Nonlinear Realization of the Local Conform-Affine Symmetry Group for Gravity in the Composite Fiber Bundle Formalism

A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz group metric are used to induce a spacetime metric. The inhomogenously transforming (under the Lorentz group) connection coefficients serve as gravitational gauge potentials used to define covariant derivatives accommodating minimal coupling of matter and gauge fields. On the other hand, the tensor valued connection forms serve as auxillary dynamical fields associated with the dilation, special conformal and deformational (shear) degrees of freedom inherent in the bundle manifold. The bundle curvature of the theory is determined. Boundary topological invariants are constructed. They serve as a prototype (source free) gravitational Lagrangian. The Bianchi identities, covariant field equations and gauge currents are obtained.Comment: 24 pages. to appear in IJGMM

Homogenization of the planar waveguide with frequently alternating boundary conditions

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the Dirichlet Laplacian and prove the uniform resolvent convergence. The spectrum of the perturbed operator consists of its essential part only and has a band structure. We construct the leading terms of the asymptotic expansions for the first band functions. We also construct the complete asymptotic expansion for the bottom of the spectrum

On spectrum of a Schroedinger operator with a fast oscillating compactly supported potential

We study the phenomenon of an eigenvalue emerging from essential spectrum of a Schroedinger operator perturbed by a fast oscillating compactly supported potential. We prove the sufficient conditions for the existence and absence of such eigenvalue. If exists, we obtain the leading term of its asymptotics expansion.Comment: The article is originally written in Russian. The translation in English is made by D. Boriso

Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.Comment: 6 pages, 4 figure

In Escherichia coli ammonia inhibits cytochrome bo3 but activates cytochrome bd-I

Interaction of two redox enzymes of Escherichia coli, cytochrome bo3 and cytochrome bd-I, with ammonium sulfate/ammonia at pH 7.0 and 8.3 was studied using high-resolution respirometry and absorption spectroscopy. At pH 7.0, the oxygen reductase activity of none of the enzymes is affected by the ligand. At pH 8.3, cytochrome bo3 is inhibited by the ligand, with 40% maximum inhibition at 100 mM (NH4 )2SO4 . In contrast, the activity of cytochrome bd-I at pH 8.3 increases with increasing the ligand concentration, the largest increase (140%) is observed at 100 mM (NH4 )2SO4 . In both cases, the effector molecule is apparently not NH4+ but NH3 . The ligand induces changes in absorption spectra of both oxidized cytochromes at pH 8.3. The magnitude of these changes increases as ammonia concentration is increased, yielding apparent dissociation constants Kdapp of 24.3 ± 2.7 mM (NH4 )2SO4 (4.9 ± 0.5 mM NH3 ) for the Soret region in cytochrome bo3, and 35.9 ± 7.1 and 24.6 ± 12.4 mM (NH4 )2SO4 (7.2 ± 1.4 and 4.9 ± 2.5 mM NH3 ) for the Soret and visible regions, respectively, in cytochrome bd-I. Consistently, addition of (NH4)2SO4 to cells of the E. coli mutant containing cytochrome bd-I as the only terminal oxidase at pH 8.3 accelerates the O2 consumption rate, the highest one (140%) being at 27 mM (NH4 )2SO4 . We discuss possible molecular mechanisms and physiological significance of modulation of the enzymatic activities by ammonia present at high concentration in the intestines, a niche occupied by E. coli

Tinnitus – a manifestation of neurodegenerative diseases

BackgroundTinnitus is a widespread hearing impairment that can be characterized by the perception of sound, such as tone or noise, in the absence of an appropriate external sound source. The cause of tinnitus and mechanism are unclear. The prevalence of tinnitus is higher in people over 60 years of age. Tinnitus is usually a manifestation of а hearing impairment. Symptoms can be acute or chronic. In most cases, tinnitus manifests as an idiopathic condition. In the clinical practice, common factors that affect the psychological and emotional well-being of people with tinnitus are: fear, stress, anxiety and depression, which in turn can cause insomnia, impaired concentration and cognitive dysfunction. Tinnitus is a heterogeneous disorder in terms of its etiology and clinic. Tinnitus is associated with hearing loss, as both symptoms often occur together, though in many clinical cases, people with hearing loss do not develop tinnitus.MethodsWe present а clinical case of a patient diagnosed with a posturographic system, along with a full otoneurological and hearing examinations. Methods of videonystagmography, video head impulse test, subjective visual vertical, audiometry, tympanometry, otoacoustic emissions test, automated auditory brainstem response were used. We provided a dental check-up and an occlusion analysis. Patient filled out questionnaires and signed a written informed consent. The aim of the team was to analyze the manifestation of tinnitus as a precursor of a neurodegenerative disease.Results and discussionFrom the literature review done chronic tinnitus is associated with anatomical brain abnormalities, including decreased cortical gray matter and decreased white matter integrity. There is also a high prevalence of cognitive impairment reported among patients with tinnitus from a clinical point of view. Tinnitus is an independent risk factor for subsequent neurodegenerative disease. There are a number of neurological conditions that can be encountered in the otorhinolaryngological and dental practice. It is important for the dentist to enrich own knowledge of the underlying neurological conditions, as they may affect the provision of dental treatment. Our findings from the examinations executed are consistent with previous studies, which show that diabetes and head injuries can be risk factors for AD and neurodegeneration.ConclusionsFurther research is needed to re-confirm the conclusions of our research and to investigate the pathophysiology of the relationship between tinnitus and the Alzheimer’s disease and tinnitus and the Parkinson’s disease in more depth

The symplectic Deligne-Mumford stack associated to a stacky polytope

We discuss a symplectic counterpart of the theory of stacky fans. First, we define a stacky polytope and construct the symplectic Deligne-Mumford stack associated to the stacky polytope. Then we establish a relation between stacky polytopes and stacky fans: the stack associated to a stacky polytope is equivalent to the stack associated to a stacky fan if the stacky fan corresponds to the stacky polytope.Comment: 20 pages; v2: To appear in Results in Mathematic

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review