On the nonsymmetric purely affine gravity

We review the vacuum purely affine gravity with the nonsymmetric connection and metric. We also examine dynamical effects of the second Ricci tensor and covariant second-rank tensors constructed from the torsion tensor in the gravitational Lagrangian.Comment: 15 pages; published versio

Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters

We present a systematic technique to construct solutions to the Yang-Baxter equation which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form. We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$ and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are known to admit non-trivial one-parameter families of infinite-dimensional and finite dimensional irreps, respectively, even for generic $q$. We develop a technique for constructing the corresponding spectral-dependent R-matrices. As examples we work out the the $R$-matrices for the three quantum algebras mentioned above in certain representations.Comment: 13 page

Integrable multiparametric quantum spin chains

Using Reshetikhin's construction for multiparametric quantum algebras we obtain the associated multiparametric quantum spin chains. We show that under certain restrictions these models can be mapped to quantum spin chains with twisted boundary conditions. We illustrate how this general formalism applies to construct multiparametric versions of the supersymmetric t-J and U models.Comment: 17 pages, RevTe

Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable equations have the Painlev\'e property, that is, all solutions are single-valued around all movable singularities. In this expository article, we review methods for analysing such singularity structure. In particular, we describe well known techniques of nonlinear regular-singular-type analysis, i.e. the Painlev\'e tests for ordinary and partial differential equations. Then we discuss methods of obtaining sufficiency conditions for the Painlev\'e property. Recently, extensions of \textit{irregular} singularity analysis to nonlinear equations have been achieved. Also, new asymptotic limits of differential equations preserving the Painlev\'e property have been found. We discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B. Grammaticos and K. Tamizhman

Geodesic and Path Motion in the Nonsymmetric Gravitational Theory

We study the problem of test-particle motion in the Nonsymmetric Gravitational Theory (NGT) assuming the four-velocity of the particle is parallel-transported along the trajectory. The predicted motion is studied on a static, spherically symmetric background field, with particular attention paid to radial and circular motions. Interestingly, it is found that the proper time taken to travel between any two non-zero radial positions is finite. It is also found that circular orbits can be supported at lower radii than in General Relativity for certain forms of motion. We present three interactions which could be used as alternate methods for coupling a test-particle to the antisymmetric components of the NGT field. One of these takes the form of a Yukawa force in the weak-field limit of a static, spherically symmetric field, which could lead to interesting phenomenology.Comment: 17 pages, REVTeX 3.0 with amssymb.st

Null dust in canonical gravity

We present the Lagrangian and Hamiltonian framework which incorporates null dust as a source into canonical gravity. Null dust is a generalized Lagrangian system which is described by six Clebsch potentials of its four-velocity Pfaff form. The Dirac--ADM decomposition splits these into three canonical coordinates (the comoving coordinates of the dust) and their conjugate momenta (appropriate projections of four-velocity). Unlike ordinary dust of massive particles, null dust therefore has three rather than four degrees of freedom per space point. These are evolved by a Hamiltonian which is a linear combination of energy and momentum densities of the dust. The energy density is the norm of the momentum density with respect to the spatial metric. The coupling to geometry is achieved by adding these densities to the gravitational super-Hamiltonian and supermomentum. This leads to appropriate Hamiltonian and momentum constraints in the phase space of the system. The constraints can be rewritten in two alternative forms in which they generate a true Lie algebra. The Dirac constraint quantization of the system is formally accomplished by imposing the new constraints as quantum operator restrictions on state functionals. We compare the canonical schemes for null and ordinary dust and emhasize their differences.Comment: 25 pages, REVTEX, no figure

Crystallographic reconstruction study of the effects of finish rolling temperature on the variant selection during bainite transformation in C-Mn high-strength steels

The effect of finish rolling temperature (FRT) on the austenite- () to-bainite () phase transformation is quantitatively investigated in high-strength C-Mn steels. In particular, the present study aims to clarify the respective contributions of the conditioning during the hot rolling and the variant selection (VS) during the phase transformation to the inherited texture. To this end, an alternative crystallographic reconstruction procedure, which can be directly applied to experimental electron backscatter diffraction (EBSD) mappings, is developed by combining the best features of the existing models: the orientation relationship (OR) refinement, the local pixel-by-pixel analysis and the nuclei identification and spreading strategy. The applicability of this method is demonstrated on both quenching and partitioning (Q&P) and as-quenched lath-martensite steels. The results obtained on the C-Mn steels confirm that the sample finish rolled at the lowest temperature (829{\deg}C) exhibits the sharpest transformation texture. It is shown that this sharp texture is exclusively due to a strong VS from parent brass {110}, S {213} and Goss {110} grains, whereas the VS from the copper {112} grains is insensitive to the FRT. In addition, a statistical VS analysis proves that the habit planes of the selected variants do not systematically correspond to the predicted active slip planes using the Taylor model. In contrast, a correlation between the Bain group to which the selected variants belong and the FRT is clearly revealed, regardless of the parent orientation. These results are discussed in terms of polygranular accommodation mechanisms, especially in view of the observed development in the hot-rolled samples of high-angle grain boundaries with misorientation axes between and

Fatty acid composition of adipose tissue triglycerides after weight loss and weight maintenance: the DIOGENES study.

Fatty acid composition of adipose tissue changes with weight loss. Palmitoleic acid as a possible marker of endogenous lipogenesis or its functions as a lipokine are under debate. Objective was to assess the predictive role of adipose triglycerides fatty acids in weight maintenance in participants of the DIOGENES dietary intervention study. After an 8-week low calorie diet (LCD) subjects with > 8 % weight loss were randomized to 5 ad libitum weight maintenance diets for 6 months: low protein (P)/low glycemic index (GI) (LP/LGI), low P/high GI (LP/HGI), high P/low GI (HP/LGI), high P/high GI (HP/HGI), and a control diet. Fatty acid composition in adipose tissue triglycerides was determined by gas chromatography in 195 subjects before the LCD (baseline), after LCD and weight maintenance. Weight change after the maintenance phase was positively correlated with baseline adipose palmitoleic (16:1n-7), myristoleic (14:1n-5) and trans-palmitoleic acid (16:1n-7t). Negative correlation was found with baseline oleic acid (18:1n-9). Lower baseline monounsaturated fatty acids (14:1n-5, 16:1n-7 and trans 16:1n-7) in adipose tissue triglycerides predict better weight maintenance. Lower oleic acid predicts lower weight decrease. These findings suggest a specific role of monounsaturated fatty acids in weight management and as weight change predictors