The sphynx's new riddle : how to relate the canonical formula of myth to quantum interaction

We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula

Comparison of stool microbiota compositions, stool alpha1-antitrypsin and calprotectin concentrations, and diarrhoeal morbidity of Indonesian infants fed breast milk or probiotic/prebiotic-supplemented formula

Aim The composition of faecal microbiota of babies is known to be influenced by diet. Faecal calprotectin and α1-antitrypsin concentrations may be associated with mucosal permeability and inflammation. We aimed to assess whether there was any difference after consumption of a probiotic/prebiotic formula on faecal microbiota composition, calprotectin and α1-antitrypsin levels, and diarrhoea in comparison with breast milk-fed Indonesian infants. Methods One hundred sixty infants, 2 to 6 weeks old, were recruited to the study. They were either breastfed or formula fed (80 per group). Faecal samples were collected at recruitment and 3 months later. Bacterial groups characteristic of the human faecal microbiota were quantified in faeces by quantitative polymerase chain reaction. Calprotectin and α1-antitrypsin concentrations were measured using commercial kits. Details of diarrhoeal morbidity were documented and rated for severity. Results The compositions of the faecal microbiota of formula-fed compared with breast milk-fed children were similar except that the probiotic strain Bifidobacterium animalis subsp. lactisâ€...DR10 was more abundant after 3 months consumption of the formula. Alpha1-antitrypsin levels were higher in breastfed compared with formula-fed infants. The occurrence of diarrhoea did not differ between the groups of babies. Conclusion Feeding Indonesian babies with a probiotic/prebiotic formula did not produce marked differences in the composition of the faecal microbiota in comparison with breast milk. Detrimental effects of formula feeding on biomarkers of mucosal health were not observed.

Global standard for the composition of infant formula: Recommendations of an ESPGHAN coordinated international expert group

The Codex Alimentarius Commission of the Food and Agriculture Organization of the United Nations (FAO) and the World Health Organization (WHO) develops food standards, guidelines and related texts for protecting consumer health and ensuring fair trade practices globally. The major part of the world's population lives in more than 160 countries that are members of the Codex Alimentarius. The Codex Standard on Infant Formula was adopted in 1981 based on scientific knowledge available in the 1970s and is currently being revised. As part of this process, the Codex Committee on Nutrition and Foods for Special Dietary Uses asked the ESPGHAN Committee on Nutrition to initiate a consultation process with the international scientific community to provide a proposal on nutrient levels in infant formulae, based on scientific analysis and taking into account existing scientific reports on the subject. ESPGHAN accepted the request and, in collaboration with its sister societies in the Federation of International Societies on Pediatric Gastroenterology, Hepatology and Nutrition, invited highly qualified experts in the area of infant nutrition to form an International Expert Group (IEG) to review the issues raised. The group arrived at recommendations on the compositional requirements for a global infant formula standard which are reported here.

Kac-Akhiezer formula for normal integral operators

The Kac-Akhiezer formula for finite section normal Wiener-Hopf integral operators is proved. This is an extension of the corresponding result for symmetric operator [2, 3, 4, 5, 6, 7].

Company taxation and tax spillovers: Separate accounting versus formula apportionment

It is observed in the real world that taxes matter for location decisions and that multinationals shift profits by transfer pricing. The US and Canada use so-called formula apportionment (FA) to tax corporate income, and the EU is debating a switch from separate accounting (SA) to FA. This paper develops a theoretical model that compares basic properties of FA to SA. The focal point of the analysis is how changes in tax rates affect capital formation, input choice, and transfer pricing, as well as on spillovers on tax revenue in other countries. The analysis shows that a move from SA to FA will not eliminate such spillovers and will, in cases identified in the paper, actually aggravate them.

Formula apportionment and transfer pricing under oligopolistic competition

This paper demonstrates that under conditions of imperfect (oligopolistic) competition, a transition from separate accounting (SA) to formula apportionment (FA) does not eliminate the problem of profit shifting via transfer pricing. In particular, if affiliates of a multinational firm face oligopolistic competition, it is beneficial for the multinational to manipulate transfer prices for tax–saving as well as strategic reasons under both FA and SA. The analysis shows that a switch from SA rules to FA rules may actually strengthen profit shifting activities by multinationals.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

An alternate form of the ramberg-osgood formula for matrix displacement analysis

A new stress-strain law, which is a three parameter representation of stress in terms of strain has been proposed for the matrix displacement analysis of structures made of non-hookean materials. This formula has been utilized to study three typical problems. These studies brought out the effectiveness and suitability of this law for matrix displacement analysis.

Investigations of superconducting bismuth cuprates of the general formula Bi2-xPbx(Ca,Sr,Y)n 1 Cun O2n 4 δ

In the (Bi,Pb)-Sr-Cu-O system we have examined many compositions which are either metallic or semiconducting. In the Bi2-xPbx(Ca, Sr)n+1 Cun O2n+4+δ system, we have established the superconducting properties of the n = 1 to 4 members. The Tc increases from n = 1 to 3 and does not increase further when n = 4. In Bi2Ca1-x,YxSr2Cu2Oy, the Tc decreases with increase in x.

On the unreasonable effectiveness of Gutzmer's formula

In this article we plan to demonstrate the usefulness of `Gutzmer's formula' in the study of various problems related to the Segal-Bargmann transform. Gutzmer's formula is known in several contexts: compact Lie groups, symmetric spaces of compact and noncompact type, Heisenberg groups and Hermite expansions. We apply Gutzmer's formula to study holomorphic Sobolev spaces, local Peter-Weyl theorems, Paley-Wiener theorems and Poisson semigroups.

A series of metallic oxides of the formula La3LnBaCu5O13+δ (Ln = rare earth or Y)

Oxides of the formula La3LnBaCu5O13+δ (Ln = Nd, Sm, Gd, Dy, or Y) exhibiting metallic resistivity have been prepared and characterized. In the case of yttrium, a composition close to La2Y2BaCu5O13+δ, which is also metallic, could be prepared.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

A formula for the solution of general Abel integral equation

A new formula for the solution of the general Abel Integral equation is derived, and an important special case is checked with the known result.