Divergent Types Research Articles

Orthogonally induced differentiation of stem cells for the programmatic patterning of vascularized organoids and bioprinted tissues.

The generation of organoids and tissues with programmable cellular complexity, architecture and function would benefit from the simultaneous differentiation of human induced pluripotent stem cells (hiPSCs) into divergent cell types. Yet differentiation protocols for the overexpression of specific transcription factors typically produce a single cell type. Here we show that patterned organoids and bioprinted tissues with controlled composition and organization can be generated by simultaneously co-differentiating hiPSCs into distinct cell types via the forced overexpression of transcription factors, independently of culture-media composition. Specifically, we used such orthogonally induced differentiation to generate endothelial cells and neurons from hiPSCs in a one-pot system containing either neural or endothelial stem-cell-specifying media, and to produce vascularized and patterned cortical organoids within days by aggregating inducible-transcription-factor and wild-type hiPSCs into randomly pooled or multicore-shell embryoid bodies. Moreover, by leveraging multimaterial bioprinting of hiPSC inks without extracellular matrix, we generated patterned neural tissues with layered regions composed of neural stem cells, endothelium and neurons. Orthogonally induced differentiation of stem cells may facilitate the fabrication of engineered tissues for biomedical applications.

Quantifying the Value of Log Sorting Based on the Location of Timber Harvest Sites Across Wisconsin

Abstract It is generally understood that sorting logs based on grade generates maximum value for all stakeholders. However, the benefits of sorting logs may depend on the location of a timber sale and distances to manufacturing mills. The objective is to quantify the potential value of log sorting through scenario-based analysis in different areas with divergent forest and mill types. An optimization model was developed to allocate logs from the timber sale to the highest profit-yielding mills. Factors considered by the model included logging and transportation cost, timber sale tract-to-mill distances, mills’ acceptance criteria, and price at the mill gate. Four timber sales from across Wisconsin were selected for the study. Three scenarios were tested, with each scenario yielding different proportions of log sorts. The results showed that log sorting increased profit by up to $41.10 per cord in certain locations but was not profitable in other locations. Study Implications The methods proposed in this study can help foresters and landowners increase the value of harvested timber. Practitioners can use the proposed method to systematically assess the gain or loss in profit associated with log sorting at each timber sale. It also provides directives on the best mill for each log sort to be sent. The proposed method should be adopted to minimize underutilization of timber, especially in areas where profits are marginal.

Combined MA-XRF, MA-XRPD and SEM-EDX analysis of a medieval stained-glass panel formerly from Notre Dame, Paris reveals its material history

As part of its conservation-restoration, the 13th century stained-glass panel ‘the Annunciation’, was examined at the micro- and macro level. This window, since 1898 in the collection of the Museum Mayer Van den Bergh (Antwerp, B), was formerly a part of the southern Rose window of the Notre Dame Cathedral (Paris, F). The insigths emerging from a first phase of the analysis, comprising non-invasive analysis techniques such as optical microscopy combined with macroscopic X-ray fluorescence (MA-XRF) and X-ray diffraction (MA-XRPD) mapping, were used to select sampling positions for the second phase of investigation that involved micro-invasive analysis, namely scanning-electron microscopy coupled to energy-dispersive X-ray analysis (SEM-EDX). The aim of the investigation was fourfold: (1) to assess the applicability of MA-XRF scanning for the characterisation of stained glass windows prior to any conservation or restoration procedure, (2) to assess the applicability of MA-XRPD scanning to identify the degradation products formed on the surface of stained glass windows, (3) to establish a method to limit the set of sampled glass fragments taken from a glass panel for quantititive analysis while maintaining sufficient representativeness and (4) to distinguish the original glass panes and grisaille paint from non-original glass panes that were inserted during various past interventions. Most of the panes in this window proved to consist of medieval potash glass, consistent with the 13th c. origin of the window while a limited number of panes were identified as non-original infills, with divergent glass compositional types and/or colorants. Most panes derive their color from the pot metal glass (i.e. homogenously colored) they were made of. Some of the panes that originally had a red flashed layer on their surface, completely or partially lost this layer due to weathering. Three main compositional glass families with similar color could be defined. With the exception of the yellow and orange panes, the chromophoric elements responsible for the dark(er) and light(er) blue (Co), green (Cu), purple (Mn) and red colors (Cu) were identified. Two different grisaille paints were encountered, part of which were restored during the 19th century. On the basis of this information, all missing pieces were replaced by glass panes with appropriate colors and the panel could be successfully conserved to its former glory. On the surface of several panes, typical glass degradation products such as calcite, syngenite and gypsum were identified, together with lead based degradation products such as anglesite and palmierite. In addition, the presence of hematite and melanotekite in the grisailles was observed; also the presence of Zn, uncorrelated to Cu, in the grissailes on the right side of the window became apparent.

