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1.
In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms.In this paper we consider the isotonic regression problem with respect to a complete order
where eachw
i
is strictly positive and eachy
i
is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n
2). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.This work was supported by the National Science and Engineering Research Council of Canada under Research Grant A8189 and an Ontario Graduate Scholarship. 相似文献
2.
Summary The exchange of Co(NH3)6]3+-ions on amberlite IRC-50 resin has been studied at room temperature. For this exchange process the cations are effective
in the order: Cs+<Rb+<K+<Na+<Li+<NH4
+<Mg2+ <Ca2+<H+ and (C2H5)4N<(CH3)4N+ ≪Cetyltrimethylammonium-ion <Cetylpyridinium-ion.
The logarithm of the selectivity coefficient gives linear graphs when plotted against the radius of the hydrated ions or the
reciprocals of theDebye-Hückel parameter?. 相似文献
3.
4.
An investigation is made of the influence of band non-parabolicity on the relation between the Fermi energies in the presence and absence of magnetic quantization in degenerate semi-conductors through derivation of a simplified form of the relation.On leave of absence from theDept. of Physics, B. N. College, Patna University, Patna 800004. 相似文献
5.
A. N. Chakravarti A. K. Chowdhury K. P. Ghatak D. R. Choudhury 《Czechoslovak Journal of Physics》1980,30(10):1161-1166
An expression is derived for the diffusivity-mobility ratio of the carriers in n-channel inversion layers on semiconductors like the ternary compounds which have strongly non-parabolic energy bands. The dependence of the ratio on alloy composition is also studied under the weak-field limit taking n-channel Hg1–xCdx.Te as an example.On leave of absence fromthe Department of Physics, Patna University, Patna, India. 相似文献
6.
Summary Cation exchange studies have been carried out between Mg-saturated bentonite and vermiculite and a number of monovalent electrolytes. According to the distribution and selectivity coefficients the cations are preferred in the order: Li Na43)4N (C2H5)4N for betonite and Li < Na < NH4 < K < Rb < Cs < H and (C2H5)4N < (CH3)4N for vermiculite. The selectivity coefficient of H+ is found to be much greater than other inorganic ions.TheG-values of the cation exchange reaction have been calculated by an equation ofBarrer. The experimental data were analyzed by the theoretical approach ofPauley too. 相似文献
7.
K. Chakravarti und G. J. Pontrelli 《Colloid and polymer science》1978,256(1):104
Ohne Zusammenfassung 相似文献
8.
K. P. Ghatak A. K. Chowdhury S. Ghosh A. N. Chakravarti 《Applied Physics A: Materials Science & Processing》1980,23(3):241-244
An analytical expression of the modified form of the Einstein relation in heavily doped semiconductors in which Gaussian band
tails are formed near the lower limit of heavy doping is derived for studying the temperature dependence of the diffusivity-mobility
ratio of the carriers in such semiconductors. It is found that, with increasing temperature from relatively low values, the
ratio first increases in a nonlinear manner and then decreases till, at high temperatures, it approaches its value corresponding
to the non-degenerate condition resulting in a peak over a narrow range of temperatures. 相似文献
9.
The Debye screening length in degenerate semiconductors having parabolic energy bands is shown for the first time to have an oscillatory dependence on magnetic field under the influence of Landau quantization when the higher lying sub-bands are occupied.The authors are indebted to Professor J. N.Bhar for his keen interest in the work. 相似文献
10.
A. N. Chakravarti 《Czechoslovak Journal of Physics》1975,25(7):778-784
The theory of electron diffusion under a temperature gradient (Soret effect) in degenerate semiconductors having non-parabolic energy bands and spherical constant-energy surfaces is worked out for the first time. An expression is given for the Soret coefficient which may be determined from the knowledge of the energy dependence of the relaxation time and can be related to the thermoelectric power. 相似文献