Narrow Results

The set of all terms of type $\tau$ is denoted by $W_{\tau }(X).$ Each element of $P(W_{\tau }(X))$ is called a tree language. A binary operation ${\cdot }_{ij}$ is an operation on $P(W_{\tau }(X))$ defined from the superposition ${Ŝ}_g^n$ on the set of all $n$-ary terms of type $\tau .$ Since ${Ŝ}_g^n$ satisfies the superposition law, $(P(W_{\tau }(X));{\cdot }_{ij})$ is a semigroup. In this paper, we study subsemigroups of the semigroup $(P(W_{\tau }(X));{\cdot }_{ij})$ including constant, left-zero, right-zero subsemigroups, rectangular bands, subgroups, and inverse subsemigroups. We also study factorization and locally factorization of the semigroup $(P(W_{\tau }(X));{\cdot }_{ij})$ and we obtain that this semigroup is neither factorizable nor locally factorizable. However, we achieve a necessary and sufficient condition for factorization of local subsemigroup $A{\cdot }_{ij}P(W_{\tau }(X)){\cdot }_{ij}A$, where $A$ is idempotent in $P(W_{\tau }(X))$. Finally, we study ${\cdot }_{ij}-$iteration and show that with special conditions, an ${\cdot }_{ij}-$iteration of idempotent is idempotent.

We study iterated transductions defined by a class of invertible Mealy automata over the binary alphabet. It is shown that in some cases the resulting orbit relation is rational and we determine the complexity of several natural computational problems associated with the iterated transductions. In particular, we show how to compute timestamps and coordinates.

Let $X$ be a klt projective variety with numerically trivial canonical divisor. A surjective endomorphism $f:X\to X$ is amplified (respectively, quasi-amplified) if $f^{\ast }D-D$ is ample (respectively, big) for some Cartier divisor $D$. We show that after iteration and equivariant birational contractions, a quasi-amplified endomorphism will descend to an amplified endomorphism. As an application, when $X$ is Hyperkähler, $f$ is quasi-amplified if and only if it is of positive entropy. In both cases, $f$ has Zariski dense periodic points. When $X$ is an abelian variety, we give and compare several cohomological and geometric criteria of amplified endomorphisms and endomorphisms with countable and Zariski dense periodic points (after an uncountable field extension).

Shared data object implementations that allow non-blocking concurrent operations are useful for in-memory data-processing, especially when they support consistent bulk operations like iterations. We propose an algorithmic implementation for concurrent iterators on shared double-ended queues (deques), building on and complementing a known lock-free deque implementation by M. Michael. The proposed construction is linearizable and wait-free. Moreover, it is read-only, so it does not execute expensive synchronization primitives and it does not interfere with update operations.

In the nonbinary low-density parity check (NB-LDPC) codes decoding algorithms, the iterative hard reliability based on majority logic decoding (IHRB-MLGD) algorithm has poor error correction performance. The essential reason is that the hard information is used in the initialization and iterative processes. For the problem of partial loss of information, when the reliability is assigned during initialization, the error correction performance is improved by modifying the assignment of reliability at initialization. The initialization process is determined by the probability of occurrence of the number of erroneous bits in the symbol and the Hamming distance. In addition, the IHRB-MLGD decoding algorithm uses the hard decision in the iterative decoding process. The improved algorithm adds soft decision information in the iterative process, which improves the error correction performance while only slightly increasing the decoding complexity, and improves the reliability accumulation process which makes the algorithm more stable. The simulation results indicate that the proposed algorithm has a better decoding performance than IHRB algorithm.

The problem of handwritten Chinese character recognition is solved by matching character stroke segments using an iteration scheme. Length and orientation similarity properties, and coordinate overlapping ratios are used to define a measure of similarity between any two stroke segments. The initial measures of similarity between the stroke segments of the input and template characters are used to set up a match network which includes all the match relationships between the input and template stroke segments. Based on the concept of at-most-one to one mapping an iteration scheme is employed to adjust the match relationships, using the contextual information implicitly contained in the match network, so that the match relationships can get into a stable state. From the final match relationships, matched stroke-segment pairs are determined by a mutually-best match strategy and the degree of similarity between the input and each template character is evaluated accordingly. Certain structure information of Chinese characters is also used in the evaluation process. The experimental results show that the proposed approach is effective. For recognition of Chinese characters written by a specific person, the recognition rate is about 96%. If the characters of the first three ranks are checked in counting the recognition rate, the rate rises to 99.6%.

