An Algorithm to Decide Feasibility of Linear Integer Constraints Occurrng in Decision Tables

Abstract-To detect errors in decision tables one needs to decide whether a given set of constraints is feasible or not. This paper describes an algorithm to do so when the constraints are linear in variables that take only integer values. Decision tables with such constraints occur frequently in business data processing and in nonnumeric applications. The aim of the algorithm is to exploit. the abundance of very simple constraints that occur in typical decision table contexts. Essentially, the algorithm is a backtrack procedure where the the solution space is pruned by using the set of simple constrains. After some simplications, the simple constraints are captured in an acyclic directed graph with weighted edges. Further, only those partial vectors are considered from extension which can be extended to assignments that will at least satisfy the simple constraints. This is how pruning of the solution space is achieved. For every partial assignment considered, the graph representation of the simple constraints provides a lower bound for each variable which is not yet assigned a value. These lower bounds play a vital role in the algorithm and they are obtained in an efficient manner by updating older lower bounds. Our present algorithm also incorporates an idea by which it can be checked whether or not an (m - 2)-ary vector can be extended to a solution vector of m components, thereby backtracking is reduced by one component.

Non-linear flapping vibrations of rotating blades

The non-linear equations of motion of a rotating blade undergoing extensional and flapwise bending vibration are derived, including non-linearities up to O (ε3). The strain-displacement relationship derived is compared with expressions derived by earlier investigators and the errors and the approximations made in some of those are brought out. The equations of motion are solved under the inextensionality condition to obtain the influence of the amplitude on the fundamental flapwise natural frequency of the rotating blade. It is found that large finite amplitudes have a softening effect on the flapwise frequency and that this influence becomes stronger at higher speeds of rotation.

On the direct parallel solution of systems of linear equations: New algorithms and systolic structures

The paper presents two new algorithms for the direct parallel solution of systems of linear equations. The algorithms employ a novel recursive doubling technique to obtain solutions to an nth-order system in n steps with no more than 2n(n −1) processors. Comparing their performance with the Gaussian elimination algorithm (GE), we show that they are almost 100% faster than the latter. This speedup is achieved by dispensing with all the computation involved in the back-substitution phase of GE. It is also shown that the new algorithms exhibit error characteristics which are superior to GE. An n(n + 1) systolic array structure is proposed for the implementation of the new algorithms. We show that complete solutions can be obtained, through these single-phase solution methods, in 5n−log2n−4 computational steps, without the need for intermediate I/O operations.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

A non-linear analogue-to-digital converter for linearization of transducer input-output relationships

Analogue and digital techniques for linearization of non-linear input-output relationship of transducers are briefly reviewed. The condition required for linearizing a non-linear function y = f(x) using a non-linear analogue-to-digital converter, is explained. A simple technique to construct a non-linear digital-to-analogue converter, based on ' segments of equal digital interval ' is described. The technique was used to build an N-DAC which can be employed in a successive approximation or counter-ramp type ADC to linearize the non-linear transfer function of a thermistor-resistor combination. The possibility of achieving an order of magnitude higher accuracy in the measurement of temperature is shown.

Image reconstruction with laterally truncated projections in helical cone-beam CT: Linear prediction based projection completion techniques

Lateral or transaxial truncation of cone-beam data can occur either due to the field of view limitation of the scanning apparatus or iregion-of-interest tomography. In this paper, we Suggest two new methods to handle lateral truncation in helical scan CT. It is seen that reconstruction with laterally truncated projection data, assuming it to be complete, gives severe artifacts which even penetrates into the field of view. A row-by-row data completion approach using linear prediction is introduced for helical scan truncated data. An extension of this technique known as windowed linear prediction approach is introduced. Efficacy of the two techniques are shown using simulation with standard phantoms. A quantitative image quality measure of the resulting reconstructed images are used to evaluate the performance of the proposed methods against an extension of a standard existing technique.