The structure of AcrIE4-F7 reveals a common strategy for dual CRISPR inhibition by targeting PAM recognition sites.

Bacteria and archaea use the CRISPR-Cas system to fend off invasions of bacteriophages and foreign plasmids. In response, bacteriophages encode anti-CRISPR (Acr) proteins that potently inhibit host Cas proteins to suppress CRISPR-mediated immunity. AcrIE4-F7, which was isolated from Pseudomonas citronellolis, is a fused form of AcrIE4 and AcrIF7 that inhibits both type I-E and type I-F CRISPR-Cas systems. Here, we determined the structure of AcrIE4-F7 and identified its Cas target proteins. The N-terminal AcrIE4 domain adopts a novel α-helical fold that targets the PAM interaction site of the type I-E Cas8e subunit. The C-terminal AcrIF7 domain exhibits an αβ fold like native AcrIF7, which disables target DNA recognition by the PAM interaction site in the type I-F Cas8f subunit. The two Acr domains are connected by a flexible linker that allows prompt docking onto their cognate Cas8 targets. Conserved negative charges in each Acr domain are required for interaction with their Cas8 targets. Our results illustrate a common mechanism by which AcrIE4-F7 inhibits divergent CRISPR-Cas types.

Thickness-Dependent Polar Domain Evolution in Strained, Ultrathin PbTiO3 Films.

Ferroelectric ultrathin films have great potential in electronic devices and device miniaturization with the innovation of technology. In the process of product commercialization, understanding the domain evolution and topological properties of ferroelectrics is a prerequisite for high-density storage devices. In this work, a series of ultrathin PbTiO3 (PTO) films with varying thicknesses were deposited on cubic KTaO3 substrates by pulsed laser deposition and were researched by Cs-corrected scanning transmission electron microscopy (STEM), reciprocal space mapping (RSM), and piezoresponse force microscopy (PFM). RSM experiments indicate the existence of a/c domains and show that the lattice constant varies continuously, which is further confirmed by atomic-scale STEM imaging. Diffraction contrast analysis clarifies that with the decrease in PTO film thickness, the critical thickness for the formation of a/c domains could be missing. When the thickness of PTO films is less than 6 nm, the domain configurations in the ultrathin PTO films are the coexistence of a/c domains and bowl-like topological structures, where the latter ones were identified as convergent and divergent types of meron. In addition, abundant 90° charged domain walls in these ultrathin PTO films were identified. PFM studies reveal clear ferroelectric properties for these ultrathin PTO films. These results may shed light on further understanding the domain evolution and topological properties in ultrathin ferroelectric PTO films.

Paradox Mindset in Management: Theory and Measurement

Purpose: This article presents an overview of the constructive functions of embracing (instead of rejecting) contradictions (otherwise known as a paradox mindset or Janusian thinking). It also demonstrates the positive impact of tension resulting from the cognitive consideration of simultaneous contradictions (as opposed to the traditional conviction that such cognitive dissonance isexperienced as uncomfortable and reduced). Additionally, this article highlights the positive impact of a paradox mindset on augmenting teams’ and institutions’ creativity and performance. It also documents a method of evaluating the propensity for embracing contradictions (i.e., a paradox mindset).Design/methodology/approach: This article documents the construction and validation of an assessment tool, i.e., the Influence of Contradictions Questionnaire (ICQ), for evaluating the level of propensity for a paradox mindset.Findings: In the validation process (n = 120 Anglophonic sample), the ICQ proved to have positive psychometric parameters (discrimination power and reliability).Social implications: The ICQ can be used for scientific purposes, e.g., for comparison between segments of society or for finding possible correlations with other personality traits (e.g., empathy). It could also serve as an evaluation tool for teams’ and individuals’ levels of propensity for conceptual blending—especially when measuring the results of training in this area.Originality/value: This is a novel approach, both in the theoretical review of various manifestations of embracing contradictions, as well as in designing a comprehensive evaluation method.Keywords: contradictions, Janusian thinking, conceptual blending, creativity, embracing contradictions, divergent thinkingPaper type: Research paper

Recombinantly Expressed Chimeric Fibers Demonstrate Discrete Type-Specific Neutralizing Epitopes in the Fowl Aviadenovirus E (FAdV-E) Fiber, Promoting the Optimization of FAdV Fiber Subunit Vaccines towards Cross-Protection in vivo.

