Surface integral and Gauss-Ostrogradskij theorem from the viewpoint of applications

Making use of a surface integral defined without use of the partition of unity, trace theorems and the Gauss-Ostrogradskij theorem are proved in the case of three-dimensional domains with a Lipschitz-continuous boundary for functions belonging to the Sobolev spaces H ^1,p () (1 p < ). The paper is a generalization of the previous author's paper which is devoted to the line integral.     

Bifurcation of periodic solutions to variational inequalities in R κ based on Alexander-Yorke theorem

Variational inequalities are studied, where K is a closed convex cone in , 3, B is a × matrix, G is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some ₀ for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some _{I 0}. Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at ₀ constructed on the basis of the Alexander-Yorke theorem as global bifurcation branches of a certain enlarged system.     

Convergence of Appell Polynomials of Long Range Dependent Moving Averages in Martingale Differences

We study limit distribution of partial sums S_N,k(t) = _{s = 1} ^{[N t]} A_k(X_s) of Appell polynomials of the long-range dependent moving average process X_t> = _{i t} b_{t - i i}, where {_i} is a strictly stationary and weakly dependent martingale difference sequence, and b_i i^{d - 1} (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums S_N,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { _i}.     

Large Deviations Behavior for the Quadratic Error of Density Estimate

For a projection estimator f_n of an unknown density f we investigate the behavior of large deviations probability P{T_n > r_n} when r_n , where T_n is appropriately centered and normed quadratic error f_n-f)².     

Physical application and optimization a shape of core for experience

We present in this work some new theoretical results concerning an influence of the shape of core on the development of magnetization. As a special case the rotary symmetric objects with non-homogeneous magnetization were investigated. The shape of core was optimized on the basis of various practical criteria.     

Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Conclusions The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.The approximation of the exact radial solution by the Taylor expansion involving also the second energy derivative of the radial function, except for the first derivative, has two advantages. First, the energy dependence of the logarithmic derivatives atr=R is better described and, therefore, the method is less sensitive to the choice of the centre of expansionE ₀ or, equivalently, acceptably accurate eigenvalues are obtained for the broader energy region aroundE ₀. The other and probably more important advantage is that the approximate radial solutions are remarkably closer to the exact radial functions inside the muffin-tin sphere. This can be of use when evaluating the measurable quantities depending on the wave functions.     

The inhibited photo-oxidation of polystyrene and styrene/HALS copolymers

The influence of molecular weight and the mode of binding of HALS stabilisers on their efficiency in the inhibited photo-oxidation of polystyrene and styrene/HALS copolymers was investigated. Photo-oxidation was performed with radiation of λ > 310 nm and 366 nm. The following functionalised HALS stabilisers were prepared: 4-methacryloylamino-2,2,6,6-tetramethylpiperidine, 4-methacryloyloxy-2,2,6,6-tetramethylpiperidine, 4-methacryloyloxy-1,2,2,6,6-pentamethylpiperidine and 15-methacryloyl-7,15-diazadispiro [5.1,5.3] hexadecane-14,16-dione. Binding by copolymerisation is substantially less efficient than addition of low molecular weight stabiliser.     

Additivity of the crossing number of graphs with connectivity 2

We prove that the crossing number of graphs with connectivity 2 has in certain cases an additive property analogous to that of crossing number of graphs with connectivity ≤1.