The existence of equilibria in certain games,separation for families of convex functions and a theorem of Borsuk-Ulam type

The existence of a Nash equilibrium in the undiscounted repeated two-person game of incomplete information on one side is established. The proof depends on a new topological result resembling in some respect the Borsuk-Ulam theorem.     

Del Pezzo surface fibrations obtained by blow-up of a smooth curve in a projective manifold

This Note is devoted to the study of the Fano manifolds X obtained by blow-up along a smooth curve C in a complex projective manifold Y. By the Mori theory, we can ensure the existence of an extremal contraction $\phi :X\to Z$ different from the blow-up $\pi :X\to Y$. Here we give the complete classification of the corresponding pairs $(Y,C)$ in the case where φ is a fiber type contraction of relative dimension 2, i.e. the general fibers of φ are del Pezzo surfaces. In Tsukioka (Thesis, Nancy University 1, 2005), the relative dimension 1 case is also considered. To cite this article: T. Tsukioka, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Labeling bipartite permutation graphs with a condition at distance two

An L(p,q)-labeling of a graph G is an assignment f from vertices of G to the set of non-negative integers {0,1,…,λ} such that |f(u)−f(v)|≥p if u and v are adjacent, and |f(u)−f(v)|≥q if u and v are at distance 2 apart. The minimum value of λ for which G has L(p,q)-labeling is denoted by λ_p,q(G). The L(p,q)-labeling problem is related to the channel assignment problem for wireless networks.In this paper, we present a polynomial time algorithm for computing L(p,q)-labeling of a bipartite permutation graph G such that the largest label is at most (2p−1)+q(bc(G)−2), where bc(G) is the biclique number of G. Since λ_p,q(G)≥p+q(bc(G)−2) for any bipartite graph G, the upper bound is at most p−1 far from optimal.     

Bandwidth of the strong product of two connected graphs

The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x)-f(y)|:xy∈E(G)} taken over all proper numberings f of G. The strong product of two graphs G and H, written as G(S_P)H, is the graph with vertex set V(G)×V(H) and with (u₁,v₁) adjacent to (u₂,v₂) if one of the following holds: (a) u₁ and v₁ are adjacent to u₂ and v₂ in G and H, respectively, (b) u₁ is adjacent to u₂ in G and v₁=v₂, or (c) u₁=u₂ and v₁ is adjacent to v₂ in H. In this paper, we investigate the bandwidth of the strong product of two connected graphs. Let G be a connected graph. We denote the diameter of G by D(G). Let d be a positive integer and let x,y be two vertices of G. Let denote the set of vertices v so that the distance between x and v in G is at most d. We define δ_d(G) as the minimum value of over all vertices x of G. Let denote the set of vertices z such that the distance between x and z in G is at most d-1 and z is adjacent to y. We denote the larger of and by . We define η(G)=1 if G is complete and η(G) as the minimum of over all pair of vertices x,y of G otherwise. Let G and H be two connected graphs. Among other results, we prove that if δ_D(H)(G)?B(G)D(H)+1 and B(H)=⌈(|V(H)|+η(H)-2)/D(H)⌉, then B(G(S_P)H)=B(G)|V(H)|+B(H). Moreover, we show that this result determines the bandwidth of the strong product of some classes of graphs. Furthermore, we study the bandwidth of the strong product of power of paths with complete bipartite graphs.     

Several contributions to soil compactibility induced by cyclic loading test

To investigate the soil compactibility during the cyclic loading, three different kinds of paddy field soils were prepared so as to clarify interrelationships among stress amplitude ratio, bulk density, soil water content and pore water pressure. The presetting values of specimen include the soil water content(percent dry basis) and bulk density of 25% d.b. and 1.1 Mg/m³ respectively. The relation between the number of cyclic loading and axial strain exhibited an asymptotically increasing trend, converging toward a specific value for each experimental condition. Possible effect caused by elastic–plastic characteristics could be recognized, when axial strain for 0.5 Hz excitation becomes greater than the one of 1.0 Hz under same stress amplitude ratio. When the stress amplitude ratio took 0.1, the absolute value of axial strain of 0.5 Hz was greater than the one of 1.0 Hz, whereas its decreasing trend was recognized in the sequence of silt, clay and silty sand. The qualitative relations between pore water pressure and number of cyclic loading were also examined to scrutinize the effect of effective water pressure to the soil compactibility.     

