Charged anisotropic compact objects by gravitational decoupling

In the present article, we have constructed a static charged anisotropic compact star model of Einstein field equations for a spherically symmetric space-time geometry. Specifically, we have extended the charged isotropic Heintzmann solution to an anisotropic domain. To address this work, we have employed the gravitational decoupling through the so called minimal geometric deformation approach. The charged anisotropic model is representing the realistic compact objects such as $RXJ1856-37$ and $SAX J1808.4-3658(SS2)$. We have reported our results in details for the compact star $RXJ1856-37$ on the ground of physical properties such as pressure, density, velocity of sound, energy conditions, stability conditions, Tolman-Oppenheimer-Volkoff equation and redshift etc

Compact star in Tolman Kuchowicz spacetime in background of Einstein Gauss Bonnet gravity

The present work is devoted to the study of anisotropic compact matter distributions within the framework of 5-dimensional Einstein-Gauss-Bonnet gravity. To solve the field equations, we have considered that the inner geometry is described by Tolman-Kuchowicz spacetime. The Gauss-Bonnet Lagrangian is coupled to Einstein-Hilbert action through a coupling constant. When this coupling tends to zero general relativity results are recovered. We analyze the effect of this parameter on the principal salient features of the model, such as energy density, radial and tangential pressure and anisotropy factor.Additionally, the behaviour of the subliminal sound speed of the pressure waves in the principal direction of the configuration and the conduct of the energy-momentum tensor throughout the star are analyzed employing causality condition and energy conditions, respectively. All these subjects are supported by mean of physical, mathematical and graphical surve

Técnicas especiales en el diagnóstico de tumores óseos

Se hace una exposición del valor actual desde el punto de vista diagnóstico y pronóstico de las técnicas especiales aplicables a los tumores óseos por el patólogo. En histoquimia se resalta el valor práctico de las técnicas de PAS y fosfatasa alcalina para el diagnóstico del sarcoma de Ewing y del osteosarcoma respectivamente. Se comenta el valor de la aplicación de la microscopía electrónica en el diagnóstico de los tumores de células redondas pequeñas (sarcoma de Ewing, tumor neuroectodérmico periférico, linfoma primitivo óseo y metástasis de neuroblastoma y de rabdomiosarcoma embrionario) y de los sarcomas fusocelulares (fibrosarcoma, leiomiosarcoma embrionario) y de los sarcoma fusocelulares (fibrosarcoma, leiomiosarcoma primitivo de hueso y sarcoma sinovial) y de la aplicación de la inmunocitoquimia en los mismos tó- picos así como el diagnóstico diferencial del condrosarcoma, cordoma y metástasis de carcinoma mucosecretor en columna. Se comenta que la citología sólo es válida cuando es utilizada por un patólogo experto en patología tumoral ósea y en citopatología y que su aplicación es muy limitada. Se hace una revisión del valor de los estudios de ploidia con las técnicas de citometría de flujo y estática, resaltando su valor en la valoración pronóstica de ciertos tumores (condrosarcoma; sarcoma de Ewing). Finalmente, se comenta la aplicación diagnóstica de los estudios citogenéticos en el sarcoma de Ewing y el futuro de dichas técnicas de esta patología.In terms of diagnosis and prognosis, the present value of different sophisticated techniques applied for the patologist on bone tumors is reviewed. Histochemically, alkaline phosphatase and PAS techniques are both very important for the diagnosis of osteosarcoma and Ewing's sarcoma respectively. The value of electronic microscopy and immunohistochemistry for diagnosis of round small cells tumors (Ewing's sarcoma, neuroectodermic tumors, primary bone lymphoma and metastatic neuroblastoma) and fusocellular sarcomas (fibrosarcoma, leiomyosarcoma of bone and synovial sarcoma) isdiscussed. The differential diagnosis of chondrosarcoma, chordoma and metastatic mucosecretor carcinoma at the spine by using immunohistochemistry is reviewed. The aplication of cytology is very limited and only useful in the hands of patologist expert in bone tumors. Recent studies on cellular ploidy using the techniques of flow and static cytometry have shown prognostic value in certain tumors such as chondrosarcoma. The future seem s to be cytogenetics as have been demostrated already for Ewing sarcoma

Contribución a la estimación de estado de sistemas de parámetros distribuidos parabólicos semilineales con aplicaciones a sistemas de reacción de transporte

Descargue en el texto completo en el repositorio institucional de la Universidade Federal de Santa Catarina: https://repositorio.ufsc.br/handle/123456789/231074Los sistemas de reacción de transporte se describen mediante ecuaciones diferenciales parciales (EDP) parabólicas semilineales y son fundamentales en aplicaciones donde los procesos de difusión deben considerarse explícitamente. El problema de la estimación del estado a partir de medidas distribuidas en el dominio no es trivial. En este trabajo, abordamos este problema para una cierta clase de sistemas de reacción de transporte. Para lograr este objetivo, proponemos estrategias de diseño de observadores en el marco de enfoques de agrupamiento temprano y tardío. Finalmente, el problema de monitoreo de la propagación del COVID-19 se aborda en la parte de aplicación de esta tesis. En particular, abordamos la estimación de estado del modelo compartimental modelado por un sistema de ecuaciones diferenciales parciales, que describe la propagación de enfermedades infecciosas en una población determinada. Se utiliza el método de diseño basado en Lyapunov y parametrización polinomial de las variables de decisión para derivar un problema de programación semidefinida cuya solución proporciona las ganancias de inyección del observador de estado tipo Luenberger. Se presentan experimentos numéricos para ilustrar la eficiencia del método.Transport–reaction systems are described by semilinear parabolic partial differential equations (PDEs) and are fundamental in applications where diffusion processes must be considered explicitly. The state estimation problem on the basis of some in-domain distributed measurements is non-trivial. In this work we address this problem for a certain class of transport-reaction systems. To achieve this task, we propose observer design strategies in the frame of both early and late lumping approaches. Regarding the early lumping approach for the state observer design, we use the Method of Weighted Residuals (MWR), that encompasses the orthogonal collocation method, to derive an approximate reduced-order model, expressed as a set of ordinary differential equations (ODEs) subject to algebraic constraints. Then, a Lyapunov-based design method is proposed for the reduced-order model which provides sufficient design conditions in terms of standard linear matrix inequalities (LMIs) aiming at the exponential convergence of the estimation error with a prescribed decay rate. The observer performance is further improved through an offline optimal sensor placement algorithm considering a parameterized reduced-order output matrix.Brasil. Ministerio de EducaciónBélgica. Ministerio de Educació