ABSTRACTVaccines against inclusion body hepatitis in chickens are complicated by the involvement of antigenically diverse fowl adenovirus types. Though immunization with fiber protein confers robust protection, type specificity of fiber antibodies is an obstacle for the desired broad coverage. In this study, we utilized information on multiple linear epitopes predicted in the Fowl Aviadenovirus E (FAdV-E) fiber head (knob) to develop chimeric fibers with an exchange between two serotypes’ sequences, each containing proposed epitopes. Two consecutive segments pertaining to amino acid positions 1 to 441 and 442 to 525/523 in the fibers of FAdV-8a and -8b, types of Fowl Aviadenovirus E that cause inclusion body hepatitis, were swapped reciprocally to result in novel chimeras, crecFib-8a/8b and crecFib-8b/8a. crecFib was indistinguishable from monospecific recombinant fibers in its eactivity with different FAdV antisera in Western blotting. However, contrary to the results for monospecific fibers, crecFib induced cross-neutralizing antibodies against both serotypes in chickens. This demonstrates three nonidentical epitopes in the FAdV-E fiber, the conserved epitope detected in Western blotting and at least two epitopes participating in neutralization, being type specific and located opposite residue position 441-442. Furthermore, we supply conformational evidence for a site in the fiber knob with accessibility critical for neutralization. With such an extended neutralization spectrum compared to those of individual fibers, crecFib was anticipated to fulfill and even extend the mechanistic basis of fiber-mediated protection toward bivalent coverage. Accordingly, crecFib, administered as a single-antigen component, protected chickens simultaneously against challenge with FAdV-8a or -8b, demonstrated by up-to-complete resistance to clinical disease, prevention of target organ-related changes, and significant reduction of viral load.IMPORTANCE The control of inclusion body hepatitis, a disease of economic importance for chicken production worldwide, is complicated by an etiology involving multiple divergent fowl adenovirus types. The fiber protein is principally efficacious in inducing neutralizing and protective antibodies in vaccinated chickens; however, it faces limitations due to its intrinsic type specificity for neutralization. In this study, based on an in silico-guided prediction of multiple epitopes in the fowl adenovirus fiber head’s loops, we designed chimeric proteins, swapping N- and C-distal fiber portions, each containing putative epitopes, between divergent types FAdV-8a and -8b. In in vitro and in vivo studies, the chimeric fiber displayed extended properties compared to those of individual monotype-specific fibers, allowing the number, distribution, functionality, and conformational bearings of epitopes of the fowl adenovirus fiber to be characterized in more detail. Importantly, the chimeric fiber induced cross-neutralizing antibodies and protective responses in chickens against infections by both serotypes, promoting the advancement of broadly protective subunit vaccination strategies against FAdV.

On the osmotic pressure of cells.

The chemical potential of water () provides an essential thermodynamic characterization of the environment of living organisms, and it is of equal significance as the temperature. For cells, is conventionally expressed in terms of the osmotic pressure (πosm). We have previously suggested that the main contribution to the intracellular πosm of the bacterium E. coli is from soluble negatively-charged proteins and their counter-ions. Here, we expand on this analysis by examining how evolutionary divergent cell types cope with the challenge of maintaining πosm within viable values. Complex organisms, like mammals, maintain constant internal πosm ≈ 0.285 osmol, matching that of 0.154 M NaCl. For bacteria it appears that optimal growth conditions are found for similar or slightly higher πosm (0.25-0.4 osmol), despite that they represent a much earlier stage in evolution. We argue that this value reflects a general adaptation for optimising metabolic function under crowded intracellular conditions. Environmental πosm that differ from this optimum require therefore special measures, as exemplified with gram-positive and gram-negative bacteria. To handle such situations, their membrane encapsulations allow for a compensating turgor pressure that can take both positive and negative values, where positive pressures allow increased frequency of metabolic events through increased intracellular protein concentrations. A remarkable exception to the rule of 0.25-0.4 osmol, is found for halophilic archaea with internal πosm ≈ 15 osmol. The internal organization of these archaea differs in that they utilize a repulsive electrostatic mechanism operating only in the ionic-liquid regime to avoid aggregation, and that they stand out from other organisms by having no turgor pressure.

