Narrow Results

In this paper, we introduce a new variant of implicit heaps, called relaxed inorder heaps. The structure is semi-implicit due to the use of 1 extra bit per node to maintain heap order and the allowance of some systematically controlled extra space. We show that relaxed inorder heaps are asymptotically more efficient than other known variants of implicit heaps. In particular, relaxed inorder heaps are especially efficient for heap merging and splitting operations, which are known to be problematic operations for implicit heaps.

Using amortized analysis, we derive several improved time bounds. Heap creation can be done in O(n) comparisons and node movements. Finding the minimum node and node insertion can each be done in O(1) comparisons and node movements. Key updating and node deletion can each be done in O(log n) comparisons and node movements. As for merging, we show that O(1) comparisons and 2k+O(1) node movements are sufficient for merging two heaps of sizes n and k. For splitting, we show that O(log n) comparisons and 1.5k+O(log n) node movements are sufficient for splitting an n-node implicit heap into two heaps of sizes k and n−k. The amount of extra space in a relaxed inorder heap is O(log n) if splitting does not occur, and O(n) otherwise.

The significance of our results is that small sophistication in the structure of implicit heaps can produce large improvements in efficiency. We have implemented the algorithms for operations on relaxed inorder heaps. The simulation results strongly indicate that relaxed inorder heaps are practical, since the constant factors recorded for the heap operations are all very small.

We have studied paramagnetic Mn²⁺ ions present in the freshwater snail, Sinotaia ingallsiana (FS), Viviparus which are abundant in Thailand. The FS shells in our study were ground into fine powder. A set of seven samples was each then separately annealed for 2 hours in air atmosphere at 300°C, 400°C, 500°C, 600°C, 700°C, 800°C and 900°C, respectively. Our detailed ESR spectral analyses of FS show that Mn²⁺ ions enter Ca²⁺ sites during a biomineralization process. The hyperfine coupling constant (A) and zero-field splitting (D) in the ESR spectrum of Mn²⁺ in calcite and aragonite were determined. The spreading of the non-central allowed transitions was analyzed and the experimental transitions were attributed. For calculating the hyperfine coupling constant, five methods for calculating the zero-field splitting, based on the analysis of the allowed and forbidden transitions, were provided. The values of the hyperfine coupling constant range from 87.50 to 89.00 G and those of the zero-field splitting range from 110.00 to 116.00 G.

We investigate the tunneling of ultracold atoms in optical traps by using the path-integral method. We obtain the decay rate for tunneling out of a single-well and discuss how the rate is affected by the level splitting caused by the presence of a second adjacent well. Our calculations show that the transition through the potential barrier can be divided into three regions: the quantum tunneling region, the thermally assisted region and the thermal activation region. The tunneling process is found to be a second-order transition. We also show that level splitting due to tunneling can increase the tunneling rate.

The problem of analyzing the bifurcation mechanisms of complex stochastic oscillations in population dynamics is considered. We study this problem on the basis of the modified Leslie–Gower prey–predator model with randomly forced Holling-II functional response. The paper focuses on the effects of noise in the Canard explosion zone. The phenomenon of noise-induced splitting of Canard cycles is discovered and studied in terms of stochastic P-bifurcations. In parametric analysis, we use the stochastic sensitivity technique with the apparatus of confidence domains to find the most noise-sensitive Canard. For the phenomenon of stochastic splitting, an underlying deterministic mechanism using critical curves near the cycle orbit and sub-/super-critical zones is revealed.

We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following.

• If G is a nonelementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group.

• If H is a nonparabolic subgroup of a relatively hyperbolic group, and if any isometric H-action on an ℝ-tree is trivial, then H is Hopfian.

• If G is a nonelementary relatively hyperbolic group whose peripheral subgroups are finitely generated, then G has a nonelementary relatively hyperbolic quotient that is Hopfian.

• Any finitely presented group is isomorphic to a finite index subgroup of Out(H) for some group H with Kazhdan property (T). (This sharpens a result of Ollivier–Wise).

