Kernel Elements Research Articles

Method of almost complete operator inversion in the theory of connected strip-slotted transmission lines

Problems concerning natural waves for a series of both screened strip transmission lines and slotted transmission lines can be formulated in the form of vector integral equations of the first kind with respect to electric-current density components on strips or electricfield intensity components on slots. The kernel elements of these integral equations implicitly contain both logarithmic and Cauchy singularities. Employing the projection-operator technique to this equation is always accompanied by a change from the singular kernel to a regular one and, therefore, introduces an incorrectness into the statement of the problem [1].

On Grassmannian description of the constrained KP hierarchy

This note develops an explicit construction of the constrained KP hierarchy within the Sato Grassmannian framework. Useful relations are established between the kernel elements of the underlying ordinary differential operator and the eigenfunctions of the associated KP hierarchy as well as between the related bilinear concomitant and the squared eigenfunction potential.

Concreteness Effects and Syntactic Modification in Written Composition

The effect of language concreteness on comprehending and recalling text has been well established, but the ways in which concreteness is incorporated in naturally occurring texts has not been studied. This study investigated whether concreteness was related to a key characteristic of written composition-the cumulative sentence with a final modifier-which has been consistently associated with higher quality writing. Forty-six 9th graders wrote informative compositions that were assessed for holistic quality, the proportion of T-units with final modifiers, and the concreteness values of the T-units' kernel elements (subject, verb, object, complement). Use of the final-modifier construction was significantly related to writing quality, and T-units with final modifiers had more concrete verbs but less concrete objects or complements. These findings are interpreted as support for the conceptual-peg hypothesis of dual coding theory, with concrete verbs providing the pegs on which cumulative sentences are composed.

Efficient 2-D Convolution Algorithm with the Single-Data Multiple Kernel Approach

A fast implementation of convolution operation is described. The implementation takes advantage of various properties of commonly used kernels. First, the kernel elements are analyzed and rearranged, grouping the kernel elements of the same absolute value together and arranging trivial multiplication cases separately. Then the sequence of computing convolution sums is modified so that all the kernel elements could be multiplied by the same data element at each step. This new algorithm significantly reduces the number of multiplication operations for most widely used kernels. Our experiment shows that the performance improvement of two to seven over the direct implementation is achievable for most kernels. The required overhead (extra memory and preprocessing) is proportional to the kernel size and is negligible.

Morphological filters--Part II: Their relations to median, order-statistic, and stack filters

This paper extends the theory of median, order-statistic (OS), and stack filters by using mathematical morphology to analyze them and by relating them to those morphological erosions, dilations, openings, closings, and open-closings that commute with thresholding. The max-min representation of OS filters is introduced by showing that any median or other OS filter is equal to a maximum of erosions (moving local minima) and also to a minimum of dilations (moving local maxima). Thus, OS filters can be computed by a closed formula that involves a max-min on prespecified sets of numbers and no sorting. Stack filters are established as the class of filters that are composed exactly of a finite number of max-min operations. The kernels of median, OS, and stack filters are collections of input signals that uniquely represent these filters due to their translation-invariance. The max-min functional definitions of these nonlinear iliters is shown to be equivalent to a maximum of erosions by minimal (with respect to a signal ordering) kernel elements, and also to a minimum of dilations by minimal kernel elements of dual filters. The representation of stack filters based on their minimal kernel elements is proven to be equivalent to their representation based on irreducible sum-of-products expressions of Boolean functions. It is also shown that median filtering (and its iterations) of any signal by convex 1-D windows is bounded below by openings and above by closings; a signal is a root (fixed point) of the median iff it is a root of both an opening and a closing; the open-closing and clos-opening yield median roots in one pass, suppress impulse noise similarly to the median, can discriminate between positive and negative noise impulses, and are computationally less complex than the median. Some similar results are obtained for 2-D median filtering.