Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Lower bounds for the number of limit cycles of trigonometric Abel equations

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New evidence of the real interest rate parity for OECD countries using panel unit root tests with breaks

This paper tests for real interest parity (RIRP) among the nineteen major OECD countries over the period 1978:Q2-1998:Q4. The econometric methods applied consist of combining the use of several unit root or stationarity tests designed for panels valid under cross-section dependence and presence of multiple structural breaks. Our results strongly support the fulfillment of the weak version of the RIRP for the studied period once dependence and structural breaks are accounted for.

Lower bounds for kernelizations

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Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

Sharpened lower bounds for cut elimination

We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our new lower bounds remove the constant of proportionality, giving an exponential stack of height equal to d − O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.

Optimal asymptotic bounds for spherical designs

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Is real GDP stationary? Evidence from a panel unit root test with cross-sectional dependence and historical data

We use historical data that cover more than one century on real GDP for industrial countries and employ the Pesaran panel unit root test that allows for cross-sectional dependence to test for a unit root on real GDP. We find strong evidence against the unit root null. Our results are robust to the chosen group of countries and the sample period. Key words: real GDP stationarity, cross-sectional dependence, CIPS test. JEL Classification: C23, E32

Fair bounds based solidarity

How should scholarships be distributed among the (public) higher education students? We raise this situation as a redistribution problem. Following the approach developed in Fleurbaey (1994) and Bossert (1995), redistribution should be based on the notion of solidarity and it re-allocates resources taking into account only agents’ relevant characteristics. We also follow Luttens (2010a), who considers that compensation of relevant characteristics must be based on a lower bound on what every individual deserves. In doing so, we use the so-called fair bound (Moulin (2002)) to define an egalitarian redistribution mechanism and characterize it in terms of non-negativity, priority in lower bound and solidarity. Finally, we apply our approach to the scholarships redistribution problem. Keywords: Redistribution mechanism, Lower bounds, Scholarship, Solidarity. JEL classification: C71, D63, D71

Dos cuestiones pendientes de la sintaxis de los pronombres átonos: enclisis como fenómeno asociado a las oraciones matrices y doble clítico en las construcciones perifrásticas = The Remainders of the Syntax of Clitics: Enclisis as a Root Phenomenon, and Clitic Doubling in Periphrastic Constructions

Conferència centrada en dos aspectes concrets de la sintaxi dels pronoms àtons: l' enclisis que es dona en algunes oracions subordinades de les variants iberromàniques modernes de l'oest peninsular i les configuracions de doble cíclic en les construccions perifràstiques

Seasonal changes of whole root system conductance by a drought-tolerant grape root system

The role of root systems in drought tolerance is a subject of very limited information compared with above-ground responses. Adjustments to the ability of roots to supply water relative to shoot transpiration demand is proposed as a major means for woody perennial plants to tolerate drought, and is often expressed as changes in the ratios of leaf to root area (AL:AR). Seasonal root proliferation in a directed manner could increase the water supply function of roots independent of total root area (AR) and represents a mechanism whereby water supply to demand could be increased. To address this issue, seasonal root proliferation, stomatal conductance (gs) and whole root system hydraulic conductance (kr) were investigated for a drought-tolerant grape root system (Vitis berlandieri×V. rupestris cv. 1103P) and a non-drought-tolerant root system (Vitis riparia×V. rupestris cv. 101-14Mgt), upon which had been grafted the same drought-sensitive clone of Vitis vinifera cv. Merlot. Leaf water potentials (ψL) for Merlot grafted onto the 1103P root system (–0.91±0.02 MPa) were +0.15 MPa higher than Merlot on 101-14Mgt (–1.06±0.03 MPa) during spring, but dropped by approximately –0.4 MPa from spring to autumn, and were significantly lower by –0.15 MPa (–1.43±0.02 MPa) than for Merlot on 101-14Mgt (at –1.28±0.02 MPa). Surprisingly, gs of Merlot on the drought-tolerant root system (1103P) was less down-regulated and canopies maintained evaporative fluxes ranging from 35–20 mmol vine−1 s−1 during the diurnal peak from spring to autumn, respectively, three times greater than those measured for Merlot on the drought-sensitive rootstock 101-14Mgt. The drought-tolerant root system grew more roots at depth during the warm summer dry period, and the whole root system conductance (kr) increased from 0.004 to 0.009 kg MPa−1 s−1 during that same time period. The changes in kr could not be explained by xylem anatomy or conductivity changes of individual root segments. Thus, the manner in which drought tolerance was conveyed to the drought-sensitive clone appeared to arise from deep root proliferation during the hottest and driest part of the season, rather than through changes in xylem structure, xylem density or stomatal regulation. This information can be useful to growers on a site-specific basis in selecting rootstocks for grape clonal material (scions) grafted to them.

On iterative performance of LDPC and Root-LDPC codes over block-fading channels

This paper presents our investigation on iterativedecoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes.Also, we show analytically that, in the case of 2 fading blocks,the iterative threshold root of Root-LDPC codes is proportional to (α1 α2)1, where α1 and α2 are corresponding fading gains.From this result, the full diversity property of Root-LDPC codes immediately follows.