Matrix analysis for associated consistency in cooperative game theory

Hamiache axiomatized the Shapley value as the unique solution verifying the inessential game property, continuity and associated consistency. Driessen extended Hamiache’s axiomatization to the enlarged class of efficient, symmetric, and linear values. In this paper, we introduce the notion of row (resp. column)-coalitional matrix in the framework of cooperative game theory. The Shapley value as well as the associated game are represented algebraically by their coalitional matrices called the Shapley standard matrix M^Sh and the associated transformation matrix M_λ, respectively. We develop a matrix approach for Hamiache’s axiomatization of the Shapley value. The associated consistency for the Shapley value is formulated as the matrix equality M^Sh = M^Sh · M_λ. The diagonalization procedure of M_λ and the inessential property for coalitional matrices are fundamental tools to prove the convergence of the sequence of repeated associated games as well as its limit game to be inessential. In addition, a similar matrix approach is applicable to study Driessen’s axiomatization of a certain class of linear values. In summary, it is illustrated that matrix analysis is a new and powerful technique for research in the field of cooperative game theory.     

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Solvent induced enhancement of nonlinear optical response of graphdiyne

Flat and crystalline materials with exceptional nonlinear optical(NLO) properties are highly desirable for their potential applications in integrated NLO photonic devices.Graphdiyne(GD),a new twodimensional(2 D) carbon allotrope,has recently evoked burgeoning research attention by virtue of its tunable bandgap along with a high carrier mobility and extended π-conjugation compared with most conventional optical materials.Here,we experimentally probe the third-order nonlinear optical response of GD dispersed in several common solvents(alcohols) using a femtosecond Z-scan technique.The measured nonlinear optical refractive index is in the order of ~10^-8 cm²/W,which is approximately one order of magnitude higher than that of most 2 D materials.In particular,we find that different NLO responses can be observed from GD when dispersed in different solvents,with the strongest NLO response when dispersed in 1-propanol.It is proposed that some intrinsic properties of the solvents,such as the polarity and viscosity,could influence the NLO response of GD materials.Our experimental results confirm the assumptions on the NLO behavior in GD and demonstrate its great potential for future generations of Kerr-effect-based NLO materials and devices.     

E-Beam—a new transfer system for isolator technology

In every aseptic filling application, the sterile transfer of goods into the aseptic area is a challenge, and there are many different ways to do it.

With isolator technology a higher sterility assurance level (SAL) is achieved. This SAL is only as good as the weakest segment in the chain of manufacturing. The transfer of goods into and out of the isolator is one of these critical segments.

Today different techniques, some already well established, others still very new, are available on the market like: dry heat tunnel, autoclave, pulsed light, rapid transfer systems (RTP), H₂O₂ tunnel, UV light, etc. all these systems are either not applicable for continuous transfer, only good for heat-compatible materials like glass, or do not guarantee a 6 log spore reduction.

E-Beam opens new perspectives in this field. With E-beam technology it is possible to transfer heat-sensitive (plastic), pre-sterilised materials at high speed, continuously into an aseptic area.

E-Beam unifies three different technologies, that result in a very efficient and high-speed decontamination machine designed for the pharmaceutical industry. First, there is the electron beam that decontaminates the goods and an accurate shielding that protects the surrounding from this beam. Second, there is the conveyor system that guarantees the output and the correct exposure time underneath the beam. And third, there is the isolator interface to provide correct differential pressure and clean air inside the tunnel as well as the decontamination of the tunnel with H₂O₂ prior to production.

The E-beam is a low-energy electron beam, capable of decontaminating any kind of surface. It penetrates only a few micrometers into the material and therefore does not deform the packaging media.

Currently, machines are being built to transfer pre-sterilised syringes, packed in plastic tubs with a Tyvek cover into an aseptic filling isolator with the following data: decontamination efficiency of 10⁶ (6 log spore reduction), decontamination speed of 6 tubs (600 syringes) per minute.

This is just one of many applications for this new technology.     

Depletion-flocculation in oil-in-water emulsions using fibrillar protein assemblies

This paper shows that low concentrations of beta-lactoglobulin fibrils can induce depletion-flocculation in beta-lactoglobulin-stabilized oil-in-water emulsions. The minimum required fibril concentration for flocculation was determined experimentally for fibril lengths of about 3 and 0.1 microm. The minimum fibril concentration for flocculation is two orders of magnitude higher for the short fibrils than for the long ones. These experimental results correspond well with a theoretical prediction based on a model of spinodal decomposition. In addition, rheological measurements were performed, verifying that flocculation was induced by a depletion mechanism. The results of this study show that the minimum concentration required for depletion-flocculation can be tuned by varying the length of the fibrils.     

On the “Tertiary Structure” of Poly‐Carbenes; Self‐Assembly of sp3‐Carbon‐Based Polymers into Liquid‐Crystalline Aggregates

The self‐assembly of poly(ethylidene acetate) (st‐PEA) into van der Waals‐stabilized liquid‐crystalline (LC) aggregates is reported. The LC behavior of these materials is unexpected, and unusual for flexible sp³‐carbon backbone polymers. Although the dense packing of polar ester functionalities along the carbon backbone of st‐PEA could perhaps be expected to lead directly to rigid‐rod behavior, molecular modeling reveals that individual st‐PEA chains are actually highly flexible and should not reveal rigid‐rod induced LC behavior. Nonetheless, st‐PEA clearly reveals LC behavior, both in solution and in the melt over a broad elevated temperature range. A combined set of experimental measurements, supported by MM/MD studies, suggests that the observed LC behavior is due to self‐aggregation of st‐PEA into higher‐order aggregates. According to MM/MD modeling st‐PEA single helices adopt a flexible helical structure with a preferred trans‐gauche syn‐syn‐anti‐anti orientation. Unexpectedly, similar modeling experiments suggest that three of these helices can self‐assemble into triple‐helical aggregates. Higher‐order assemblies were not observed in the MM/MD simulations, suggesting that the triple helix is the most stable aggregate configuration. DLS data confirmed the aggregation of st‐PEA into higher‐order structures, and suggest the formation of rod‐like particles. The dimensions derived from these light‐scattering experiments correspond with st‐PEA triple‐helix formation. Langmuir–Blodgett surface pressure–area isotherms also point to the formation of rod‐like st‐PEA aggregates with similar dimensions as st‐PEA triple helixes. Upon increasing the st‐PEA concentration, the viscosity of the polymer solution increases strongly, and at concentrations above 20 wt % st‐PEA forms an organogel. STM on this gel reveals the formation of helical aggregates on the graphite surface–solution interface with shapes and dimensions matching st‐PEA triple helices, in good agreement with the structures proposed by molecular modeling. X‐ray diffraction, WAXS, SAXS and solid state NMR spectroscopy studies suggest that st‐PEA triple helices are also present in the solid state, up to temperatures well above the melting point of st‐PEA. Formation of higher‐order aggregates explains the observed LC behavior of st‐PEA, emphasizing the importance of the “tertiary structure” of synthetic polymers on their material properties.     

Exact categories

We survey the basics of homological algebra in exact categories in the sense of Quillen. All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3×3$3\times 3$-lemma and the snake lemma. We briefly discuss exact functors, idempotent completion and weak idempotent completeness. We then show that it is possible to construct the derived category of an exact category without any embedding into abelian categories and we sketch Deligne's approach to derived functors. The construction of classical derived functors with values in an abelian category painlessly translates to exact categories, i.e., we give proofs of the comparison theorem for projective resolutions and the horseshoe lemma. After discussing some examples we elaborate on Thomason's proof of the Gabriel–Quillen embedding theorem in an appendix.