The relative Lefschetz and Nielsen fixed-point theorems are generalized for compact absorbing contractions on ANR-spaces and nilmanifolds. The nontrivial Lefschetz number implies the existence of a fixedpoint in the closure of the complementary domain. The relative Nielsen numbers improve the lower estimate of the number of coincidences on the total space or indicate the location of fixed-point...

This paper presents two techniques for the design of digital filters with bit-constrained coefficients, the “bit-flipping” algorithm [1] and the Downhill Simplex Method modified to deliver fixedpoint filter coefficients [2]. Both techniques can be applied both to design filters from scratch and to optimise their floating-point equivalents. They are comparatively presented through an example of ...

This letter addresses the problem of fetal electrocardiogram (FECG) extraction. A class of source extraction algorithms is proposed, which uses a combination of two different approaches: Barros’s source extraction approach and Hyvärinen’s fixedpoint approach. The proposed algorithms can rapidly extract the desired FECG with little noise, and can work well in some bad situations. The validity an...

This paper is devoted to the study of the following nonlocal p -Laplacian functional differential equation −φp(x′(t)) )′ = λ f (t,x(t),x ′ (t)) (∫ 1 0 f (s,x(s),x′ (s))ds )n , 0 < t < 1, subject to multi point boundary conditions. We obtain some results on the existence of at least one (when n ∈ Z+ ) or triple (when n = 0) pseudo-symmetric positive solutions by using fixedpoint theory in cone. ...

Within the framework of exact renormalization group flow equations, a scale-dependent transformation of the field variables provides for a continuous translation of UV to IR degrees of freedom. Using the gauged NJL model as an example, this translation results in a construction of partial bosonization at all scales. A fixedpoint structure arises which makes it possible to distinguish between fu...

Digital linear filters are used in a variety of applications (sound treatment, control/command, etc.), implemented in software, in hardware, or a combination thereof. For safety-critical applications, it is necessary to bound all variables and outputs of all filters. We give a compositional, effective abstraction for digital linear filters expressed as block diagrams, yielding sound, precise bo...

Taking Löb's Axiom in modal provability logic as a running thread, we discuss some general methods for extending modal frame correspondences, mainly by adding fixedpoint operators to modal languages as well as their correspondence languages. Our suggestions are backed up by some new results – while we also refer to relevant work by earlier authors . But our main aim is advertizing the perspecti...

This paper describes a Modelica package for fixedpoint arithmetics and automatic fixed point code generation for embedded systems and FPGA applications. Using Dymola [1] to investigate the dynamic behavior of the original model a fixed point representation is automatically generated. The model can then be simulated, using fixed point arithmetics to verify the fixed-point representation. Finally...

We discuss QCD condensate contributions to the gluon propagator both in the fixedpoint gauge and in covariant gauges for the external QCD vacuum gluon fields with the conclusion that a covariant gauge is essential to obtain a gauge invariant QCD vacuum energy density difference and to retain the unitarity of the quark scattering amplitude. The gauge-invariant QCD condensate contributions to the...