Jacobi polynomials for first-order generalized Reed--Muller codes

In this paper, we give the Jacobi polynomials for first-order generalized Reed--Muller codes. We show as a corollary the nonexistence of combinatorial $3$-designs in these codes.Comment: 15 page

Classification of bifurcation diagrams in coupled phase-oscillator models with asymmetric natural frequency distributions

Synchronization among rhythmic elements is modeled by coupled phase-oscillators each of which has the so-called natural frequency. A symmetric natural frequency distribution induces a continuous or discontinuous synchronization transition from the nonsynchronized state, for instance. It has been numerically reported that asymmetry in the natural frequency distribution brings new types of bifurcation diagram having, in the order parameter, oscillation or a discontinuous jump which emerges from a partially synchronized state. We propose a theoretical classification method of five types of bifurcation diagrams including the new ones, paying attention to the generality of the theory. The oscillation and the jump from partially synchronized states are discussed respectively by the linear analysis around the nonsynchronized state and by extending the amplitude equation up to the third leading term. The theoretical classification is examined by comparing with numerically obtained one.Comment: 18 pages, 14 figure

Generation of polarization entanglement from spatially-correlated photons in spontaneous parametric down-conversion

We propose a novel scheme to generate polarization entanglement from spatially-correlated photon pairs. We experimentally realized a scheme by means of a spatial correlation effect in a spontaneous parametric down-conversion and a modified Michelson interferometer. The scheme we propose in this paper can be interpreted as a conversion process from spatial correlation to polarization entanglement.Comment: 4 pages, 4 figure

Effect of Air or Medium Temperature on Occurrence of Leaf-yellow-spot in Chrysanthemum 'Seikou-no-makoto'

Leaf-yellow-spot, a physiological abnormality occurring in leaves of several chrysanthemum (Chrysanthemum x morifolium) cultivars is a very serious production problem in Japan. High temperature or high irradiation are possible physiological factors, which may lead to leaf-yellow-spot. In the present study, effects of air or medium temperature on the occurrence of leaf-yellow-spot in 'Seikou-nomakoto' were investigated. The nodal position with spotted leaves and rate of leaf-yellow-spot increased with increasing day/night temperature. The nodal position with spotted leaves and rate of leaf-yellow-spot of plants grown on 30°C night air temperature were smaller than those grown on 25°C or ambient night air temperature. The days to first occurrence of leaf-yellow-spot showed no differences among medium temperatures. As occurrence of leaf-yellow-spot was not affected by root zone temperature, we recognized that occurrence of leaf-yellow-spot was promoted by high temperature or solar radiation on shoot, especially leaf. Occurrence of leaf-yellow-spot was reduced by long period high temperature and/or high solar radiation as plant growth reduced. Therefore, we thought that occurrence of leaf-yellow-spot was promoted by environmental condition as plant growth would promote.キク（Chrysanthemum × morifolium）‘精興の誠’の葉身で発生する黄斑に及ぼす気温および培地温度の影響を調査した．昼夜温を40/30℃，35/25℃，なりゆきの3区で栽培した場合，昼夜温が高いほど生育は抑制され，黄斑の発生は早くなったが，黄斑発生度は40/30℃区と比較してなりゆき区で高くなる傾向がみられた．夜温を30℃，25℃となりゆき区で栽培した場合，黄斑発生度は30℃区と比較してなりゆき区で有意な差がみられた．生育が抑制されるほどの長期間の強光や高温は黄斑発生を抑制させたことから，生育が旺盛な環境条件における外的要因により黄斑発生は助長されると考えられた．地下部の温度は黄斑発生に影響しなかったことから黄斑発生は地上部，特に葉身部位の高温により助長されることが明らかになった

Tomographic Image Reconstruction Based on Minimization of Symmetrized Kullback-Leibler Divergence

Iterative reconstruction (IR) algorithms based on the principle of optimization are known for producing better reconstructed images in computed tomography. In this paper, we present an IR algorithm based on minimizing a symmetrized Kullback-Leibler divergence (SKLD) that is called Jeffreys’ J-divergence. The SKLD with iterative steps is guaranteed to decrease in convergence monotonically using a continuous dynamical method for consistent inverse problems. Specifically, we construct an autonomous differential equation for which the proposed iterative formula gives a first-order numerical discretization and demonstrate the stability of a desired solution using Lyapunov’s theorem. We describe a hybrid Euler method combined with additive and multiplicative calculus for constructing an effective and robust discretization method, thereby enabling us to obtain an approximate solution to the differential equation.We performed experiments and found that the IR algorithm derived from the hybrid discretization achieved high performance