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21.
In this paper, we present examples of codes all of whose weight classes support 1‐designs, with duals whose classes include two that support 2‐designs. We can find these examples in the triply even binary codes of length 48, which have been classified by Betsumiya and Munemasa. 相似文献
22.
The current work entails development of rapid, sensitive, and inexpensive high-performance liquid chromatographic method of quercetin dihydrate using the quality by design approach. Quality target method profile was defined and critical analytical attributes (CAAs) were earmarked. Chromatographic separation was accomplished on a C18 column using acetonitrile and ammonium acetate buffer (35:65) %v/v (containing 0.1% acetic acid, pH 3.5) as mobile phase at 0.7?mL/min flow rate with UV detector at 237?nm. Screening studies using fractional factorial design revealed that organic modifier, injection volume, column temperature, and buffer strength have significant influence on method CAAs, namely, peak area, retention time, and peak tailing. The critical method parameters were systematically optimized using Box–Behnken design. Response surface mapping was used along with numerical optimization and desirability function for identifying the optimal chromatographic conditions. Linearity was observed in the drug concentration ranging between 2 and 50?µg/mL. Accuracy analysis revealed mean % recovery between 93.6 and 96.2%, while precision study revealed mean % recovery between 93.7 and 96.5%. Limits of detection and quantification of the developed method were found to be 12.1 and 36.6?ng/mL. Overall, the studies construed successful development of chromatographic method of quercetin with enhanced method performance. 相似文献
23.
We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1‐factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1‐factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D. Stones. 相似文献
24.
A q‐ary code of length n, size M, and minimum distance d is called an code. An code with is said to be maximum distance separable (MDS). Here one‐error‐correcting () MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 53, 3)5 and (5, 73, 3)7 codes and equivalence classes of (5, 83, 3)8 codes. The codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q, called Graeco‐Latin cubes. 相似文献
25.
《Photonics and Nanostructures》2014,12(1):23-33
We present an efficient parallel topology optimization framework for design of large scale 3D nanophotonic devices. The code shows excellent scalability and is demonstrated for optimization of broadband frequency splitter, waveguide intersection, photonic crystal-based waveguide and nanowire-based waveguide. The obtained results are compared to simplified 2D studies and we demonstrate that 3D topology optimization may lead to significant performance improvements. 相似文献
26.
By a T
*(2, k, v)-code we mean a perfect4-deletion-correcting code of length 6 over an alphabet of size v, which is capable of correcting anycombination of up to 4 deletions and/or insertions of letters that occur in transmission of codewords. Thethird author (DCC Vol. 23, No. 1) presented a combinatorial construction for such codes and prove thata T
*(2, 6, v)-code exists for all positive integers v 3 (mod 5), with 12 possible exceptions of v. In this paper, the notion of a directedgroup divisible quasidesign is introduced and used to show that a T
*(2, 6,v)-code exists for all positive integers v 3 (mod 5), except possiblyfor v {173, 178, 203, 208}. The 12 missing cases for T
*(2,6, v)-codes with v 3 (mod 5) are also provided, thereby the existenceproblem for T
*(2, 6, v)-codes is almost complete. 相似文献
27.
Malcolm Greig 《Designs, Codes and Cryptography》2002,27(1-2):25-47
Batten and Beutelspacher have characterized Finite Linear Spaces with lines of size n,n + 1 and n + 2, and with v (n + 1)2for n 22, and some of the cases for smaller n. In this article, using the structuredapproach we presented in our earlier article [8], we complete this characterization for smalln. 相似文献
28.
Kreher and Rees 3 proved that if h is the size of a hole in an incomplete balanced design of order υ and index λ having minimum block size , then, They showed that when t = 2 or 3, this bound is sharp infinitely often in that for each h ≥ t and each k ≥ t + 1, (t,h,k) ≠(3,3,4), there exists an ItBD meeting the bound. In this article, we show that this bound is sharp infinitely often for every t, viz., for each t ≥ 4 there exists a constant Ct > 0 such that whenever (h ? t)(k ? t ? 1) ≥ Ct there exists an ItBD meeting the bound for some λ = λ(t,h,k). We then describe an algorithm by which it appears that one can obtain a reasonable upper bound on Ct for any given value of t. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 256–281, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10014 相似文献
29.
In this paper properties and construction of designs under a centered version of the -discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.
30.
Konrad J. Swanepoel 《Proceedings of the American Mathematical Society》1999,127(7):2155-2162
A hollow axis-aligned box is the boundary of the cartesian product of compact intervals in . We show that for , if any of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any of a collection of hollow axis-aligned rectangles in have non-empty intersection, then the whole collection has non-empty intersection. The values for and for are the best possible in general. We also characterize the collections of hollow boxes which would be counterexamples if were lowered to , and to , respectively.