Application of Maclaurin Series in Structural Analysis

In the simple theory of flexure of beams, the slope, bending moment, shearing force, load and other quantities are functions of a derivative of y with respect to x. It is shown that the elastic curve of a transversely loaded beam can be represented by the Maclaurin series. Substitution of the values of the derivatives gives a direct solution of beam problems. In this paper the method is applied to derive the Theorem or three moments and slope deflection equations. The method is extended to the solution of a rigid portal frame. Finally the method is applied to deduce results on which the moment distribution method of analyzing rigid frames is based.

WISENOM. A formal organic chemical nomenclature system

A formal chemical nomenclature system WISENOM based on a context-free grammar and graph coding is described. The system is unique, unambiguous, easily pronounceable, encodable, and decodable for organic compounds. Being a formal system, every name is provable as a theorem or derivable as a terminal sentence by using the basic axioms and rewrite rules. The syntax in Backus-Naur form, examples of name derivations, and the corresponding derivation trees are provided. Encoding procedures to convert connectivity tables to WISENOM, parsing, and decoding are described.

A computational algorithm for the verification of tautologies in propositional calculus

A computational algorithm (based on Smullyan's analytic tableau method) that varifies whether a given well-formed formula in propositional calculus is a tautology or not has been implemented on a DEC system 10. The stepwise refinement approch of program development used for this implementation forms the subject matter of this paper. The top-down design has resulted in a modular and reliable program package. This computational algoritlhm compares favourably with the algorithm based on the well-known resolution principle used in theorem provers.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Generalized pencils of rays in statistical wave optics

The recently introduced generalized pencil of Sudarshan which gives an exact ray picture of wave optics is analysed in some situations of interest to wave optics. A relationship between ray dispersion and statistical inhomogeneity of the field is obtained. A paraxial approximation which preserves the rectilinear propagation character of the generalized pencils is presented. Under this approximation the pencils can be computed directly from the field conditions on a plane, without the necessity to compute the cross-spectral density function in the entire space as an intermediate quantity. The paraxial results are illustrated with examples. The pencils are shown to exhibit an interesting scaling behaviour in the far-zone. This scaling leads to a natural generalization of the Fraunhofer range criterion and of the classical van Cittert-Zernike theorem to planar sources of arbitrary state of coherence. The recently derived results of radiometry with partially coherent sources are shown to be simple consequences of this scaling.

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem o limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (xi(gamma)) is determined. On account of interference, the magnitude of xi(gamma) is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.

On the Arrangement of Cliques in Chordal Graphs with respect to the Cuts

A cut (A, B) (where B = V - A) in a graph G = (V, E) is called internal if and only if there exists a vertex x in A that is not adjacent to any vertex in B and there exists a vertex y is an element of B such that it is not adjacent to any vertex in A. In this paper, we present a theorem regarding the arrangement of cliques in a chordal graph with respect to its internal cuts. Our main result is that given any internal cut (A, B) in a chordal graph G, there exists a clique with kappa(G) + vertices (where kappa(G) is the vertex connectivity of G) such that it is (approximately) bisected by the cut (A, B). In fact we give a stronger result: For any internal cut (A, B) of a chordal graph, and for each i, 0 <= i <= kappa(G) + 1 such that vertical bar K-i vertical bar = kappa(G) + 1, vertical bar A boolean AND K-i vertical bar = i and vertical bar B boolean AND K-i vertical bar = kappa(G) + 1 - i. An immediate corollary of the above result is that the number of edges in any internal cut (of a chordal graph) should be Omega(k(2)), where kappa(G) = k. Prompted by this observation, we investigate the size of internal cuts in terms of the vertex connectivity of the chordal graphs. As a corollary, we show that in chordal graphs, if the edge connectivity is strictly less than the minimum degree, then the size of the mincut is at least kappa(G)(kappa(G)+1)/2 where kappa(G) denotes the vertex connectivity. In contrast, in a general graph the size of the mincut can be equal to kappa(G). This result is tight.

Do elasmobranch reactions to magnetic fields in water show promise for bycatch mitigation?