A generalized Finch-Skea class one static solution

In the present article, we discuss relativistic anisotropic solutions of the Einstein field equation for the spherically symmetric line element under the class I condition. To do so we apply the embedding class one technique using Eisland condition. Within this approach, one arrives at a particular differential equation that links the two metric components $e^{\nu}$ and $e^{\lambda}$. In order to obtain the full space-time description inside the stellar configuration we ansatz the generalized form of metric component $g_{rr}$ corresponding to the Finch-Skea solution. Once the space-time geometry is specified we obtain the complete thermodynamic description i.e. the matter density $\rho$, the radial, and tangential pressures $p_r$ and $p_t$, respectively. Graphical analysis shows that the obtained model respects the physical and mathematical requirements that all ultra-high dense collapsed structures must obey. The $M-R$ diagram suggests that the solution yields stiffer EoS as parameter $n$ increases. The $M-I$ graph is in agreement with the concepts of Bejgar et al. \cite{bej} that the mass at $I_{max}$ is lesser by few percent (for this solution $\sim 3\%$) from $M_{max}$. This suggests that the EoSs is without any strong high-density softening due to hyperonization or phase transition to an exotic state.Comment: 14 figures, Accepted in European Physical Journal

Quantum aspects of the gravitational-gauge vector coupling in the Ho\v{r}ava-Lifshitz theory at the kinetic conformal point

This work presents the main aspects of the anisotropic gravity-vector gauge coupling at all energy scales \i.e., from the IR to the UV point. This study is carry out starting from the 4+1 dimensional Ho\v{r}ava-Lifshitz theory, at the kinetic conformal point.The Kaluza-Klein technology is employed as a unifying mechanism to couple both interactions. Furthermore, by assuming the so-called cylindrical condition, the dimensional reduction to 3+1 dimensions leads to a theory whose underlying group of symmetries corresponds to the diffeomorphisms preserving the foliation of the manifold and a U(1) gauge symmetry. The counting of the degrees of freedom shows that the theory propagates the same spectrum of Einstein-Maxwell theory. The speed of propagation of tensorial and gauge modes is the same, in agreement with recent observations. This point is thoroughly studied taking into account all the $z=1,2,3,4$ terms that contribute to the action. In contrast with the 3+1 dimensional formulation, here the Weyl tensor contributes in a non-trivial way to the potential of the theory. Its complete contribution to the 3+1 theory is explicitly obtained. Additionally, it is shown that the constraints and equations determining the full set of Lagrange multipliers are elliptic partial differential equations of eighth-order. To check and assure the consistency and positivity of the reduced Hamiltonian some restrictions are imposed on the coupling constants. The propagator of the gravitational and gauge sectors are obtained showing that there are not ghost fields, what is more they exhibit the $z=4$ scaling for all physical modes at the high energy level. By evaluating the superficial degree of divergence and considering the structure of the second class constraints, it is shown that the theory is power-counting renormalizable

Unified first law of thermodynamics in Gauss-Bonnet gravity on an FLRW background

Employing the thermodynamic unified first law through the thermodynamic-gravity conjecture, in this article, we derive for a FLRW universe the Friedmann equations in the framework of Gauss-Bonnet gravity theory. To do this, we project this generalized first law along the Kodama vector field and along the direction of an orthogonal vector to the Kodama vector. The second Friedmann equation is obtained by projecting on the Kodama vector, while the first is obtained by projecting along the flux on the Cauchy hypersurfaces. This result does not assume a priory temperature and an entropy, so the Clausius relation is not used here. Nevertheless, it is used to obtain the corresponding Gauss-Bonnet entropy. In this way, the validity of the generalized second law of thermodynamics is proved for the Gauss-Bonnet gravity theory.Comment: 10 pages, 2 figure

A new model of regular black hole in (2+1)(2+1) dimensions

We provide a new regular black hole solution in $(2+1)$ dimensions with presence of matter fields in the energy momentum tensor, having its core a flat or (A)dS structure. Since the first law of thermodynamics for regular black holes is modified by the presence of the matter fields, we provide a new version of the first law, where a local definition of the variation of energy is defined, and, where the entropy and temperature are consistent with the previously known in literature. It is shown that the signs of the variations of the local definition of energy and of the total energy coincide. Furthermore, at infinite, the usual first law $dM=TdS$ is recovered. It is showed that the formalism used is effective to compute the total energy of regular black holes in $(2+1)$ with presence of matter in the energy momentum tensor. This latter suggests the potential applicability of this formalism to calculate the mass of other models of regular black holes in $d \ge 4$ dimensions.Comment: accepted for publication in EP