On measuring changes in welfare when changes in consumption bundles are small

The paper examines three extensively used propositions regarding changes in utility and social welfare attributable to small changes in consumption bundles. It is shown that, though these propositions are valid when the changes in consumption bundles are ``infinitesimally small,''' none of the propositions can be sustained when we have finite changes in consumption bundles, even when such finite changes are arbitrarily small. This drastically reduces the usefulness of the propositions for any practical purpose. The paper discusses the underlying formal structure of the problem and identifies the reason why the propositions run into difficulties in the case of finite changes.

Koherentno upravljanje spektrom spontane emisije u dvojno tjeranom atomu tipa Y

We have studied the dynamic control of the spontaneous emission spectrum in a Y-type atomic system driven by two coherent fields. In different dynamic conditions, the evolution of coherent spectral features in the bare-state model, has been analyzed by using the dressed-state model. For the system under purely dissipative environment, it has been shown that the behaviour of spectral components can be coherently controlled by changing the values of the Rabi frequencies and detunings of external fields. At the condition of resonant evolution of spectra, present work highlights that the emission line shape can be strongly modified for unequal decay rates of the uppermost doublet states. In this situation, the phenomenon of constructive quantum interference gives rise to the emergence of a single peak at a certain spectral position when two distinct peaks disappear at the other spectral positions. Owing to the mutual orientation of polarizations of the fields interacting with the atom in a specific configuration, we have incorporated the static phase-variation effect to exhibit phase-dependent spectra. We consider the present model with a typical field configuration such that the frequency mismatch between two coherent fields introduces the dynamic phase-variation effect. This phenomenon leads to obtain anomalous peak-shifting effect accompanied by the selective quenching of emission within the spectral profile.Proučavamo dinamičko upravljanje spektrom spontane emisije atomskog sustava tipa Y koji tjeraju dva koherentna polja. Proučavamo ovisnost svojstava koherentnog spektra o različitim uvjetima, u oguljenom sustavu i primjenom potpunog sustava. Ako sustav troši energiju, onda svojstvima spektralnih sastavnica možemo koherentno upravljati mijenjanjem Rabijevih frekvencija i narušavanjem ugodbe vanjskih polja. Uz uvjet rezonantnog razvoja spektra, pokazujemo kako se oblik emisijske linije može jako promijeniti uz nejednoliko raspadanje gornjeg dubleta. U tim uvjetima konstruktivna kvantna interferencija uzrokuje nastanak jednog vrha na određenom mjestu u spektru kada dva jasna vrha nestanu u drugim dijelovima spektra. Radi međusobne orijentacije polarizacija polja koja djeluju na atom u nekom stanju, uključili smo i učinak promjene statičke faze da bismo prikazali faznoovisne spektre. Ovaj model predstavljamo s tipičnim oblikom polja tako da nesklad frekvencija dovodi do dinamičkih promjena faze. Ta pojava vodi na anomalne pomake vrhova i mogućnost odabira gušenja emisije unutar spektralnog područja