Pathwise least-squares estimator for linear SPDEs with additive fractional noise

This paper deals with the drift estimation in linear stochastic evolution equations (with emphasis on linear SPDEs) with additive fractional noise (with Hurst index ranging from 0 to 1) via least-squares procedure. Since the least-squares estimator contains stochastic integrals of divergence type, we address the problem of its pathwise (and robust to observation errors) evaluation by comparison with the pathwise integral of Stratonovich type and using its chain-rule property. The resulting pathwise LSE is then defined implicitly as a solution to a non-linear equation. We study its numerical properties (existence and uniqueness of the solution) as well as statistical properties (strong consistency and the speed of its convergence). The asymptotic properties are obtained assuming fixed time horizon and increasing number of the observed Fourier modes (space asymptotics). We also conjecture the asymptotic normality of the pathwise LSE.

Library Services Through Mobile Apps- Development and use by Indian Libraries

This paper aims to report on the adoption and use of mobile apps, including in-house and available in the app store by the Indian libraries for carrying out library services. An online survey was conducted to collect data from 229 LIS professionals from divergent types of libraries across the country. The study found that only 27 libraries developed their dedicated library mobile apps for catering services to the patron. The primary services offered were e-resources facility (92.60%), reference query (88.88%) and SMS alert (77.77%). The study also found the effective integration of social media apps by the libraries for sharing information regarding library services (74.67%) and upcoming events (68.12%), highlighting the library collection (62%), reference advisory (55.45%) and streaming videos lively (26.20%). The most used social media apps were WhatsApp (69.43%), Facebook (66.37%) and YouTube (65.93%). However, the unavailability of apps in offline mode and storage problems were the major hurdles cited by the professionals in using apps. The study results suggest opportunities for libraries to develop their library app to satisfy users’ information needs.

Hyperbolicity of a class of first-order quasilinear covariant equations of divergent type

Hyperbolicity of a class of first-order quasilinear covariant equations of divergent type

Assessment of Palatal Throat Form in Lateral Cephalogram and its Correlation with the Skeletal Base and Facial Divergence: An Institutional Based Study

Background Along with peripheral seal, palatal throat form also has significant value to achieve good retention and stability of maxillary complete denture. The palatal throat form also determines the posterior extention of maxillary dentures and affects the comfortability of the patients.
 Objective To analyse the palatal throat form in a Nepalese population based on age, gender malocclusion and facial divergence.
 Method This study consisted of 300 randomly selected radiographs with a mean age of 21.46±5.62 years. Skeletal malocclusion in lateral palatal throat form outlines. Patient were also categorized according to different Schudy’s facial divergence angle (SNMP). The obtained data was tabulated based on the age, gender, palatal throat form, type of malocclusion and facial divergence. The results obtained were subjected to a statistical analysis to find the relation between variants of the soft palate and types of malocclusion in different gender groups.
 Result Proportion between palatal throat form and malocclusion found to be significant. There is no significant difference in proportion of different class of palatal throat form between genders. Whereas Class II palatal throat form found to be most common in all facial divergence.
 Conclusion It was observed that Class II malocclusion was most common among three types. The relation between palatal throat form and malocclusion, was found to be statistically significant.

Extracellular vesicles from mesenchymal stem cells of dental pulp and adipose tissue display distinct transcriptomic characteristics suggestive of potential therapeutic targets.

