The Nonexistence of Ternary [38, 6, 23] Codes

It has been shown by Bogdanova and Boukliev [1] that there exist a ternary [38,5,24] code and a ternary [37,5,23] code. But it is unknown whether or not there exist a ternary [39,6,24] code and a ternary [38,6,23] code. The purpose of this paper is to prove that (1) there is no ternary [39,6,24] code and (2) there is no ternary [38,6,23] code using the nonexistence of ternary [39,6,24] codes. Since it is known (cf. Brouwer and Sloane [2] and Hamada and Watamori [14]) that (i) n₃(6,23) = 38> or 39 and d₃(38,6) = 22 or 23 and (ii) n₃(6,24) = 39 or 40 and d₃(39,6) = 23 or 24, this implies that n₃(6,23) = 39, d₃(38,6) = 22, n₃(6,24) = 40 and d₃(39,6) = 23, where n3<>(k,d) and d<>3(n,k) denote the smallest value of n and the largest value of d, respectively, for which there exists an [n,k,d] code over the Galois field GF(3).     

Convergence of a penalty-finite element approximation for an obstacle problem

Summary This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is where is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality.     

Wellposedness of abstract Cauchy problems for second order differential equations

This paper concerns the abstract Cauchy problem (ACP) for an evolution equation of second order in time. LetA be a closed linear operator with domainD(A) dense in a Banach spaceX. We first characterize the exponential wellposedness of ACP onD(A ^k+1),k teN. Next let {C(t);t teR} be a family of generalized solution operators, on [D(A ^k)] toX, associated with an exponentially wellposed ACP onD(A ^k+1). Then we define a new family {T(t); Ret>0} by the abstract Weierstrass formula. We show that {T(t)} forms a holomorphic semigroup of class (H _k) onX. Research of the second-named author was partially supported by Grant-in-Aid for Scientific Research (No. 63540139), Ministry of Education, Science and Culture.     

On spectra of doubly regular asymmetric digraphs ofRH-type

Spectra of doubly regular asymmetric digraph of regular Hadamard type are determined.     

Mass spectrometric studies on gibberellins

Based on the element maps of twenty-two gibberellin methyl esters fragmentations are discussed, which are characteristic of the common structural features as well as structural modification in gibberellin homologues.     

Nearly triply regular Drad’s ofRH type

Nearly triply regular (4m ², 2m ²−m,m ²−m) DRAD’s, wherem is an even power of 2, are constructed.     

Reinterpretation of two-photon interference experiment using advanced field

The recent two-photon interference experiments by Wang, Zou, and Mandel, with and without a time-dependent light switch introduced into one of interferometer arms, indicate the collapse of photon waves along empty arms, not travelled by the detected photon, at a critical moment on the light cone backwards from the detected photon. It is proposed to interpret the Schrödinger's retarded wave equation as an operator acting on the advanced field satisfying the final condition of the experiment. In this time-symmetrical formulation the advanced field of the detected particle guides the retarded wave from the particle source not to enter empty arms, and the critical moment is interpreted as the time of the passage of the advanced field through the light switch. By changing the relative optical lengths of interferometer arms and observing the independence of the result of the experiment on the relative position of the detectors, we could conceive of the unarousal of the empty wave destined to collapse.     

Oxo-tethered ruthenium(II) complex as a bifunctional catalyst for asymmetric transfer hydrogenation and H2 hydrogenation

Newly developed oxo-tethered Ru amido complexes (R,R)-1 and their HCl adducts (R,R)-2 exhibited excellent catalytic performance for both asymmetric transfer hydrogenation and the hydrogenation of ketonic substrates under neutral conditions without any cocatalysts to give chiral secondary alcohols with high levels of enantioselectivity.