The number of self-dual cyclic codes of length p (k) over GR(p (2), m) is determined by the nullity of a certain matrix M(p (k) , i (1)). With the aid of Genocchi numbers, we determine the nullity of M(p (k) , i (1)) and hence determine completely the number of such codes.
In this paper, we mainly consider the quasi-cyclic (QC) codes over finite chain ring R =3D F(p)m + u F(p)m + ... + u(3-1) F(p)m, where p is a prime number and m, s are positive integers such that s >=3D 2 and u(s) =3D 0. We investigate the structural properties of the QC codes over R, regarding them as subcodes of cyclic codes over some Galois extension rings of R. This point of view leads to construct the 1-generator QC codes with index s over finite field F(p)m. Further, we study the structural properties of annihilators of the 1-generator QC codes. For the case s=3D2, under the conditions gcd(n,p) =3D 1 and gcd(vertical bar p(m vertical bar)vertical bar(n),l) =3D 1, we discuss the enumeration of the distinct 1-generator QC codes and describe how to obtain one and the only one generator for each 1-generator QC code. Finally, we give some examples to illustrate the main work in this paper. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
In this paper we define the sequence space BV theta (M, p, q, s) on a seminormed complex linear space by using an Orlicz function. We give various properties and some inclusion relations on this space.
Chen, Yafeng
Liu, Jie
Li, Yunpeng
Sadiq, Rehan
Deng, Yong
Weather system is a relative complex dynamic system, the factors of the system are mutually influenced P M (2.5) concentration. In this paper, a new method is proposed to quantify the influence on P M (2.5) by other factors in the weather system and identify the most important factors for P M (2.5) with limited resources. The relation map (RM) is used to figure out the direct relation matrix of 14 factors in P M (2.5). The decision making trial and evaluation laboratory(DEMATEL) is applied to calculate the causal relationship and extent to a mutual influence of 14 factors in P M (2.5). According to the ranking results of our proposed method, the most important key factors is sulfur dioxide (SO (2)) and nitrogen oxides (NO (X) ). In addition, the other factors, the ambient maximum temperature (T (max)), concentration of P M (10), and wind direction (W (d i r) ), are important factors for P M (2.5). The proposed method can also be applied to other environment management systems to identify key factors.
P–M equation proposed by Perona and Malik can not only perform scale-space, but also preserve edges while smoothing an image. In this paper, we employ this property to construct a new multiscale decomposition method, by which an image can be decomposed into a sequence of detail images and a base image, and the initial image can be perfectly reconstructed by adding up these decomposed images. This decomposition method is applied to multisensor image fusion. The source images are first decomposed into the detail images and the base image. Then, these images are combined according to the given fusion rules. Finally, the fused image is reconstructed by adding up the fused detail images and base image. Compared with conventional methods based on multiscale decomposition, experimental results over multifocus images, visible and infrared images, and medical images demonstrate the superiority of our method in terms of visual inspection and objective measures.
A subgroup K of G is M (p) -supplemented in G if there exists a subgroup B of G such that G =3D KB and TB < G for every maximal subgroup T of K with |K: T| =3D p (alpha). We study the structure of the chief factor of G by using M (p) -supplemented subgroups and generalize the results of Monakhov and Shnyparkov by involving the relevant results about the p-modular subgroup O (p) (G) of G.
Link, Timothy E.
Bisson, Erica
Horgan, Michael A.
Tranmer, Bruce I.
Raymond M. P. Donaghy was one of the true pioneers of modern neurosurgery. His restless dedication, innovation, and desire to humbly disseminate his knowledge facilitated the advancement of the field of microneurosurgery. Many of his trainees-most notably M. Gazi Yasargil-continued to advance the field. developing innovative microsurgical instruments and techniques. The history of microneurosurgery is incomplete without a glimpse at the life of this remarkable man. (DOI: 10.3171/2009.6.JNS09539)
The pure vibrational transition frequencies of magnetically trapped cold XH molecules are useful to detect the variance in the proton-to-electron mass ratio beta (X: alkali-earth atom). This paper compares the accuracies of the vibrational transition frequencies for different XH molecules.
All of the M and P isomers of optically pure oligophenylenes with 6, 8, 10, and 12 phenyl rings were synthesized and fully characterized. The Suzuki cross-coupling reaction has been revealed to be a viable strategy in the syntheses of tetraphenylene derivatives, which, together with the copper-mediated oxidative cross-coupling reaction, were employed in the quest for the oligophenylenes. X-ray diffraction analysis in combination with specific rotation and circular dichroism spectroscopy unambiguously identified the unique covalent double-helical frameworks of these oligophenylene molecules.