Koherentno upravljanje spektrom spontane emisije u dvojno tjeranom atomu tipa Y

We have studied the dynamic control of the spontaneous emission spectrum in a Y-type atomic system driven by two coherent fields. In different dynamic conditions, the evolution of coherent spectral features in the bare-state model, has been analyzed by using the dressed-state model. For the system under purely dissipative environment, it has been shown that the behaviour of spectral components can be coherently controlled by changing the values of the Rabi frequencies and detunings of external fields. At the condition of resonant evolution of spectra, present work highlights that the emission line shape can be strongly modified for unequal decay rates of the uppermost doublet states. In this situation, the phenomenon of constructive quantum interference gives rise to the emergence of a single peak at a certain spectral position when two distinct peaks disappear at the other spectral positions. Owing to the mutual orientation of polarizations of the fields interacting with the atom in a specific configuration, we have incorporated the static phase-variation effect to exhibit phase-dependent spectra. We consider the present model with a typical field configuration such that the frequency mismatch between two coherent fields introduces the dynamic phase-variation effect. This phenomenon leads to obtain anomalous peak-shifting effect accompanied by the selective quenching of emission within the spectral profile.Proučavamo dinamičko upravljanje spektrom spontane emisije atomskog sustava tipa Y koji tjeraju dva koherentna polja. Proučavamo ovisnost svojstava koherentnog spektra o različitim uvjetima, u oguljenom sustavu i primjenom potpunog sustava. Ako sustav troši energiju, onda svojstvima spektralnih sastavnica možemo koherentno upravljati mijenjanjem Rabijevih frekvencija i narušavanjem ugodbe vanjskih polja. Uz uvjet rezonantnog razvoja spektra, pokazujemo kako se oblik emisijske linije može jako promijeniti uz nejednoliko raspadanje gornjeg dubleta. U tim uvjetima konstruktivna kvantna interferencija uzrokuje nastanak jednog vrha na određenom mjestu u spektru kada dva jasna vrha nestanu u drugim dijelovima spektra. Radi međusobne orijentacije polarizacija polja koja djeluju na atom u nekom stanju, uključili smo i učinak promjene statičke faze da bismo prikazali faznoovisne spektre. Ovaj model predstavljamo s tipičnim oblikom polja tako da nesklad frekvencija dovodi do dinamičkih promjena faze. Ta pojava vodi na anomalne pomake vrhova i mogućnost odabira gušenja emisije unutar spektralnog područja

On arithmetic functions of balancing and Lucas-balancing numbers

For any integers $ngeq1$ and $kgeq0,$ let $phi(n)$ and $sigma_{k}(n)$ denote the Euler phi function and the sum of the $k$-th powers of the divisors of $n$, respectively. In this article, the solutions to some Diophantine equations about these functions of balancing and Lucas-balancing numbers are discussed

Proučavanje učinaka brzinski-ovisnih sudara na lambovu udubinu i prijelazne rezonancije u sustavu s tri stanja

We discuss the effects of phase-dephasing and velocity-changing collisions on saturated absorption line shapes studied in an open V-type system under the semi-classical density-matrix formalism. It has been noted that the traces of Lamb dips and crossover resonance dip lying within the Doppler-broadened contour can vanish in the presence of a strong saturating field if a sufficient contribution of collisional dephasing effect is present. Asymmetry may be introduced in the wings of saturated line profiles for a small contribution of collision kernel.Raspravljamo učinke otklanjanja faze i sudara s promjenom brzine na oblike linija zasićenih apsorpcijom za otvoren V-sustav, primjenom poluklasičnog formalizma matrice gustoće. Primijetili smo da tragovi Lambovih udubina i prijelaznih rezonancija unutar linija proširenih Dopplerovih učinkom mogu nestati pod djelovanjem snažnog zasićujećeg polja uz dovoljan doprinos učinka sudarnog otklanjanja faza. U ramenima zasićenih linija može se postići nesimetrija za male doprinose sudarne jezgre

Proučavanje učinaka brzinski-ovisnih sudara na lambovu udubinu i prijelazne rezonancije u sustavu s tri stanja

We discuss the effects of phase-dephasing and velocity-changing collisions on saturated absorption line shapes studied in an open V-type system under the semi-classical density-matrix formalism. It has been noted that the traces of Lamb dips and crossover resonance dip lying within the Doppler-broadened contour can vanish in the presence of a strong saturating field if a sufficient contribution of collisional dephasing effect is present. Asymmetry may be introduced in the wings of saturated line profiles for a small contribution of collision kernel.Raspravljamo učinke otklanjanja faze i sudara s promjenom brzine na oblike linija zasićenih apsorpcijom za otvoren V-sustav, primjenom poluklasičnog formalizma matrice gustoće. Primijetili smo da tragovi Lambovih udubina i prijelaznih rezonancija unutar linija proširenih Dopplerovih učinkom mogu nestati pod djelovanjem snažnog zasićujećeg polja uz dovoljan doprinos učinka sudarnog otklanjanja faza. U ramenima zasićenih linija može se postići nesimetrija za male doprinose sudarne jezgre