We propose a class of models exhibiting instanton crystal phase. In this phase, the minimum free energy corresponds to configuration with an imaginary-time-dependent order parameter in form chain alternating instantons and antiinstantons. The resulting characteristic feature state is that average over imaginary time vanishes. study model broad region parameters quantitatively, prove existence w...

The imagination and creativity of children is often puzzling to the adult mind. Pretend play and make-believe friends are often prevalent in the life of a child. Past research shows a relationship between the use of the imagination in children’s play and their social, cognitive, and emotional development. Furthermore, there are a number of gender differences in the type of imaginary play and pr...

This article deals with channel estimation (CE) in orthogonal frequency division multiplexing (OFDM)/OQAM. After a brief presentation of the OFDM/OQAM modulation scheme, we present the CE problem in OFDM/OQAM. Indeed, OFDM/OQAM only provides real orthogonality therefore the CE technique used in cyclic prefix-OFDM cannot be applied in OFDM/OQAM context. However, some techniques based on imaginar...

Our remark concerns the structure of the pencil of conics containing three degenerate conics of which two represent conjugate imaginary line pairs, i.e. the pencil defined by Eq. (24) in [1]. In what follows we will demonstrate that Campbell’s claim that also the third singular conic ‘must be a conjugate imaginary line pair’ is false, because this conic is, in fact, a real line pair. The proof ...

This paper is concerned with α– and D–negative imaginary systems. The definition of α–negative imaginary transfer functions is firstly introduced. Then, the relationship between negative imaginary and α–negative imaginary transfer functions is studied. By means of the generalized inverse, an α–negative imaginary lemma is proposed to test the α–negative imaginary property of transfer functions. ...

An imaginary cube is a three dimensional object which has square projections in three orthogonal directions just as a cube has. In this paper, we study imaginary cubes and present sculptures based on imaginary cubes. We show that there are 16 kinds of minimal convex imaginary cubes. The list of 16 representative minimal convex imaginary cubes contains, as well as a regular tetrahedron and a cub...

Even though the two term recurrence relation satisfied by the incomplete gamma function is asymptotically stable in at least one direction, for an imaginary second argument there can be a considerable loss of correct digits before stability sets in. We present an approach to compute the recurrence relation to full precision, also for small values of the arguments, when the first argument is neg...

The evolution of QCD coupling constant at finite temperature is considered by making use of the finite temperature renormalization group equation up to the one-loop order in the background field method with the Feynman gauge and the imaginary time formalism. The results are compared with the ones obtained in the literature. We point out, in particular, the origin of the discrepancies between di...

whereX0(N) is the complete curve overQ which classifies pairs of elliptic curves related by a cyclic N -isogeny. The curve E is equipped with the collection of Heegner points defined over ring class fields of suitable imaginary quadratic fields. More precisely, let K be an imaginary quadratic field in which all rational primes dividing N are split and let O be the order of K of conductor c prim...