Can playing Spirograph lead to an ordered structure in self-propelled particles?

In the present study we introduce a simple model of self-propelled particles with constant linear velocity which captures the essential features of microorganism aggregation as well as the dynamics around an attractive point.

Fixed Point and Acute Point Theorems for New Mappings in a Banach Space

In a Hilbert space, concepts of attractive point and acute point are studied by many researchers. Moreover, these concepts extended to Banach space. In this paper, we introduce a new class of mappings on Banach space corresponding to the class of all widely more generalized hybrid mappings on Hilbert space. Moreover, we introduce some extensions of acute point and prove some acute point theorems.

Ergodic and fixed point theorems for sequences and nonlinear mappings in a Hilbert space

In this paper, we introduce the notion of 2-generalized hybrid sequences, extending the notion of nonexpansive and hybrid sequences introduced and studied in our previous work [Djafari Rouhani B., Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. thesis, YaleUniversity, 1981; and other published in J. Math. Anal. Appl., 1990, 2002, and 2014; Nonlinear Anal., 1997, 2002, and 2004], and prove ergodic and convergence theorems for such sequences in a Hilbert space H. Subsequently, we apply our results to prove new fixed point theorems for 2-generalized hybrid mappings, first introduced in [Maruyama T., Takahashi W., Yao M., Fixed point and mean ergodic theorems for new nonlinear mappings in Hilbert spaces, J. Nonlinear Convex Anal., 2011, 12, 185-197] and further studied in [Lin L.-J., Takahashi W., Attractive point theorems and ergodic theorems for nonlinear mappings in Hilbert spaces, Taiwanese J. Math., 2012, 16, 1763-1779], defined on arbitrary nonempty subsets of H.

TUBERCULOUS PERICARDITIS AND PLEURITIS;

Background: Diagnosis of Tubercles Pericarditis and Pleuritis remains thegreatest challenge for clinicians. WHO has recommended GeneXpert MTB/RIF assay as ascreening test for substitution of conventional methods for the initial diagnosis and prognosisof the extra pulmonary and pulmonary tuberculosis in developing countries. Objectives: Tofind out the diagnostic validity of GeneXpert assay for detection of Myco-bacterium tuberculosisin the pericardial and pleural effusions samples, keeping MTB culture as “Gold Standard”.Material and Methods: Total number of 286 samples of effusions (pericardial 128, pleural 158)were received, and processed for Zn smear microscopy, LJ culture, GeneXpert MTB/RIF assayaccording standard protocols. Efficacy for the detection of MTB was evaluated comparatively.Results: Out of 286effusions samples AFB was detected by Zn smear in 11 (3.8%) samples whileGeneXpert detected MTB in 43 (15.0%) and LJ culture 51 (17.8%). Zn smear showed sensitivity18.2%, specificity, 98.1%, Positive predictive value 81.8%, Negative predictive value 85.4 %, incomparison GeneXpert showed high sensitivity 84.3%, specificity 100%, with Positive predictivevalue 100%, and Negative predictive value 96.7%. Conclusion: GeneXpert assay is innovativetool in resource limited settings for prompt detection of MTB along with drug résistance. It isdefinitely an attractive point of care test, with High sensitivity and specificity along with turnouttime of two hours which facilitates timely diagnoses and appropriate management of tuberclePleuritis and Pericarditis.

On the number of bound states of point interactions on hyperbolic manifolds

We study the bound state problem for [Formula: see text] attractive point Dirac [Formula: see text]-interactions in two- and three-dimensional Riemannian manifolds. We give a sufficient condition for the Hamiltonian to have [Formula: see text] bound states and give an explicit criterion for it in hyperbolic manifolds [Formula: see text] and [Formula: see text]. Furthermore, we study the same spectral problem for a relativistic extension of the model on [Formula: see text] and [Formula: see text].