We consider (1+1)-dimensional directed polymers in a random potential and provide sufficient conditions guaranteeing joint localization. Joint localization means that for typical realizations of the environment, started at different starting points, all associated endpoint distributions localize common region does not grow with length polymer. In particular, we prove holds when reference walk p...

The exact range of the joined values of several Rényi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied.

2. Capsule afferents in the hip discharged only when the joint was rotated into its limit of movement along a single axis of rotation. 2. The optimal axis of rotation for an afferent was determined by the part of the capsule that was loaded by the rotation and by the location of the receptor in the capsule. Afferents were activated by rotations along the axes of abduction, adduction, and intern...

in this article, aimed at promoting iranian statutes and increasing their applicatory aspects and for providing more and more financial security of society, the legal rule of i‘rāḍ (avoidance, abandonment) is deliberated on, which is a rule that is not clearly and extensively discussed but is the basis of some rules in iranian civil law. this has caused some obscurities, and sometimes, hasty de...

spatial patterns of soil fertility parameters, and other extrinsic factors need to be iden-tified to develop farming practices that match agricultural inputs with local crop needs. little is known about the spatial structure of yield and weed density across fields. in this study, geostatistics was used to describe and map spatial patterns of soil total nitrogen, available phosphorus, available ...