Class Of Measures Research Articles

On measurability of real-valued functions in infinite-dimensional topological vector spaces

Abstract Some related questions concerning the measurability properties of real-valued functions with respect to a certain class of measures are discussed.

New generalised divergence measure for increasing functions

New generalised divergence measure for monotonically increasing functions is proposed and properties, bounds, some relations are derived. Further, new divergence measure of this new generalised measure's class is introduced as well with properties, bounds and numerical verification.

Sorting N-Elements Using Natural Order: A New Adaptive Sorting Approach

Problem statement: Researchers focused their attention on optimally ad aptive sorting algorithm and illustrated a need to develop tools f or constructing adaptive algorithms for large class es of measures. In adaptive sorting algorithm the run time for n input data smoothly varies from O(n) to O(nlogn), with respect to several measures of disor der. Questions were raised whether any approach or technique would reduce the run time of adaptive sor ting algorithm and provide an easier way of implementation for practical applications. Approach: The objective of this study is to present a new method on natural sorting algorithm with a run time for n input data O(n) to O(nlogm), where m defines a positive value and surrounded by 50% of n . In our method, a single pass over the inputted data creates some blocks of data or buffers accordi ng to their natural sequential order and the order can be in ascending or descending. Afterward, a bottom up approach is applied to merge the naturally sorted subsequences or buffers. Additionally, a par allel merging technique is successfully aggregated in our proposed algorithm. Results: Experiments are provided to establish the best, wo rst and average case runtime behavior of the proposed method. The simulation statistics provide same harmony with the theoretical calculation and proof the method ef ficiency. Conclusion: The results indicated that our method uses less time as well as acceptable memory to sort a data sequence considering the natural order behavior and applicable to the realistic rese arches. The parallel implementation can make the algorithm for efficient in time domain and will be the future research issue.