This paper deals with analyzing and comparing several key thinning algorithms in terms of various different methodologies. From these analyses and comparisons, a new sequential model thinning algorithm using heuristic, hybrid methods is presented. It intends to produce, based on past experience, thinned skeletons of thickness one from input patterns, keep connectivity, and eliminate unnecessary pixels. Several illustrative examples on various patterns were tested and the results compared. The parallel model thinning algorithm is still open.

This paper proposes a new iteration method for chaotifying and controlling dynamical systems. By applying this iteration method, the dimension of the given dynamical system can be reduced from to n to n-1. Moreover, the chaotified system is not necessarily Hurwitz stable originally. The iteration method is applied to three-dimensional systems for demonstration, for which a sufficient condition is obtained for chaotification. In addition, the iteration method can be used to control a class of chaotic systems. These results are illustrated via simulations on the Duffing oscillator and the Chen system.

We consider the family of entire transcendental maps given by F_λ,m(z)=λz^mexp(z) where m≥2. All functions F_λ,m have a superattracting fixed point at z=0, and a critical point at z = -m. In the dynamical plane we study the topology of the basin of attraction of z=0. In the parameter plane we focus on the capture behavior, i.e. λ values such that the critical point belongs to the basin of attraction of z=0. In particular, we find a capture zone for which this basin has a unique connected component, whose boundary is then nonlocally connected. However, there are parameter values for which the boundary of the immediate basin of z=0 is a quasicircle.

An iterative compatible cell mapping (CCM) method with the digraph theory is presented in this paper to compute the global invariant manifolds of dynamical systems with high precision and high efficiency. The accurate attractors and saddles can be simultaneously obtained. The simple cell mapping (SCM) method is first used to obtain the periodic solutions. The results obtained by the generalized cell mapping (GCM) method are treated as a database. The SCM and GCM are compatible in the sense that the SCM is a subset of the GCM. The depth-first search algorithm is utilized to find the coarse coverings of global stable and unstable manifolds based on this database. The digraph GCM method is used if the saddle-like periodic solutions cannot be obtained with the SCM method. By taking this coarse covering as a new cell state space, an efficient iterative procedure of the CCM method is proposed by combining sort, search and digraph algorithms. To demonstrate the effectiveness of the proposed method, the classical Hénon map with periodic or chaotic saddles is studied in far more depth than reported in the literature. Not only the global invariant manifolds, but also the attractors and saddles are computed. The computational efficiency can be improved by up to 200 times compared to the traditional GCM method.

In this paper, we study rational functions of the form $R_{n,a,c}(z)=z^n+\frac{a}{z^n}+c,$ with $n$ fixed and at least $3$, and hold either $a$ or $c$ fixed while the other varies. We locate some homeomorphic copies of the Mandelbrot set in the $c$-parameter plane for certain ranges of $a$, as well as in the $a$-plane for some $c$-ranges.

We use techniques first introduced by Douady and Hubbard [1985] that were applied for the subfamily $R_{n,a,0}$ by Devaney [2006]. These techniques involve polynomial-like maps of degree two.

We study free profinite subgroups of free profinite semigroups of the same rank using, as main tools, iterated continuous endomorphisms, subword complexity, and the associated entropy. Main results include a general scheme to produce such subgroups and a proof that the complement of the minimal ideal in a free profinite semigroup on more than one generator is closed under all implicit operations that do not lie in the minimal ideal and even under their infinite iteration.

In this paper, a new notion of super coalescence hidden-variable fractal interpolation function (SCHFIF) is introduced. The construction of SCHFIF involves choosing an IFS from a pool of several non-diagonal IFS at each level of iteration. Further, the integral of a SCHFIF is studied and shown to be a SCHFIF passing through a different set of interpolation data.

