77,252 research outputs found

### Design of a New Step-like Frame FBAR for Suppression of Spurious Resonances

Film bulk acoustic wave resonators (FBARs) are of great interest for wireless applications due to its inherent advantages at microwave frequencies. However, the presence of spurious modes near the main resonance degrades the performance of resonators and requires development of new methods to suppress such unwanted modes. Different techniques are used to suppress these spurious modes. In this paper, we present design of a new step-like frame structure film bulk acoustic wave resonator operating near 1.5 GHz. The simulated results are compared with simple frame-like structure. The spurious resonances are eliminated effectively and smooth pass band is obtained with effective coupling coefficient of 5.68% and quality factor of 1800. The equivalent electrical mBVD model of the FBAR based on impedance response is also presented. These highly smooth phase response and passband skirt steepness resonators are most demanding for the design of low cost, small size and high performance filters, duplexers and oscillators for wireless systems

### On Rational Sets in Euclidean Spaces and Spheres

IFor a positive rational $l$, we define the concept of an $l$-elliptic and an
$l$-hyperbolic rational set in a metric space. In this article we examine the
existence of (i) dense and (ii) infinite $l$-hyperbolic and $l$-ellitpic
rationals subsets of the real line and unit circle. For the case of a circle,
we prove that the existence of such sets depends on the positivity of ranks of
certain associated elliptic curves. We also determine the closures of such sets
which are maximal in case they are not dense. In higher dimensions, we show the
existence of $l$-ellitpic and $l$-hyperbolic rational infinite sets in unit
spheres and Euclidean spaces for certain values of $l$ which satisfy a weaker
condition regarding the existence of elements of order more than two, than the
positivity of the ranks of the same associated elliptic curves. We also
determine their closures. A subset $T$ of the $k$-dimensional unit sphere $S^k$
has an antipodal pair if both $x,-x\in T$ for some $x\in S^k$. In this article,
we prove that there does not exist a dense rational set $T\subset S^2$ which
has an antipodal pair by assuming Bombieri-Lang Conjecture for surfaces of
general type. We actually show that the existence of such a dense rational set
in $S^k$ is equivalent to the existence of a dense $2$-hyperbolic rational set
in $S^k$ which is further equivalent to the existence of a dense 1-elliptic
rational set in the Euclidean space $\mathbb{R}^k$.Comment: 20 page

### Friedmann model with viscous cosmology in modified $f(R,T)$ gravity theory

In this paper, we introduce bulk viscosity in the formalism of modified
gravity theory in which the gravitational action contains a general function
$f(R,T)$, where $R$ and $T$ denote the curvature scalar and the trace of the
energy-momentum tensor, respectively within the framework of a flat
Friedmann-Robertson-Walker model. As an equation of state for prefect fluid, we
take $p=(\gamma-1)\rho$, where $0 \leq \gamma \leq 2$ and viscous term as a
bulk viscosity due to isotropic model, of the form $\zeta
=\zeta_{0}+\zeta_{1}H$, where $\zeta_{0}$ and $\zeta_{1}$ are constants, and
$H$ is the Hubble parameter. The exact non-singular solutions to the
corresponding field equations are obtained with non- viscous and viscous
fluids, respectively by assuming a simplest particular model of the form of
$f(R,T) = R+2f(T)$, where $f(T)=\alpha T$ ( $\alpha$ is a constant). A big-rip
singularity is also observed for $\gamma<0$ at a finite value of cosmic time
under certain constraints. We study all possible scenarios with the possible
positive and negative ranges of $\alpha$ to analyze the expansion history of
the universe. It is observed that the universe accelerates or exhibits
transition from decelerated phase to accelerated phase under certain
constraints of $\zeta_0$ and $\zeta_1$. We compare the viscous models with the
non-viscous one through the graph plotted between scale factor and cosmic time
and find that bulk viscosity plays the major role in the expansion of the
universe. A similar graph is plotted for deceleration parameter with
non-viscous and viscous fluids and find a transition from decelerated to
accelerated phase with some form of bulk viscosity.Comment: 19 pages, 3 figures, the whole paper has been revised to improve the
quality of paper. Some references added. arXiv admin note: text overlap with
arXiv:1307.4262 by other author

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