Arithmetic Algorithms in a Negative Base

Algorithms are described for the basic arithmetic operations and square rooting in a negative base. A new operation called polarization that reverses the sign of a number facilitates subtraction, using addition. Some special features of the negative-base arithmetic are also mentioned.

Simple Coding Scheme For Modular Arithmetic

A dual representation scheme for performing arithmetic modulo an arbitrary integer M is presented. The coding scheme maps each integer N in the range 0 <= N < M into one of two representations, each being identified by its most significant bit. The encoding of numbers is straightforward and the problem of checking for unused combinations is eliminated.

A new parallel algorithm for parsing arithmetic infix expressions

A new parallel algorithm for transforming an arithmetic infix expression into a par se tree is presented. The technique is based on a result due to Fischer (1980) which enables the construction of the parse tree, by appropriately scanning the vector of precedence values associated with the elements of the expression. The algorithm presented here is suitable for execution on a shared memory model of an SIMD machine with no read/write conflicts permitted. It uses O(n) processors and has a time complexity of O(log2n) where n is the expression length. Parallel algorithms for generating code for an SIMD machine are also presented.

The mean geometry of the peptide unit from crystal structure data

The average dimensions of the peptide unit have been obtained from the data reported in recent crystal structure analyses of di- and tripeptides. The bond lengths and bond angles agree with those in common use, except for the bond angle C---N---H, which is about 4° less than the accepted value, and the angle C2α---N---H which is about 4° more. The angle τ (Cα) has a mean value of 114° for glycyl residues and 110° for non-glycyl residues. Attention is directed to these mean values as observed in crystal structures, as they are relevant for model building of peptide chain structures.

The non-planar peptide unit II. Comparison of theory with crystal structure datastar, open

The theoretical results derived in Part I (Ramachandran, G.N., Lakshminarayan, A.V. and Kolaskar, A.S. (1973) Biochim. Biophys. Acta 303, 8–13) that the three bonds of the peptide unit meeting at N can have a pyramidal structure is confirmed by an analysis of 14 published crystal structures of small peptides. It is shown that the dihedral angles θN and Δω are correlated, while θC, is small and is uncorrelated with Δω, showing that the non-planar distortion at C′ is generally small.

The nonplanar peptide unit III. Quantum chemical calculations for related compounds and experimental X-ray diffraction data

The possible nonplanar distortions of the amide group in formamide, acetamide, N-methylacetamide, and N-ethylacetamide have been examined using CNDO/2 and INDO methods. The predictions from these methods are compared with the results obtained from X-ray and neutron diffraction studies on crystals of small open peptides, cyclic peptides, and amides. It is shown that the INDO results are in good agreement with observations, and that the dihedral angles N and defining the nonplanarity of the amide unit are correlated approximately by the relation N = -2, while C is small and uncorrelated with . The present study indicates that the nonplanar distortions at the nitrogen atom of the peptide unit may have to be taken into consideration, in addition to the variation in the dihedral angles (,), in working out polypeptide and protein structures.

[B4O9H2] Cyclic Borate Units as the Building Unit in a Family of Zinc Borate Structures

A solvothermal reaction of ZnO, boric acid (B(OH)(3)), and aliphatic airlines in a water-pyridine mixture gave four zinc borate phases of different dimensionalities: [Zn(B4O8H2)(C3H10N2)], I (one-dimensional); [Zn(B4O8H2)(C3H10N2)] H2O, II (two-dimensional); [Zn(B5O10H3)(C10H24N4)]center dot H2O, III (two-dimensional): and [Zn-2(B8O15H2)(C3H10N2)(2)], IV (three-dimensional). The structures are formed by the connectivity involving polyborate chains and layers with Zn2+ species. In all the compounds, the amine molecules act its file ligand binding either the same or different zn centers. The formation of two different structures, II and IV, from the same amine by varying the reaction time is noteworthy. Transformation studies on II indicate that the formation of IV. from II, is facile and has been investigated for the first time. Two of file compounds, I and III, exhibit activity for second-order nonlinear optical behavior. The UV exposure of the sample indicates the absorption of all the UV radiation suggesting that the zinc borate compounds could be exploited for UV-blocking applications. The compounds have been characterized by powder X-ray diffraction, infrared spectroscopy, thermogravimetric analysis, UV-vis, photoluminescence, and NMR studies.

