Remarks on Characterizations of Malinowska and Szynal

The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. To this end, one will depend on the characterizations of this distribution which provide conditions under which the underlying distribution is indeed that particular distribution. In this work, several characterizations of Malinowska and Szynal (2008) for certain general classes of distributions are revisited and simpler proofs of them are presented. These characterizations are not based on conditional expectation of the kth lower record values (as in Malinowska and Szynal), they are based on: (i) simple truncated moments of the random variable, (ii) hazard function

A new 3D-beam finite element including non-uniform torsion with the secondary torsion moment deformation effect

In this paper, a new 3D Timoshenko linear-elastic beam finite element including warping torsion will be presented which is suitable for analysis of spatial structures consisting of constant open and hollow structural section (HSS) beams. The analogy between the 2ndorder beam theory (with axial tension) and torsion (including warping) was used for the formulation of the equations for non-uniform torsion. The secondary torsional moment deformation effect and the shear force effect are included into the local beam finite element stiffness matrix. The warping part of the first derivative of the twist angle was considered as an additional degree of freedom at the finite element nodes. This degree of freedom represents a part of the twist angle curvature caused by the bimoment. Results of the numerical experiments are discussed, compared and evaluated. The importance of the inclusion of warping in stress-deformation analyses of closed-section beams is demostrated

Attention explores space periodically at the theta frequency

Voluntary attention is at the core of a wide variety of cognitive functions. