Defining length

The ciphered code is indicated with a defined length, i.e., a fixed hit/byte length. A hash code of 32 bits could have 2 (or 4 294 976 296) possible values, whereas one of 64 bits could have 2 values, However, due to tbe fixed length, several diverse data entries could assign the same hash code ( address collision ), The probability of collision rises if the number of input data is increased in relation to the range of values (bit length). In fact, the limits of hash coding are reached with about 10 000 compounds with 32 bits and over 100 million with 64 bits, to avoid collisions in databases [97. ... 

A lower bound on the overall effect of crossover, which can both create and destroy instances of a given schema, can be estimated by calculating the probability, Pc S), that crossover leaves a schema S unaltered. Let be the probability that the crossover operation will be applied to a string. Since a schema S will be destroyed by crossover if the operation is applied anywhere within its defining length, the probability that S will be destroyed is equal to Pc x 6 S)/ K — 1), where 6 S) is the defining length of S. Hence, the probability of survival ps = 1 — PcS S)/ K — 1), and equation 11.9 takes the updated form ... 

Numerical values defining length and height of the carbene "tences" are listed in Table II. Not surprisingly, all aryl-substituted carbenes possess nearly the same... 

ELPs can be produced via chemical synthesis and biosynthetically. For chemical synthesis via solid phase peptide synthesis, the attainable polymer length is limited, and if long polymers with a defined length are required then the biosynthetic approach is more appropriate. An advantage of chemical synthesis is, however, that it enables the facile introduction of functional residues in the polypeptide [27]. 

Figure 40-7. The polymerase chain reaction is used to amplify specific gene sequences. Double-stranded DNA is heated to separate it into individual strands. These bind two distinct primers that are directed at specific sequences on opposite strands and that define the segment to be amplified. DNA polymerase extends the primers in each direction and synthesizes two strands complementary to the original two. This cycle is repeated several times, giving an amplified product of defined length and sequence. Note that the two primers are present in excess.

Fig. 14. A,B. A living polymerization of mannose-substituted norbornene derivatives can be used to produce materials of defined lengths for biological testing. B The relationship between polymer length and biological activity was explored...

Time is one of the so-called base units within the SI system, and so is length. Whereas volume can be expressed in terms of a length (for example, a cube has a volume l3 and side of area l2), we cannot define length in terms of something simpler. Similarly, whereas a velocity is a length per unit time, we cannot express time in terms of something simpler. In fact, just as compounds are made up of elements, so all scientific units are made up from seven base units length, time, mass, temperature, current, amount of material and luminous intensity. 

Molecules are made up of two or more atoms these atoms are held together by chemical bonds, a form of electronic glue. Chemical bonds have defined lengths and directions in space. Water and carbon-based molecules are the foundation of the molecules of living organisms. 

Yao, J., Lowary, P.T., and Widom, J. (1990) Direct detection of linker DNA bending in defined-length oligomers of chromatin. Proc. Natl. Acad. Sci. USA 87, 7603-7607. 

The number of DNA molecules doubles in each cycle of the process, so that after 30 cycles, say, we have molecules (approximately 10 copies). However, there is another, less obvious feature that makes the PCR even more useful. In the second cycle, two of the newly synthesized single-stranded chains will be of defined length. They will consist of the target area plus two primers the 5 -ends of the... 

The validity of the Forster theory was tested and confirmed in a number of model studies with compounds that contained a donor and an acceptor separated by well-defined rigid spacers. This work has been reviewed 5] In a classical study, a naphthyl group (donor) was attached to the C-terminal and a dansyl group (acceptor) to the N-terminal of poly-L-proline oligomers (1-12 proline residues) 61 These proline oligomers assume a trans helical conformation in ethanol and thus represent spacers of well-defined length (12-46 A). A continuous decrease in the transfer efficiency from 100% at a donor-acceptor separation of... 

On the basis of these examples, we can see that using templates connected by covalent bonds, we can produce a new class of copolymers - semi-ladder block copolymers -with blocks of ladder-type structure. By hydrolysis, the template can be removed and block copolymers with defined length of block can be obtained. Such synthesis by conventional copolymerization is very difficult and sometimes impossible. 

As indicated in the introduction, we have also extended our studies to oligomeric single and double strands of well-defined length [13]. An example is shown in Fig. 3, where... 

The vector should be linearized with a restriction enzyme before the transcription reaction m order to obtain transcripts of a defined length. Using intact plasmid DNA as template for transcription will result m heterogeneous transcripts of different sizes... 

U. Balucani and M. Zoppi, Dynamics of the Liquid State, Claredon, Oxford, 1994. Page 193, Table 5.1 for the value of the diffusion coefficient. Page 261, Table 6.1 for the viscosity value. Page 264, using the effective particle radius instead of the defined length scale a. 

Nucleic acid-based detection may be more specific and sensitive than immunological-based detection. Furthermore, the polymerase chain reaction (PCR) can be easily coupled to enhance the sensitivity of nucleic acid-based assays. Target nucleic segments of defined length... 

A 3D crystal has its atoms arranged such that many different planes can be drawn through them. It is convenient to be able to describe these planes in a systematic way and Fig. 4 shows how this is done. It illustrates a 2D example, but the same principle applies to the third dimension. The crystal lattice can be defined in terms of vectors a and b, which have a defined length and angle between them (it is c in the third dimension). The box defined by a and b (and c for 3D) is known as the unit cell. The dashed lines in Fig. 4A show one set of lines that can be drawn through the 2D lattice (they would be planes in 3D). It can be seen that these lines chop a into 1 piece and b into 1 piece, so these are called the 11 lines. The lines in B, however, chop a into 2 pieces, but still chop b into 1 piece, so these are the 21 lines. If the lines are parallel to an axis as in C, then they do not chop that axis into any pieces so, in C, the lines chopping a into 1 piece and which are parallel to b are the 10 lines. This is a simple rule. The numbers that are generated are known as the Miller indices of the plane. Note that if the structure in Fig. 6.4 was a 3D crystal viewed down the c axis, the lines would be planes. In these cases, the third Miller index would be zero (i.e., the planes would be the 110 planes in A, the 210 planes in B, and the 100... 

He also defines length, breadth and depth as follows. 

The 145.7 MHz proton noise decoupled 31p nmR spectra of the poly(dA-dT) duplex in 10 mM cacodylate buffer between 28° and 54°C are presented in Figure 9. A broad symmetrical unresolved resonance is observed at 28°C. By contrast, two resolved narrow resonances separated by 90.2 ppm have been observed for 150 base pair long (dA-dT)n (41). Thus, though the resolution of dT dA and dApdT phosphodiesters cannot be achieved at the synthetic DNA level in solution (18), it has been observed for the same sequence at a shorter well defined length (41). More recently, two resolved 31p resonances have also been reported in poly(dA-dT) fibers oriented parallel to the direction to the magnetic field by solid state 3lp nmr spectroscopy (42). 

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