Uniqueness of certain differential polynomial of L-functions and meromorphic functions sharing a polynomial

The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main theorem of the paper extends and improves all the results in {W. J. Hao and J. F. Chen, Uniqueness of L-functions concerning certain differential polynomials, Discrete Dyn. Nat. Soc., 2018, DOI. 10.1155/2018/4673165}, {F. Liu, X. M. Li and H. X. Yi, Value distribution of L-functions concerning shared values and certain differential polynomials, Proc. Japan. Acad. Ser. A, 93 (2017), 41-46} and {P. Sahoo and S. Haldar, Uniqueness results related to L-functions and certain differential polynomials, Tbilisi Math. J., 11(4) (2018), 67-78}

The 32nd CDC: Robust stabilizer synthesis for interval plants using Nevanlina-pick theory

The synthesis of robustly stabilizing compensators for interval plants, i.e., plants whose parameters vary within prescribed ranges is discussed. Well-known H(sup infinity) methods are used to establish robust stabilizability conditions for a family of plants and also to synthesize controllers that would stabilize the whole family. Though conservative, these methods give a very simple way to come up with a family of robust stabilizers for an interval plant

Lipschitz Estimates and an application to trace formulae

In this note, we provide an elementary proof for the expression of $f(U)-f(V)$ in the form of a double operator integral for every Lipschitz function $f$ on the unit circle \cir and for a pair of unitary operators $(U,V)$ with U-V\in\mathcal{S}_{2}(\hilh) (the Hilbert-Schmidt class). As a consequence, we obtain the Schatten $2$-Lipschitz estimate \|f(U)-f(V)\|_2\leq \|f\|_{\lip(\cir)}\|U-V\|_2 for all Lipschitz functions f:\cir\to\C. Moreover, we develop an approach to the operator Lipschitz estimate for a pair of contractions with the assumption that one of them is a strict contraction, which significantly extends the class of functions from results known earlier. More specifically, for each $p\in(1,\infty)$ and for every pair of contractions $(T_0,T_1)$ with $\|T_0\|0$ such that $\|f(T_1)-f(T_0)\|_p\leq d_{f,p, T_0}\|T_1-T_0\|_p$ for all Lipschitz functions on \cir. Using our Lipschitz estimates, we establish a modified Krein trace formula applicable to a specific category of pairs of contractions featuring Hilbert-Schmidt perturbations.Comment: Improved article presentation; revised Section

Regulation of T-reg/Th-17 Balance: One Step Closer Towards Immunotherapy Against Malaria Infection

According to World Malaria Report 2020, the rate of decline in malaria case incidence and deaths caused by malaria has ceased in latter half of the past decade. Though Artemisinin Combination Therapy (ACT) is still the major therapeutic approach globally to treat malaria patients, increased resistance of Plasmodium sp. to artemisinin can be looked upon as a major factor responsible for the rate of decline. In the present world, immunotherapeutic approaches are in the limelight to treat several infections, autoimmune disorders, cancers but application of such therapeutic measures in case of malaria are yet not available. Among different immune cells, T-regulatory cells (T-reg) and Th-17 cells and the balance between them, helps in determining the outcome of the immune response in host during both lethal and non-lethal malaria. TGFβ and IL-6 are two major cytokines that play important role in fine tuning the Treg/Th-17 balance by modulating dendritic cell responses, specially by regulating the ratio between myeloid DC and plasmacytoid DC (mDC/pDC). Studies in rodent malaria models have revealed that neutralization of IL-6 by using anti IL-6 monoclonal antibodies in-vivo has been found effective in declining the parasitemia, malaria induced deaths and also in reverting back the altered T-reg/Th-17 balance to normal levels. Apart from these, autophagy is one of the major factors which also contributes to regulate the T-reg/Th-17 balance. In malaria infected mice, autophagy induction has been found to normalise the dysregulated T-reg/Th-17 ratio and promote anti-inflammatory Th-2 pathway by supressing pro-inflammatory Th-1 pathway. So, Treg/Th-17 balance and its associated regulators can be important immunotherapeutic targets for malaria prevention in near future

Ross syndrome: a case report

Ross syndrome is a rare partial dysautonomic syndrome of unknown aetiology, characterized by segmental hypo/ anhidrosis associated with Holmes-Adie syndrome (tonic pupil and hypo/areflexia). The hypohydrosis or anhydrosis is patchy initially, later it becomes segmental or diffuse. This is due to affection of postganglionic cholinergic parasympathetic and sympathetic fibers involvement. There are a very few cases (approximately 50) have been reported in the literature since its original description. Author report a 22 years old male with classical features of Ross syndrome

Calculation of true coincidence summing correction factor for a Broad Energy Germanium (BEGe) detector using standard and fabricated sources

The true coincidence summing (TCS) correction factor for a Broad Energy Germanium (BEGe) detector has been calculated at far and close geometry measurement using multi-energetic radioactive $\gamma$-ray sources $^{60}$Co, $^{133}$Ba and $^{152}$Eu. The correction factors were calculated using experimental method and analytical method. Photopeak efficiency and total efficiency required to calculate the correction factor were obtained using Geant4 Monte Carlo simulation code. A few standard as well as fabricated mono-energetic sources were also included in the $\gamma$-ray efficiency measurements. The simulated efficiencies of mono-energetic $\gamma$-ray sources were matched to experimental $\gamma$-ray efficiencies by optimizing the detector parameters. The same parameters were used to obtain the photopeak and total efficiency for $\gamma$-ray of our interest and coincident $\gamma$-ray. Analytical correction factors and experimental correction factors were found in good agreement with each other

A mosaic of RNA binding and protein interaction motifs in a bifunctional mitochondrial tRNA import factor from Leishmania tropica

Proteins that participate in the import of cytosolic tRNAs into mitochondria have been identified in several eukaryotic species, but the details of their interactions with tRNA and other proteins are unknown. In the kinetoplastid protozoon Leishmania tropica, multiple proteins are organized into a functional import complex. RIC8A, a tRNA-binding subunit of this complex, has a C-terminal domain that functions as subunit 6b of ubiquinol cytochrome c reductase (complex III). We show that the N-terminal domain, unique to kinetoplastid protozoa, is structurally similar to the appended S15/NS1 RNA-binding domain of aminoacyl tRNA synthetases, with a helix–turn–helix motif. Structure-guided mutagenesis coupled with in vitro assays showed that helix α1 contacts tRNA whereas helix α2 targets the protein for assembly into the import complex. Inducible expression of a helix 1-deleted variant in L. tropica resulted in formation of an inactive import complex, while the helix 2-deleted variant was unable to assemble in vivo. Moreover, a protein-interaction assay showed that the C-terminal domain makes allosteric contacts with import receptor RIC1 complexed with tRNA. These results help explain the origin of the bifunctionality of RIC8A, and the allosteric changes accompanying docking and release of tRNA during import