Hydrothermal synthesis and structural characterization of novel alpha-Keggin unit-supported Cu(II)- and Mn(II)-bipyridine complexes from a tri-lacunary precursor

Blue [{Cu(2,2'-bipy)(2)}(2){alpha-SiW12O40}] (bipy = bipyridyl) (1) and pale yellow [Mn(2,2'-bipy)(3)](2)[alpha-SiW12O40] (2) have been synthesized hydrothermally and characterized by IR spectroscopy and single crystal X-ray structure analysis. In 1, the [alpha-SiW12O40](4-) ion acts as a bridge between the two [{Cu(2,2'-bipy)(2)](2+) moieties via coordination through the terminal oxygen atoms, while in 2, the [Mn(2,2'-bipy)(3)](2+) ion balances the charge on the polyoxo anion without forming any covalent bond. To the best of our knowledge, this is the first example of transition metal-mediated transformation of [alpha-SiW9O34](10-) to [alpha-SiW12O40](4-).

Hybrid algorithms for power system unit commitment

Four hybrid algorithms has been developed for the solution of the unit commitment problem. They use simulated annealing as one of the constituent techniques, and produce lower cost schedules; two of them have less overhead than other soft computing techniques. They are also more robust to the choice of parameters. A special technique avoids the generating of infeasible schedules, and thus reduces computation time.

Spectral analysis of noise in the neonatal intensive care unit

Objective To perform spectral analysis of noise generated by equipments and activities in a level III neonatal intensive care unit (NICU) and measure the real time sequential hourly noise levels over a 15 day period. Methods Noise generated in the NICU by individual equipments and activities were recorded with a digital spectral sound analyzer to perform spectral analysis over 0.5–8 KHz. Sequential hourly noise level measurements in all the rooms of the NICU were done for 15 days using a digital sound pressure level meter. Independent sample t test and one way ANOVA were used to examine the statistical significance of the results. The study has a 90% power to detect at least 4 dB differences from the recommended maximum of 50 dB with 95 % confidence. Results The mean noise levels in the ventilator room and stable room were 19.99 dB (A) sound pressure level (SPL) and 11.81 dB (A) SPL higher than the maximum recommended of 50 dB (A) respectively (p < 0.001). The equipments generated 19.11 dB SPL higher than the recommended norms in 1–8 KHz spectrum. The activities generated 21.49 dB SPL higher than the recommended norms in 1–8 KHz spectrum (p< 0.001). The ventilator and nebulisers produced excess noise of 8.5 dB SPL at the 0.5 KHz spectrum.Conclusion Noise level in the NICU is unacceptably high. Spectral analysis of equipment and activity noise have shown noise predominantly in the 1–8 KHz spectrum. These levels warrant immediate implementation of noise reduction protocols as a standard of care in the NICU.

Optimal auctions for multi-unit procurement with volume discount bids

Our attention, is focused on designing an optimal procurement mechanism which a buyer can use for procuring multiple units of a homogeneous item based on bids submitted by autonomous, rational, and intelligent suppliers. We design elegant optimal procurement mechanisms for two different situations. In the first situation, each supplier specifies the maximum quantity that can be supplied together with a per unit price. For this situation, we design an optimal mechanism S-OPT (Optimal with Simple bids). In the more generalized case, each supplier specifies discounts based on the volume of supply. In this case, we design an optimal mechanism VD-OPT (Optimal with Volume Discount, bids). The VD-OPT mechanism uses the S-OPT mechanism as a building block. The proposed mechanisms minimize the cost to the buyer, satisfying at the same time, (a) Bayesian, incentive compatibility and (b) interim individual rationality.

Computing a matrix symmetrizer exactly using modified multiple modulus residue arithmetic

A symmetric solution X satisfying the matrix equation XA = AtX is called a symmetrizer of the matrix A. A general algorithm to compute a matrix symmetrizer is obtained. A new multiple-modulus residue arithmetic called floating-point modular arithmetic is described and implemented on the algorithm to compute an error-free matrix symmetrizer.

The dimensions of the ester unit

The dimensions of the ester unit, which is a component of the depsipeptide unit has been obtained by analysing the data on crystal structures of compounds having the ester unit. The dimensions indicate that this unit is slightly different from the peptide unit both as far as the bond length and bond angles are concerned.

An integer arithmetic method to compute generalized matrix inverse and solve linear equations exactly

An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.