Objective: Mesenchymal stem cells (MSCs) are isolated from various human tissues and used for therapy, in which beneficial effects are attributed mainly to mesenchymal stem cell-derived extracellular vesicles (MSC-EVs). Whereas MSCs of diverse tissue types share cardinal stem cell features, it is becoming evident that MSCs of each tissue type possess unique properties as well. For designing efficient stem cellbased therapies, it is crucial to understand the unique properties associated with MSCs and MSC-EVs of each tissue type. Such unique properties can be analyzed through transcriptomic approaches using comprehensive gene expression databases and sophisticated analytical tools. Here, we comparatively studied the transcriptomes in MSC-EVs of dental pulp and adipose tissue. Additionally, the transcriptomes of MSC-EVs were compared with the cellular transcriptomes of MSCs for the same tissue types. Methods: MSCs were cultured from human dental pulp and adipose tissue specimens. Conditioned culture media were collected to prepare MSC-EVs, from which RNAs were isolated and subjected to next-generation sequencing for transcriptomic analysis. Gene expression signatures in MSC-EVs of each tissue type were investigated using gene set analysis. Results: MSC-EVs obtained from dental pulp-derived MSCs showed distinct transcriptomic signatures of neurogenesis and neural retina development while MSC-EVs of adipose tissue-derived MSCs showed signatures of mitochondrial activity and skeletal system development. The transcriptomes of MSC-EVs resembled the cellular transcriptomes of MSCs, and the genes associated with neurogenesis were highly expressed in both MSCs and MSC-EVs of dental pulp. Adipose tissue-derived MSCs and MSC-EVs highly expressed genes associated with angiogenesis, hair growth, and dermal matrices. Conclusion: The clear and distinct signatures of neurogenesis and neural retina development in dental pulp-derived MSC-EVs imply neurodegenerative disorders and retinal diseases as putative therapeutic targets. In contrast, the transcripts in adipose tissue-derived MSC-EVs could be useful in rejuvenating the skin and musculoskeletal system. Further insights into MSC-EVs of divergent tissue types may expand the list of potential therapeutic targets.

Scattering of light by a parity-time-symmetric dipole beyond the first Born approximation

The scattering of light by localized three-dimensional dielectrics having gain and loss defies the usual Born approximation, since the material can increase the amplitude of the incident field within the scatterer, making the weak-scattering assumption invalid. The convergence of the Born series is rarely discussed in analytical treatments, as the state of exhaustion is reached after calculating the very first few terms of the series. Even if all the terms are obtained, the series will certainly be of a divergent type in general, thus invalidating the equality of the scattered field to its Taylor-series representation. We present here a simple localized material model of a dielectric having parity-time ($\mathcal{PT}$) symmetry, consisting of a $\mathcal{PT}$-symmetric dipole, such that all the terms in the Born series are analytically evaluated and a closed-form expression is obtained in the far-zone approximation. The scattered field is then analyzed by using Pad\'e approximants in order to obtain convergent representations of the scattered radiation and to compare with the exact solution. This allows us to study the role of the gain and loss parameter in strong-scattering regimes and to demonstrate the remarkable properties of Pad\'e approximants when applied to scattering.

Resolutivity and invariance for the Perron method for degenerate equations of divergence type

We consider Perron solutions to the Dirichlet problem for the quasilinear elliptic equation divA(x,∇u)=0 in a bounded open set Ω⊂Rn. The vector-valued function A satisfies the standard ellipticity assumptions with 1<p<∞ and a p-admissible weight w. We show that arbitrary perturbations on sets of (p,w)-capacity zero of continuous (and certain quasicontinuous) boundary data f are resolutive and that the Perron solutions for f and such perturbations coincide. As a consequence, we prove that the Perron solution with continuous boundary data is the unique bounded solution that takes the required boundary data outside a set of (p,w)-capacity zero.

Inequalities for Jensen-Sharma-Mittal and Jeffreys-Sharma-Mittal Type f-Divergences.

In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback–Leibler types of divergences, are provided in order to show a few applications of new divergences.

Differential Implications of CSF3R Mutations in t(8;21) and CEBPA Double Mutated Acute Myeloid Leukemia

