Inhomogeneous Group Research Articles

Age and weak indivisibility

A relational structure H is homogeneous if every isomorphism between finite induced substructures has an extension to an automorphism of H.A relational structure R is indivisible if for every partition (A,B) of the set of elements of R, there is a copy of R in A or in B. The structure R is weakly indivisible if for every partition (A,B) of the set of elements of R for which some finite induced substructure of R does not have a copy in A, there exists a copy of R in B. The structure R is age indivisible if for every partition (A,B) of the elements of R every finite induced substructure of R has an embedding into A or every finite induced substructure of R has an embedding into B. It follows that indivisibility implies weak indivisibility which in turn implies age indivisibility. There are many examples of countable infinite homogeneous structures which are weakly indivisible but not indivisible; see Sauer (2000) [17] and the end of Section 3.1 of this paper.In general, it is difficult to find structures which are age indivisible but not weakly indivisible. One such example (see Pouzet et al. (2011) [16]) is obtained via the inhomogeneous general linear group of vector spaces over finite fields. Finding such an example for homogeneous structures seems to be even more difficult. The only one that I obtained, together with L. Nguyen Van Thé, is a countable homogeneous metric subspace of the Hilbert sphere ℓ2 (see Nguyen Van Thé and Sauer (2010) [13]). Both of the examples above are relational structures with infinitely many relations. One of the still open questions then is: Are there countable infinite homogeneous structures with finite signature which are age but not weakly indivisible? We will show that the generic “free amalgamation” homogeneous structures are weakly indivisible; see Section 3.1.Countable “Urysohn metric spaces” (see the next section), with finite distance sets, are indivisible (see Sauer (2013) [19]). Countable Urysohn metric spaces are age indivisible, which follows from the Hales–Jewett theorem (Hales and Jewett (1963) [7]; see Delhommé et al. (2007) [2]). For non-Urysohn homogeneous countable metric spaces, except for the example mentioned above, the weak indivisibility question is completely open. We will show, in this paper, that a countable homogeneous ultrametric space is age indivisible if and only if it is weakly indivisible.

Diagnostic tools in neurodegenerative disorders of adult-elderly

Neurodegenerative disorders are an inhomogeneous group of neurological diseases that affect a large part of the population because of the rise in life expectancy. Although clinical manifestations are important to make the correct diagnosis, the new advanced imaging technique represent a very useful tool for the diagnostic work-up.

Relativistic Chasles' theorem and the conjugacy classes of the inhomogeneous Lorentz group

This work is devoted to the relativistic generalization of Chasles' theorem, namely, to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the frame displacement of an observer which moves with constant acceleration and constant angular velocity. The acceleration and angular velocity can be chosen either aligned or perpendicular, and in the latter case the angular velocity can be chosen equal or smaller than the acceleration. We start reviewing the classical Euler's and Chasles' theorems both in the Lie algebra and group versions. We recall the relativistic generalization of Euler's theorem and observe that every (infinitesimal) transformation can be recovered from information of algebraic and geometric type, the former being identified with the conjugacy class and the latter with some additional geometric ingredients (the screw axis in the usual non-relativistic version). Then the proper orthochronous inhomogeneous Lorentz Lie group is studied in detail. We prove its exponentiality and identify a causal semigroup and the corresponding Lie cone. Through the identification of new Ad-invariants we classify the conjugacy classes, and show that those which admit a causal representative have special physical significance. These results imply a classification of the inequivalent Killing vector fields of Minkowski spacetime which we express through simple representatives. Finally, we arrive at the mentioned generalization of Chasles' theorem.

