The objective of the study in this paper is to define M₁,M₂-direction curves and M₁,M₂-donor curves of the spacelike curve γ via the Bishop frame of type-2 in E₁³. We obtained the necessary and sufficient conditions when the associated curves to be slant helices and general helices via the Bishop frame of type-2 in E₁³. After defining the spherical indicatrices of the associated curves, we obta...

In this paper, we propose a delay constrained spatio-temporal video rate control method for lossy channels where the effective channel rate available to the video encoder is time-varying. Target bit-rate constraint for encoding is derived, which guarantees in-time delivery of video frames. By using empirically obtained rate-quantization and distortionquantization relations of video, the distort...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.

We describe techniques to establish local frames over point-sampled manifold surfaces. The tangential alignment of local frames is determined using a wave front algorithm starting from a set of pre-defined directions and conquering the remaining points. The repeated application of this algorithm is a relaxation procedure that maximizes coherence along the surface and minimizes the discrepancy t...

We describe the so-called method of virtual components for tight wavelet framelets to increase their approximation order and vanishing moments in the multivariate setting. Two examples of the virtual components for tight wavelet frames based on bivariate box splines on three or four direction mesh are given. As a byproduct, a new construction of tight wavelet frames based on box splines under t...

Initial geometric imperfections are unavoidable in steel members and frames due to erection manufacturing tolerances. These include frame out-of-plumbness, member out-of-straightness cross-sectional imperfections, can have a significant influence on the response resistance of structures. Thus, they need be accounted for analysis design structures, especially when advanced procedures adopted. On...