Narrow Results

In procedural programming languages, the order of executing the statements may follow a regular pattern, including sequences of statements, conditional and branching statements and loops. On the other hand, regular languages can be represented by finite state acceptors (finite automata), by regular expressions and by (a special form of) railroad diagrams (syntax diagrams) allowing alternatives, option, concatenation and iteration. Context-free languages can also be described by (the general form of) railroad diagrams allowing also recursion. Based on the analogy of finite automata and railroad diagrams, the transformation between node-labelled and edge-labelled graphs, special infinite state automata, namely the fractal automata, are established to characterize the class of context-free languages. Deterministic and linear variants are also investigated. To establish these connections, we also define such variants of pushdown automata that accept the deterministic context-free and linear languages by empty stack. A transformation between the pushdown automata and fractal automata is also shown. The proposed model gives some new insights and a new view of context-free languages, deterministic context-free languages, linear context-free and deterministic linear context-free languages.

Jacobi elliptic functions play a central role in nonlinear evolution equations. We show how with one recursive call we can calculate the Jacobi elliptic functions sn, cn, and dn. We give an implementation using C++.

The global reliability of a connected network reflects the probability of having a connected path between every pair of processors. Given any network, there are several ways of finding this reliability measure such as path set and cut set methods. These methods are computation extensive for large networks and do not utilize the symmetry of the networks. In this paper, we present a generalization of a special class of networks called Braided-Line networks and derive the reliability expressions for these networks using recursive techniques. These recursive techniques utilize the symmetry of the networks thus reducing the computation time of the global reliability substantially.

In this paper, we describe the recursion relations between two parameter HOMFLY and Kauffman polynomials of framed links. These relations correspond to embeddings of quantized universal enveloping algebras. The relation corresponding to embeddings g_n ⊃ g_k × sl_n-k where g_n is either so_2n+1, so_2n or sp_2n is new.

The Bourrée Part I from Johann Sebastian Bach's Cello Suite No. 3 provides a clear example of structural scaling. The recursive form of this structure can be visualized in the manner of a well known fractal construction — the Cantor set.

Ideology plays a vital role in politics, but not only so. Also in consumer life, ideologically based attitudes and stances are immanent. Building on four different business models within the fashion industry, a model with two axes is presented. The two axes are conceptual recursion and consumption as social ideology. Fashion easily contains a progressive attitude; the social environment creates a milieu where consumers and businesses operate, and in this ambiance of ideas they will be able to (inside-out or outside-in) foot themselves in ideology. Hence, fashion can be said to uphold ideological attitudes, whether explicit or not. The model captures these ideological mindsets. It makes clear how the business models in themselves are ridden by ideology and the expression of brands, as well as bringing an overall understanding of the role ideology plays in entrepreneurship and enterprise development in the fashion industry.

We prove some interesting multiplicative relations which hold between the coefficients of the logarithmic derivatives obtained in a few simple ways from 𝔽_q-linear formal power series. Since the logarithmic derivatives connect power sums to elementary symmetric functions via the Newton identities, we establish, as applications, new identities between important quantities of function field arithmetic, such as the Bernoulli–Carlitz fractions and power sums as well as their multivariable generalizations. Resulting understanding of their factorizations has arithmetic significance, as well as applications to function field zeta and multizeta values evaluations and relations between them. Using specialization/generalization arguments, we provide much more general identities on linear forms providing a switch between power sums for positive and negative powers.

Synaptic communication, nonsynaptic diffusion neurotransmission and glial activity each update the morphology of the other two. These interactions lead to an endogenous structure of causal entailment. It has internal ambiguities rendering it incomputable. The entailed effects are bizarre. These include abduction of novelty in response to conflicting cues, a resolution of the seeming conflict between freewill and determinism, and anticipatory behavior. Such inherent ambiguity of the causal entailment structure does not preclude the implementation of brain-like activities artificially. Although an algorithm is incapable of neuromimetically reproducing self-referential character of the brain, there is a currently-feasible strategy for wiring a "human in the loop" to use the cognitive powers of anticipation and unconscious integration to provide dramatic improvement in the operation of large engineered systems.

In this paper we present some analytical integration formulae for computing integrals of rational functions of bivariate polynomial numerator with linear and bilinear denominator over a 2-square |ξ| = 1, |η| = 1 in the local parametric space (ξ, η). These integrals arise in finite element formulations of second order partial differential equations of plane and axisymmetric problems in continuum mechanics to computer the components of element stiffness matrices. In case of a rational integrals of n-th degree bivariate polynomial numerator with a linear of bilinear denominator there are exactly rational integrals of monomial numerators with the same linear denominator. By an expansion it is shown that these integrals can be computed in two ways, accordingly we have presented an explicit and a recursive scheme. By use of the recursive scheme such integrals can be computed efficiently with less computational effort whenever (n + 1) integrals of order zero to n in one of the variates are known by explicit integration formulae. Integration formulae from zeroth to octic order are, for clarity and reference summarized in tabular forms. Finally to show the application of the derived formulae three application examples to compute the Prandtl stress function values and the torsional constant k are considered. A computer code based on the present integration scheme to obtain the element stiffness matrices for plane problems is also developed.

The weighted Tower of Hanoi problem is a new generalization of the classical Tower of Hanoi problem, where a move of a disc between two pegs $i$ and $j$ is weighted by a positive real $w_{ij}$. This new problem generalizes the concept of finding the minimum number of moves to solve the Tower of Hanoi, to find a sequence of moves with the minimum total weight. We present an optimal dynamic algorithm to solve the weighted Tower of Hanoi problem, as well as some of its properties. We also show the link of this generalization to the Tower of Hanoi variants with restricted disc moves, and how this new problem can generalize the concept of restricting a disc move.

We present a neural-symbolic learning model of sentence production which displays strong semantic systematicity and recursive productivity. Using this model, we provide evidence for the data-driven learnability of complex yes/no-questions.

A new approach, to analysis of statistical data collected in contingent valuation surveys, is introduced. In data collecting, randomly sampled respondents may freely self-select any interval that contains their willingness-to-pay (WTP-) point. Here, the presence of self-selected intervals, with rounded ends, is an essential feature. We avoid put restrictions on dependencies between the selfselected intervals and their associated WTP-points. Two-step sampling designs are proposed. Based on an estimated coverage probability, a practical rule to stop sampling in the first step is suggested. Then division intervals are generated and they are used on the second step of data collecting. A recursion is applied to maximize the log likelihood corresponding to data collected on the second step. The consistent maximum likelihood (ML-) estimates of WTPdistribution, projected on the division intervals, are found. Their accuracies may be consistently estimated by resampling methods.