Elasmobranchs are under increasing pressure from targeted fisheries worldwide, but unregulated bycatch is perhaps their greatest threat. This study tested five elasmobranch bycatch species (Sphyrna lewini, Carcharhinus tilstoni, Carcharhinus amblyrhynchos, Rhizoprionodon acutus, Glyphis glyphis) and one targeted teleost species (Lates calcarifer) to determine whether magnetic fields caused a reaction response and/or change in spatial use of an experimental arena. All elasmobranch species reacted to magnets at distances between 0.26 and 0.58 m at magnetic strengths between 25 and 234 gauss and avoided the area around the magnets. Contrastingly, the teleosts showed no reaction response and congregated around the magnets. The different reactions of the teleosts and elasmobranchs are presumably driven by the presence of ampullae of Lorenzini in the elasmobranchs; different reaction distances between elasmobranch species appeared to correlate with their feeding ecology. Elasmobranchs with a higher reliance on the electroreceptive sense to locate prey reacted to the magnets at the greatest distance, except G. glyphis. Notably, this is the only elasmobranch species tested with a fresh- and saltwater phase in their ecology, which may account for the decreased magnetic sensitivity. The application of magnets worldwide to mitigate the bycatch of elasmobranchs appears promising based on these results.

A Case of Simple Tool Use in Wild Liontailed Macaques (Macaca silenus)

Three members of a group of liontailed macaques (Macaea silenus) were seen to use leaves for food preparation. Other examples of prey-selection and hunting behaviour in liontailed macaques reflect individual- and group-specific skills. The absence of similar patterns in bonnet macaques (Macaca radiata) living in the same habitat might be related to differences in the social design and indicate the high significance of social aspects for the occurrence and manifestation of innovative behaviour.

Foldable compatibility matrix for the folding of programmable logic arrays

This paper describes a switching theoretic algorithm for the folding of programmable logic arrays (PLA). The algorithm is valid for both column and row folding, although it has been presented considering only the simple column folding. The pairwise compatibility relations among all the pairs of the columns of the PLA are mapped into a square matrix, called the compatibility matrix of the PLA. A foldable compatibility matrix (FCM), a new concept introduced by the author, is then derived from the compatibility matrix. A new theorem called the folding theorem is then proved. The theorem states that the existence of an m by 2m FCM is both necessary and sufficient to fold 2m columns of the n column PLA (2m ≤ n). Once an FCM is obtained, the ordered pairs of foldable columns and the re-ordering of the rows are readily determined.

Stresses around two equal circular elastic inclusions in a pressurised cylindrical shell

The stress problem of two equal circular elastic inclusions in a pressurised cylindrical shell has been solved by using single inclusion solutions together with Graf’s addition theorem. The effect of the inter-inclusion distance on the interface stresses in the shell as well as in the inclusion is studied. The results obtained for small values of curvature parameter fi @*=(a*/8Rt) [12(1-v*)]“*, a, R, t being inclusion radius and shell radius and thickness) when compared with the flat-plate results show good agreement. The results obtained in non-dimensional form are presented graphically.

New genetic loci link adipose and insulin biology to body fat distribution

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10−8). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms.

On the implication of the recently discovered 5 millisecond binary pulsar PSR 1855+09

e argue that the extraordinary fact that all three known millisecond pulsars are very close to the galactic plane implies that there must be ~100 potentially observable millisecond pulsars within ~4 kpc from the Sun. Our other main conclusion is that the dipole magnetic fields or old neutron stars probably saturate around 5 x 108 gauss.

Improvement On Brooks Chromatic Bound For A Class Of Graphs

Brooks' Theorem says that if for a graph G,Δ(G)=n, then G is n-colourable, unless (1) n=2 and G has an odd cycle as a component, or (2) n>2 and Kn+1 is a component of G. In this paper we prove that if a graph G has none of some three graphs (K1,3;K5−e and H) as an induced subgraph and if Δ(G)greater-or-equal, slanted6 and d(G)<Δ(G), then χ(G)<Δ(G). Also we give examples to show that the hypothesis Δ(G)greater-or-equal, slanted6 can not be non-trivially relaxed and the graph K5−e can not be removed from the hypothesis. Moreover, for a graph G with none of K1,3;K5−e and H as an induced subgraph, we verify Borodin and Kostochka's conjecture that if for a graph G,Δ(G)greater-or-equal, slanted9 and d(G)<Δ(G), then χ(G)<Δ(G).

Marker selection by Akaike information criterion and Bayesian information criterion

We carried out a discriminant analysis with identity by descent (IBD) at each marker as inputs, and the sib pair type (affected-affected versus affected-unaffected) as the output. Using simple logistic regression for this discriminant analysis, we illustrate the importance of comparing models with different number of parameters. Such model comparisons are best carried out using either the Akaike information criterion (AIC) or the Bayesian information criterion (BIC). When AIC (or BIC) stepwise variable selection was applied to the German Asthma data set, a group of markers were selected which provide the best fit to the data (assuming an additive effect). Interestingly, these 25-26 markers were not identical to those with the highest (in magnitude) single-locus lod scores.