A simple model for explaining Galaxy Rotation Curves

A new simple expression for the circular velocity of spiral galaxies is proposed and tested against HI Nearby Galaxy Survey (THINGS) data set. Its accuracy is compared with the one coming from MOND.Comment: 9 pages, 3 figures, 2 tables; this article is connected to arXiv:1705.0413

Do sewn singularities falsify the Palatini cosmology?

We investigate further (cf. arXiv:1512.01199, JCAP01 (2016) 040) Starobinsky cosmological model $R+\gamma R^2$ in the Palatini formalism with Chaplygin gas and baryonic matter as a source. For this aim we use dynamical system theory. The dynamics is reduced to the 2D sewn dynamical system of a Newtonian type (a piecewise-smooth dynamical system). We classify all evolutional paths in the model as well as trajectories in the phase space. We demonstrate the presence of a degenerate freeze singularity (glued freeze type singularities) for the positive $\gamma$. In this case it is a generic feature of early evolution of the universe. We point out that a degenerate type III of singularity can be considered as an endogenous model of inflation between the matter dominating epoch and the dark energy phase. We also investigate cosmological models with negative $\gamma$. It is demonstrated that $\gamma$ equal zero is a bifurcation parameter and dynamics qualitatively changes in comparison to positive $\gamma$. Instead of the big bang the sudden bounce singularity of a finite scale factor appears and there is a generic class of bouncing solutions sewn along the line $a=a_{\text{sing}}$. And we argue that the presence of sudden singularities in an evolutional scenario of the Universe falsifies the negative $\gamma$ in the Palatini cosmology. Only very small values of $\Omega_{\gamma}$ parameter are admissible if we requires that agreements physics with the $\Lambda$CDM model. From the statistical analysis of astronomical observations, we deduce that the case of negative values of $\Omega_\gamma$ can be rejected even if it may fit better to the data.Comment: 26 pages, 15 figures, v3: change of title, more discussion on singularitie

Inflationary cosmology with Chaplygin gas in Palatini formalism

We present a simple generalisation of the $\Lambda$CDM model which on the one hand reaches very good agreement with the present day experimental data and provides an internal inflationary mechanism on the other hand. It is based on Palatini modified gravity with quadratic Starobinsky term and generalized Chaplygin gas as a matter source providing, besides a current accelerated expansion, the epoch of endogenous inflation driven by type III freeze singularity. It follows from our statistical analysis that astronomical data favors negative value of the parameter coupling quadratic term into Einstein-Hilbert Lagrangian and as a consequence the bounce instead of initial Big-Bang singularity is preferred.Comment: 19 pages, 6 figures, typos corrected; version accepted by JCA

Expression of SATB1 protein in the ductal breast carcinoma tissue microarrays — preliminary study

Abstract: Special AT-rich sequence-binding protein 1 (SATB1) is a nuclear matrix protein which interacts with specific regions of DNA, ensuring its proper organization and function in the cell. The expression of SATB1 was primarily found in thymocytes, but its increased levels were observed in various types of cancers. However, the knowledge of the function and application possibilities of this protein is still limited. The aim of this study was to investigate the expression of SATB1 protein using immunohistochemistry and tissue microarray (TMA) technique and determine its possible relationship with the proliferative marker Ki-67, estrogen a (ER) and progesterone (PR) receptors as well as grade of histological malignancy (G). The study was performed on material of 48 archival invasive ductal breast cancers (IDC). The TMAs were prepared with the use of 0.6 mm diameter punches. Immunohistochemical reactions were carried out using antibodies against Ki-67, ER, PR and SATB1 proteins. The intensity of the nuclear reaction was evaluated using a light microscope and computer-assisted image analysis. Expression of Ki-67 and SATB1 protein was observed in 89.58% and 31.25% of cancer cases, respectively. 62.5% of tumors were classified as ER-positive, and 47.92% as PR-positive. Statistical analysis showed a moderate positive correlation between Ki-67 and SATB1 expression (r = 0.291, p = 0.045 independently on the receptor status, and r = 0.392, p = 0.032 in ER-negative tumors). The expression of the Ki-67 antigen increased with higher grade of histological malignancy (G). The results suggest that SATB1 protein may play an indirect role in the cell proliferation and should be evaluated in relation to the other markers. Further studies concerning determination of its role in cancer progression and metastasis, in terms of application as therapeutic target and prognostic marker, are recommended

The expression of selected immunocytochemical diagnostic markers in the case of chondrosarcoma with a mesenchymal component

The case of 52-year-old man is presented, who had suffered from pains in his right brachial region and in whom, upon admission to the Lower Silesia Centre of Oncology, a tumour of 20 cm in diameter and restricted mobility was disclosed in the right brachial region and proximal 1/3 of his right arm. Radiograms of his right humerus disclosed non-uniform restructuring of the osseous tissue, dominated by osteosclerosis in the upper half of his right humerus, while in the surrounding dift tissues of the proximal portion non-uniform shades were seen of calcified appearance. The patient was qualified to surgical biopsy and histopathological examination of the sample disclosed Chondrosarcoma G II. Following amputation of the right upper extremity together with the scapula, the tumour was subjected to histopathological and immunocytochemical examination in the Department of Pathomorphology, Lower Silesia Centre of Oncology. In numerous samples of the tumour dedifferentiated chondrosarcoma was diagnosed with a dominating component of malignant fibrous histiocytoma (MFH), which was confirmed by detecting a high expression of alpha-1-antichymotrypsin (ACT) within the spindle-shaped cell component of the chondrosarcoma. Spindle-shaped elements in dedifferentiated chondrosarcoma (DChSa) may represent patterns of fibrosarcoma, osteosarcoma or the malignant fibrohistiocytoma (MFH) type and they are present as if in the form of restricted fields with no reciprocal infiltrates. Moreover, due to the worse prognosis in the case of the MFH component in dedifferentiated chondrosarcoman as compared to that in classical chondrosarcoma, common evaluation of the material was made by a surgeon, radiologist and histopathologist, accompanied by a minimum panel of immunocytochemical tests (ACT, Vimentyna, Desmina, S-100). This enabled a final diagnosis for all tumour components to be established and prognosis to be made regarding the further fate of the patient

Invariant solutions and Noether symmetries in Hybrid Gravity

Symmetries play a crucial role in physics and, in particular, the Noether symmetries are a useful tool both to select models motivated at a fundamental level, and to find exact solutions for specific Lagrangians. In this work, we consider the application of point symmetries in the recently proposed metric-Palatini Hybrid Gravity in order to select the $f({\cal R})$ functional form and to find analytical solutions for the field equations and for the related Wheeler-DeWitt (WDW) equation. We show that, in order to find out integrable $f({\cal R})$ models, conformal transformations in the Lagrangians are extremely useful. In this context, we explore two conformal transformations of the forms $d\tau=N(a) dt$ and $d\tau=N(\phi) dt$. For the former conformal transformation, we found two cases of $f({\cal R})$ functions where the field equations admit Noether symmetries. In the second case, the Lagrangian reduces to a Brans-Dicke-like theory with a general coupling function. For each case, it is possible to transform the field equations by using normal coordinates to simplify the dynamical system and to obtain exact solutions. Furthermore, we perform quantization and derive the WDW equation for the minisuperspace model. The Lie point symmetries for the WDW equation are determined and used to find invariant solutions.Comment: 12 pages, 1 figur