Pulsations driven by theɛ-mechanism in post-merger remnants: First results

Helium-rich subdwarfs are a rare subclass of hot subdwarf stars which constitute a small and inhomogeneous group showing varying degrees of helium enrichment. Only one star, LS IV °14 116 has been found to show multiperiodic luminosity variations. The variability of LS IV °14 116 has been explained as the consequence of nonradial g-mode oscillations, whose excitation is difficult to understand within the frame of the standard κ-mechanism driving pulsations in sdBV stars. In a recent study, we have proposed that the pulsations of LS IV °14 116 might be driven through the ɛ-mechanism acting in unstable He-burning zones in the interior of the star, that appear before the quiescent He-burning phase. One of the few accepted scenarios for the formation of He-rich subdwarfs is the merger of two He-core white dwarfs. As part of this project, we present a study of the ɛ-mechanism in post-merger remnants, and discuss the results in the light of the pulsations exhibited by LS IV °14 116.

A multi-field two-fluid concept for transitions between different scales of interfacial structures

This paper presents a concept for the CFD-modelling of multiphase flows where both segregated and dispersed flow structures occur simultaneously. Transitions between such morphologies, characterized by different scales of interfacial structures, are investigated and a new multi-field two-fluid strategy for a generalized two-phase flow (GENTOP) is presented. The GENTOP-approach extends the inhomogeneous Multiple Size Group (MUSIG)-model by adding an additional continuous gas phase. Within the MUSIG-framework, mass transfers between different bubble size groups due to coalescence and breakup as well as gas–liquid transfers are described. By modelling an additional mass transfer between the polydispersed and continuous gas phase, transitions between the different gas morphologies can be considered dependent on the flow situation. The continuous gas phase summarizes gas structures which are large enough to be resolved within the computed mesh. Therefore a free surface detection and generalized formulations for interfacial transfer models are introduced. The appearance of one particular gas phase due to mass transfer from another gaseous morphology is demonstrated by means of two demonstration cases: the impingement of a liquid jet on a free surface with an associated entrainment of dispersed bubbles as well as an evolving vertical bubble column showing a wide spectrum of bubble sizes.

Relativistic implications of the quantum phase

The quantum phase leads to projective representations of symmetry groups in quantum mechanics. The projective representations are equivalent to the unitary representations of the central extension of the group. A celebrated example is Wigner's formulation of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group. However, Wigner's formulation makes no mention of the Weyl-Heisenberg group and the hermitian representation of its algebra that are the Heisenberg commutation relations fundamental to quantum physics.We put aside the relativistic symmetry and show that the maximal quantum symmetry that leaves the Heisenberg commutation relations invariant is the projective representations of the conformally scaled inhomogeneous symplectic group. The Weyl-Heisenberg group and noncommutative structure arises directly because the quantum phase requires projective representations.We then consider the relativistic implications of the quantum phase that lead to the Born line element and the projective representations of an inhomogeneous unitary group that defines a noninertial quantum theory. (Understanding noninertial quantum mechanics is a prelude to understanding quantum gravity.) The remarkable properties of this symmetry and its limits are studied.

Inhomogeneous Quantum Invariance Group of Multi-Dimensional Multi-parameter Deformed Boson Algebra

We investigate the inhomogeneous invariance quantum group of the d-dimensional d-parameter deformed boson algebra. It is found that the homogeneous part of this quantum group is given by the d-parameter deformed general linear group. We construct the R-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case.

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The current paper presents the prediction results of a bubbly flow under plunging jet conditions using multiphase mono- and poly-dispersed approaches. The models consider interfacial momentum transfer terms arising from drag, lift, and turbulent dispersion force for the different bubble sizes. The turbulence is modeled by an extended k–ɛ model which accounts for bubble induced turbulence. Furthermore in case of a poly-dispersed air–water flow the bubble size distribution, bubble break-up and coalescence processes as well as different gas velocities in dependency on the bubble diameter are taken into account using the Inhomogeneous MUSIG model. This model is a generalized inhomogeneous multiple size group model based on the Eulerian modeling framework which was developed in the framework of a cooperative work between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf (FZD). The latter is now implemented into the CFD code CFX.According to the correlation on the lateral lift force obtained by Tomiyama (1998); this force changes its sign in dependence on the bubble size. Consequently the entrained small bubbles are trapped below the jet. They can escape from the bubble plume only by turbulent fluctuations or by coalescence. If the size of the bubbles generated by coalescence exceeds the size at which the lift force changes its sign these large bubbles go out from the plume and rise to the surface.A turbulent model based on an additional source term for turbulence kinetic energy and turbulence eddy dissipation equation is compared to the common concept for modeling the turbulence quantities proposed by Sato et al. (1981). It has been found that the large bubble distribution is slightly affected by the turbulence modeling which affects particularly the bubble coalescence and break-up process.