The aim of this paper is the numerical treatment of some convection systems with stiff relaxation source-terms. We will first define the notion of stiffness for such systems and will select some prototypical and physical problems. We will introduce a new numerical method in order to solve accurately this type of systems. Numerical comparisons will be performed on the evoked problems.

We propose a toy model for self-organized road traffic taking into account the state of orderliness in drivers’ behavior. The model is reminiscent of the wide family of generalized second-order models (GSOM) of road traffic. It can also be seen as a phase-transition model. The orderliness marker is evolved along vehicles’ trajectories and it influences the fundamental diagram of the traffic flow. The coupling we have in mind is non-local, leading to a kind of “weak decoupling” of the resulting $2\times 2$ system; this makes the mathematical analysis similar to the analysis of the classical Keyfitz–Kranzer system. Taking advantage of the theory of weak and renormalized solutions of one-dimensional transport equations [Panov, 2008], which we further develop on this occasion in the Appendix, we prove the existence of admissible solutions defined via a mixture of the Kruzhkov and the Panov approaches; note that this approach to admissibility does not rely upon the classical hyperbolic structure for $2\times 2$ systems. First, approximate solutions are obtained via a splitting strategy; compactification effects proper to the notion of solution we rely upon are carefully exploited, under general assumptions on the data. Second, we also address fully discrete approximation of the system, constructing a BV-stable Finite Volume numerical scheme and proving its convergence under the no-vacuum assumption and for data of bounded variation. As a byproduct of our approach, an original treatment of local GSOM-like models in the BV setting is briefly discussed, in relation to discontinuous-flux LWR models.

We investigate a ring R with the property that for every right R-module M and every ideal I of R the annihilator of I in M is a direct summand of M, and determine conditions under which such a ring is semisimple Artinian.

In this paper, a new conservative and splitting fourth-order compact difference scheme is proposed and analyzed for solving two-dimensional linear Schrödinger equations. The proposed splitting high-order compact scheme in two dimensions has the excellent property that it preserves the conservations of charge and energy. We strictly prove that the scheme satisfies the charge and energy conservations and it is unconditionally stable. We also prove the optimal error estimate of fourth-order accuracy in spatial step and second-order accuracy in time step. The scheme can be easily implemented and extended to higher dimensional problems. Numerical examples are presented to confirm our theoretical results.

Nickel phthalocyanines (NiPc) substituted by trifluorosulfonyl or trimethylsilylethynyl groups have been prepared and characterized using NMR and electronic absorption spectroscopy. In particular, when trifluorosulfonyl groups are introduced to two, so-called, α-benzo positions of one benzene ring of the Pc skeleton, the Q-band splits similarly to the Q-bands of metal-free phthalocyanines. The splitting width of the Q-bands can be interpreted as due mainly to splitting of the LUMOs by the substituents, although splitting between the HOMO-1 and HOMO-2 is also effective to a lesser extent.

To develop a high-quality TTS system, an appropriate segmentation of continuous speech into the syllabic units plays a vital role. The significant objective of this research work involves the implementation of an automatic syllable-based speech segmentation technique for continuous speech of the Hindi language. Here, the parameters involved in the segmentation process are optimized to segment the speech syllables. In addition to this, the proposed iterative splitting process containing the optimum parameters minimizes the deletion errors. Thus, the optimized iterative incorporation can discard more insertions without merging the frequent non-iterative incorporation. The mixture of optimized iterative and iterative incorporation provides the best accuracy with the least insertion and deletion errors. The segmentation output based on different text signals for the proposed approach and other techniques namely GA, PSO and SOM is accurately segmented. The average accuracy obtained for the proposed approach is high with 97.5% than GA, PSO and SOM. The performance of the proposed algorithm is also analyzed and gives better-segmented accuracy when compared with other state-of-the-art methods. Here, the syllable-based segmented database is suitable for the speech technology system for Hindi in the travel domain.