A Pseudo-Random Frequency Modulation Continuous Wave Coherent Lidar Using an Optical Field Correlation Detection Method

We propose a new detection method for a pseudo-random frequency modulation continuous wave (RM-CW) coherent lidar. The feature of this method is modulation of local beam with a time delayed pseudo-random sequence. Heterodyne detection and correlation detection between the received beam and the local beam are simultaneously carried out in an optical field. In the RM-CW coherent lidar using the optical field correlation detection method, the received equipment is greatly simplified. We carried out preliminary experiments and demonstrated that the new method is effective for detection of a CW coherent lidar.     

A study on the effect of filling factor for laser action in dielectric random media

In a random system composed of dielectric materials, laser action is expected to occur from the light localization caused by multiple scattering and interference effect. The wavelengths at which the laser oscillation occurs in random media depend on the mean free path of continuous scattering. Since the mean free path of continuous scattering is dependent on the filling factor, it is important to investigate systematically the effect of the filling factor for the laser action. In the present study, we calculate the Poynting vectors of the light emitted from two-dimensional random media consisting of dielectric rods with population inversion modeled by the negative imaginary part of relative permittivity. The spectra of the radiated Poynting vectors from the two-dimensional random media are shown for several different filling factors and for various values of population inversion. We try to find laser generation which occurs at low population inversion and discuss about the threshold of laser action occurring in dielectric structures with different filling factors. We also study the spacial distribution of the electric field amplitude in several frequency regions where light strongly amplifies.     

Diagnostics of laser-induced plasma with soft X-ray (13.9 nm) bi-mirror interference microscopy

X-ray interference microscopy diagnostics of a nanosecond-pulse pumped Al (Z=13) plasma are presented. A transient picosecond Ni-like Ag X-ray laser (13.9 nm) is used as the probe beam and a wavefront division bi-mirror interferometer is adopted as the diagnosis tool. From the fringe shifts, the two-dimensional plasma density profile at 1 ns after the peak of the heating pulse is deduced. Opposite fringe shifts during the plasma development are observed and possible explanations for this behavior are discussed. This study will contribute to the validation of 1D and 2D hydrodynamic codes as well as to the better understanding of the physics during the development of laser produced plasmas. PACS 41.50.+h; 41.85.Ew; 42.55.Vc     

Dual Meissner effect and magnetic displacement currents

The dual Meissner effect is observed without monopoles in quenched SU(2) QCD with Landau gauge fixing. Magnetic displacement currents that are time-dependent Abelian magnetic fields act as solenoidal currents squeezing Abelian electric fields. Monopoles are not always necessary for the dual Meissner effect. A mean-field calculation suggests that the dual Meissner effect through the mass generation of the Abelian electric field is related to a gluon condensate A(a)(mu)A(a)(mu) not equal 0 of mass dimension 2.     

Interrogation of fiber-Bragg-grating temperature and strain sensors with a temperature-stabilized VCSEL

The interrogation of fiber-Bragg-grating (FBG) sensors using a vertical-cavity surface-emitting laser (VCSEL) is discussed. A long-wavelength (1.54 μm) VCSEL was used as a wavelength-tunable source by variation in the current. Temperature stabilization was performed with a thermoelectric device. Characteristics of temperature and strain sensing were investigated. FBGs with different reflectivities were compared. For temperature sensing, the root-mean-square error in the measurement was reduced to 1/3 that without temperature stabilization. The dependence of the measurement error on the reflectivities of the FBGs was investigated. The measurement error was larger for FBGs with lower reflectivities in both temperature and strain sensing. Improvement on the sensing with low-reflectivity FBGs is discussed.