A connected plane graph taken with its interior faces forms an (r, q)-polycycle if the interior faces are all r-gons (where r = const > 3), while all interior vertices are of the maximal possible degree, denoted by q (where q = const > 3); see [1]. Any finite (r, q)-polycycle is homeomorphic to a disc and its boundary is homeomorphic to a circle. The cyclic sequence q1q2 . . . qm formed by the ...

We describe how the nonlinear development of the R-mode instability of neutron stars influences spin up to millisecond periods via accretion. When nearly resonant interactions of the l = m = 2 R-mode with pairs of ”daughter modes” are included, the R-mode saturates at the lowest amplitude which leads to significant excitation of a pair of modes. The lower bound for this threshold amplitude is p...

We prove the existence of a solution for the nonlinear boundary value problem u = f ( x, u, u′′, . . . , u ) , x ∈ [0, 1], u(0) = 0 = u(1), 0 ≤ i ≤ m + 1, where f : [0, 1] × R → R is continuous. The technique used here is a monotone method in the presence of upper and lower solutions. We introduce a new maximum principle which generalizes one due to Bai which in turn was an improvement of a max...

Fourier spectrum of the boundary values of functions in the complex Hardy Space H(C+) is characterized for p ∈ (0, 2). First, functions f in the L(R) can be decomposed into a sum g + h, where g and h are the non-tangential boundary limits of function in H(C+) and H(C−) in the sense of L(R), where H(C+) and H(C−) are the Hardy spaces in the upper and lower complex plane C+ and C−, respectively. ...

We analyze a piecewise deterministic PDE consisting of the diffusion equation on a finite interval Ω with randomly switching boundary conditions and diffusion coefficient. We proceed by spatially discretizing the diffusion equation using finite differences and constructing the Chapman–Kolmogorov (CK) equation for the resulting finite-dimensional stochastic hybrid system. We show how the CK equa...

in this article, we investigate sufficient conditions for existence of maximal and minimalsolutions to a coupled system of highly nonlinear differential equations of fractional order with mixedtype boundary conditions. to achieve this goal, we apply monotone iterative technique togetherwith the method of upper and lower solutions. also an error estimation is given to check theaccuracy of the me...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...

As long ago as 1962 Nitsche [8] conjectured that a harmonic homeomorphism h : A(r,R) onto −→ A(r∗, R∗) between planar annuli exists if and only if R∗ r∗ > 1 2 ` R r + r R ́ . We prove this conjecture when the domain annulus is not too wide; explicitly, when log R r 6 3 2 . For general A(r, R) the conjecture is proved under additional assumption that either h or its normal derivative have vanishi...