1,721,442 research outputs found
On regular polytope numbers
No full textLagrange proved a theorem which states that every nonnegative integer can be written as a sum of four squares. This result can be generalized as the polygonal number theorem and the Hilbert-Waring problem. In this paper, we shall generalize Lagrange's sum of four squares theorem further. To each regular polytope V in a Euclidean space, we will associate a sequence of nonnegative integers which we shall call regular polytope numbers, and consider the problem of finding the order g (V) of the set of regular polytope numbers associated to V.X112sciescopu
EVALUATION OF ZETA FUNCTION OF THE SIMPLEST CUBIC FIELD AT NEGATIVE ODD INTEGERS (VOL 124, PG 551, 2007)
No full textX11sciescopu
Maximum distance separable poset codes
No full textWe derive the Singleton bound for poset codes and define the MDS poset codes as linear codes which attain the Singleton bound. In this paper, we study the basic properties of MDS poset codes. First, we introduce the concept of I-perfect codes and describe the MDS poset codes in terms of I -perfect codes. Next, we study the weight distribution of an MDS poset code and show that the weight distribution of an MDS poset code is completely determined. Finally, we prove the duality theorem which states that a linear code C is an MDS P-code if and only if C(perpendicular to) is an MDS (P) over tilde -code, where C(perpendicular to) is the dual code of C and (P) over tilde is the dual poset of P.X1113sciescopu
Evaluation of zeta function of the simplest cubic field at negative odd integers
No full textIn this paper, we are interested in the evaluation of the zeta function of the simplest cubic field. We first introduce Siegel's formula for values of the zeta function of a totally real number field at negative odd integers. Next, we will develop a method of computing the sum of a divisor function for ideals, and will give a full description for a Siegel lattice of the simplest cubic field. Using these results, we will derive explicit expressions, which involve only rational integers, for values of a zeta function of the simplest cubic field. Finally, as an illustration of our method, we will give a table for zeta values for the first one hundred simplest cubic fields.X115sciescopu
On optimal superimposed codes
No full textA (w,r) cover-free family is a family of subsets of a finite set such that no intersection of w members of the family is covered by a union of r others. A binary (w,r) superimposed code is the incidence matrix of such a family. Such a family also arises in cryptography as a concept of key distribution patterns. In this paper, we develop a method of constructing superimposed codes and prove that some superimposed codes constructed in this way are optimal. (C) 2003 Wiley Periodicals, Inc.X114243sciescopu
A comparative study of shade-matching performance using intraoral scanner, spectrophotometer, and visual assessment
Full text linkThis study aimed to explore the clinical applicability of the shade-matching function in intraoral scanners. This study measured the tooth colors of maxillary anterior dentitions of 83 adults using visual matching, a spectrophotometer, and a scanner according to two color systems: VITA Classical (VC) and VITA 3D-Master (V3D). Agreement between each method was assessed by weighted Cohen’s kappa coefficient (KW, α = 0.05). For V3D, the overall agreement between the scanner and spectrophotometer (KW = 0.498) was higher than that between the scanner and visual matching (KW = 0.473). Similarly, the agreement between the scanner and spectrophotometer (KW = 0.283) was higher than that between a scanner and visual matching (KW = 0.140) for VC. Regarding tooth position, the highest agreement between the scanner and spectrophotometer was observed on the right central incisor (KW = 0.542) for V3D. Tooth color measurement with a scanner was comparable to that with a spectrophotometer, especially on the central incisors when using the VITA 3D-Master system. A scanner could serve as an alternative to a spectrophotometer for shade selection. However, color matching should still be visually verified
Comparative study on sustained release of human growth hormone from semi-crystalline poly(L-lactic acid) and amorphous poly(D,L-lactic-co-glycolic acid) microspheres: morphological effect on protein release
No full textRecombinant human growth hormone (rhGH) was encapsulated by a double emulsion solvent evaporation method within two biodegradable microspheres having different polymer compositions. Semi-crystalline poly(L-lactic acid) (PLA) and amorphous poly(D,L-lactic-co-glycolic acid) (PLGA) were used for the encapsulation of hGH. Protein release profiles from the two rnicrospheres were comparatively evaluated with respect to their morphological difference. Both of the microspheres similarly exhibited rugged surface and porous internal structures, but their inner pore wall morphologies were quite different. The slowly degrading PLA microspheres had many nano-scale reticulated pores on the wall, while the relatively fast degrading PLGA microspheres had a non-porous and smooth wall structure. From the PLA microspheres, hGH was released out in a sustained manner with an initial similar to 20% burst, followed by constant release, and almost 100% complete release after a 1-month period. In contrast, the PLGA microspheres showed a similar burst level of similar to 20%, followed by much slower release, but incomplete release of similar to 50% after the same period. The different hGH release profiles between PLA and PLGA microspheres were attributed to different morphological characters of the pore wall structure. The inter-connected nano-porous structure of PLA microspheres was likely to be formed due to the preferable crystallization of PLA during the solvent evaporation process. (C) 2004 Elsevier B.V. All rights reserved.Center for Advanced Functional Polymers at KAIST
and the Korea Science and Engineering Foundation,
Republic of Korea
New Inequalities for q-ary constant-weight codes
No full textUsing double counting, we prove Delsarte inequalities for -ary codes and their improvements. Applying the same technique to -ary constant-weight codes, we obtain new inequalities for -ary constant-weight codes.X110sciescopu
Association schemes and MacWilliams dualities for generalized Niederreiter-Rosenbloom-Tsfasman posets
No full textLet P be a poset on the set [m] x [n], which is given as the disjoint sum of posets on 'columns' of [m] x [n], and let P be the dual poset of P. Then P is called a generalized Niederreiter Rosenbloom Tsfasman poset (gNRTp) if all further posets on columns are weak order posets of the 'same type'. Let G (resp. (sic)) be the group of all linear automorphisms of the space F-q(m x n) preserving the P-weight (resp. (sic)-weight). We define two partitions of F-q(m x n), one consisting of 'P-orbits' and the other of '(sic)-orbits'. If P is a gNRTp, then they are respectively the orbits under the action of G on F-q(m x n) and of (sic) on F-q(m x n). Then, under the assumption that P is not an antichain, we show that (1) P is a gNRTp if (2) the P-orbit distribution of C uniquely determines the (sic)-orbit distribution of C-perpendicular to for every linear code C in F-q(m x n) iff (3) G acts transitively on each P-orbit iff (4) F-q(m x n) together with the classes given by '(u, v) belongs to a class iff u - v belongs to a P-orbit' is a symmetric association scheme. Furthermore, a general method of constructing symmetric association schemes is introduced. When P is a gNRTp, using this, four association schemes are constructed. Some of their parameters are computed and MacWilliams-type identities for linear codes are derived. Also, we report on the recent developments in the theory of poset codes in the Appendix.X115sciescopu
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