Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields, assuming that their associated L-functions are analytic L-functions. Moreover, we obtain lower bounds for the conductor of elliptic curves and abelian varieties over Q with specified bad reduction, under the same hypothesis. As an application, we prove, for certain number fields, the non-existence of abelian varieties with analytic L-function and with everywhere good reduction.
We establish an integration by parts formula for the semigroup in time T>0 of the kinetic Brownian motion in the Euclidean plane together with its velocity in the circle. The stochastic differential equation of our kinetic Brownian motion is driven here by one real-valued Brownian motion constructed from an orthonormal basis of L^2([0,T],) and an independent sequence of (0,1) random variables. Our method is based on an explicit computation of a Malliavin dual in the Gaussian space. We are mainly interested in large time T. From our integration by parts, we obtain gradient estimates including a reverse Poincaré inequality for the semigroup. As a direct consequence, we also obtain a Liouville property for the generator of the kinetic Brownian motion and its speed: all bounded harmonic functions are constant.
The pyrolysis of lignocellulosic biomass offers an effective route to produce carbon rich solids that serve as intermediates for hydrogen generation via steam gasification. This study investigates the structural and compositional evolution of pine wood biochars produced under well controlled conditions in two reactor systems: a thermogravimetric analyzer (TGA) for wood powder and a laboratory scale fixed-bed reactor for wood pellets. Pyrolysis experiments were performed at 400–900 °C with heating rates of 10–100 °Cmin−1. Raman spectroscopy, SEM–EDX, and oxidation tests were employed to characterize the resulting chars. Raman analysis showed that increasing temperature promotes carbon ordering, with the D band shifting from 1378 to 1335 cm−1 and the HD/HG ratio rising from 0.60 to 0.87. SEM–EDX revealed progressive surface roughening, pore formation, and mineral enrichment (mainly K and Ca), accompanied by a decline in O/C ratio from 0.663 to 0.083. Oxidation reactivity tests indicated reduced char reactivity with increasing pyrolysis severity, consistent with enhanced structural ordering and deoxygenation. This study characterizes the pyrolysis stage char precursor rather than the gasification step itself; by linking pyrolysis parameters to carbon ordering, deoxygenation, and mineral (K, Ca) enrichment, it provides a structural basis for selecting char preparation conditions in the subsequent steam gasification route to hydrogen, which is the subject of ongoing work.
In 1996, F & agrave;brega and Fiol introduced the g-extra connectivity of Gas an important parameter for the fault tolerance of an interconnection network. A subset of vertices S is said to be a cutset if G-S is not connected. A cutset S is called an Rg-cutset, where g is a non-negative integer, if every component of G-S has at least g + 1 vertices. If G has at least one Rg-cutset, the g-extra connectivity of G, denoted by kappa g(G), is then defined as the minimum cardinality over all Rg-cutsets of G. In this paper, we obtain the exact values of the g-extra connectivity of some special graph classes, and show that & LeftFloor; n-3 & RightFloor; 1 <= kappa g(G) <= n-2g-2 for 0 <= g <= 2 , and graphs with kappa g(G) = 1, 2, 3 and trees with kappa g(Tn) = n-2g-2 are characterized, respectively. We also derive three extremal results for the g-extra connectivity. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
As the James Webb Space Telescope (JWST) pursues its observing journey, several thousands of icy-grain spectra are expected to be measured and analysed. The inventory of ices in particular, via the observations of background sources, is accessible for hundreds of lines of sight (LOSs) per molecular-cloud region, opening the possibility to add strong constraints on the solid phase chemistry in a vast domain of cloud densities. SynthIceSpec is a synthetic infrared (IR) spectrum generator that has been designed as a tool to support observing proposals and to test the outcome of chemical models. It is based on laboratory measurements of pure and mixed ices, where each vibrational component is fitted by a sum of Gaussian profiles. Given an initial ice chemical composition (either set by the user or the outputs of a chemical model), a full JWST spectrum is generated, to which the contribution of silicates; continuum, stellar photospheric absorption bands; and extinction law can be added. For the continuum, stellar photospheric models for a wide range of spectral types can be selected by the program, or, Spectral Energy Distribution (SEDs). We present a few use cases of SynthIceSpec: we probed the impact of dust temperature on CO2 ice formation using IR data and gas-grain modelling. Next, we used SynthIceSpec to explore the detectability of the main feature of CH3CN at 4.45 & micro;m in a cold core environment with the JWST, which was previously tentatively detected in YSOs. The detection thresholds we derive are reasonably low and observable, but identification is directly impacted by the photosphere absorptions that can greatly hinder identification. For some photostellar types, it could remain feasible. Coupled with the Estimated Time Calculator of the Space Telescope Science Institute, SynthIceSpec can be used to find the optimum observational setup for new observations.
