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These two mechanisms will have a final net effect **on** disposable income, which will have effects **on** welfare through changes in consumption. In order to quantify **the** welfare effect of **the** different fiscal policies, I use a measure of **the** consumption equivalent variation. I quantify **the** welfare effect of a given policy framework for an individual by asking: by how much **the** consumption has to change in all future periods and in **the** initial steady state, so that **the** expected utility equals **the** one after **the** transition, under a specific policy frame- work? In other words, by how much, in consumption terms, **the** agents benefit or lose from a specific fiscal policy framework in an economic downturn context? In order to **study** **the** **distributional** effects, I compute **the** Gini coefficient in **the** initial steady state, and I compare it with **the** Gini coefficients that result from **the** transition of each policy framework.

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lattices. **On** **the** other hand, using **the** **q**-analog of **the** quantum theory of angular momentum [20–23] we can obtain several results for **the** **q**-**polynomials**, some of which are nontrivial from **the** viewpoint of **the** theory of orthogonal **polynomials** (see, e.g., **the** nice surveys [24, 25]). In fact, in this paper we present a detailed **study** of some **q**-analogs of **the** Racah **polynomials** u α,β n (x(s), a, b) **q** and u e

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In this paper we **study** in detail a **q**-extension of **the** generalized Hermite **polynomials** of Szeg˝ o. A continuous orthogonality property **on** R with respect to **the** positive weight function is established, a **q**-difference equation and a three-term recurrence relation are derived for this family of **q**-**polynomials**.

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Let us also point out that there are also **the** so-called discrete (see e.g. [8]) and **q**-discrete Sobolev type orthogonal **polynomials** associated with **the** classical discrete and **q**-classical functionals [23, 24]. In both cases **the** corresponding **polynomials** can be reduced to **the** Krall-type one (except for **the** **q**-case when **the** mass is added at zero where a more careful **study** is needed [23, 24]) since **the** differences ∆f (x) = f (x + 1) − f(x) and D **q** f(x) = (f (qx) − f(x))/(qx − x).

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In 1940, H. L. Krall [19] obtained three new classes of **polynomials** orthogonal with respect to measures which are not absolutely continuous with respect to **the** Lebesgue measure. In fact, his **study** is related to an extension of **the** very well known characteri- zation of classical orthogonal **polynomials** by S. Bochner. This kind of measures was not considered in [28]. Moreover, in his paper H. L. Krall obtain that these three new families of orthogonal **polynomials** satisfy a fourth order dierential equation. **The** corresponding measures are given in **the** following table.

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User acceptability has become a critical issue for **the** successful imple- mentation of transport pricing measures and policies. Although several studies have addressed **the** public acceptability of road pricing, little evidence can be found of **the** effects of pricing strategies. **The** accept- ability of alternative schemes for a toll network already in operation is an issue to be tackled. This paper contributes to **the** limited literature in this ﬁeld by exploring perceptions toward road-pricing schemes among toll road users. **On** **the** basis of a nationwide survey of toll road users in Spain, **the** **study** developed several binomial logit models to analyze user acceptability of three approaches: express toll lanes, a time-based pricing approach, and a ﬂat fee (vignette) system. **The** results show notable differences in user acceptability by **the** type of charging scheme proposed. Express toll lanes were more acceptable by travelers who perceived greater beneﬁts from saving travel time. **The** acceptability of time-based approaches (peak versus off-peak) decreased for users who felt forced to use **the** toll road, whereas this was not an aspect that signiﬁcantly inﬂuenced users’ support for ﬂat fee schemes. In addi- tion, a ﬂat fee strategy was more acceptable for long-distance trips and truck drivers who regularly used **the** toll facilities. **The** results from this analysis can inform policy makers and planners for **the** promotion of more efﬁcient, socially inclusive, and publicly acceptable road-pricing schemes.

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It is well known that **the** classical families of Jacobi, Laguerre, Hermite, and Bessel **polynomials** are characterized as eigenvectors of a second order linear differential operator with polynomial coefﬁcients, Rodrigues formula, etc. In this paper we present a uniﬁed **study** of **the** classical discrete **polynomials** and **q**-**polynomials** of **the** **q**-Hahn tableau by using **the** difference calculus **on** linear-type lattices. We obtain in a straightforward way several characterization theorems for **the** classical discrete and **q**-**polynomials** of **the** “**q**-Hahn tableau”. Finally, a detailed discussion of a characterization by Marcellán et al. is presented.

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In **the** last decade an increasing interest **on** **the** so called **q**-orthogonal **polynomials** (or basic orthogonal **polynomials**) is observed ( for a review see [1], [2] and [3]). **The** reason is not only of purely intrinsic nature but also because of **the** so many applications in several areas of Math- ematics ( e.g., continued fractions, eulerian series, theta functions, elliptic functions,...; see for instance [4] and [5]) and Physics ( e.g., angular momentum [6] and [7] and its **q**-analog [8]-[11], **q**-Shrodinger equation [12] and **q**-harmonic oscillators [13]-[19]). Moreover, it is well known **the** connection between **the** representation theory of quantum algebras (Clebsch-Gordan coecients, 3j and 6j symbols) and **the** **q**-orthogonal **polynomials**, (see [20], [21] (Vol. III), [22], [23], [24] ), and **the** important role that these **q**-algebras play in physical applications (see for instance [26]-[31] and references therein).

