Extended Birkhoff’s theorem in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">T</Emphasis>) gravity

f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, Eur. Phys. J. (2011), ], we prove that Birkhoff’s theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss, respectively, the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of Birkhoff’s theorem in the frame of f(T) gravity via a conformal transformation by regarding the Brans–Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.     

Permutations with extremal number of fixed points

We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting permutations we study their generating polynomials by number of excedances. Several techniques are used: Désarménien's desarrangement combinatorics, Gessel's hook-factorization and the analytical properties of two new permutation statistics “DEZ” and “lec.” Explicit formulas for the maximal case are derived by using symmetric function tools.     

Linear response in the strong field domain

We show that, while it is well-known that first-order perturbation theory leads to linear response (of, e.g., a material system to an external field), the reverse is not true: linear response does not necessarily imply the validity of first-order perturbation theory, nor does it follow from it that the external perturbation is weak. We do so by analyzing the intensity dependence in the photoexcitation followed by dissociation or isomerization of a bound molecular system by a shaped broadband laser pulse. We show that, in certain cases where strong field effects are definitely present, the observed photoexcitation yield as a function of intensity may exhibit linear dependence over a wide range of intensities. The behavior is shown to coexist with a rather extensive range of coherent control over the branching ratios, an effect that was shown in the past to be impossible in the single precursor state (e.g., in the first-order perturbation theory) domain. For example, we demonstrate computationally that when (flat continuum-mediated) Raman transitions are present, appropriate pulse shaping can lead to a linear yield with intensity over a wide range of intensities, while coherent control over the branching ratio is significant. Thus, it is not necessary to invoke external bath effects (as is currently being done) to explain present-day experiments where coherent control is observed in the linear response regime.     

Extracting muon momentum scale corrections for hadron collider experiments

The quark condensate is calculated within the world-line effective-action formalism, by using for the Wilson loop an ansatz provided by the stochastic vacuum model. Starting with the relation between the quark and the gluon condensates in the heavy-quark limit, we diminish the current quark mass down to the value of the inverse vacuum correlation length, finding in this way a 64?% decrease in the absolute value of the quark condensate. In particular, we find that the conventional formula for the heavy-quark condensate cannot be applied to the c-quark, and that the corrections to this formula can reach 23?% even in the case of the b-quark. We also demonstrate that, for an exponential parametrization of the two-point correlation function of gluonic field strengths, the quark condensate does not depend on the non-confining non-perturbative interactions of the stochastic background Yang?CMills fields.     

Evaluation of natural recharge of Chingshui geothermal reservoir using tritium as a tracer

Naturally existing tritium in groundwater was applied as a tracer to evaluate the natural recharge of the Chingshui geothermal reservoir. The residence time (or, age) of Chingshui geothermal water was first determined with tritium data at 15.2 and 11.3 year using the plug flow and dispersive model, respectively. The annual natural recharge was then estimated by combining the use of the residence time and the fluid-in-place of the Chingshui geothermal reservoir. The natural recharge for Chingshui geothermal reservoir was estimated at 5.0 × 10⁵ and 6.7 × 10⁵ m³ year^?1 using the plug flow and dispersive model, respectively. Chingshui geothermal water is largely from a fractured zone in the Jentse Member of the Miocene Lushan Formation. The dispersive model more adequately represents the fracture flow system than the simple plug flow model.     

Two-dimensional ‘hat-scratch’ periodic structures induced by a single femtosecond laser pulse on silica glass

Two-dimensional ‘hat-scratch’ structures are fabricated on silica glass by the interference of three non-coplanar beams originating from a single femtosecond laser pulse. The scanning electron microscope (SEM) characterizations show that the as-formed structures are composed of hat holes and scratch marks. The experimental results indicate that the structures are dependent on the intensity of laser beam. The formation of the two-dimensional ‘hat-scratch’ structures is mainly due to the combined laser ablation effects including ionization, shock wave, plasma expansion, and phase explosion.     

A FAMILY OF DIFFERENCE SCHEMES WITH FOURNEAR-CONSERVED QUANTITIES FOR THE KdV EQUATION

1.IntroductionInthispaper,weareconcernedwiththesemi--discretizeddifferencemethodswhicharecapableofapproximatingtotheKdVequationtoaconsiderableextent.Considertheperiodicillitial-boundaryproblem:at aam uxxx~0,~co0(1.l)u(x 1,t)~u(x,t),~co0(…     

High-Q exterior whispering-gallery modes in a metal-coated microresonator

We propose a kind of plasmonic whispering-gallery mode highly localized on the exterior surface of a metal-coated microresonator. This exterior (EX) surface mode possesses high quality factors at room temperature, and can be efficiently excited by a tapered fiber. The EX mode can couple to an interior (IN) mode and this coupling produces a strong anticrossing behavior, which not only allows conversion of IN to EX modes, but also forms a long-lived antisymmetric mode. As a potential application, the EX mode could be used for a biosensor with a sensitivity high of up to 500 nm per refraction index unit, a large figure of merit, and a wide detection range.     

Combretastatin A-4 derivatives: synthesis and evaluation of 2,4,5-triaryl-1H-imidazoles as potential agents against H1299 (non-small cell lung cancer cell)

A number of 2,4,5-triaryl-1H-imidazole derivatives were synthesized and evaluated for their antiproliferative activities against the growth of five cell lines including three non-small cell lung cancers (H460, H1299, and A549), one breast cancer (MCF-7), and one normal diploid embryonic lung cell line (MRC-5). Preliminary results indicated that both 2-(5-bromofuran-2-yl)-4,5-bis{4-[3-(dimethylamino) propoxy] phenyl}-1H-imidazole (10f) and 4,5-bis{4-[3-(dimethylamino)propoxy]phenyl}-2-(5-nitrofuran-2-yl)-1H -imidazole (10g) were selectively active against the growth of H1229 with an IC₅₀ of less than 0.1???M, thus were more active than topotecan (IC₅₀ >?10.0??? M). However, both 10f and 10g exhibited only marginal cytotoxicity against H460, A549, MCF-7, and MRC-5 requiring an IC ₅₀ of at least 4.16???M. Our results also indicated that 10f induced H1299 cell cycle arrest at G0/G1 through the inactivation of p38 MAPK, JNK, ERK, as well as the expression of SIRT1 and survivin. These results suggested that 10f might have therapeutic potential against H1299 (non-small cell lung cancer cell).     

Copper as an electron trap in GaAs0.6P0.4

An electron trap having an energy level of 0.14 eV from the conduction band edge was found in the bulk of copper-diffused VPE-grown n-GaAs_0.6P_0.4 by conventional DLTS measurements and by pulse-duration dependent capacitance amplitude measurements. The capture cross section at room temperature is about 1.0×10^–21 cm² and has a weak temperature dependence. These properties are attributed to a non-repulsive center having a capturing mechanism which involves multiphonon emission processes with hardly any lattice relaxation. Evolution of the spatial distributions of the traps with time under junction electric field were studied. The results suggest that the trap is positively charged and has a high diffusivity under electric field. The center can thus be identified as positively charged interstitial copper ion rather than some form of copper complexes.