Manyeconomicmodels andoptimizationproblemsgenerate (endogenous) shadow prices—alias dual variables or Lagrange multipliers. Frequently the “slopes” of resulting price curves—that is, multiplier derivatives—are of great interest. These objects relate to the Jacobian of the optimality conditions. That particular matrix often has block structure. So, we derive explicit formulas for the inverse of ...

(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems are defined bounded intervals or domains. Therefore, it is important both theory application to construct all possible wavelets some desired properties from (bi)orthogonal line. Vanishing moments compactly supported key property for sparse wavelet representa...

Highly efficient arithmetic operations are necessary to achieve the desired performance in many real-time systems and digital image processing applications. In all these applications, one of the important arithmetic operations frequently performed is to multiply and accumulate with small computational time. In this paper, a 4-bit serial parallel multiplier, which can perform both positive and n...

A simple way of obtaining multivariate wavelets is the tensor product of univariate wavelets. Multivariate wavelets are of interest in both theory and application. In this paper, we study the projection method, an inverse operation in some sense to the tensor product method, to investigate various properties of multivariate refinable function vectors and multivariate multiwavelets. To illustrat...

It is shown how orthogonal compact-support multiwavelets may be used for the solution of quantum mechanical eigenvalue problems subject to specific boundary conditions. Special scaling functions and wavelets with convenient limiting behaviors at the edges of an interval are constructed in analogy to earlier work on single wavelet families. All of the integrals required for Hamiltonian matrix el...

.The basic elements of an algorithm for designing multiplier blocks for matrices are presented. The new algorithm often produces results superior to the best of the older algorithms applied only to columns.

This paper reports on the veriication of two of the IFIP WG10.5 benchmarks | the multi-plier and systolic matrix multiplier. The circuit implementations are timed, detailed gate-level descriptions, and the speciication is given using the temporal logic TL n , a quaternary-valued temporal logic. A practical, integrated theorem-proving/model checking system based on the compositional theory for T...

In this chapter, we propose to use a parametric multiplier approach to deriving parametric Lyapunov functions for robust stability analysis of linear systems involving uncertain parameters. This new approach generalizes the traditional multiplier approach used in the absolute stability literature where the multiplier is independent of the uncertain parameters. Our main result provides a general...

A procedure for the construction of balanced orthogonal nonseparable quincunx multiwavelets, having filters with good lowpass properties, is introduced. Thematrix filter bank is viewed as the polyphasematrix of other filters, uponwhich the lowpass condition is imposed. The multiscaling functions obtained are plotted by means of the cascade algorithm. The process of transforming an image with th...

In this paper, we give explicit construction of multiwavelets on polygonal region in R 2 that is associated with a nested triangular tessellation. Two di erent constructions will be presented. The rst construction is very similar to Alpert's construction in [3], but unlike the latter 1-D construction, in which case symmetry of basis functions comes in almost automatically, the multiwavelets fro...