Copper Based Shape Memory Alloy a Modern Opportunity to Change Classic Casting Dental Alloys

Gurau, Irena; Gurău, Gheorghe; Gurău, Carmela

doi:10.1002/9781118663547.ch123

Cited by 4 publications

(9 citation statements)

References 15 publications

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“…Indeed, parameterizing the Young diagram ∆ by the numbers m i which counts the number of lines of the same length i in the diagram (i.e., for instance, for ∆ = [4,2,2,1], m 1 = 1, m 2 = 2, m 3 = 0, and m 4 = 1) and taking into account that, in these terms, z ∆ = i:mi =0 i mi m i ! with the product over all i with non-zero m i , obtains…”

Section: The Problemmentioning

confidence: 99%

“…Tensor models [1] look superintegrable [3] and can be exactly solved [4,5] by combinatorial methods [5,6] just like their matrix model prototypes [7]. However, original presentations [5,6] rely too much on the theory of symmetric groups and therefore can not attract much attention from physicists, generically unfamiliar with this subject.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we start with the rectangular complex matrix model (RCM ) [13], which has a straightforward generalization to rainbow [4] tensor models [1]- [5], with well-studied Aristotelian (rank r = 3) model [3] as the first non-trivial example. Our goal is to pose the problem of how ( 1) is generalized to r > 2 and suggest a possible way to solve it.…”

Section: Introductionmentioning

confidence: 99%

“…Say, at level n = 2, allowed at the r.h.s. are only [1,1], [2] while the other four [1,1], [1,1] are forbidden. We introduced here an abbreviated notation…”

Section: Introductionmentioning

confidence: 99%

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Tensorial generalization of characters

Itoyama

Mironov

Морозов

2019

J. High Energ. Phys.

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In rainbow tensor models, which generalize rectangular complex matrix model (RCM) and possess a huge gauge symmetry U (N1) × . . . × U (Nr), we introduce a new sub-basis in the linear space of gauge invariant operators, which is a redundant basis in the space of operators with non-zero Gaussian averages. Its elements are labeled by r-tuples of Young diagrams of a given size equal to the power of tensor field. Their tensor model averages are just products of dimensions: χR 1 ,...,Rr ∼ CR 1 ,...,Rr DR 1 (N1) . . . DR r (Nr) of representations Ri of the linear group SL(Ni), with CR 1 ,...,Rr made of the Clebsch-Gordan coefficients of representations Ri of the symmetric group. Moreover, not only the averages, but the operators χ R themselves exist only when these C R are non-vanishing. This sub-basis is much similar to the basis of characters (Schur functions) in matrix models, which is distinguished by the property character ∼ character, which opens a way to lift the notion and the theory of characters (Schur functions) from matrices to tensors. In particular, operators χ R are eigenfunctions of operators which generalize the usual cut-and-join operatorsŴ ; they satisfy orthogonality conditions similar to the standard characters, but they do not form a full linear basis for all gauge-invariant operators, only for those which have non-vanishing Gaussian averages.

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Section: The Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Say, at level n = 2, allowed at the r.h.s. are only [1,1], [2] while the other four [1,1], [1,1] are forbidden. We introduced here an abbreviated notation…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tensorial generalization of characters

Itoyama

Mironov

Морозов

2019

J. High Energ. Phys.

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“…In this letter, we explain what happens in still another generalization: from matrices to tensors [13][14][15][16][17]. As explained in [18], in this case of Gaussian measure, there is a large kernel, still the rainbow tensor models [19] remain super-integrable in the sense that beyond the kernel one can still find an explicit basis with nicely factorized and explicitly calculable averages.…”

mentioning

confidence: 94%

Complete solution to Gaussian tensor model and its integrable properties

2020

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Similarly to the complex matrix model, the rainbow tensor models are superintegrable in the sense that arbitrary Gaussian correlators are explicitly expressed through the Clebsh-Gordan coefficients. We introduce associated (Ooguri-Vafa type) partition functions and describe their W -representations. We also discuss their integrability properties, which can be further improved by better adjusting the way the partition function is defined. This is a new avatar of the old unresolved problem with non-Abelian integrability concerning a clever choice of the partition function. This is a part of the long-standing problem to define a non-Abelian lift of integrability from the fundamental to generic representation families of arbitrary Lie algebras.

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Chitosan Containing Supported Ionic Liquid Phase Materials for CO₂ Absorption

Põhako‐Esko

Bahlmann

Schulz

et al. 2016

Ind. Eng. Chem. Res.

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Here we present novel CO2 sorbents based on chitosan ionogels. The powder sorbents called inverse supported ionic liquid phase (SILP) materials were prepared by dissolving chitosan in various ionic liquids (ILs) followed by encapsulation of the ionogel droplets with nanoporous fumed silica. CO2 absorption was determined at 40 °C in the range of 200 to 5500 mbar. At 1 bar, absorption capacities of these materials were 0.1–0.8 mol kg–1; at 5 bar, values of 0.2–1.5 mol kg–1 were reached. A comparison of inverse SILP materials with and without chitosan dissolved in the applied IL indicated that the presence of chitosan increased the CO2 absorption efficiency of the materials. The aim of the study was also to compare the CO2 absorption in pure chitosan and chitosan dissolved in ILs. It was found that dissolution increases the absorption capacity of chitosan about 10 times.

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Copper Based Shape Memory Alloy a Modern Opportunity to Change Classic Casting Dental Alloys

Cited by 4 publications

References 15 publications

Tensorial generalization of characters

Tensorial generalization of characters

Complete solution to Gaussian tensor model and its integrable properties

Chitosan Containing Supported Ionic Liquid Phase Materials for CO₂ Absorption

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Copper Based Shape Memory Alloy a Modern Opportunity to Change Classic Casting Dental Alloys

Cited by 4 publications

References 15 publications

Tensorial generalization of characters

Tensorial generalization of characters

Complete solution to Gaussian tensor model and its integrable properties

Chitosan Containing Supported Ionic Liquid Phase Materials for CO2 Absorption

Contact Info

Product

Resources

About

Chitosan Containing Supported Ionic Liquid Phase Materials for CO₂ Absorption