5 Existing research provides no systematic, limited information procedure for handling 6 non-invertibility, despite the well-known inference problem it causes as well as its 7 presence in many types of dynamic systems. Non-invertibility means that structural 8 shocks cannot be recovered from a history of observed variables. It can arise from 9 a form of delayed responses due to, among other thi...

We consider the invertibility (injectivity) of a nonparametric nonseparable demand system. Invertibility of demand is important in several contexts, including identi…cation of demand, estimation of demand, testing of revealed preference, and economic theory exploiting existence of an inverse demand function or (in an exchange economy) uniqueness of Walrasian equilibrium prices. We introduce the...

We consider the so-called Berezin ?-sequence, where ? is an operator valued inner function, for operators on vector Hardy space H2E (D), and study invertibility of some model K? = ?H2E via ?-sequence. By applying symbols technique Toeplitz corona problem in Bergman L2a(D) studied. Moreover, C-invertibility C-unitarity are also defined

In this paper, we consider a certain class of discrete pseudo-differential operators in a sharp convex cone and describe their invertibility conditions in L2-spaces. For this purpose we introduce a concept of periodic wave factorization for elliptic symbol and show its applicability for the studying. Key–Words: Discrete operator, Multidimensional periodic Riemann problem, Periodic wave factoriz...

<p><span data-preserver-spaces="true">The demands of 21st Century learning are now in the Industrial Revolution Era 4.0 with 4C characters. Educators must develop their creativity to improve quality so that students can be more creative learning. </span><em>Instrumental Analytical Chemistry</em><span data-preserver-spaces="true"> is a course studies modern in...

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2, we investigate a concept of invertibility and the invertibility of the composition of random functions defined on finite sets. In Section 3, we resolve some questions concerning the number of samples required to ensure the accuracy of maximum likelihood estimatio...

Using a novel Wintner-type formulation of the classical Peano’s existence theorem [Math. Ann. 37 (1890), 182-228], we enhance Ważewski’s result on invertibility of maps defined on closed balls [Ann. Soc. Pol. Math. 20 (1947), 81-125] securing the size of the domain of invertibility that agrees with the bounds derived by John [Comm. Pure Appl. Math. 21 (1968), 77-110] and Sotomayor [Z. Angew. Ma...