equal to 4 except for $K_{6,10}$, $K_{5,n}$ and $K_{6,n}$ with $n=5,6,7,8$. We determine the basis number of some particular non-planar graphs such as $K_{5,n}$ and $K_{6,n}$, $n=5,6,7,8$, and $r$-cages for $r=5,6,7,8$, and the Robertson graph.
The bathymetric range of 149 digenean species recorded deeper than 200 m, the approximate depth of the continental shelf/slope break, are presented in graphical form. It is found that only representatives of the four families Lepocreadiidae, Fellodistomidae, Derogenidae and Hemiuridae reach to abyssal regions (>4,000 m). Three other families, the Lecithasteridae, Zoogonidae and Opecoelidae, have truly deep-water forms reaching deeper than 3,000 m. Bathymetric data are available for the Acanthocolpidae, Accacoeliidae, Bucephalidae, Cryptogonimidae, Faustulidae, Gorgoderidae, Monorchiidae and Sanguinicolidae showing that they reach deeper than 200 m. No bathymetric data are available for the members of the Bivesiculidae and Hirudinellidae which are reported from deep-sea hosts. These results indicate that only seventeen out of the 150 or so digenean families are reported in the deep sea.
We investigate the Bergman kernel function for the intersection of two complex ellipsoids {(z,w1,w2) 2 Cn+2 : |z1|2+. . .+|zn|2+|w1|q
<1, |z1|2+. . .+|zn|2+|w2|r < 1}. We also compute the kernel function for {(z1,w1,w2) 2 C3 : |z1|2/n + |w1|q < 1, |z1|2/n + |w2|r < 1} and show deflation type identity between these two domains. Moreover in the case that q = r = 2 we express the Bergman kernel in terms of the Jacobi polynomials. The explicit formulas of the Bergman kernel function for these domains enables us to investigate whether the Bergman kernel has zeros or not. This kind of problem is called a Lu Qi-Keng problem., Tomasz Beberok., and Seznam literatury
Although the fluid therapy plays a fundamental role in the
management of polytrauma patients (PP), a tool which could
determine it appropriately is still lacking. The aim of this study
was to evaluate the application of a bioimpedance spectroscopy
(BIS) for body fluids volume and distribution monitoring in these
patients. This prospective, observational study was performed on
25 severe PP and 25 healthy subjects. The body fluids
composition was repeatedly assessed using BIS between days 3
to 11 of intensive care unit stay while the impact of fluid intake
and balance was evaluated. Fluid intake correlated significantly
with fluid excess (FE) in edemas, and their values were
significantly higher in comparison with the control group. FE was
strongly associated with cumulative fluid balance (p<0.0001,
r=0.719). Furthermore, this parameter was associated with the
entire duration of mechanical ventilation (p=0.001, r=0.791)
independently of injury severity score. In conclusion, BIS
measured FE could be useful in PP who already achieved
negative fluid balance in prevention the risk of repeated
hypovolemia through inappropriate fluid restriction. What is
more, measured FE has a certain prognostic value. Further
studies are required to confirm BIS as a potential instrument for
the improvement of PP outcome.
The paper deals with a special way of the construction of the boundary conditions for the compressible gas flow. The solution of the Riemann problem is used at the boundary. It can be shown, that the unknown one-side initial condition for this problem can be partially replaced by the suitable complementary condition. Authors work with such complementary conditions (by the preference of pressure, velocity, total quantities,...) in order to match the physically relevant data. Algorithms were coded and used within the own developed code for the solution of the Euler, NS, and the RANS equations, using the finite volume method. Numerical example shows superior behavior of these boundary conitions in comparison with some other boundary conditions. and Obsahuje seznam literatury
The main purpose of this paper is to prove the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space.
The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.