We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain Ω under the general outflow condition. Let T be a 2-dimensional straight channel R × (−1, 1). We suppose that Ω ∩ {x1 < 0} is bounded and that Ω ∩ {x1 > −1} = T ∩ {x1 > −1}. Let V be a Poiseuille flow in T and µ the flux of V . We look for a solution which tends to V as x1 → ∞. Assuming that the domain and the boundary data are symmetric with respect to the x1-axis, and that the axis intersects every component of the boundary, we have shown the existence of solutions if the flux is small (Morimoto-Fujita [8]). Some improvement will be reported in this note. We also show certain regularity and asymptotic properties of the solutions.
We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1/16. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π and M.
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In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.
H. Weyl, jeden z prvních, kdo se zabýval rolí symetrie v kvantové mechanice, podal následující definici symetrie [1]: „Věc je symetrická, pokud se s ní dá něco udělat tak, že i po dokončení toho udělání vypadá stejně jako před tím.“ Tato věta se dá přeložit do poněkud exaktnějšího jazyka pomocí teorie grup - matematické disciplíny, která byla ještě na začátku 20. století považována za nepraktickou, spíše poněkud exotickou doménu ryze teoretického bádání. Především zásluhou fyziků se v následujících desetiletích z teorie grup stal jeden z nejdůležitějších nástrojů k uchopení reality. Fyzikální svět je plný symetrií!, Pavel Cejnar., and Obsahuje seznam literatury
The present paper introduces a group of transformations on the collection of all multivariate copulas. The group contains a subgroup which is of particular interest since its elements preserve symmetry, the concordance order between two copulas and the value of every measure of concordance.
Properties of $n$-ary groups connected with the affine geometry are considered. Some conditions for an $n$-ary $rs$-group to be derived from a binary group are given. Necessary and sufficient conditions for an $n$-ary group $<\theta ,b>$-derived from an additive group of a field to be an $rs$-group are obtained. The existence of non-commutative $n$-ary $rs$-groups which are not derived from any group of arity $m<n$ for every $n\ge 3$, $r>2$ is proved.
The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.
In this paper I defend the rejection of fatalism about the past by showing that there are possible circumstances in which it would be rational to attempt to bring about by our decisions and actions a necessary and sufficient condition, other things being equal, for something which we see as favorable to have occurred in the past. The examples I put forward are analogous to our attempts to bring about the occurrence of future events, and demonstrate the symmetry between the past and the future in this respect., V tomto příspěvku hájím odmítnutí fatalismu o minulosti tím, že dokazuji, že existují možné okolnosti, za kterých by bylo rozumné pokusit se o naše rozhodnutí a činy učinit nezbytnou a dostatečnou podmínkou, jiné věci jsou rovnocenné, za něco, co jsme v minulosti bylo příznivé. Příklady, které jsem předložil, jsou analogické s našimi pokusy o nastolení budoucích událostí a v tomto ohledu ukazují symetrii mezi minulostí a budoucností., and Gal Yehezkel