Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups

Given a complete non-compact Riemannian manifold (M, g) with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries G of (M, g) that characterizes the coerciveness of G in the sense of Skrzypczak and Tintarev (Arch Math 101(3): 259–268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). We also consider the case of non-compact Randers-type Finsler manifolds with finite reversibility constant inheriting similar embedding properties as their Riemannian companions; sharpness of such constructions are shown by means of the Funk model. As an application, a quasilinear PDE on Randers spaces is studied by using the above compact embeddings and variational arguments.

Molecular Parameters of Tert-Butyl Chloride and Its Isotopologues Determined from High-Resolution Rotational Spectroscopy

A broadband chirped-pulse Fourier transform microwave spectrometer was used to detect the rotational spectra of the products of a chemical reaction in the gas phase from 1-18 GHz under the supersonic expansion condition. In natural abundance, pure rotational energy level transitions of tert-butyl chloride and its isotopologues (13C, 37Cl) were observed and assigned. The rotational spectral parameters (rotational constant, quadrupole coupling constant and centrifugal distortion constant) of these isotopologues were determined. The experimental results are in great agreement with the calculated values of quantum chemistry and the spectral parameters in the literature. The accuracy and the capability for chemical detection of our homemade rotational spectrometer were verified by this experiment.

Some Krasnosel’skii-type fixed point theorems for Meir–Keeler-type mappings

In this paper, inspired by the idea of Meir–Keeler contractive mappings, we introduce Meir–Keeler expansive mappings, say MKE, in order to obtain Krasnosel’skii-type fixed point theorems in Banach spaces. The idea of the paper is to combine the notion of Meir–Keeler mapping and expansive Krasnosel’skii fixed point theorem. We replace the expansion condition by the weakened MKE condition in some variants of Krasnosel’skii fixed point theorems that appear in the literature, e.g., in [T. Xiang, R. Yuan, A class of expansive-type Krasnosel’skii fixed point theorems, Nonlinear Anal., Theory Methods Appl., 71(7–8):3229–3239, 2009].

Complexity analysis of dynamical spherically-symmetric dissipative self-gravitating objects in modified gravity

In this paper, we have worked on the concept of complexity factor for nonstatic spherically-symmetric self-gravitating source filled with anisotropic fluid distribution in [Formula: see text] gravity theory. The definition of complexity for dynamical sources, proposed by Herrera, is examined in the framework of [Formula: see text] gravity. We intended to analyze the behavior of complexity factor in modified theory. For this, we defined the scalar functions through orthogonal splitting of Reimann tensor in [Formula: see text] gravity and worked out the structure scalars. We considered the structure scalar [Formula: see text] as a complexity factor to evaluate the complexity of the structure of dynamical system and also to analyze the complexity of the evolutionary patterns of the system under consideration. We took into account the homologous condition and homogeneous expansion condition in order to present the simplest mode of evolution, and found that homologous evolution is the simplest one. We considered both dissipative and nondissipative cases and found that shearing behavior of the fluid is not the same in both cases, however it remained geodesic in both cases. In the end, we established the results for the vanishing of the complexity factor. It has been found that zero complexity condition is satisfied if the energy density inhomogeneity and pressure anisotropy of the fluid configuration cancel each other.

Anisotropic stellar filaments evolving under expansion-free condition in f(R,T) gravity

In this paper, we have analyzed the role of a viable [Formula: see text] model, i.e. [Formula: see text], while exploring the unstable regions of cylindrically symmetric gravitational source, where, [Formula: see text] and [Formula: see text] correspond to the Ricci invariant and trace of energy momentum tensor, respectively. The matter distribution is considered to be anisotropic and gravitating system evolves under zero expansion condition. The collapse equation of cylindrical star has been obtained by applying perturbation scheme on modified field equations and conservation equations. Dynamical instability has been discussed in N and pN regimes, stability constraints have also been developed. We found that adiabatic index [Formula: see text] is meaningless for the discussion of stability of gravitating sources carrying expansion-free condition, and stability variations are determined by physical properties of the fluid.

Tissue Source and Cell Expansion Condition Influence Phenotypic Changes of Adipose-Derived Stem Cells

Stem cells derived from the subcutaneous adipose tissue of debrided burned skin represent an appealing source of adipose-derived stem cells (ASCs) for regenerative medicine. Traditional tissue culture uses fetal bovine serum (FBS), which complicates utilization of ASCs in human medicine. Human platelet lysate (hPL) is one potential xeno-free, alternative supplement for use in ASC culture. In this study, adipogenic and osteogenic differentiation in media supplemented with 10% FBS or 10% hPL was compared in human ASCs derived from abdominoplasty (HAP) or from adipose associated with debrided burned skin (BH). Most (95–99%) cells cultured in FBS were stained positive for CD73, CD90, CD105, and CD142. FBS supplementation was associated with increased triglyceride content and expression of adipogenic genes. Culture in hPL significantly decreased surface staining of CD105 by 31% and 48% and CD142 by 27% and 35% in HAP and BH, respectively (p<0.05). Culture of BH-ASCs in hPL also increased expression of markers of osteogenesis and increased ALP activity. These data indicate that application of ASCs for wound healing may be influenced by ASC source as well as culture conditions used to expand them. As such, these factors must be taken into consideration before ASCs are used for regenerative purposes.