Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Kinetic Ising model: Some exact solutions

Exact expressions for the response functions of kinetic Ising models are reported. These results valid for magnetisation in one dimension are based on a general formalism that yield the earlier results of Glauber and Kimball as special cases.

X-Pro peptides. A theoretical study of the hydrogen bonded conformations of (alpha-aminoisobutyryl-L -prolyl)n sequences

Intramolecularly hydrogen bonded conformations of (Aib-Pro)n sequences have been analysed theoretically. Both 4-1 (C10 and 3-1 (C7 hydrogen bonded regular structures are shown to be stereochemically feasible. Conformational energies for the helical structures have been estimated using classical potential energy methods. Both C10 and C7 conformations have very similar energies. Pyrrolidine ring puckering has a pronounced effect on the energies, and only Cv-endo puckered Pro residues can be accommodated. The theoretical calculations using spectroscopic data suggest that the recently proposed novel 310 helical conformation for benzyloxycarbonyl(Aib-Pro)4-methyl ester is in solution, is indeed energetically and stereochemically favourable.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.

Exact, self-similar, time-dependent free surface flows under gravity

A class of exact, self-similar, time-dependent solutions describing free surface flows under gravity is found which extends the self-propagating class of solutions discovered earlier by Freeman (1972) to those which decay with time.

Exact analysis of simply supported rhombic plates under uniform pressure

The simply supported rhombic plate under transverse load has received extensive attention from elasticians, applied mathematicians and engineers. All known solutions are based on approximate procedures. Now, an exact solution in a fast converging explicit series form is derived for this problem, by applying Stevenson's tentative approach with complex variables. Numerical values for the central deflexion and moments are obtained for various corner angles. The present solution provides a basis for assessing the accuracy of approximate methods for analysing problems of skew plates or domains.

Conformation of the LL and LD hairpin bends with internal hydrogen bonds in proteins and peptides

The conformation of three linked peptide units having an internal 4 → 1 type of hydrogen bond has been studied in detail, and the low energy conformations are listed. These conformations all lead to the reversal of the chain direction, and may therefore be called as “hairpin bends” or “U-bends”. Since this bend can occur at the end of two chains hydrogen-bonded in the antiparallel β-conformation, it is also known as the “β-bend”. Two types of conformation are possible when the residues at the second and third Cα atoms are both of type L (the LL bend), while only one type is possible for the LD and the DL bend. The LL bend can also accommodate the sequences LG, GL, GG (G = glycine), while the LD bend can accommodate the sequences LG, GD and GG. The conformations for the sequences DD and DL are exact inverses (or mirror images) of those for the sequences LL and LD, respectively, and have dihedral angles (phi2, ψ2), (phi3, ψ3) of the same magnitudes, but of opposite signs as those for the former types, which are listed, along with the characteristics (length, angle and energy) of the hydrogen bonds. A comparison of the theoretical predictions with experimental data (from X-ray diffraction and NMR studies) on proteins and peptides, show reasonably good agreement. However, a systematic trend is observable in the experimental data, slightly deviating from theory, which indicates that some deformations occur in the shapes of the peptide units forming the bend, differing from that of the standard planar peptide unit.

X-Pro peptides. A theoretical study of the hydrogen bonded conformations of (a-aminoisobutyryl-L -prolyl)n sequences

Intramolecularly hydrogen bonded conformations of (Aib-Pro)n sequences have been analysed theoretically. Both 4�1 (C10 and 3�1 (C7 hydrogen bonded regular structures are shown to be stereochemically feasible. Conformational energies for the helical structures have been estimated using classical potential energy methods. Both C10 and C7 conformations have very similar energies. Pyrrolidine ring puckering has a pronounced effect on the energies, and only Cγ-endo puckered Pro residues can be accommodated. The theoretical calculations using spectroscopic data suggest that the recently proposed novel 310 helical conformation for benzyloxycarbonyl(Aib-Pro)4-methyl ester is in solution, is indeed energetically and stereochemically favourable.