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It is well known that **the** Lie Groups Representation Theory plays a very important role in **the** Quantum Theory and in **the** Special Function Theory. **The** group theory is an ef- fective tool for **the** investigation of **the** properties of dierent special functions, moreover, it gives **the** possibility to unify various special functions systematically. In a very simple and clear way, **on** **the** basis of group representation theory concepts, **the** Special Function Theory was developed in **the** classical book of N.Ya.Vilenkin [1] and in **the** monography of N.Ya.Vilenkin and A.U.Klimyk [2], which have an encyclopedic character.

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tion of **the** non-standard **q**-Racah **polynomials** was considered in detail. This is an important example for two reasons: 1) it is **the** first family of **the** Krall- type **polynomials** **on** a non-linear type lattice that has been studied in detail and 2) almost all modifications (via **the** addition of delta Dirac masses) of **the** classical and **q**-classical **polynomials** can be obtained from them by taking appropriate limits (as it is shown for **the** dual **q**-Hahn, **the** Racah, and **the** **q**- Hahn **polynomials** in section 4.2). Let us also mention here that an instance of **the** Krall-type **polynomials** obtained from **the** Askey-Wilson **polynomials** (with a certain choice of parameters), by adding two mass points at **the** end of **the** orthogonality has been mentioned in [20, §6, page 330]. This Askey-Wilson-Krall-type **polynomials** solve **the** so-called bi-spectral problem associated with **the** Askey-Wilson operator. Then, it is an interesting open problem to **study** **the** general Krall-type Askey-Wilson **polynomials** and to obtain their main properties. This will be considered in a forthcoming paper. Acknowledgements:

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Suslov, The theory of dierene analogues of speial funtions of hypergeometri. type[r]

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Mellin integral transforms for some families of basic hypergeometric **polynomials** from **the** Askey scheme [15] were considered in [7].Derivation of these Mellin transform pairs is essentially based **on** **the** use of Ramanujan’s **q**-extension [17,4,5] of **the** Euler integral representation for **the** gamma function

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In **the** ﬁrst section we consider **the** Aron-Berner extension. We begin with **the** Arens product in a commutative Banach algebra, a very speciﬁc extension of a bilinear function, but nevertheless an extension in which some of **the** main points of more general extensions already appear, such as lack of symmetry and **the** notion of regularity. We then deﬁne and **study** **the** Aron-Berner extension, an extension of **polynomials** from a Banach space to its bidual. In **the** second section, we consider extensions from E to G. Here all solutions stem from **the** existence of a continuous linear extension morphism for linear forms E −→ G , a condition obviously stronger than Hahn-Banach, and not satisﬁed in all cases. Section 3 is devoted to Hahn-Banach type extensions. We are naturally drawn to ‘linearization’ of **polynomials**, and thus to preduals of spaces of **polynomials**. **The** space of ‘extendible’ **polynomials** is considered also.

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(a small subset of **the** **q**-world). Here we need to point out that exits two dierent point of view in **the** **study** of **the** **q**-**polynomials**. **The** rst one, in **the** framework of **the** **q**-basic hypergeometric series [6], [8], [9] and **the** second, in **the** framework of **the** theory of dierence equations developed by Nikiforov et al. [12], [13], [14]. In this work we will use **the** second one because it gives us **the** possibility to provide an uniform treatment of several classes of orthogonal **polynomials** and, probably, it is **the** best way to nd further applications.

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(x), whih satises ontinuous orthogonality on the whole real line R with respet.. to the positive weight funtion..[r]

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lae, epigastric lobes semicircular, anteriorly not well delimited, frontal sur- face flat, postgastric pits present, branchio-urogastric, branchio-cardiac, and branchio-intestinal grooves narrow, urogastric groove not demarcated; ab- dominal segments III to VI fused, but suture 3/4 still visible in males, abdo- men triangular, outer margins slightly concave, telson triangular, with outer margin slightly sinuous (Fig. 18 G); first pereiopods heterochelous; merus of chela in large males with distal spine **on** external margin, carpus with promi- nent, acute, distal spine **on** internal margin, palm with small, spine **on** up- per margin near articulation of dactylus, fingers elongated (1.6 times **the** length of palm) with longitudinal ridges, not gaping when closed (Fig. 18 I). First male gonopod tapering to apex, recurved laterally; mesial side con- cave; lateral side slightly convex; margin regularly displaced to mesocephalic surface and emerging **on** caudal surface near apex; lateral lobe absent (Fig. 18 A – C); apex outline V-shape, opening below corneous prominent spine- like process (Fig. 18 E); apical translucent spines, decreasing in size distally, forming continuous patch over caudal and lateral surfaces, mesial side with rows of translucent spines, basal lateral side with conspicuous long setae (Fig. 18 A – E). Second gonopod considerable longer than first; recurved mesially in form of question mark (Fig. 18 F).

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We underline that, in a different context (cf. [2, Theorem 2]), the characterization of solutions of an integrable system was established in terms of the derivative of the polynomials a[r]

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In particular, an explicit form of the squared norms for these q-extensions of the Hermite functions (or the wave functions of the linear harmonic oscillator in [r]

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