First-order equivalent to Einstein-Hilbert Lagrangian

A first-order Lagrangian L ∇ variationally equivalent to the second-order Einstein- Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by L ∇ is proved to be regular and its Hamiltonian formulation is studied, including its covariant Hamiltonian attached to ∇ .

Integrability of second-order Lagrangians admitting a first-order Hamiltonian formalism

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) necessary and sufficient conditions for the Poincaré–Cartan form of a second-order Lagrangian on an arbitrary fibred manifold p : E → N to be projectable onto J 1 E are explicitly determined; ii) for each of such Lagrangians, a first-order Hamiltonian formalism is developed and a new notion of regularity is introduced; iii) the variational problems of this class defined by regular Lagrangians areprovedtobeinvolutive

Stability switches in a first-order complex neutral delay equation

Stability of the first-order neutral delay equation x’ (t) + ax’ (t – τ) = bx(t) + cx(t – τ) with complex coefficients is studied, by analyzing the existence of stability switches.

European elections: from ‘second-order’ elections to ‘first-order supranational’ elections, How can a ‘first-order supranational’ European election be created? European Policy Brief No. 34, April 2014

Starting from the idea that European elections cannot be considered as purely second order elections, the author gathers some proposals in order to encourage a more effective electoral process. According to the author, if political leaders adopt these reforms, it could transform gradually the European elections into genuine ‘first-order supranational elections’.

European elections: from ‘second-order’ elections to ‘first-order supranational’ elections: How can a ‘first-order supranational’ European election be created?. European Policy Brief No. 35, April 2015

Starting from the idea that European elections cannot be considered as purely second order elections, the author gathers some proposals in order to encourage a more effective electoral process. According to the author, if political leaders adopt these reforms, it could transform gradually the European elections into genuine ‘first-order supranational elections’.

Complete problems in the first-order predicate calculus /

"UILU-ENG 79 1726."

Statistical-physical models of man-made and natural radio noise : part IV, Determination of the first-order parameters of class A and B interference /

Issued Sept. 1978.

Operator, organizational, direct support, general support, and depot maintenance manual : theodolite, directional, 2/10 sec graduation, first-order, with accessories, trivet, tripod, and cases (Kern model DKM3M) FSN 6675-455-9200.

Includes index.

A First Order Predicate Logic Formulation of the 3D Reconstruction Problem and its Solution Space

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 x 5 voxel space gives 10 to 10(7) solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

Point-by-point inscription of first-order fiber Bragg grating for C-band applications

The influence of the fiber geometry on the point-by-point inscription of fiber Bragg gratings using a femtosecond laser is highlighted. Fiber Bragg gratings with high spectral quality and strong first-order Bragg resonances within the C-band are achieved by optimizing the inscription process. Large birefringence (1.2×10-4) and high degree of polarizationdependent index modulation are observed in these gratings. Potential applications of these gratings in resonators are further illustrated.

Femtosecond inscription of the first order Bragg gratings in pure fused silica

The fabrication of sub-micron periodic structures beyond diffraction limit is a major motivation for the present paper. We describe the fabrication of the periodic structure of 25 mm long with a pitch size of 260 nm which is less than a third of the wavelength used. This is the smallest reported period of the periodic structure inscribed by direct point-by-point method. A prototype of the add-drop filter, which utilizes such gratings, was demonstrated in one stage fabrication process of femtosecond inscription, in the bulk fused silica.

Femtosecond inscription of the first order Bragg gratings in pure fused silica

The fabrication of sub-micron periodic structures beyond diffraction limit is a major motivation for the present paper. We describe the fabrication of the periodic structure of 25 mm long with a pitch size of 260 nm which is less than a third of the wavelength used. This is the smallest reported period of the periodic structure inscribed by direct point-by-point method. A prototype of the add-drop filter, which utilizes such gratings, was demonstrated in one stage fabrication process of femtosecond inscription, in the bulk fused silica.

Analytical first order comparison of amplitude and phase noise in single and dual Mach-Zehnder interferometer detection schemes for DQPSK transmission systems

An analytical first order calculation of the impact of Gaussian white noise on a novel single Mach-Zehnder Interferometer demodulation scheme for DQPSK reveals a constant Q factor ratio to the conventional scheme.