On an inequality of Bynum and Drew

AbstractAn extension of the Bynum-Drew inequality in the abstract Lp space, 1 < p ⩽ 2, is presented. The extended inequality is applied to show the strong uniqueness of best approximations and existence of fixed points for uniformly Lipschitzian mappings and to prove an estimate for the self-Jung constants

Fast multidimensional Bernstein-Lagrange algorithms

In this paper we present two fast algorithms for the Bézier curves and surfaces of an arbitrary dimension. The first algorithm evaluates the Bernstein-Bézier curves and surfaces at a set of specific points by using the fast Bernstein-Lagrange transformation. The second algorithm is an inversion of the first one. Both algorithms reduce the initial problem to computation of some discrete Fourier transformations in the case of geometrical subdivisions of the d-dimensional cube. Their orders of computational complexity are proportional to those of corresponding d-dimensional FFT-algorithm, i.e. to O (N logN) + O (dN), where N denotes the order of the Bernstein-Bézier curves

Algorithms for multi-secret hierarchical sharing schemes of shamir type

In this paper there are presented algorithms for multilevel hierarchical threshold secret sharing schemes based on the interpolation of Hermite type, which use either traditional Shamir's keys or polynomial and orthogonal polynomial keys. These algorithms enable to compute the probability of authenticity of shares during the process of recovering the keys. In addition, two models of secret sharing are considered, which enlarge their security against attacks and decrease their rate of computations by applying FFT-algorithm

Fast algorithms for polynomial evaluation and differentiation at special knots

We present fast evaluating and differentiating algorithms for the Hermite interpolating polynomials with the knots of multiplicity 2, which are generated dynamically in a field K = (K,+,⋅) by the recurrent formula of the formX^i = αx^i-1+β (i=1,2,..,n-1; x^0=γ).As in the case of Lagrange-Newton interpolating algorithms, the running time of these algorithms is C(n) + O(n) base operations from the field K, where C(n) = O(nlog n) denotes the time needed to compute the wrapped convolution in Kn

Fast interpolating algorithms in cryptography

We present two fast polynomial interpolating algorithms with knots generated in a field K by the recurrent formula of the form xf = axj_l + ft (z = 1,2,..,« -1; x0 = . The running time of them is C(n) + 0(n) base operations from K, where C(n) = 0(n\og2 n) denotes the time needed to compute the wrapped convolution in K. Moreover, we give an application of these algorithms to threshold secret sharing schemes in cryptography

Stany graniczne użytkowalności belek żelbetowych z betonu wysokowartościowego z dodatkiem włókien

The article presents the results of research and analysis of reinforced high performance concrete beams with steel and polypropylene fibres at service load. The beams were bent in the 4-point model. Research was carried out for three different rectangular reinforced concrete beams in terms of the quantity and the type of reinforcement. The beam B1 was constructed conventionally with reinforced steel rods. The beams B2 and B3, instead of the compressive rods and the stirrups the fibre reinforcement of variable fibre volume percentage was applied. In the tests a non-contact system for three-dimensional measurements of deformation – ARAMIS was used. The analysis of the behaviour of the beams under static load for serviceability was based on: images of cracks, strain and force – displacement curves.W artykule przedstawiono wyniki i analizy badań belek żelbetowych wykonanych z betonu wysokowartościowego z dodatkiem włókien stalowych i&nbsp;polipropylenowych poddanych zginaniu w schemacie 4-punktowym przy obciążeniach eksploatacyjnych. Badania przeprowadzono dla trzech prostokątnych belek żelbetowych zróżnicowanych pod względem ilości i rodzaju zbrojenia. W belce B1 skonstruowano tradycyjne zbrojenie prętami stalowymi. W belkach B2 i B3 zamiast prętów górnych i&nbsp;strzemion zastosowano zbrojenie rozproszone o zmiennej procentowej objętości włókien. W&nbsp;badaniach wykorzystano system pomiarowy do bezkontaktowych trójwymiarowych pomiarów odkształceń – ARAMIS. Analizy zachowania belek pod obciążeniem statycznym w&nbsp;zakresie użytkowalności przedstawiono w oparciu o: obrazy zarysowania i odkształcenia oraz zależności siła-przemieszczenie

Analiza numeryczna niesprężystych belek żelbetowych z betonu wysokiej wytrzymałości o niskim stopniu zbrojenia

Numerical modelling of flexural behavior of the reinforced highstrength concrete beams with low reinforcement ratio is discussed in this paper. Modelling mechanism of failure reinforced concrete beams under static load, static deformation processes of the reinforced high-strength concrete beams with regard to the physical nonlinearities of the structural materials (i.e. concrete and reinforcement steel) were developed using finite element analysis. The comparison of the numerical and experimental results as well as theoretical solutions, were presented. The compared results indicate correctness of the constitutive models of the structural materials: concrete and reinforcing steel and effectiveness of the solution method.W artykule przedstawiono analizę wytężenia zginanych belek żelbetowych wykonanych z betonu wysokiej wytrzymałości o niskim stopniu zbrojenia. Modelowanie deformacji elementów pod obciążeniem statycznym do zniszczenia włącznie z uwzględnieniem nieliniowości fizycznych betonu i stali zbrojeniowej przeprowadzono z wykorzystaniem zasad metody elementów skończonych. W celu zweryfikowania przyjętych modeli materiałów konstrukcyjnych wyniki analiz numerycznych przedstawiono na tle wyników eksperymentalnych dostępnych w literaturze