A 3D-printed polarization-independent low-cost lightweight and flexible frequency selective surface based dual-band microwave absorber is presented in this paper. Two concentric square loops fabricated at different heights using 3D printing technology are responsible for exhibiting dual-band responses at 3.32 GHz (S-band) and 5.46 GHz (C-band) with more than 97% absorptivities. The corresponding full widths at half maximum bandwidths are observed as 230 MHz (3.21–3.44 GHz) and 450 MHz (5.27–5.72 GHz). The proposed topology is polarization-insensitive owing to the four-fold symmetry. The absorption phenomenon is explained with the analysis of current distributions at the surface and impedance curves at the frequencies of resonance. Further, the performance has been evaluated for both planar and curved surfaces with different angles of curvature, and the good agreement between the measured and simulated responses confirms the flexible behavior of the proposed structure.

This article presents a novel miniaturized (0.105λ0 × 0.105λ0) flexible complementary frequency selective surfaces (CFSS) structure with sharp band edge selectivity and very high angular stability. To explore two diverse applications as a passband and stopband filter, a novel complementary convoluted square loop (CCSL) type structure has been designed and investigated on ultrathin dielectric material of thickness 0.0023λ0. The second-order wide controllable passband with fractional bandwidth of 19.23% (−3 dB) and remarkably wide stopband of 64.7% (−10 dB) and 54.8% (−20 dB) respectively have been achieved by using a cascaded resonating structure which is composed of asymmetrical meandered CCSL array, arranged on two ultrathin dielectric layers with air foam separation. This particular format would lead to sharp band edge selectivity with steep roll-off (72.43 dB/GHz) and an excellent passband selectivity factor (0.731). An equivalent lumped LC circuit in conjunction with the transmission line model has also been adopted to comprehend the physical mechanism of the proposed single layer and double layer structures. Further, better passband and stopband angular stability at an oblique incident angle of 45° and the bending characteristics have also been investigated thoroughly for the proposed flexible CFSS to check their employability in different conformal structures with WiMAX passband and WLAN stopband application.

Objective: The objective of this study was to directly compare the cost of conformal radiotherapy used with the RTo1 trial with that of non-conformal radiotherapy of the prostate.

Method: Two methods were employed to establish the cost, a simplistic top-down method and the more complicated bottom-up method that involved breaking down the cost elements of the respective treatments and undertaking a non-participative timing study on 37 patients undergoing radiotherapy. Costs were then ascribed based on the time the staff and equipment were utilised.

Results: The total cost of radiotherapy using the top-down method for both non-conformal radiotherapy and 32 fraction conformal radiotherapy was £2890.88, compared with £3342.58 for conformal radiotherapy using 37 fractions. The costs of the bottom-up method were £2485.67 for non-conformal radiotherapy, £2717.67 for 32 fraction conformal radiotherapy and £3110.52 for conformal radiotherapy using a 37 fraction regime.

Conclusions: Conformal radiotherapy of the prostate costs significantly more than non-conformal radiotherapy which reflects the increase in complexity of the technique. Cost differences arose due to increased time in the planning stage and in the actual treatment because of an increase in equipment and staffing costs during treatment.

Conformally invariant functionals on the space of knots are introduced via extrinsic conformal geometry of knots and integral geometry on the space of spheres. Our functionals are expressed in terms of a complex-valued 2-form, which can be considered as the cross-ratio of a pair of infinitesimal segments of the knot. We show that our functionals detect the unknot as the total curvature does, and that their values explode if a knot degenerates to a singular knot with double points.

AMS 2000 Mathematics subject classification: Primary 57M25; 53A30. Secondary 57R17

The paper extends the rigidity of the mixing expanding repellers theorem of D. Sullivan announced at the 1986 IMC. We show that, for a regular conformal, satisfying the ‘Open Set Condition’, iterated function system of countably many holomorphic contractions of an open connected subset of a complex plane, the Radon–Nikodym derivative dμ/dm has a real-analytic extension on an open neighbourhood of the limit set of this system, where m is the conformal measure and μ is the unique probability invariant measure equivalent with m. Next, we introduce the concept of nonlinearity for iterated function systems of countably many holomorphic contractions. Several necessary and sufficient conditions for nonlinearity are established. We prove the following rigidity result: If h, the topological conjugacy between two nonlinear systems F and G, transports the conformal measure mF to the equivalence class of the conformal measure mG, then h has a conformal extension on an open neighbourhood of the limit set of the system F. Finally, we prove that the hyperbolic system associated to a given parabolic system of countably many holomorphic contractions is nonlinear, which allows us to extend our rigidity result to the case of parabolic systems.