We have extracted a ball from an urn which contains n− 1 black balls and one white ball. A witness to the drawing announces that the extracted ball is white; we demand the probability of this exit. If the number n is very great, that which renders extraordinary the exit of the white ball, the probability of the error or of the falsehood of the witness becomes quite near to certitude, that which...

Given a family ~ ~ {0, 1 } "' of binary vectors of length m, a set W ~ { I ..... m} is called a witness set for r ~ .~, if for all other r' • ~. there exists a coordinate c • W such that r,.~r',.. The smallest cardinality of a witness set for r •b~ is denoted w(r) = t ry( r ) . In this note we show that Y~r~ w(r)= O(1,~'13/2) and constructions are given to show that this bound is tight. Further...

This open access book is the biography of one Britain’s foremost animal welfare campaigners and world activism, science, politics she inhabited. In 1964, Ruth Harrison’s bestseller Animal Machines triggered a gear change in modern protection by popularising term ‘factory farming’ alongside new way thinking about welfare. Here, historian Claas Kirchhelle explores avant-garde upbringing, Quakeris...

Witness is someone who has relevant information about a crime. They have to make an oath or solemnly state the truth in court. Witnesses are important constituent of administration justice. perform duty assisting court discover truth. Hostile witnesses unfavourable can cause unjust acquittal guilty. turning hostile major issue our country and it be due reason which been mentioned this paper. Th...