Fixed points of fuzzy mappings in Hilbert spaces

In this paper we work out two fixed point theorems for fuzzy mappings on Hilbert spaces. The proofs rely on the paralellogram law in Hilbert spaces

Salt Crystal Growth in Interacting Drops of a Complex Biopolymer: Statistical Characterization Using FESEM Images

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.  A simple colloidal drop generally forms ring like patterns after drying. The deposition morphology of the dried drop changes significantly when such a drop dries in the vicinity of another similar drop. Here we present an observational study and statistical analysis of the patterns formed inside an isolated as well as interacting drops of gelatin containing sodium sulfate (Na2SO4). In all the cases, multiple concentric regions of solute particles combined with the polymer gel appear as the drops dry up. Needle crystals of sulfur and coacervates of salt and gelatin are visible in some regions. The outer region becomes non-uniform, so does the size distribution of the needle crystals and coacervates. The non-uniformity increases with proximity of the drops. Here we propose a novel mechanism of growing patterns inside the single drop during drying and correlate that with the results obtained for interacting drops. This study and the proposed mechanism provide insights into the future studies of drying drops under different physical conditions. Further we explore the statistical characteristics of the single and interacting drops using the field emission scanning electron microscopy (FESEM) images. Next, we report fractal and image texture analyses along with object shape statistics of the drop FESEM images, under various experimental conditions. Several statistical hypothesis tests have been carried out to identify the most significant features.SERB, IndiaGovt. of Indi

Generalized Model for Λ\Lambda-Dark Energy

Einstein field equations under spherically symmetric space-times are considered here in connection to dark energy investigation. A set of solutions are obtained for a kinematical $\Lambda$ model, viz., $\Lambda \sim (\dot a/a)^2$ without assuming any {\it a priori} value for the curvature constant and the equation of state parameter $\omega$. Some interesting results, such as the nature of cosmic density $\Omega$ and deceleration parameter $q$, have been obtained with the consideration of two-fluid structure instead of usual uni-fluid cosmological model.Comment: 8 Latex page

Effect of vitrification techniques on post-thaw survivability and in vitro maturation of immature bovine oocytes

The present study was conducted to evaluate the effectiveness of single-step and two-step vitrification techniques on post-thaw survivability and subsequent in vitro maturation of immature bovine oocytes. In two-step vitrification method, oocytes were first equilibrated in vitrification solution-I and then vitrification solution–II of 3.5M or 4.0M and 7.0M or 8.0M glycerol + ethylene glycol (GLY+EG) cryoprotectant respectively. In single-step vitrification technique oocytes were directly exposed to final vitrification solution (7 M or 8 M of GLY+EG) for 45, 60 and 75 sec to find out the suitable exposure time based on post-thaw survivability and subsequent development in vitro. In single step vitrification the per cent morphologically normal oocyte, cumulus cells expansion and polar body formation was found to be significantly highest in oocytes of least exposure (45 seconds) period for 8M of GLY+EG. The per cent recovery of morphologically normal oocytes was found to be higher in two steps (91.81±1.42 and 91.18±1.17) than single step vitrification technique (87.94±3.49 and 85.72±2.24 of 45 sec exposure time) for both 7M and 8M of GLY+EG. The rate of cumulus cells expansion and polar body formation was significantly higher in two-steps (81.34±2.65% and 76.54±3.60% and 56.93±1.52% and 51.76±2.87%) than single step vitrification technique (57.33±3.90% and 56.91±4.66% and 33.17±5.34% and 32.70±2.91%). From the study it was concluded that two-step vitrification technique was more effective on post-thaw survivability and subsequent in vitro maturation of immature bovine oocytes

Triviality Bound on Lightest Higgs Mass in NMSSM

We study the implication of triviality on Higgs sector in next to minimal supersymmetric model (NMSSM) using variational field theory. It is shown that mass of the lightest Higgs boson in NMSSM has an upper bound $\sim 10\, M_W$ which is of the same order as that in standard model.Comment: Plain Tex, 12 page

Dark energy models with time-dependent gravitational constant

Two phenomenological models of $\Lambda$, viz. $\Lambda \sim (\dot a/a)^2$ and $\Lambda \sim \ddot a/a$ are studied under the assumption that $G$ is a time-variable parameter. Both models show that $G$ is inversely proportional to time as suggested earlier by others including Dirac. The models considered here can be matched with observational results by properly tuning the parameters of the models. Our analysis shows that $\Lambda \sim \ddot a/a$ model corresponds to a repulsive situation and hence correlates with the present status of the accelerating Universe. The other model $\Lambda \sim (\dot a/a)^2$ is, in general, attractive in nature. Moreover, it is seen that due to the combined effect of time-variable $\Lambda$ and $G$ the Universe evolved with acceleration as well as deceleration. This later one indicates a Big Crunch.Comment: Latex, 6 page

Chemical equilibration and thermal dilepton production from the quark gluon plasma at finite baryon density

The chemical equilibration of a highly unsaturated quark-gluon plasma has been studied at finite baryon density. It is found that in the presence of small amount of baryon density, the chemical equilibration for gluon becomes slower and the temperature decreases less steeply as compared to the baryon free plasma. As a result, the space time integrated yield of dilepton is enhanced if the initial temperature of the plasma is held fixed. Even at a fixed initial energy density, the suppression of the dilepton yields at higher baryo-chemical potential is compensated, to a large extent, by the slow cooling of the plasma.Comment: Latex, 19 pages, 8 postscript figures. To appear in Phys. Rev.

Don't Stop Thinking About Leptoquarks: Constructing New Models

We discuss the general framework for the construction of new models containing a single, fermion number zero scalar leptoquark of mass $\simeq 200-220$ GeV which can both satisfy the D0/CDF search constraints as well as low energy data, and can lead to both neutral and charged current-like final states at HERA. The class of models of this kind necessarily contain new vector-like fermions with masses at the TeV scale which mix with those of the Standard Model after symmetry breaking. In this paper we classify all models of this type and examine their phenomenological implications as well as their potential embedding into SUSY and non-SUSY GUT scenarios. The general coupling parameter space allowed by low energy as well as collider data for these models is described and requires no fine-tuning of the parameters.Comment: Modified text, added table, and updated reference

Neutral Gauge Boson Contributions to the Dimuon Charge Asymmetry in B Decays

Recently, the D0 Collaboration measured the CP-violating like-sign dimuon charge asymmetry in neutral B decays, finding a 3.2sigma difference from the standard-model (SM) prediction. A non-SM charge asymmetry a_sl^s suggests a new-physics (NP) contribution to Bs-Bsbar mixing. In this case, in order to explain the measured value of a_sl^s within its 1sigma range, NP must be present in Gamma_12^s, the absorptive part of the mixing. In this paper, we examine whether such an explanation is possible in models with flavor-changing Z (ZFCNC) or Z' (Z'FCNC) gauge bosons. The models must also reproduce the measured values of the indirect CP asymmetry S_psi-phi in Bs -> J/psi phi, and Delta Gamma_s, the Bs-Bsbar width difference. We find that the ZFCNC model cannot reproduce the present measured values of S_psi-phi and a_sl^s within their 1sigma ranges. On the other hand, in the Z'FCNC model, the values of all three observables can be simultaneously reproduced.Comment: 18 pages, 7 figures, JHEP format. Some ZFCNC equations corrected, ZFCNC analysis redone, references added, conclusions unchange