Systematic Construction of Linear Transform Based Full-Diversity, Rate-One Space-Time Frequency Codes

In this paper, we generalize the existing rate-one space frequency (SF) and space-time frequency (STF) code constructions. The objective of this exercise is to provide a systematic design of full-diversity STF codes with high coding gain. Under this generalization, STF codes are formulated as linear transformations of data. Conditions on these linear transforms are then derived so that the resulting STF codes achieve full diversity and high coding gain with a moderate decoding complexity. Many of these conditions involve channel parameters like delay profile (DP) and temporal correlation. When these quantities are not available at the transmitter, design of codes that exploit full diversity on channels with arbitrary DIP and temporal correlation is considered. Complete characterization of a class of such robust codes is provided and their bit error rate (BER) performance is evaluated. On the other hand, when channel DIP and temporal correlation are available at the transmitter, linear transforms are optimized to maximize the coding gain of full-diversity STF codes. BER performance of such optimized codes is shown to be better than those of existing codes.

Linear time geometrical design rule checker based on quadtree representation of VLSI mask layouts

An efficient geometrical design rule checker is proposed, based on operations on quadtrees, which represent VLSI mask layouts. The time complexity of the design rule checker is O(N), where N is the number of polygons in the mask. A pseudoPascal description is provided of all the important algorithms for geometrical design rule verification.

New initiators for the ring-opening thermal polymerization of hexachlorocyclotriphosphazene: synthesis of linear poly(dichlorophosphazene) in high yields

Ring-opening thermal polymerization of hexachlorocyclotriphosphazene (N3P3C&h)a s been investigated at 250 "C and at 1.333-Pa pressure using chlorocyclotriphosphazenes N3P3C15(N=PPh3) and N3P3Cl,.,(NMe2), (n = 2-4), salt hydrates, triphenylphosphine, and benzoic acid as initiators. The linear poly (dich1orophosphazene) products are phenoxylated, and the phenoxy polymers are characterized by gel permeation chromatography and dilute solution viscometry. Among the various initiators investigated, CaS04.2H20b rings about a high conversion (>60%) of N3P3C&to the linear [NPC12], polymer which possesses a high molecular weight (>5 X lo6). The rationale for the choice of the initiators and possible mechanism(s) of polymerization is discussed. Several mixed substituent polymers, [NP(OPh),(OC6H4Me-p)2,1, and [NP(OPh),(OCHzCF3)2,]nh, ave been prepared and their thermal properties evaluated.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

A new algorithm for parallel solution of linear equations

Abstract is not available.

Representation of functional dependencies in relational databases using linear graphs

Functional dependencies in relational databases are investigated. Eight binary relations, viz., (1) dependency relation, (2) equipotence relation, (3) dissidence relation, (4) completion relation, and dual relations of each of them are described. Any one of these eight relations can be used to represent the functional dependencies in a database. Results from linear graph theory are found helpful in obtaining these representations. The dependency relation directly gives the functional dependencies. The equipotence relation specifies the dependencies in terms of attribute sets which functionally determine each other. The dissidence relation specifies the dependencies in terms of saturated sets in a very indirect way. Completion relation represents the functional dependencies as a function, the range of which turns out to be a lattice. Depletion relation which is the dual of the completion relation can also represent functional dependencies and similarly can the duals of dependency, equipotence, and dissidence relations. The class of depleted sets, which is the dual of saturated sets, is defined and used in the study of depletion relations.

Comment: Eigenvalue sensitivity method for optimal stabilisation of linear systems

In a letter RauA proposed a new method for designing statefeedback controllers using eigenvalue sensitivity matrices. However, there appears to be a conceptual mistake in the procedure, or else it is unduly restricted in its applicability. In particular the equation — BR~lBTK = A/.I, in which K is a positive-definite symmetric matrix.

Non-linear dynamic analysis of rotors by finite element method

Non-linear natural vibration characteristics and the dynamic response of hingeless and fully articulated rotors of rectangular cross-section are studied by using the finite element method. In the formulation of response problems, the global variables are augmented with appropriate additional variables, facilitating direct determination of sub-harmonic response. Numerical results are given showing the effect of the geometric non-linearity on the first three natural frequencies. Response analysis of typical rotors indicates a possibility of substantial sub-harmonic response especially in the fully articulated rotors widely adopted in helicopters.

A simple, wide-range, linear thermistor-based temperature indicator

A novel thermistor-based temperature indicator using an RC oscillator and an up/down counter has been developed and described. The indicator provides linear performance over a wide dynamic temperature range of 0-100°C. This indicator is free from the error due to lead resistances of the thermistor and gives a maximum error of ±0 · 1°C in the range 0-100°C. Test results are given to support the theory.