Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

Triples of Positive Integers with the same Sum and the same Product

It is proved that for every k there exist k triples of positive integers with the same sum and the same product.

An Invariant Theory of Surfaces in the Four-Dimensional Euclidean or Minkowski Space

2010 Mathematics Subject Classification: 53A07, 53A35, 53A10.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

On a Generalization of a Theorem due to Larcombe on the Sum of a 3F2 Series

MSC 2010: 33C20

Weighted Sum of Correlated Lognormals: Convolution Integral Solution

Probability density function (pdf) for sum of n correlated lognormal variables is deducted as a special convolution integral. Pdf for weighted sums (where weights can be any real numbers) is also presented. The result for four dimensions was checked by Monte Carlo simulation.

Variable 360° Vector-Sum Phase Shifter With Coarse and Fine Vector Scaling

A CMOS vector-sum phase shifter covering the full 360° range is presented in this paper. Broadband operational transconductance amplifiers with variable transconductance provide coarse scaling of the quadrature vector amplitudes. Fine scaling of the amplitudes is accomplished using a passive resistive network. Expressions are derived to predict the maximum bit resolution of the phase shifter from the scaling factor of the coarse and fine vector-scaling stages. The phase shifter was designed and fabricated using the standard 130-nm CMOS process and was tested on-wafer over the frequency range of 4.9–5.9 GHz. The phase shifter delivers root mean square (rms) phase and amplitude errors of 1.25° and 0.7 dB, respectively, at the midband frequency of 5.4 GHz. The input and output return losses are both below 17 dB over the band, and the insertion loss is better than 4 dB over the band. The circuit uses an area of 0.303 mm2 excluding bonding pads and draws 28 mW from a 1.2 V supply.

How Much Greater Than the Sum of Its Parts? Evaluating Interactions Between Complex Policies

This presentation focuses on methods for the evaluation of complex policies. In particular, it focuses on evaluating interactions between policies and the extent to which two or more interacting policies mutually reinforce or hinder one another, in the area of environmental sustainability. Environmental sustainability is increasingly gaining recognition as a complex policy area, requiring a more systemic perspective and approach (e.g. European Commission, 2011). Current trends in human levels of resource consumption are unsustainable, and single solutions which target isolated issues independently of the broader context have so far fallen short. Instead there is a growing call among both academics and policy practitioners for systemic change which acknowledges and engages with the complex interactions, barriers and opportunities across the different actors, sectors, and drivers of production and consumption. Policy mixes, and the combination and ordering of policies within, therefore become an important focus for those aspiring to design and manage transitions to sustainability. To this end, we need a better understanding of the interactions, synergies and conflicts between policies (Cunningham et al., 2013; Geels, 2014). As a contribution to this emerging field of research and to inform its next steps, I present a review on what methods are available to try to quantify the impacts of complex policy interactions, since there is no established method among practitioners, and I explore the merits or value of such attempts. The presentation builds on key works in the field of complexity science (e.g. Anderson, 1972), revisiting and combining these with more recent contributions in the emerging field of policy and complex systems, and evaluation (e.g. Johnstone et al., 2010). With a coalition of UK Government departments, agencies and Research Councils soon to announce the launch of a new internationally-leading centre to pioneer, test and promote innovative and inclusive methods for policy evaluation across the energy-environment-food nexus, the contribution is particularly timely.

Effect of channel aging on the sum rate of uplink massive MIMO systems

This paper investigates the achievable sum-rate of uplink massive multiple-input multiple-output (MIMO) systems considering a practical channel impairment, namely, aged channel state information (CSI). Taking into account both maximum ratio combining (MRC) and zero-forcing (ZF) receivers at the base station, we present tight closed-form lower bounds on the sum-rate for both receivers, which provide efficient means to evaluate the sum-rate of the system. More importantly, we characterize the impact of channel aging on the power scaling law. Specifically, we show that the transmit power of each user can be scaled down by 1/√(M), which indicates that aged CSI does not affect the power scaling law; instead, it causes only a reduction on the sum rate by reducing the effective signal-to-interference-and-noise ratio (SINR).

Achievable sum-rate of multiuser massive MIMO downlink in ricean fading channels

We investigate the achievable ergodic sum-rate of multi-user multiple-input multiple-output systems in Ricean fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by utilizing the Mullen's inequality, which is then used to analyze the effect of channel mean information on the achievable sum-rate. With these results, a novel statistical-eigenmode space-division multipleaccess downlink transmission scheme is proposed. For this scheme, we derive an exact closed-form expression for the achievable ergodic sum-rate. Our results show that the achievable ergodic sum-rate converges to a saturation value in the high signal-to-noise ratio (SNR) region and reaches to a lower limit value in the lower Ricean K-factor range. In addition, we present tractable upper and lower bounds, which are shown to be tight for any SNR and Ricean K-factor value. Finally, the theoretical analysis is validated via numerical simulations.