We introduced and studied GF-regular modules as a generalization of π-regular rings to modules as well as regular modules (in the sense of Fieldhouse). An R-moduleM is called GF-regular if for each x ∈ M and r ∈ R, there exist t ∈ R and a positive integer n such that rntrnx = rx. The notion of G-pure submodules was introduced to generalize pure submodules and proved that an RmoduleM isGF-regula...

As soon as we have established (10) and (11) we can complete the discussion in the customary manner. An m-chain will be exact if its derivative vanishes, it will be derived if it is the derivative of some (m 1)-chain. By (10), every derived chain will be exact; therefore, the group GD' of all derived m-chains will be a subgroup of the group GE of all exact m-chains. The residue group GE mod GD ...

Injective Pure Type Systems form a large class of Pure Type Systems for which one can compute by purely syntactic means two sorts elmt(?jM) and sort(?jM), where ? is a pseudo-context and M is a pseudo-term, and such that for every sort s, ? ` M : A ^ ? ` A : s) elmt(?jM) = s ? ` M : s) sort(?jM) = s By eliminating the problematic clause in the (abstraction) rule in favour of constraints over el...

In order to use optical tweezers as a force measuring tool inside a viscoelastic medium such as the cytoplasm of a living cell, it is crucial to perform an exact force calibration within the complex medium. This is a nontrivial task, as many of the physical characteristics of the medium and probe, e.g., viscosity, elasticity, shape, and density, are often unknown. Here, we suggest how to calibr...

Cai(1996b) proposed a wavelet method, BlockShrink, for estimating regression functions of unknown smoothness from noisy data by thresholding empirical wavelet co-eecients in groups rather than individually. The BlockShrink utilizes the information about neighboring wavelet coeecients and thus increases the estimation accuracy of the wavelet coeecients. In the present paper, we ooer insights int...

A Golomb ruler with M marks can be defined as a set {ai} of integers so that all differences δij = aj − ai, i 6= j, are distinct. An order 2 Golomb ruler is a Golomb ruler such that all differences δijk` = |δk` − δij |, {i, j} 6 = {k, `}, are distinct as much as possible. Contruction of optimum order 2 Golomb ruler, i.e., of rulers of minimum length, is a highly combinatorial problem which has ...