Functional nasolacrimal duct obstruction – a nonexistent condition? Concepts in lacrimal dynamics and a practical course of treatment

The term functional nasolacrimal duct obstruction (FNLDO; watering with patent drainage) is misleading as it implies occluded drainage and solely nasolacrimal duct pathology. ‘Normal’ tear dynamics cannot be defined, comprising of a complex interplay of tear production, evaporation and drainage, with variability due to anatomical differences, variation in movements, environmental factors and age-related changes. FNLDO is due to several scenarios and therefore comprises an inhomogeneous group of patients for whom treatment should, logically, be sequential. First, medical measures to reduce inflammatory mediators include bathing the ocular surface and drainage system; next, lateral canthus elevation where lateral tear spillage is present; if medial spillage continues, dacryocystorhinostomy is performed; and last, secondary placement of a canalicular bypass tube will generally control symptoms where they persist after dacryocystorhinostomy.

Analytical nonautonomous soliton solutions for the cubic–quintic nonlinear Schrödinger equation with distributed coefficients

In this paper, we find the exact bright, dark and gray analytical nonautonomous soliton solutions of the generalized CQNLSE with spatially inhomogeneous group velocity dispersion (GVD) and amplification or attenuation by the similarity transformation method under certain parametric conditions. As an example, we investigate their propagation dynamics in the soliton control system. In addition, the interaction of two neighboring solitary waves is discussed, and the results show that the interaction of two neighboring solitary waves can be restricted by choosing the distributed coefficients appropriately. Finally, the stability of the solutions is checked by direct numerical simulation.

Projective representations of the inhomogeneous Hamilton group: Noninertial symmetry in quantum mechanics

Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary representations of the central extension of the group. The formulation of the inertial states of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group, and its nonrelativistic limit in terms of the Galilei group, are fundamental examples. Interestingly, neither of these symmetries include the Weyl–Heisenberg group; the hermitian representations of its algebra are the Heisenberg commutation relations that are a foundation of quantum mechanics. The Weyl–Heisenberg group is a one dimensional central extension of the abelian group and its unitary representations are therefore a particular projective representation of the abelian group of translations on phase space. A theorem involving the automorphism group shows that the maximal symmetry that leaves the Heisenberg commutation relations invariant is essentially a projective representation of the inhomogeneous symplectic group. In the nonrelativistic domain, we must also have invariance of Newtonian time. This reduces the symmetry group to the inhomogeneous Hamilton group that is a local noninertial symmetry of the Hamilton equations. The projective representations of these groups are calculated using the Mackey theorems for the general case of a nonabelian normal subgroup.

Endoscopic and surgical management of serrated colonic polyps

Serrated polyps are an inhomogeneous group of lesions that harbour precursors of colorectal cancer. Current research has been directed at further defining the histopathological characteristics of these lesions, but definitive treatment recommendations are unclear. The aim was to review the current literature regarding classification, molecular genetics and natural history of these lesions in order to propose a treatment algorithm for surgeons to consider. The PubMed database was searched using the following search terms: serrated polyp, serrated adenoma, hyperplastic polyp, hyperplastic polyposis, adenoma, endoscopy, surgery, guidelines. Papers published between 1980 and 2010 were selected. Sixty papers met the selection criteria. Most authors agree that recommendations regarding endoscopic or surgical management should be based on the polyp's neoplastic potential. Polyps greater than 5 mm should be biopsied to determine their histology so that intervention can be directed accurately. Narrow-band imaging or chromoendoscopy may facilitate the detection and assessment of extent of lesions. Complete endoscopic removal of sessile serrated adenomas in the left or right colon is recommended. Follow-up colonoscopy is recommended in 2-6 months if endoscopic removal is incomplete. If the lesion cannot be entirely removed endoscopically, segmental colectomy is strongly recommended owing to the malignant potential of these polyps. Left-sided lesions are more likely to be pedunculated, making them more amenable to successful endoscopic removal. Even though the neoplastic potential of certain subtypes of serrated polyp is heavily supported, further studies are needed to make definitive endoscopic and surgical recommendations.

