In this chapter we survey several recent results on the existence of frames with prescribed norms and frame operator. These results are equivalent to Schur-Horn type theorems which describe possible diagonals of positive self-adjoint operators with specified spectral properties. The first infinite dimensional result of this type is due to Kadison who characterized diagonals of orthogonal projec...

well-known seismic design codes have offered an alternative equivalent static procedure for practical purposes instead of verifying design trials with complicated step-y-step dynamic analyses. such a pattern of base-shear distribution over the building height will enforce its special stiffness and strength distribution which is not necessarily best suited for seismic design. the present study, ...

Abstract We prove that the existence of a measurable cardinal is equivalent to normal space whose modal logic coincides with Kripke frame isomorphic powerset two element set.

The parameterized model of the tension machine frame is established through Solidworks software, and then optimization function ANSYS Workbench used to optimize design frame. Under condition meeting strength, weight reduction completed. Compared with original scheme, maximum equivalent stress overall shape optimized scheme will be lower, reduced by 7.11%, effect significant, thus reducing cost ...

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual relationship. We will show that controlled frames are equivalent to standard frames and so this concept gives a generalized way to check the frame condition, while ...

Frames with a large minimum angle between any two distinct frame vectors are desirable in many present day applications. For unit norm frame, the absolute value of cosine is also known as coherence. Two frames equivalent if one can be obtained from other via left action an invertible linear operator. Frame angles change under Most existing works solve different optimization problems to find opt...

In this work, a general method for the design of concentric braced steel frames (CBF) with active tension diagonal bracings, applicable to single- and multi-storey structures, is presented. The based on use an elastic modal analysis response spectrum, which carried out using appropriate modified stiffness bracings. reliability proposed validated through significant case studies, making series n...

The conventional discussion of the observed distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations, from a stationary frame, of : (i) objects moving with constant velocity and uniformly illuminated during a short time τL (their ‘Luminous Proper Time’) in their rest frame; these may be called ‘Transient...