Aimed at its elegance, the rigid-body-based procedure for geometric nonlinear analysis is extended to including the plastic-hinge concept for elasto-plastic analysis of framed structures. To this end, the rigid body test for initially stressed elements is first briefed, followed by derivation of the tangent stiffness of the 2D elasto-plastic beam element using the initial and full yield surfaces to consider gradual yielding of the cross-section. Of theoretical importance, the tangent and geometric stiffnesses are jointly tested by the rigid body rule for initially stressed elements. The above concepts are contained in the global and localstrategies, respectively, for tracing the load–deflection curves and for performing the trial-and-error iterations. The former can deal with the formation of multi plastic hinges, in addition to multi-critical points, whereas the latter is strongly rooted in the rigid body rule and thus is free of fictitious forces (source of slow convergence). The accuracy and efficiency of the solutions obtained are confirmed by comparison with the existing ones. In conclusion, the procedure proposed in its entity makes the elasto-plastic analysis simpler and faster. The more complicated the problem is, the greater the saving in computation time using the proposed procedure. Since only minimal mathematical operations are required, this procedure has the potential of being widely accepted by structural engineers in routine analysis.

Identification of the latent trend component is a vital procedure for further evaluating the measured signal. Many methods have been presented to extract the trend component. However, some essential parameters used in these methods need to be selected depending on much prior knowledge or experience. To avoid the inherent flaws in current methods, we introduce a novel signal decomposition method called variational mode decomposition (VMD) to cope with this issue. Firstly, the parameters involved in VMD method are discussed according to the universal characteristics of trend component. Then, a novel data-driven method based on the iterative VMD is proposed to identify the intricate trend component. Moreover, a criterion called normalized euclidean distance (NED) is presented to evaluate the converging property of the proposed method. Finally, the simulated time series and the collected extensive experimental cases are employed to illustrate the effectiveness of the proposed method. The analysis results show that the proposed method delivers a good performance for the trend component extraction and outperforms the benchmark method, i.e., empirical mode decomposition (EMD)-based method, for which more than one intrinsic mode function (IMF) is regarded as the underlying trend component.

In this paper, the three-dimensional dynamic problem for an infinite elastic medium weakened by a crack of infinite length and finite width is analyzed, while the crack surfaces are subjected to mode I transient linear tractions. The integral transform approach is applied to reduce the governing differential equations to a pair of coupled singular integral equations, whose solutions can be obtained with the typical iteration method. The analytical solution of the stress intensity factor when the first wave and the first scattered wave reach the investigated crack tip is obtained. Numerical results are presented for different values of the width-to-longitudinal distance ratio z/l. It is found that the stress intensity factor decreases with the arrival of the first scattered longitudinal wave and increases with the arrival of the first scattered Rayleigh wave and tends to be stable. The static value considering both the first scattered wave and the first wave is about 50% greater than that considering only the first wave, and then the effect of the reflected wave is remarkable and deserves further study.

This paper deals with analyzing and comparing several key thinning algorithms in terms of various different methodologies. From these analyses and comparisons, a new sequential model thinning algorithm using heuristic, hybrid methods is presented. It intends to produce, based on past experience, thinned skeletons of thickness one from input patterns, keep connectivity, and eliminate unnecessary pixels. Several illustrative examples on various patterns were tested and the results compared. The parallel model thinning algorithm is still open.

Iterating a unary operation f defined on an n-element set A one obtains the descending chain

We consider surjective endomorphisms f of degree > 1 on the projective n-space ℙⁿ with n = 3, and f⁻¹-stable hypersurfaces V. We show that V is a hyperplane (i.e., deg(V) = 1) but with four possible exceptions; it is conjectured that deg(V) = 1 for any n ≥ 2; cf. [7], [3].

The problem of handwritten Chinese character recognition is solved by matching character stroke segments using an iteration scheme. Length and orientation similarity properties, and coordinate overlapping ratios are used to define a measure of similarity between any two stroke segments. The initial measures of similarity between the stroke segments of the input and template characters are used to set up a match network which includes all the match relationships between the input and template stroke segments. Based on the concept of at-most-one to one mapping, an iteration scheme is employed to adjust the match relationships, using the contextual information implicitly contained in the match network, so that the match relationships can get into a stable state. From the final match relationships, matched stroke-segment pairs are determined by a mutually-best match strategy and the degree of similarity between the input and each template character is evaluated accordingly. Certain structure information of Chinese characters is also used in the evaluation process. The experimental results show that the proposed approach is effective. For recognition of Chinese characters written by a specific person, the recognition rate is about 96%. If the characters of the first three ranks are checked in counting the recognition rate, the rate rises to 99.6%.