Kolorektale Lebermetastasen: Aktueller Stand der multimodalen Therapie

Surgical resection is the only chance of cure for patients with colorectal liver metastases und significantly improves patient survival. The percentage of patients who can undergo curative resection as well as the survival after liver resection can be increased by using modern multimodal treatment algorithms. This has been achieved by not only innovations in pre- and postoperative chemotherapy but also by new surgical and interventional techniques and last but not least by individualisation of chemotherapeutic regimens. Due to the high number of new treatment modalities, a generally accepted treatment algorithm cannot be provided so far for all subgroups of the inhomogeneous group of patients with colorectal liver metastases. In the present review the current status of multimodal therapy is outlined and the pending questions mentioned.

Funktionelle Abdominalschmerzen

Functional abdominal pain is an inhomogeneous group of disorders concerning aetiology and clinical presentation. Support for classification is provided by the ROME-Foundation with its criteria catalogue, ROME-III being the most recent one. However, basic approach consists of exclusion of somatic or psychiatric as well as psychosomatic disorders that are sharply defined and readily diagnosable. This article outlines a pragmatic gastroenterological approach by exemplary means of dyspepsia and irritable bowel syndrome. Dyspepsia includes a broad complex of mainly epigastric located symptoms, whereas irritable bowel syndrome is symptomatic with altered bowel habits and mid-abdominal pain in the majority. Gastreoenterologic therapy modalities are mainly based on empirical and symptomatic grounds, more than on precisely explaining pathophysioligic understanding.

Numerical study of a bubble plume generated by bubble entrainment from an impinging jet

The current paper presents the prediction results of a bubbly flow under plunging jet conditions using multiphase mono- and poly-dispersed approaches. The models consider interfacial momentum transfer terms arising from drag, lift, and turbulent dispersion force for the different bubble sizes. The turbulence is modeled by an extended k– ɛ model which accounts for bubble induced turbulence. Furthermore in case of a poly-dispersed air–water flow the bubble size distribution, bubble break-up and coalescence processes as well as different gas velocities in dependency on the bubble diameter are taken into account using the Inhomogeneous MUSIG model. This model is a generalized inhomogeneous multiple size group model based on the Eulerian modeling framework which was developed in the framework of a cooperative work between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf (FZD). The latter is now implemented into the CFD code CFX. According to the correlation on the lateral lift force obtained by Tomiyama (1998); this force changes its sign in dependence on the bubble size. Consequently the entrained small bubbles are trapped below the jet. They can escape from the bubble plume only by turbulent fluctuations or by coalescence. If the size of the bubbles generated by coalescence exceeds the size at which the lift force changes its sign these large bubbles go out from the plume and rise to the surface. A turbulent model based on an additional source term for turbulence kinetic energy and turbulence eddy dissipation equation is compared to the common concept for modeling the turbulence quantities proposed by Sato et al. (1981). It has been found that the large bubble distribution is slightly affected by the turbulence modeling which affects particularly the bubble coalescence and break-up process.

The search for reliable biomarkers of disease in multiple chemical sensitivity and other environmental intolerances.

