Tables of the common logarithms and trigonometrical functions to six places of decimals.

"With an appendix containing a table of natural functions and circular measures of angles to each minute of arc to five places of decimals."

The functions of experimental participatory experiences in the learning-teaching process /

Mode of access: Internet.

The functions of societies and the evolution of group living: Spider societies as a test case

Many models have been advanced to suggest how different expressions of sociality have evolved and are maintained. However these models ignore the function of groups for the particular species in question. Here we present a new perspective on sociality where the function of the group takes a central role. We argue that sociality may have primarily a reproductive, protective, or foraging function, depending on whether it enhances the reproductive, protective or foraging aspect of the animal's life (sociality may serve a mixture of these functions). Different functions can potentially cause the development of the same social behaviour. By identifying which function influences a particular social behaviour we can determine how that social behaviour will change with changing conditions, and which models are most pertinent. To test our approach we examined spider sociality, which has often been seen as the poor cousin to insect sociality. By using our approach we found that the group characteristics of eusocial insects is largely governed by the reproductive function of their groups, while the group characteristics of social spiders is largely governed by the foraging function of the group. This means that models relevant to insects may not be relevant to spiders. It also explains why eusocial insects have developed a strict caste system while spider societies are more egalitarian. We also used our approach to explain the differences between different types of spider groups. For example, differences in the characteristics of colonial and kleptoparasitic groups can be explained by differences in foraging methods, while differences between colonial and cooperative spiders can be explained by the role of the reproductive function in the formation of cooperative spider groups. Although the interactions within cooperative spider colonies are largely those of a foraging society, demographic traits and colony dynamics are strongly influenced by the reproductive function. We argue that functional explanations help to understand the social structure of spider groups and therefore the evolutionary potential for speciation in social spiders.

Structure and regulation of type 2 transglutaminase in relation to its physiological functions and pathological roles

This chapter contains sections titled: Introduction Structure and Regulation Physiologic Functions of TG2 Disruption of TG2 Functions in Pathologic Conditions Perspectives for Pharmacologic Interventions Concluding Comments Acknowledgements References

Complete Systems of Hermite Associated Functions

It is proved that if the increasing sequence {kn} n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of C\R then the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

Applications of the Owa-Srivastava Operator to the Class of K-Uniformly Convex Functions

2000 Mathematics Subject Classification: Primary 30C45, 26A33; Secondary 33C15

Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function

AMS Subject Classification 2010: 11M26, 33C45, 42A38.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica

ACM Computing Classification System (1998): G.1.2.

On the Residuum of Concave Univalent Functions

2000 Mathematics Subject Classification: 30C25, 30C45.

Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions

2000 Mathematics Subject Classification: 47A10, 47A13.

The Deformed Trigonometric Functions of two Variables

MSC 2010: 33B10, 33E20

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

MSC 2010: 33E12, 30A10, 30D15, 30E15

Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

On the construction of new bent functions from the max-weight and min-weight functions of old bent functions

Given a bent function f (x) of n variables, its max-weight and min-weight functions are introduced as the Boolean functions f + (x) and f − (x) whose supports are the sets {a ∈ Fn2 | w( f ⊕la) = 2n−1+2 n 2 −1} and {a ∈ Fn2 | w( f ⊕la) = 2n−1−2 n 2 −1} respectively, where w( f ⊕ la) denotes the Hamming weight of the Boolean function f (x) ⊕ la(x) and la(x) is the linear function defined by a ∈ Fn2 . f + (x) and f − (x) are proved to be bent functions. Furthermore, combining the 4 minterms of 2 variables with the max-weight or min-weight functions of a 4-tuple ( f0(x), f1(x), f2(x), f3(x)) of bent functions of n variables such that f0(x) ⊕ f1(x) ⊕ f2(x) ⊕ f3(x) = 1, a bent function of n + 2 variables is obtained. A family of 4-tuples of bent functions satisfying the above condition is introduced, and finally, the number of bent functions we can construct using the method introduced in this paper are obtained. Also, our construction is compared with other constructions of bent functions.