On the existence of exponential polynomials with prefixed gaps

This paper shows that the conjecture of Lapidus and Van Frankenhuysen on the set of dimensions of fractality associated with a nonlattice fractal string is true in the important special case of a generic nonlattice self-similar string, but in general is false. The proof and the counterexample of this have been given by virtue of a result on exponential polynomials P(z), with real frequencies linearly independent over the rationals, that establishes a bound for the number of gaps of RP, the closure of the set of the real projections of its zeros, and the reason for which these gaps are produced.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

The Gaia-ESO Survey: The analysis of high-resolution UVES spectra of FGK-type stars

Context. The ongoing Gaia-ESO Public Spectroscopic Survey is using FLAMES at the VLT to obtain high-quality medium-resolution Giraffe spectra for about 105 stars and high-resolution UVES spectra for about 5000 stars. With UVES, the Survey has already observed 1447 FGK-type stars. Aims. These UVES spectra are analyzed in parallel by several state-of-the-art methodologies. Our aim is to present how these analyses were implemented, to discuss their results, and to describe how a final recommended parameter scale is defined. We also discuss the precision (method-to-method dispersion) and accuracy (biases with respect to the reference values) of the final parameters. These results are part of the Gaia-ESO second internal release and will be part of its first public release of advanced data products. Methods. The final parameter scale is tied to the scale defined by the Gaia benchmark stars, a set of stars with fundamental atmospheric parameters. In addition, a set of open and globular clusters is used to evaluate the physical soundness of the results. Each of the implemented methodologies is judged against the benchmark stars to define weights in three different regions of the parameter space. The final recommended results are the weighted medians of those from the individual methods. Results. The recommended results successfully reproduce the atmospheric parameters of the benchmark stars and the expected Teff-log  g relation of the calibrating clusters. Atmospheric parameters and abundances have been determined for 1301 FGK-type stars observed with UVES. The median of the method-to-method dispersion of the atmospheric parameters is 55 K for Teff, 0.13 dex for log  g and 0.07 dex for [Fe/H]. Systematic biases are estimated to be between 50−100 K for Teff, 0.10−0.25 dex for log  g and 0.05−0.10 dex for [Fe/H]. Abundances for 24 elements were derived: C, N, O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Mo, Ba, Nd, and Eu. The typical method-to-method dispersion of the abundances varies between 0.10 and 0.20 dex. Conclusions. The Gaia-ESO sample of high-resolution spectra of FGK-type stars will be among the largest of its kind analyzed in a homogeneous way. The extensive list of elemental abundances derived in these stars will enable significant advances in the areas of stellar evolution and Milky Way formation and evolution.

Chemical diversity and potential biological functions of the pygidial gland secretions in two species of Neotropical dung roller beetles

Dung roller beetles of the genus Canthon (Coleoptera: Scarabaeinae) emit an odorous secretion from a pair of pygidial glands. To investigate the chemical composition of these secretions, we used stir bar sorptive extraction (SBSE), coupled with gas chromatography–mass spectrometry (GC–MS) for analysis of extracts of pygidial gland secretions secreted by the dung roller beetles Canthon femoralis femoralis and Canthon cyanellus cyanellus. Chemical analyses of volatiles collected from pygidial gland secretions comprise a great diversity of the functional groups. Chemical profile comparisons showed high intra- and interspecific variability. The pygidial gland secretion of Canthon f. femoralis was dominated by sesquiterpene hydrocarbons, whereas the profile of Canthon c. cyanellus was dominated by carboxylic acids. The different pygidial secretions have a high diversity of chemical compounds suggesting a multifunctional nature involving some key functions in the biology. We discuss the biological potential of these compounds found in the pygidial glands of each species with respect to their ecological and behavioral relevance.

Bis(arylene-ethynylene)-s-tetrazines: A Promising Family of n-Type Organic Semiconductors?

We theoretically describe in this work the n-type semiconducting behavior of a set of bis(arylene-ethynylene)-s-tetrazines ((ArCC)2Tz), by comparing their electronic properties with those of their parent diaryl-s-tetrazines (Ar2Tz) after the introduction of ethynylene bridges. The significantly reduced internal reorganization energy for electron transfer is ascribed to an extended delocalization of the LUMO for (ArCC)2Tz as opposite to that for Ar2Tz, which was described mostly localized on the s-tetrazine ring. The largest electronic coupling and the corresponding electron transfer rates found for bis(phenyl-ethynylene)-s-tetrazine, as well as for some halogenated derivatives, are comparable to those reported for the best performing n-type organic semiconductor materials such as diimides and perylenes. The theoretical mobilities for the studied compounds turn out to be in the range 0.3–1.3 cm2 V–1 s–1, close to values experimentally determined for common n-type organic semiconductors used in real devices. In addition, ohmic contacts can be expected when these compounds are coupled to metallic cathodes such as Na, Ca, and Sm. For these reasons, the future application of semiconducting bis(phenyl-ethynylene)-s-tetrazine and its fluorinated and brominated derivatives in optoelectronic devices is envisioned.

On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.

A note on the real projection of the zeros of partial sums of Riemann zeta function

This paper proves that the real projection of each simple zero of any partial sum of the Riemann zeta function ζn(s):=∑nk=11ks,n>2 , is an accumulation point of the set {Res : ζ n (s) = 0}.

Computing the zeros of the partial sums of the Riemann zeta function

In this paper, we introduce a formula for the exact number of zeros of every partial sum of the Riemann zeta function inside infinitely many rectangles of the critical strips where they are situated.