Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X-valued functions on Rn. We characterize Kato’s square root estimates ‖ √ Lu‖p h ‖∇u‖p and the H-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp spac...

This paper presents a new class AB programmable square-root domain (SRD) filter. The main advantages of the proposed circuits are low power consumption, wide input dynamic range with small standby current and potential for low-voltage operation. Simulation results confirm the validity of the proposed design technique and the high performance of the proposed circuits. Key-Words: Square-root doma...

In certain bodies, like the Council of the EU, the member states have a voting weight which depends on the population of the respective state. IN this article we ask the question which voting weight guarantees a ‘fair’ representation of the citizens in the union. The traditional answer, the square-root law by Penrose, is that the weight of a state (more precisely: the voting power) should be pr...

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

This paper presents the operation and the implementation of novel fixed point square root algorithms with an input range of 0 to 1 into CMOS. These algorithms are referred to as non-restoring and restoring algorithm and were compared with a square root implementation into a lookup table (LUT). The power consumption, the area consumption and the propagation delay were investigated and the result...

Allowing for the inclusion of the parity operator, it is possible to construct a model of an oscillator whose Hamiltonian admits an exact square root which is rather different from the conventional approach based on creation and annihilation operators. We outline such a model, the method of solution and some generalisations. 03.65.Ge, 03.65.Fd Typeset using REVTEX In memory of Lorella M Jones w...

This paper presents a program transformation that removes square roots and divisions from functional programs without recursion, producing code that can be exactly computed. This transformation accepts different subsets of languages as input and it provides a certifying mechanism when the targeted language is Pvs. In this case, we provide a relation between every function definition in the outp...

The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute the eigenvalues where the basis functions in the formulae are...

465 news & views of amplifiers and logic devices based on graphene, actually enables a new class of nonlinear radiofrequency electronic devices. Frequency multipliers 5,6, , high-frequency mixers 7 and digital modulators 8,9 have all been recently demonstrated using this principle, with operating frequencies as high as 16 GHz and radiofrequency efficiencies in excess of 90% (ref. 10). Infrared ...