Multiple positive solutions of singular nonlinear Sturm-Liouville problems with caratheodory perturbed term

By employing a well-known fixed point theorem, we establish the existence of multiple positive solutions for the following fourth-order singular differential equation Lu=p(t)f(t,u(t),u′′(t))-g(t,u(t),u′′(t)),0<t<1,α1u(0)-β1u'(0)=0,γ1u(1)+δ1u'(1)=0,α2u′′(0)-β2u′′′(0)=0,γ2u′′(1)+δ2u′′′(1)=0, with αi,βi,γi,δi≥0 and βiγi+αiγi+αiδi>0,    i=1,2, where L denotes the linear operator Lu:=(ru′′′)'-qu′′,r∈C1([0,1],(0,+∞)), and q∈C([0,1],[0,+∞)). This equation is viewed as a perturbation of the fourth-order Sturm-Liouville problem, where the perturbed term g:(0,1)×[0,+∞)×(-∞,+∞)→(-∞,+∞) only satisfies the global Carathéodory conditions, which implies that the perturbed effect of g on f is quite large so that the nonlinearity can tend to negative infinity at some singular points

Analysis of Laser ARPES from Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta} in superconductive state: angle resolved self-energy and fluctuation spectrum

We analyze the ultra high resolution laser angle resolved photo-emission spectroscopy (ARPES) intensity from the slightly underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ in the superconductive (SC) state. The momentum distribution curves (MDC) were fitted at each energy \w employing the SC Green's function along several cuts perpendicular to the Fermi surface with the tilt angle $\theta$ with respect to the nodal cut. The clear observation of particle-hole mixing was utilized such that the complex self-energy as a function of $\omega$ is directly obtained from the fitting. The obtained angle resolved self-energy is then used to deduce the Eliashberg function \alpha^2 F^{(+)}(\th,\w) in the diagonal channel by inverting the d-wave Eliashberg equation using the maximum entropy method. Besides a broad featureless spectrum up to the cutoff energy $\omega_c$, the deduced $\alpha^2 F$ exhibits two peaks around 0.05 eV and 0.015 eV. The former and the broad feature are already present in the normal state, while the latter emerges only below $T_c$. Both peaks become enhanced as $T$ is lowered or the angle $\th$ moves away from the nodal direction. The implication of these findings are discussed.Comment: 7 pages, 5 figures, summited to PR

Exact solution of gyration radius of individual's trajectory for a simplified human mobility model

Gyration radius of individual's trajectory plays a key role in quantifying human mobility patterns. Of particular interests, empirical analyses suggest that the growth of gyration radius is slow versus time except the very early stage and may eventually arrive to a steady value. However, up to now, the underlying mechanism leading to such a possibly steady value has not been well understood. In this Letter, we propose a simplified human mobility model to simulate individual's daily travel with three sequential activities: commuting to workplace, going to do leisure activities and returning home. With the assumption that individual has constant travel speed and inferior limit of time at home and work, we prove that the daily moving area of an individual is an ellipse, and finally get an exact solution of the gyration radius. The analytical solution well captures the empirical observation reported in [M. C. Gonz`alez et al., Nature, 453 (2008) 779]. We also find that, in spite of the heterogeneous displacement distribution in the population level, individuals in our model have characteristic displacements, indicating a completely different mechanism to the one proposed by Song et al. [Nat. Phys. 6 (2010) 818].Comment: 4 pages, 4 figure

Genomic diversity among Basmati rice (Oryza sativa L) mutants obtained through 60Co gamma radiations using AFLP markers

Mutation breeding can be considered successful in obtaining new cultivars and broadening the genetic base of rice crop. In order to obtain new varieties of rice with improved agronomic and grain characteristics, gamma radiation (60Co) has been used to generate novel mutants of the Basmati rice. In this study rice cultivars; Basmati-370 and Basmati-Pak, were exposed to different doses of gamma radiations and stable mutants along with parents were studied for genomic diversity on the basis of molecular marker (AFLP). Morphological data showed that mutants of Basmati-370 performed well for yield and yield components and grain physical parameters whereas, the mutant EL-30-2-1 has extra long rain trait as compared to the parent (Basmati-Pak). The genetic variations determined through AFLP revealed a total of 282 scorable bands, out of which 108 (37.81%) were polymorphic. The number of fragments produced by various primers combinations ranged from 11 - 26 with an average of 17.63fragments per primer combination. Maximum 26 bands were amplified with P-AAG/M-CAG primer combination and minimum one band was amplified with P-ATG/M-CTA primer combination. Two groups of genotypes were detected; group-A had DM-1-30-3-99, DM-1-30-34-99 and EF-1-20-52-04 mutants along with parent Basmati-370, whereas the group-B contained EL-30-2-1 and parent Basmati-Pak. The results of AFLP analysis indicated that the rate of polymorphism was 4.43% (DM-1-30-3-99), 4.25% (DM-1-30-34-99) and 6.38% (EF-1-20-52-04) among the genomes of mutants and parent Basmati-370, respectively, whereas polymorphism rate was 5.32% between genome of EL-30-2-1 and Basmati-Pak. The study further confirmed that the use of gamma radiations is an effective approach for creating new rice germplasm