Graham’s pebbling conjecture on product of complete bipartite graphs

The pebbling number of a graph G, f(G), is the least n such that, no matter how n pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. Graham conjectured that for any connected graphs G and H, f( G x H) ⩽ f( G) f( H). We show that Graham’s conjecture holds true of a complete bipartite graph by a graph with the two-pebbling property. As a corollary, Graham’s conjecture holds when G and H are complete bipartite graphs.     

Suppression of the Resonant Scattering in Imperfect Acoustic Cloaking with a Lossy Medium in R^3

It has been realized that resonance frequencies of imperfect the transformation acoustics in R^2 are located near Dirichlet acoustic cloaking based on a small perturbation of eigenvalues of the cloaked region [Chin. Phys. Lett. 26 （2009） 014301; 29 （2012） 124301]. In this work, we study the performance of the three-dimensional approximate cloaking system based on the transformation acoustics and show that the cloaking effect may be deteriorated at zeroth order Neumann eigenvalues of the concealed region. In particular, transmitted fields into the concealed region can be extremely resonated at frequencies corresponding to the zeroth-order Neumann eigenvalues while scattered fields are suppressed well for any frequency. To enhance the cloaking effect at resonance frequencies, we introduce a lossy medium inside the cloaked region and show that the new proposal can reduce the intensity of transmitted fields significantly due to the lossy medium.     

A CONCENTRATED MASS ON THE SPINNING UNCONSTRAINED BEAM SUBJECTED TO A THRUST

The dynamic stability of a spinning unconstrained beam subjected to a pulsating follower forceP₀ +P₁cos Ωt is analyzed. A concentrated mass is located at an arbitrary location on the beam, and the stability of the beam is studied with the mass at various locations. The beam is analyzed using the Timoshenko-type shear deformation theory with the rotary inertia. Hamilton's principle is used to derive the equations of motion, and the spinning speed of the beam with various non-dimensional parameters subjected to a pulsating follower force is investigated. The finite element method is applied to analyze the spinning beam model, and the method of multiple scales is used to investigate the dynamic stability characteristics. A pulsating follower force is applied, and then the stability regions are changed with the transitions of the stability area in many regions. The results show that the concentrated mass increases the dynamic stability of the spinning unconstrained beam subjected to a thrust. As the spinning speed of the beam is increased, the instability regions are reduced, but various slight instability regions are additionally developed.     

带阻尼项非等熵流方程组解的大时间状态估计

利用能量估计的方法及压力函数 p (v,s)的性质 ,研究了带阻尼项非等熵流方程组解的大时间状态 ,证明了解在 L 2-模意义下的大时间状态收敛速度的衰减估计 .     

HF SAR image cross-correlation technique for high accuracy orbit positioning

A novel technique to determine the position of spacecraft orbits is proposed. The technique is based on the cross-correlation function of HF SAR images and is able to determine the relative position of orbits with an accuracy of ～ /4 or better, where is the wavelength of the HF radar pulse at its center frequency. The performance of the proposed technique was confirmed by simulation which was carried out under the condition of design facts of the SELENE LRS mission. The highly accurate orbit positioning ena...     

Photovoltaic and Electroluminescence Bifunctional Devices with Starburst Amine and Rare-Earth-Complexes

We fabricate the organic photovoltaic （PV） devices, in which 4,4＇,4＂-tris-（2-methylphenylphenylamino）triphenylamine （m-MTDATA） and rare earth （RE） （dibenzoylmethanato）a（bathohenanthroline） （RE（DBM）abath） （RE = Nd or Pr） are used as electron donor and acceptor, and investigate their PV properties. The PV diode fabricated in the optimum processing conditions shows the open-circuit voltage of 1.91 V, short-circuit current of 0.1 mA/cm^2, fill factor of 0.38, and the overall power conversion efficiency of 1.9% when it is irradiated under UV light （4 m W/cm^2）. The photocurrent density exhibits an increase of 20% at least when a very thin LiF layer is inserted between the RE-complexes and the A1 cathode. A strong electroluminescence from the interface is also observed and the maximum luminance of a yellow emission resulted from the exciplex is 580 cd/m^2 at 17 V bias.     

Guiding Properties of a Tapered Photonic Crystal Fiber Compared with Those of a Tapered Single-Mode Fiber

We have fabricated tapered photonic crystal fibers using a fusion splicer and experimentally observed the near-field mode distribution and the beam divergence of it. We have also compared characteristics of the tapered photonic crystal fiber with those of a tapered standard single-mode fiber. Unlike a tapered standard single-mode fiber, the mode field profile of a tapered photonic crystal fiber shows a good confinement of its field within the core region. The numerical apertures of tapered photonic crystal fibers are increased as the diameter of the fiber is decreased.     

A model for the value of a business, some optimization problems in its operating procedures and the valuation of its debt

Corresponding author, email pw{at}oxfordfinancial.co.uk; also at: Imperial College, London In this paper we present a model for the value of a firm basedon observable variables and parameters: the annual turnover,the expenses, interest rates. This value is the solution ofa parabolic partial differential equation. We show how the valueof the company depends on its legal status such as its liability(that is, whether it is a Limited Company or a sole trader/partnership).We give examples of how the operating procedures can be optimized(for example, whether the firm should close down, relocate etc.).Finally, we show how the model can be used to value the debtissued by the firm.     

PORPHYRIN-SENSITIZED PHOTOREACTIONS IN THE PRESENCE OF ASCORBATE: OXIDATION OF CELL MEMBRANE LIPIDS AND HYDROXYL RADICAL TRAPS

Abstract— Photooxidation reactions in ascorbate (AH)-containing erythrocyte membrane suspensions have been studied in broad perspective by simultaneously monitoring lipid peroxidation in the membrane compartment and formation of hydrogen peroxide (H₂O₂) and hydroxyl radical (OH) in the aqueous compartment. Non-bound uroporphyrin (UP) and membrane-bound protoporphyrin (PP) were used as sensitizers. Photoreduction of UP to the radical anion (UP^-) was detected by electron spin resonance when UP/AH/membrane mixtures were irradiated anaerobically. Aerobic irradiation resulted in a strong AH^--stimulation of lipid peroxidation, H₂O₂ formation, and OH^- generation (detected with 2-deoxyribose (DOR) and the spin trap 5,5-dimethyl-l-pyrroline-N-oxide). Use of diagnostic agents (e.g. catalase, desferrioxamine, mannitol) revealed that OH^- is involved in light-stimulated DOR oxidation, but not in lipid peroxidation. Similar irradiation in the presence of PP resulted in far greater lipid peroxidation than observed with UP, but less DOR oxidation, and insignificant accumulation of H₂O₂. This suggests that photoreduction of membrane-bound PP is less efficient, possibly due to hindered access of AH^-.