BackgroundFew data are available exploring mutations of the colony-stimulating factor 3 receptor (CSF3R) in acute myeloid leukemia (AML) in an all-round and systematic manner. The purpose of this study was to analyze the CSF3R mutations (CSF3Rmut) in AML with recurrent genetic abnormalities for potential synergistic pathomechanism. Patients and MethodsWe retrospectively screened 1102 adult de novo AML patients with available next-generation sequencing (NGS) information on 132 genes related to hematologic disorders. The χ2, Mann-Whitney U tests were used to analyze their associations with clinicopathologic characteristics, and a propensity score matching (PSM) followed by Kaplan-Meier method was applied to measure their prognostic effects. ResultsOverall, CSF3Rmut were detected in 40 (3.6%) of 1102 patients with adult de novo AML. CSF3Rmut were predominantly enriched in AML with the CEBPA double mutations (CEBPAdm) (16/122, 13.1%), t(8;21) (12/186, 6.5%) and mutated RUNX1 (3/50, 6.0%), respectively. The CSF3Rmut loci and types differed according to AML subtypes, with frameshift-indels and premature stop confined in the t(8;21) AML [10/12 (83.3%)], and missense recurrently aggregated in the CEBPAdm AML [16/16 (100%)]. Cases with CSF3Rmut had a lower WBC count versus those with CSF3R wild-type (CSF3Rwt) in the t(8;21) AML cohort, with a borderline significance [median 5.45 (range 0.94-20.30) × 109/L) vs. 8.80 (range 0.96-155.00) × 109/L, P = .046]. CSF3Rmut were non-significantly associated with higher WBC counts [median 33.6 (range 6.8-287.6) × 109/L vs. 18.1 (range 1.7-196.0) × 109/L, P = .156] and significantly with lower immunophenotypic CD15 positivity [0/8 (0%) vs. 44/80 (55%), P = .009] as compared to CSF3Rwt in the CEBPAdm AML cohort. After propensity score matching followed by Kaplan-Meier analysis, CSF3Rmut cases had comparable disease-free survival (DFS) and overall survival (OS) to those with CSF3Rwt (P = .607 and P = .842, respectively) in the t(8;21) AML cohort. By contrast, CSF3Rmut showed an inclination towards inferior DFS compared to CSF3Rwt in the CEBPAdm AML cohort [median DFS 19.8 (95%CI 3.1-36.5) months vs. not reached (NR), P = .086]. No significant difference was found for OS between CSF3Rmut and CSF3Rwt cases (P = .943). ConclusionWe concluded that CSF3Rmut were frequently enriched in patients with t(8;21) and CEBPAdm subtypes among AML, but showed divergent clinicopathologic features, mutation loci and types and differing prognostic aspects.

Responses of the atmospheric boundary layer to a low‐latitude mesoscale SST front

AbstractThe responses of the atmospheric boundary layer at low latitudes (20°N) to forcing by an ocean‐mesoscale sea surface temperature (SST) front are investigated under the conditions that the background wind intersects with the SST front (i.e., there are cross‐frontal and along‐frontal wind components) through ideal numerical experiments. The simulation results show that the responses of the atmospheric boundary layer are sensitive to the background wind speed and its direction relative to the SST front. The type of convergence and divergence of Ekman transport and that of the background wind can be constructive or destructive, depending on the relative orientation of the background wind and the SST front. When the two kinds of convergence and divergence are constructive, they can cause strong convergence and divergence in the boundary layer near the SST front; further, the unbalanced state forced over the SST front will excite inertial gravity waves propagating into the free atmosphere. The vertical velocity excited in this case is much greater than that when there is only a cross‐frontal background wind component with an equivalent magnitude. On the contrary, when the two kinds of convergence and divergence are destructive, the resultants of convergence and divergence are reduced significantly, and the interaction between the boundary layer and the aloft atmosphere decays rapidly with height. The significance of the results obtained for the analysis of coastal precipitation are discussed.

Linearized dispersion relations in viscous relativistic hydrodynamics

We compute the dispersion relations for scalar, vector and tensor modes of a viscous relativistic fluid, linearized around an equilibrium solution, for a divergence type theory (which, in the linearized theory, includes Israel-Stewart theory and anisotropic hydrodynamics as particular cases) and contrast them to the corresponding results derived from kinetic theory under the relaxation time approximation, and from causal first order theories. We conclude that all approaches give similar dynamics for the scalar and vector modes, while the particular divergence type theory presented here also contains propagating damped tensor waves, in agreement with kinetic theory. Nonhydrodynamic tensor modes are also a feature of holographic fluids. These results support the application of hydrodynamics in problems involving the interaction between fluids and gravitational waves.

Comparison Geometry for an Extension of Ricci Tensor

For a complete Riemannian manifold M with a (1,1)-elliptic Codazzi self-adjoint tensor field A, we use the divergence type operator \({L_A}(u): = div(A\nabla u)\) and an extension of the Ricci tensor to extend some major comparison theorems in Riemannian geometry. In fact we extend theorems such as mean curvature comparison theorem, Bishop–Gromov volume comparison theorem, Cheeger–Gromoll splitting theorem and some of their famous topological consequences. Also we get an upper bound for the end of manifolds by restrictions on the extended Ricci tensor. The results can be applied to some Riemannian hypersurfaces of Riemannian or Lorentzian space forms.