The boundary layer equations for the non-Newtonian power law fluid are examined under the classical conditions of uniform flow past a semi infinite flat plate. We investigate the behavior of the similarity solution and employing the Crocco-like transformation we establish the power series representation of the solution near the plate.
The limit behaviour of solutions of a singularly perturbed system is examined in the case where the fast flow need not converge to a stationary point. The topological convergence as well as information about the distribution of the values of the solutions can be determined in the case that the support of the limit invariant measure of the fast flow is an asymptotically stable attractor.
Let $R$ be a commutative ring, $M$ an $R$-module and $G$ a group of $R$-automorphisms of $M$, usually with some sort of rank restriction on $G$. We study the transfer of hypotheses between $M/C_M(G)$ and $[M,G]$ such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose $[M,G]$ is $R$-Noetherian. If $G$ has finite rank, then $M/C_M(G)$ also is $R$-Noetherian. Further, if $[M,G]$ is $R$-Noetherian and if only certain abelian sections of $G$ have finite rank, then $G$ has finite rank and is soluble-by-finite. If $M/C_M(G)$ is $R$-Noetherian and $G$ has finite rank, then $[M,G]$ need not be $R$-Noetherian., Bertram A. F. Wehrfritz., and Obsahuje bibliografické odkazy
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
We study the solutions and attractivity of the difference equation xn+1 = xn−3/(−1 + xnxn−1xn−2xn−3) for n = 0, 1, 2, . . . where x−3, x−2, x−1 and x0 are real numbers such that x0x−1x−2x−3 ≠ 1.
We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded., Marek T. Malinowski, Ravi P. Agarwal., and Obsahuje bibliografii
A subgroup H of a finite group G is said to be ss-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is s-permutable in K. In this paper, we first give an example to show that the conjecture in A.A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group G is solvable if every subgroup of odd prime order of G is ss-supplemented in G, and that G is solvable if and only if every Sylow subgroup of odd order of G is ss-supplemented in G. These results improve and extend recent and classical results in the literature., Jiakuan Lu, Yanyan Qiu., and Obsahuje seznam literatury
Consider boundary value problems for a functional differential equation ( x (n) (t) = (T +x)(t) − (T −x)(t) + f(t), t ∈ [a, b], lx = c, where T +, T − : C[a, b] → L[a, b] are positive linear operators; l: ACn−1 [a, b] → R n is a linear bounded vector-functional, f ∈ L[a, b], c ∈ ℝ n , n ≥ 2. Let the solvability set be the set of all points (T +, T −) ∈ ℝ + 2 such that for all operators T +, T − with kT ±kC→L = T ± the problems have a unique solution for every f and c. A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started in R. Hakl, A. Lomtatidze, J. Šremr: Some boundary value problems for first order scalar functional differential equations. Folia Mathematica 10, Brno, 2002.