Equivalential algebras with conjunction on the regular elements

We introduce the definition of the three-element equivalential algebra R with conjunction on the regular elements. We study the variety generated by R and prove the Representation Theorem. Then, we construct the finitely generated free algebras and compute the free spectra in this variety.

Sub-Doppler infrared spectroscopy of resonance-stabilized hydrocarbon intermediates: ν3/ν4 CH stretch modes and CH2 internal rotor dynamics of benzyl radical

Sub-Doppler spectroscopy of benzyl radicals reveals how resonance stabilization provides for rovibrationally well resolved and relatively perturbation-free spectra in the CH stretch region.

Spectral phase measurement of complex pulses using delay controlled fringe free interferometry technique

The shortcomings in complex femtosecond pulse measurement of conventional spectral phase interferometry for direct electric-field reconstruction (SPIDER) are commented in this paper. To solve the problem, we propose an improved version of SPIDER, where single replica of the unknown pulse upconverts synchronously with two frequency-shifted narrow-banded long pulses. With the introduction of a suitable small delay between the upconverted pulses, the spectral phase of the unknown pulse can be directly calculated from the fringe-free spectra and Fourier-transform filtering is not required. The results of numerical simulation show that the accuracy of the new method in complex pulse measurement is higher than conventional SPIDER.

ON FREE SPECTRA OF A CLASS OF FINITE INVERSE MONOIDS

For a finite Clifford inverse algebra $A$, with natural order meet-semilattice ${Y}_{A} $ and group of units ${G}_{A} $, we show that the inverse monoid obtained as the semidirect product ${ Y}_{A}^{1} {\mathop{\ast }\nolimits}_{\rho } {G}_{A} $ has a log-polynomial free spectrum whenever $\rho $ is a term-expressible left action of ${G}_{A} $ on ${Y}_{A} $ and all subgroups of $A$ are nilpotent. This yields a number of examples of finite inverse monoids satisfying the Seif conjecture on finite monoids whose free spectra are not doubly exponential.

ON FREE ALGEBRAS IN VARIETIES GENERATED BY ITERATED SEMIDIRECT PRODUCTS OF SEMILATTICES

We present a new solution of the word problem of free algebras in varieties generated by iterated semidirect products of semilattices. As a consequence, we provide asymptotical bounds for free spectra of these varieties. In particular, each finite [Formula: see text]-trivial (and, dually, each finite [Formula: see text]-trivial) semigroup has a free spectrum whose logarithm is bounded above by a polynomial function.

ON FREE SPECTRA OF VARIETIES OF LOCALLY THRESHOLD TESTABLE SEMIGROUPS

A semigroup S is said to be ℓ-threshold k-testable if it satisfies all identities u = v where u, v is an arbitrary pair of words over a finite alphabet Σ such that they simultaneously belong or fail to belong to any ℓ-threshold k-testable (regular) language. We give an asymptotic formula for the free spectrum of the variety [Formula: see text] of all ℓ-threshold k-testable semigroups, thereby providing an asymptotic upper bound on the size of an arbitrary finitely generated locally threshold testable semigroup. The combinatorial interpretation of this task yields an enumeration problem for particular edge labelings of de Bruijn graphs.