On the out of phase appearance of large-scale diffuse magnetic field of the sun with respect to sunspots

We assume the large-scale diffuse magnetic field of the Sun to originate from the poloidal component of a dynamo operating at the base of the convection zone, whereas the sunspots are due to the toroidal component. The evolution of the poloidal component is studied to model the poleward migration of the diffuse field seen on the solar surface and the polar reversal at the time of sunspot maxima (Dikpati and Choudhuri 1994, 1995).

The algebra and geometry of SU(3) matrices

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimensional real Linear vector space, are developed in an SU(3) covariant manner. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is developed as a generalization of that for SU(2), and the specifically new features are brought out. Application to the dynamics of three-level systems is outlined.

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling

For the successful performance of a granular filter medium, existing design guidelines, which are based on the particle size distribution (PSD) characteristics of the base soil and filter medium, require two contradictory conditions to be satisfied, viz., soil retention and permeability. In spite of the wider applicability of these guidelines, it is well recognized that (i) they are applicable to a particular range of soils tested in the laboratory, (ii) the design procedures do not include performance-based selection criteria, and (iii) there are no means to establish the sensitivity of the important variables influencing performance. In the present work, analytical solutions are developed to obtain a factor of safety with respect to soil-retention and permeability criteria for a base soil - filter medium system subjected to a soil boiling condition. The proposed analytical solutions take into consideration relevant geotechnical properties such as void ratio, permeability, dry unit weight, effective friction angle, shape and size of soil particles, seepage discharge, and existing hydraulic gradient. The solution is validated through example applications and experimental results, and it is established that it can be used successfully in the selection as well as design of granular filters and can be applied to all types of base soils.

Algorithmic aspects of k-tuple total domination in graphs

For a fixed positive integer k, a k-tuple total dominating set of a graph G = (V. E) is a subset T D-k of V such that every vertex in V is adjacent to at least k vertices of T Dk. In minimum k-tuple total dominating set problem (MIN k-TUPLE TOTAL DOM SET), it is required to find a k-tuple total dominating set of minimum cardinality and DECIDE MIN k-TUPLE TOTAL DOM SET is the decision version of MIN k-TUPLE TOTAL DOM SET problem. In this paper, we show that DECIDE MIN k-TUPLE TOTAL DOM SET is NP-complete for split graphs, doubly chordal graphs and bipartite graphs. For chordal bipartite graphs, we show that MIN k-TUPLE TOTAL DOM SET can be solved in polynomial time. We also propose some hardness results and approximation algorithms for MIN k-TUPLE TOTAL DOM SET problem. (c) 2012 Elsevier B.V. All rights reserved.

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Note on high aspect-ratio SU-8 micromechanical structures using mask-less direct laser writing

We report high aspect-ratio micromechanical structures made of SU-8 polymer, which is a negative photoresist. Mask-less direct writing with 405 nm laser is used to pattern spin-cast SU-8 films of thickness of more than 600 um. As compared with X-ray lithography, which helps pattern material to give aspect ratios of 1:50 or higher, laser writing is a less expensive and more accessible alternative. In this work, aspect ratios up to 1:30 were obtained on narrow pillars and cantilever structures. Deep vertical patterning was achieved in multiple exposures of the surface with varying dosages given at periodic intervals of sufficient duration. It was found that a time lag between successive exposures at the same location helps the material recover from the transient changes that occur during exposure to the laser. This gives vertical sidewalls to the resulting structures. The time-lags and dosages were determined by conducting several trials. The micromechanical structures obtained with laser writing are compared with those obtained with traditional UV lithography as well as e-beam lithography. Laser writing gives not only high aspect ratios but also narrow gaps whereas e-beam can only give narrow gaps over very small depths. Unlike traditional UV lithography, laser writing does not need a mask. Furthermore, there is no adjustment for varying the dosage in traditional UV lithography. A drawback of this method compared to UV lithography is that the writing time increases. Some test structures as well as a compliant microgripper are fabricated.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

Baryon squishing in synthetic dimensions by effective SU(M) gauge fields

The ``synthetic dimension'' proposal A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with M internal states (''flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an M-sites-wide square lattice strip. We investigate the physics of SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles with SU(M) symmetric interactions] experiencing an SU(M) Zeeman field at each lattice site and a non-Abelian SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For M particles, concomitantly, the SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (''squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the SU(M) random flux model, inconceivable in conventional experimental systems.

