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This g means that the smallest value of d (T ) = x Ci g(d(x, T )) is obtained when each g block Ci contains a member ti of T for 1 i k and the actual value is d (T ) = k 2 2 i=1 (|Ci | 1)r = (|S| k)r Consider now a partition = {C1 , C1 , C2 , , Ck }, where C1 = C1 C1 , so < Choose r to be a positive number such that r < r and de ne the dissimilarity d on S such that d (x, y) = r if x = y and x y and d (x, y) = d(x, y) g otherwise Clearly, d is a -transformation of d.

The minimal value for d (T ) will be achieved when T consists of k + 1 points, one in each of the block of ; as a result, the value of the clustering function for d will be = , which shows that no clustering function obtained by this technique is consistent..

>>> t[0]=10 Traceback (most recent call last): File "<stdin>", line 1, in <module> TypeError: tuple object does not support item assignment >>>

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Examples of reducing agents in non-aqueous solvents are Cr(II), Sn(II), Fe(II), Ti(III), ascorbic acid and organic radical anions. In DMF containing 0.05 M HCl, the potential of Cr(III)/Cr(II) is 0.51 V, that of Ti(IV)/Ti(III) is 0.00 V, and that of Fe(III)/Fe(II) is 0.405 V (vs aqueous SCE). Although Cr(II) is a strong reducing agent, the titration with it must be carried out under nitrogen atmosphere. Ti(III) is used in DMF to titrate inorganic substances like Cu(II), Fe(III), Sb(V), I2 and Br2 and organic substances like azo dyes, quinones, nitro and nitroso compounds, and oximes. Coulometric titrations, in which Ti(II) is generated by electroreduction of TiCl4, have also been carried out [14]. The radical anions of organic compounds are strong reducing agents and applicable as titrants. The standard solutions of radical anions are prepared by reducing the organic compounds in aprotic solvents, either with sodium metal or by cathodic reductions. However, because the radical anions usually react with oxygen, the titrations must be carried out under oxygen-free atmosphere. Coulometric titrations are convenient. For example, coulometric titrations of such organic compounds as anthracene, nitromethane, nitrobenzene, benzophenone and azobenzene have been carried out using biphenyl radical anions, which were coulometrically generated in DMF, THF and DME. The titration reactions are rapid and the end-point can be detected either potentiometrically or visually using the color of the radical anions.

3:56

Aliasing is the phenomenon whereby periodic structures in an object are not faithfully represented in the object image, but instead by a false period that can be mistaken for being real. Aliasing (from the Latin alius, meaning another, other, or different) is an imaging artifact and is a property inherent to all detectors with periodic structures such as raster lines or pixels. We commonly observe aliasing on television. This occurs when there is insufficient magnification produced by the lens of a TV camera focused on periodic structures such as the pattern of pinstripes in an announcer s shirt, bricks in the wall of a house, or seats in an empty stadium. Under these conditions the images of these objects exhibit false patterns of wide bands. An example of aliasing in a diatom imaged by video microscopy is shown in Figure 13-12. Aliasing has its origins in signal sampling theory and can be described mathematically. If the image of a specimen with periodic structure (a sine wave target or the periodic pattern of pores in a diatom) is reconstructed from sample points that occur at a much higher frequency than detail in the specimen, it is possible to reconstruct and display an accurate image of the specimen. However, at the point where the sampling frequency is less than twice the specimen frequency, it is no longer possible to represent the signal accurately, and a false period (aliasing) is observed. Below this sampling limit, the display of periodic elements in the image actually increases as the sampling frequency becomes further reduced. The factor of 2 requirement for oversampling is

Then, the voltage and current eigenvector matrices and the characteristic impedance matrix are given by ! 1 1 Sv 1 1 2 3 1 1 6Z Z2 7 7 SI 6 1 4:3:9 41 15 Z1 Z2 ! 1 Z1 Z2 Z1 Z2 Zc 2 Z1 Z2 Z1 Z2 where L11 L12 Z1 C11 C12 !1=2 L11 L12 Z2 C11 C12 !1=2 4:3:10

The impairment of the hormonal axes is a main symptom of AN and was included as a diagnostic guideline in the ICD-10 as well as in the DSM-IV. Involvement of the hypothalamo-pituitary-gonadal axis is associated with primary or secondary amenorrhoea, depending on the age of the patient at rst manifestation. Although endocrine disorders are not a part of the diagnostic criteria of BN, 20 to 50% of BN patients are found to

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