A statistical analysis of audience sound absorption (A)

The absorption produced by the audience in concert halls is considered a random variable. Beranek's proposal [L. L. Beranek, Music, Acoustics and Architecture (Wiley, New York, 1962), p. 543] that audience absorption is proportional to the area they occupy and not to their number is subjected to a statistical hypothesis test. A two variable linear regression model of the absorption with audience area and residual area as regressor variables is postulated for concert halls without added absorptive materials. Since Beranek's contention amounts to the statement that audience absorption is independent of the seating density, the test of the hypothesis lies in categorizing halls by seating density and examining for significant differences among slopes of regression planes of the different categories. Such a test shows that Beranek's hypothesis can be accepted. It is also shown that the audience area is a better predictor of the absorption than the audience number. The absorption coefficients and their 95% confidence limits are given for the audience and residual areas. A critique of the regression model is presented.

A formate bridged Ni(II) sheet and its 3D analogue in presence of a linear organic linker: Synthesis, crystal structure and magnetic properties

Reaction of formamide with Ni(NO3)(2)center dot 6H(2)O under hydrothermal condition in a mixture of MeOH/H2O forms a two-dimensional formate bridged sheet Ni(HCOO)(2)(MeOH)(2) (1). X-ray structure analysis reveals the conversion of formamide to formate which acts as a bridging ligand in complex 1 where the axial sites of Ni(II) are occupied by methanol used as a solvent. An analogous reaction in presence of 4,4'-bipyridyl (4,4'-bipy) yielded a three-dimensional structure Ni(HCOO)(2)(4,4'-bpy) (2). DC magnetic measurements as a function of temperature and field established the presence of spontaneous magnetization with T-c (Curie temperature) = 17 and 20.8 K in 1 and 2, respectively, which can be attributed due to spin-canting. DFT calculations were performed to corroborate the magnetic results of 1 and 2. (C) 2010 Elsevier Ltd. All rights reserved.

An optimal local approximation algorithm for max-min linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0 for nonnegative matrices A and C. We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.

Epoch extraction from linear prediction residual for identification of closed glottis interval

In voiced speech analysis epochal information is useful in accurate estimation of pitch periods and the frequency response of the vocal tract system. Ideally, linear prediction (LP) residual should give impulses at epochs. However, there are often ambiguities in the direct use of LP residual since samples of either polarity occur around epochs. Further, since the digital inverse filter does not compensate the phase response of the vocal tract system exactly, there is an uncertainty in the estimated epoch position. In this paper we present an interpretation of LP residual by considering the effect of the following factors: 1) the shape of glottal pulses, 2) inaccurate estimation of formants and bandwidths, 3) phase angles of formants at the instants of excitation, and 4) zeros in the vocal tract system. A method for the unambiguous identification of epochs from LP residual is then presented. The accuracy of the method is tested by comparing the results with the epochs obtained from the estimated glottal pulse shapes for several vowel segments. The method is used to identify the closed glottis interval for the estimation of the true frequency response of the vocal tract system.

Local approximability of max-min and min-max linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ΔI positive elements, and each row ck of C has at most ΔK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ΔI ≥ 2, ΔK ≥ 2, and ε > 0 there exists a local algorithm that achieves the approximation ratio ΔI (1 − 1/ΔK) + ε. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ΔI (1 − 1/ΔK) for any ΔI ≥ 2 and ΔK ≥ 2.

A new classification and linear sequence of extant gymnosperms

A new classification and linear sequence of the gymnosperms based on previous molecular and morphological phylogenetic and other studies is presented. Currently accepted genera are listed for each family and arranged according to their (probable) phylogenetic position. A full synonymy is provided, and types are listed for accepted genera. An index to genera assists in easy access to synonymy and family placement of genera.

A linear sequence of extant families and genera of lycophytes and ferns

Throughout the history of the classification of extant ferns (monilophytes) and lycophytes, familial and generic concepts have been in great flux. For the organisation of lycophytes and ferns in herbaria, books, checklists, indices and spore banks and on the internet, this poses a problem, and a standardized linear sequence of these plants is therefore in great need. We provide here a linear classification to the extant lycophytes and ferns based on current phylogenetic knowledge; this provides a standardized guide for organisation of fern collections into a more natural sequence. Two new families, Diplaziopsidaceae and Rhachidosoraceae, are here introduced.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

An efficient algorithm for linear programming

A simple but efficient algorithm is presented for linear programming. The algorithm computes the projection matrix exactly once throughout the computation unlike that of Karmarkar’s algorithm where in the projection matrix is computed at each and every iteration. The algorithm is best suitable to be implemented on a parallel architecture. Complexity of the algorithm is being studied.

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

A note on resolving infeasibility in linear programs by constraint relaxation

We study the problem of finding a set of constraints of minimum cardinality which when relaxed in an infeasible linear program, make it feasible. We show the problem is NP-hard even when the constraint matrix is totally unimodular and prove polynomial-time solvability when the constraint matrix and the right-hand-side together form a totally unimodular matrix.