Biochemical Characterization of Nonamer Binding Domain of RAG1 Reveals its Thymine Preference with Respect to Length and Position

RAG complex consisting of RAG1 and RAG2 is a site-specific endonuclease responsible for the generation of antigen receptor diversity. It cleaves recombination signal sequence (RSS), comprising of conserved heptamer and nonamer. Nonamer binding domain (NBD) of RAG1 plays a central role in the recognition of RSS. To investigate the DNA binding properties of the domain, NBD of murine RAG1 was cloned, expressed and purified. Electrophoretic mobility shift assays showed that NBD binds with high affinity to nonamer in the context of 12/23 RSS or heteroduplex DNA. NBD binding was specific to thymines when single stranded DNA containing poly A, C, G or T were used. Biolayer interferometry studies showed that poly T binding to NBD was robust and comparable to that of 12RSS. More than 23 nt was essential for NBD binding at homothymidine stretches. On a double-stranded DNA, NBD could bind to A:T stretches, but not G:C or random sequences. Although NBD is indispensable for sequence specific activity of RAGs, external supplementation of purified nonamer binding domain to NBD deleted cRAG1/cRAG2 did not restore its activity, suggesting that the overall domain architecture of RAG1 is important. Therefore, we define the sequence requirements of NBD binding to DNA.

MIXED NORM ESTIMATES FOR THE RIESZ TRANSFORMS ON SU (2)

In this paper we prove mixed norm estimates for Riesz transforms on the group SU(2). From these results vector valued inequalities for sequences of Riesz transforms associated to Jacobi differential operators of different types are deduced.

Evaluación temporal y espacial en el bosque de Pinus oocarpa Schiede y su impacto sobre la fijación de carbono en el municipio de Dipilto

El objetivo de este estudio fue a nalizar el cambio de uso de suelo durante un periodo de 18 años en las áreas de bosque de pino y su influencia en la fijación de bióxido de carbono en el Municipio de Dipilto, Nueva Segovia . Se seleccionaron 3 Fincas : San Martín, El Sarrete y Campofresco que presentaron estados de desarrollo: bosque maduro, bosque joven y bosque en regeneración. Se establecieron 9 parcelas temporales (con predominancia P. oocarpa ), utilizándose una parcela temporal para cada es tado d esarrollo. En cada estado de desarrollo se derribó un árbol tipo, se separó en tallo, ramas y follaje. La mayor par te de biomasa seca se encuentra en la finca San Martin con 99.12 Mg/ha estado en desarrollo maduro , estado en desarrollo joven con 77.70 Mg/ ha y estado en desarrollo regeneración 38.63 Mg/ha . El Factor de expansión de biomasa en San Martin 1.59 esta do en desarrollo regeneración, El Sarrete para el estado en desarrollo maduro 1 .40 y finca Campofresco 1.27 estado desarrollo joven . El total de ca rbono almacenado lo presentó San Martín para el estado en desarrollo maduro con 27.13 Mg/ha , joven 22.06 Mg/ha y estado en desarrollo regeneraci ón con 9.82 Mg/ha . El contenido de carbono en el suelo 826.89 Mg/ha regeneración, 503.96 Mg/ha Joven , 294.55 Mg/ ha maduro en San Martín de 0 a 20 cm de profundidad. En un 38.49 % de esa área se emitieron entre 0 - 15 Mg/ha . Emisiones de 26 - 30 Mg/ha se presentaron en un 17.8 1 % del área. Existe un 48.19 % del área total que fijo rangos de 26 - 30 Mg/ha y un 38. 49 % de las áreas fij aron entre 0 - 15 Mg /ha . Se encontró un balance neto positivo de 2925. 2 1 hectáreas, de las cuales 1981.25 hectáreas fijaron rangos de 26 - 30 Mg/ha, 606.06 hectáre as fijaron en un rango entre 0 - 15 Mg /ha y el rango 16 - 25 Mg/ha 337.89 hect áreas .