6-Amino-9H-purine-1,7-diium bis­(4-methyl­benzene­sulfonate) monohydrate

The asymmetric unit of the title compound, C5H7N5 2+·2C7H7O3S−·H2O, consists of one diprotonated adeninium cation, two p-toluene­sulfonic acid anions and one water mol­ecule. In the crystal, the cations and anions are connected through N—H⋯O hydrogen bonds forming R 2 2(8) and R 2 2(9) graph-set motifs. The solvent water mol­ecule links cations and anions through O—H⋯O and N—H⋯O hydrogen bonds, generating a two-dimensional layer parallel to (10)

N-(2-Hydroxy­ethyl)-1,8-naphthalimide

In the mol­ecule of the title compound, C14H11NO3, the naphthalimide ring system is nearly planar (r.m.s. deviation 0.0139 Å). In the crystal structure, inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into centrosymmetric dimers forming R 2 2(14) ring motifs. π–π contacts between the naphthalimide rings [centroid–centroid distances = 3.648 (3), 3.783 (3), 3.635 (3), 3.722 (3) and 3.755 (3) Å] may further stabilize the structure

Categorification of a linear algebra identity and factorization of Serre functors

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre functor of a finite dimensional triangular algebra A has always a lift, up to shift, to a product of suitably defined reflection functors in the category of perfect complexes over the trivial extension algebra of A.Comment: 18 pages; Minor changes, references added, new Section 2.

4-Thioxo-3,5-dithia-1,7-hepta­nedioic acid

The complete molecule of the title compound, C5H6O4S3, is generated by crystallographic twofold symmetry with the C=S group lying on the rotation axis. The molecules are linked through weak hydrogen-bond contacts by glide-plane operations to form R 2 2(20) rings and ladder-like C(4) chains along the c axis

Octa­aqua­bis(μ2-1H-pyrazole-3,5-di­carboxyl­ato)tricopper(II) tetra­hydrate

In the trinucler CuII complex mol­ecule of the title compound, [Cu3(C5HN2O4)2(H2O)8]·4H2O, the central CuII atom is located on an inversion centre and is coordinated in a distorted octa­hedral geometry. The equatorial sites are occupied by two N and two O atoms from two pyrazole-3,5-dicarboxyl­ate ligands and the axial positions are occupied by two water mol­ecules. The two other symmetry-related CuII atoms are penta­coordinated and assume a square-pyramidal geometry. In the crystal structure, coordinated and uncoordinated water mol­ecules and carboxyl­ate O atoms are linked by O—H⋯O hydrogen bonds

Convolution-type derivatives, hitting-times of subordinators and time-changed C0C_0-semigroups

In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators similar to the fractional derivatives. Furthermore we will discuss the concept of time-changed $C_0$-semigroup in case the time-change is performed by means of the hitting-time of a subordinator. We will show that such time-change give rise to bounded linear operators not preserving the semigroup property and we will present their governing equations by using again integro-differential operators. Such operators are non-local and therefore we will investigate the presence of long-range dependence.Comment: Final version, Potential analysis, 201

(7R,8S,9S,12S)-1-Benz­yloxy-13,14-didehydro-12-hy­droxy-2,13-dimeth­oxy-N-methyl­morphinane

In the title compound, C26H31NO4, a sinomenine derivative, the angle between the two aromatic rings is 53.34 (4)°. The N-containing ring is in a chair conformation, while the other two non-planar rings are in a half-boat conformation. In the crystal, mol­ecules are linked by O—H⋯N inter­actions into a C(8) chain along [100]

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice

Deducing the \u3csup\u3e237\u3c/sup\u3eU(\u3cem\u3en,f\u3c/em\u3e) Cross Section Using the Surrogate Ratio Method

We have deduced the cross section for 237U(n, f) over an equivalent neutron energy range from 0 to 20 MeV using the surrogate ratio method. A 55 MeV4He beam from the 88 inch cyclotron at Lawrence Berkeley National Laboratory was used to induce fission in the following reactions: 238U(α, αf) and 236U(α, αf). The 238U reaction was a surrogate for 237U(n, f), and the 236U reaction was used as a surrogate for 235U(n, f). Scattered α particles were detected in a fully depleted segmented silicon telescope array over an angle range of 35° to 60° with respect to the beam axis. The fission fragments were detected in a third independent silicon detector located at backward angles between 106° and 131°