Splicing P systems are a class of distributed parallel computing models in the framework of membrane computing, which are inspired by the recombination of DNA molecules under the influence of restriction enzymes. In this work, a variant of P machine, called splicing P machine, is presented, which can provide an automata approach to investigate splicing P systems. It is shown that such a device can do what the splicing P system does. Several examples are given to illustrate that splicing P machine can provide the same results as the corresponding splicing P system. This work provides an answer to an open problem formulated by G. Ciobaun and M. Gontineac.
Treating PCl5 with C12H8Li2, generated from either C12H10, C12H8Br2, or C12H8I2, affords three products in different ratios depending on the source of the lithiated biphenyl. Hellwinkel's salt [P(C12H8)(2)][P(C12H8)(3)] ([1][2]) and another product [P(C12H8)(C24H16)][P(C12H8)(3)] ([1'][2]) were obtained by reacting PCl5 with 2,2'-dilithiobiphenyl [Route A: 2.5 equiv.; obtained from biphenyl, n-BuLi, and TMEDA; Route B: 3.0 equiv.; obtained from 2,2'-diiodobiphenyl and n-BuLi; Route C: 4.0 equiv.; obtained from 2,2'-dibromobiphenyl and n-BuLi]. The synthesis, isolation, and characterization of the chiral spiro-compound [1'][2] and the characterization of the pentavalent phosphorane [P(C12H8)(2)(C12H9)] (3) are reported. The complex [1'][2] was characterized by P-31{H-1} NMR spectroscopy, X-ray crystallography, and mass spectrometry. The pentavalent compound (3) was characterized by P-31{H-1} NMR spectroscopy and X-ray crystallography.
We prove an asymptotic formula for the number of primes of the shape , thereby refining the well known work of Friedlander and Iwaniec (Ann Math (2) 148(3):945-1040, 1998). Along the way, we prove a result on equidistribution of primes up to x, in which the moduli may be almost as large as x(2).
We present a high-resolution (R similar or equal to 20 000) near-infrared (9100-13 500 angstrom) long-slit spectrum of P Cygni obtained with the newly commissioned WINERED spectrograph in Japan. In the obtained spectrum, we have found that the velocity profiles of the [Fe II] emission lines are resolved into two peaks at a velocity of similar or equal to 220 km s(-1) with a moderate dip in between and with additional sub-peaks at similar or equal to +/- 100 km s(-1). The sub-peak component is confirmed with the long-slit echellogram to originate in the known shell with a radius of similar or equal to 10 arcsec, which was originally created by the outburst in 1600 AD. On the other hand, the similar or equal to 220 km s(-1) component, which dominates the [Fe II] flux from P Cygni, is found to be concentrated closer to the central star with an apparent spatial extent of similar or equal to 3 arcsec. The extent is much larger than the compact (< 0.1 arcsec) regions traced with hydrogen, helium, and metal permitted lines. The velocity, estimated mass, and dynamical time of the extended emission-line region suggest that the region is an outer part of the stellar wind region. We suggest that the newly identified emission-line region may trace a reverse shock due to the stellar wind overtaking the outburst shell.
Acar, Tuncer
Agrawal, Purshottam Narain
Kumar, A. Sathish
In the present paper, we construct and investigate a variant of modified (p, q)-Szasz-Mirakyan operators, studied in Acar (Math Methods Appl Sci 39(10):2685-2695, 2016), which reproduce the test function The order of approximation of the operators via Peetre -functional, weighted approximation properties and approximation for functions in a Lipschitz space are discussed.