Whilst facing a worldwide fast increase of food and environmental allergies, the medical community is also confronted with another inhomogeneous group of environment-associated disabling conditions, including multiple chemical sensitivity (MCS), fibromyalgia, chronic fatigue syndrome, electric hypersensitivity, amalgam disease and others. These share the features of poly-symptomatic multi-organ cutaneous and systemic manifestations, with postulated inherited/acquired impaired metabolism of chemical/physical/nutritional xenobiotics, triggering adverse reactions at exposure levels far below toxicologically-relevant values, often in the absence of clear-cut allergologic and/or immunologic involvement. Due to the lack of proven pathogenic mechanisms generating measurable disease biomarkers, these environmental hypersensitivities are generally ignored by sanitary and social systems, as psychogenic or “medically unexplained symptoms”. The uncontrolled application of diagnostic and treatment protocols not corresponding to acceptable levels of validation, safety, and clinical efficacy, to a steadily increasing number of patients demanding assistance, occurs in many countries in the absence of evidence-based guidelines. Here we revise available information supporting the organic nature of these clinical conditions. Following intense research on gene polymorphisms of phase I/II detoxification enzyme genes, so far statistically inconclusive, epigenetic and metabolic factors are under investigation, in particular free radical/antioxidant homeostasis disturbances. The finding of relevant alterations of catalase, glutathione-transferase and peroxidase detoxifying activities significantly correlating with clinical manifestations of MCS, has recently registered some progress towards the identification of reliable biomarkers of disease onset, progression, and treatment outcomes.

Ultrashort self-similar solutions of the cubic-quintic nonlinear Schrödinger equation with distributed coefficients in the inhomogeneous fiber

By means of the similarity transformation, we obtain exact self-similar solutions (similaritons) of the generalized cubic-quintic (CQ) nonlinear Schrödinger equation with spatially inhomogeneous group velocity dispersion, CQ nonlinearity and amplification or attenuation. Exact balance conditions between the dispersion, nonlinearity and the gain/loss have been obtained. As an example, we investigate their propagation dynamics in the dispersion decreasing fiber (DDF). Considering the fluctuation of the fiber parameter in real application, the exact balance conditions do not satisfy, and so we perform direct numerical analysis with initial 10% white noise for the bright similariton in both the DDF and the periodic distributed amplification system. Numerical calculations indicate stable propagation of the bright similariton over tens of dispersion lengths. These ultrashort self-similar optical waves are potentially useful for all-optical data-processing schemes and the design of beam compressors and amplifiers.

Noninertial symmetry group with invariant Minkowski line element consistent with Heisenberg quantum commutation relations

The maximal symmetry of a quantum system with Heisenberg commutation relations is given by the projective representations of the automorphism group of the Weyl-Heisenberg algebra. The automorphism group is the central extension of the inhomogeneous symplectic group with a conformal scaling that acts on extended phase space. We determine the subgroup that also leaves invariant a degenerate Minkowski orthogonal line element. This defines noninertial relativistic symmetry transformations that have the expected classical limit as c → ∞.

S02-04 - Ressource-Oriented Treatment of Addiction - the Orpheus Programme

Major problems in treating patients suffering from addictions derive from the fact that the diagnostic category dependence syndrome covers a highly inhomogeneous patient group. Therefore uniform therapeutic approaches inflexibly following treatment guidelines have not fulfilled prognostic expectations. This was the starting point for developing a new modular resource-oriented treatment program in the Anton Proksch Institute Vienna.Changing paradigms in the treatment of addiction, the Orpheus Programme offers a host of different modules designed to help patients to discover their own aims, objectives, values, and resources. The main task of the Orpheus modules is an increasing autonomous and joyful life. Abstinence represents no longer the only final goal of therapy, but is an important step to offer space and possibilities for the patients’ new life. When life becomes once again beautiful and filled with joy and meaning, addictive substances lose their seductive power: The more beautiful and attractive the patient's life, the less the drugs attractiveness. As illustrated by Orpheus, who defeated the sirens (as a symbol for addictive agents) by making the better, louder, and more attractive music, it becomes the patients’ main task to make a better “music of life”; the Orpheus modules are not training programs telling the patients how the better life looks like (as in former moral therapy); they intend to provide places, spaces and atmospheres encouraging and promoting the patients to make possible the possible.

THE INHOMOGENEOUS INVARIANCE QUANTUM GROUP OF Q-DEFORMED BOSON ALGEBRA WITH CONTINUOUS PARAMETERS

We present a q-deformed boson algebra using continuous momentum parameters and investigate its inhomogeneous invariance quantum group.