Differential Topology

This paper proposes a new differential topology that features a stacked multiloop inductor. Comparative studies of stacked one-to four-loop spiral inductors with and without patterned ground shields (PGSs) for silicon-based radio-frequency integrated circuits (RFICs) were conducted, and lumped-element circuit models were developed for these inductors. The partialelement equivalent-circuit method that can accurately analyze mutual inductive couplings among different spirals in these multiloop geometries was employed for capturing the frequencydependent inductances and resistances of inductors at low frequencies. A good agreement between numerical results and measurements is obtained. It is demonstrated that a stacked multiloop spiral inductor with differential topology and PGS has a larger inductance and a higher Q-factor as compared with the same inductor without differential topology and PGS. This hybrid methodology could provide a promising technique for developing new silicon-based passive devices used in RFICs.

Las nociones de Variedad Diferenciable y Variedad Algebraica son similares sin embargo,
su diferencia radica y muy importante, es que una variedad algebraica puede tener puntos singulares mientras que una variedad diferenciable no tiene. A partir de lo anterior, se formula la siguiente pregunta ¿cuando una variedad dierenciable puede verse como una variedad algebraica?.
Para responder esta pregunta usaremos el siguiente objeto: “Si M es una variedad diferenciable y X es una variedad algebráica afín no-singular difeomorfa a M, se dice que X es un Modelo Algebraico de M”, así podemos reformular la pregunta anterior ¿Cuando
una variedad diferenciable tiene un modelo algebraico?.

A high data transfer rate quadrature phase shift keying (QPSK) demodulator is proposed for wireless implantable electronic medical devices. The QPSK demodulator is an improved version from our previous binary phase shift keying (BPSK) demodulator, which is based on a modified Costas loop. Simulated QPSK model under Matlab Simulink obtained a data transmission rate of 8 Mbps with 13.56 MHz carrier frequency. Also, implemented differential topology of the proposed circuit using a 0.18µm CMOS technology achieves a data transmission rate up to 4Mbps with the same carrier frequency. The simulated power dissipation of the schematic is 0.75mw under 1.8V power supply.

For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group isomorphic to Z/r. As an application we construct the first examples of manifolds which possess infinitely many metrics of nonnegative sectional curvature with pairwise non-homeomorphic homogeneous souls of codimension three with trivial normal bundle, such that their curvatures and the diameters of the souls are uniformly bounded. These manifolds are the first examples of manifolds fulfilling such geometric conditions and they serve as solutions to a problem posed by I. Belegradek, S. Kwasik and R. Schultz.

Let T(\gamma) be the total space of the canonical line bundle \gamma over CP^1 and r an integer which is greater than one and coprime to six. We prove that L_r^3\times T(\gamma) admits an infinite sequence of metrics of nonnegative sectional curvature with pairwise non-homeomorphic souls, where L_r^3 is the standard 3-dimensional lens space with fundamental group isomorphic to Z/r. We classify the total spaces of S^1-fibre bundles over S^2\times S^2 with fundamental group isomorphic to Z/r up to diffeomorphism and use these results to give examples of manifolds N which admit two complete metrics of nonnegative sectional curvature with souls S and S' of codimension two such that S and S' are diffeomorphic whereas the pairs (N,S) and (N,S') are not diffeomorphic. This solves a problem posed by I. Belegradek, S. Kwasik and R. Schultz.

Two compact and simple to design differential phase shifter topologies, based on high/low impedance transmission line sections and open-ended coupled line sections, are presented for the first time. The basic circuit theory for single section topologies is reviewed, leading to design equations and graphs for direct circuit synthesis. Balanced topologies and multiple section designs are also proposed improving the performance and feasibility of the phase shifters. Two planar microstrip single section differential phase shifter hybrids, at a centre frequency of 12 GHz and a 45° and 135° phase difference have been designed and manufactured. The designs have a simulated 0.5 dB amplitude and 1° phase imbalance over more than 25% and 40% bandwidth, respectively. Experimental results verify the circuit performance and feasibility of the proposed differential phase shifters.

In this paper, differential low-noise amplifiers are presented as a very powerful solution for radio astronomy applications. A fully differential amplifier topology has been analyzed and implemented in microstrip technology with discrete surface mount components. The amplifier design is made for an active receiving dense antenna array. Thus, the differential amplifier source impedance is no longer 50 , but 150 from the proposed bunny-ear antennas. A full characterization in terms of gain and noise has been undertaken. Source-pull measurements have been included in order to evaluate the performance of the amplifiers operating with variable source impedances. Noise temperatures below 55 K have been obtained for the differential design in the 300-1000-MHz band for the 150impedance. In addition, the results for different scanning angles are also presented.

"Let (M, g) be a compact, connected riemannian manifold that is homogeneous, i.e. each pair of points p, q ∈ M have isometric neighborhoods. This paper is a first step towards an understanding of the extent to which it is true that for each "generic" initial condition ff/∂t = Δgf, f(⋅, 0) = f0 is such that for sufficiently large t, f(⋅ t) is a minimal Morse function, i.e., a Morse function whose total number of critical points is the minimal possible on M. In this paper we show that this is true for flat tori and round spheres in all dimensions."