Functional Transformation Research Articles

An empirical investigation of part-whole hierarchical relations

ABSTRACTPrevious research has shown classification type (“class/member”) hierarchical responding as relational framing. The aim of this study was to use the same paradigm to investigate analysis type (“part-whole”) hierarchical responding. A total of 10 participants were exposed to (1) a procedure involving non-arbitrarily related multi-dimensional stimuli, the aim of which was to establish two arbitrary shapes as contextual cues for “part of” and “includes” relational responding respectively; and (2) a procedure that employed these cues to establish a network of arbitrary stimuli in particular hierarchical relations with each other and then test for derivation of further untrained hierarchical relations as well as for transformation of functions (TOF). Resultant patterns of relational framing consistently showed features of asymmetrical mutual entailment and transitive combinatorial entailment but, in contrast with results for classification type hierarchical responding, there was no consistent trend for TOF. Implications and future research directions are discussed.

Generation of Exactly Solvable Potentials of Position-Dependent Mass Schrödinger Equation from Hulthen Potential

Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.

Synthesis of 2,6‐Dioxatetracyclo[6.3.0.01,10.07,8]undecane and 2,7,12‐Trioxatetracyclo[6.3.1.04,11.05,9]dodecane

AbstractThe oxa‐cage compounds 1 and 2 are synthesized from the alcohol 3 by a series of functional trans formations. Syntheses of novel skeletons 6 and 8 are also de scribed.

Functional transformations in AI discovery systems

The power of scientific discovery systems derives from two main sources: a set of heuristics that determines when to apply a creative operator (an operator for forming new operators and concepts) in a space that is being explored; and a set of creative operators that determines what new operators and concepts will be created for that exploration. This paper is mainly concerned with the second issue. A mechanism called functional transformation (FT) shows promising power in creating new and useful creative operators during exploration. This paper discusses the definition, creation, and application of functional transformations, and describes, as a demonstration of the power of FT, how the system ARE, starting with a small set of creative operations and a small set of heuristics, uses FTs to create all the concepts attained by Lenat's AM system [4], and others as well. Besides showing an alternative way, of Lenat's eurisko [5], to meet the criticisms of too much pre-programmed knowledge [6] that have been leveled against AM, ARE provides a route to discovery systems that are capable of “refreshing” themselves indefinitely by continually creating new operators.

Functional method for solving gravitational field equations

A new method for solving the equations of a gravitational field (G field), which is based on functional transformations (FT), which replace holonomic transformations (HT), is discussed. The method is equivalent to nonholonomic transformations (NT) of the field functions and makes it possible to use a known solution to construct a new set of solutions in the same coordination, which contains a fixed number (up to 12) of arbitrary functions. The FT method can be used to solve the Cauchy problem for a non-steady-state G field, to eliminate singularities in the field, etc.