Optical Barker sequences and self-orthogonal convolutional codes

The relation between optical Barker codes and self-orthogonal convolutional codes is pointed out. It is then used to update the results in earlier publication.

Multilevel aperiodic Huffman sequences

Certain sequences that have zero aperiodic autocorrelation except for zero and the maximum shifts are described. They are useful in radar pulse compression.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Comments on "Diffuse sound reflection by maximum length sequences"

Some improvements are suggested to Schroeder's scheme [J. Acoust. Soc. Am. 57, 149–150 (1975)] of achieving diffuse sound reflection in concert halls.Subject Classification

Immunological studies on nucleic-acids and their components .6. Antibodies specific to two deoxyribotrinucleotide sequences

Antibodies to the deoxyribotrinucleotides dpApTpA and dpApApT were prepared by injecting the bovine serum albumin conjugates of the respective haptens in rabbits. The specificities of the antibodies were determined by estimating the inhibition of the binding of the tritiated haptens to the immunoglobulins by various nonradioactive mono- and oligonucleotides, using nitrocellulose membrane binding assay. Anti-dpApTpA and anti-dpApApT antisera were found to contain antibodies which were highly specific to the respective hapten sequence.

Polypurine/polypyrimidine sequences as cis-acting transcriptional regulators

Genome sequence information has generated increasing evidence for the claim that repetitive DNA sequences present within and around genes could play a important role in the regulation of gene expression. Polypurine/polypyrimidine sequences [poly(Pu/Py)] have been observed in the vicinity of promoters and within the transcribed regions of many genes. To understand whether such sequences influence the level of gene expression, we constructed several prokaryotic and eukaryotic expression vectors incorporating poly(Pu/Py) repeats both within and upstream of a reporter gene, lacZ (encoding β-galactosidase), and studied its expression in vivo. We find that, in contrast to the situation in Escherichia coli, the presence of poly(Pu/Py) sequences within the gene does not significantly inhibit gene expression in mammalian cells. On the other hand, the presence of such sequences upstream of lacZ leads to a several-fold reduction of gene expression in mammalian cells. Similar down-regulation was observed when a structural cassette containing poly(Pu/Py) sequences upstream of lacZ was integrated into yeast chromosome V. Sequence analysis of the nine totally sequenced yeast chromosomes shows that a large number of such sequences occur upstream of ORFs. On the basis of our experimental results and DNA sequence analysis, we propose that these sequences can function as cis-acting transcriptional regulators.

Analysis of the amino acid sequences of plant Bowman-Birk inhibitors

Plant seeds contain a large number of protease inhibitors of animal, fungal, and bacterial origin. One of the well-studied families of these inhibitors is the Bowman-Birk family(BBI). The BBIs from dicotyledonous seeds are 8K, double-headed proteins. In contrast, the 8K inhibitors from monocotyledonous seeds are single headed. Monocots also have a 16K, double-headed inhibitor. We have determined the primary structure of a Bowman-Birk inhibitor from a dicot, horsegram, by sequential edman analysis of the intact protein and peptides derived from enzymatic and chemical cleavage. The 76-residue-long inhibitor is very similar to that ofMacrotyloma axillare. An analysis of this inhibitor along with 26 other Bowman-Birk inhibitor domains (MW 8K) available in the SWISSPROT databank revealed that the proteins from monocots and dicots belong to related but distinct families. Inhibitors from monocots show larger variation in sequence. Sequence comparison shows that a crucial disulphide which connects the amino and carboxy termini of the active site loop is lost in monocots. The loss of a reactive site in monocots seems to be correlated to this. However, it appears that this disulphide is not absolutely essential for retention of inhibitory function. Our analysis suggests that gene duplication leading to a 16K inhibitor in monocots has occurred, probably after the divergence of monocots and dicots, and also after the loss of second reactive site in monocots.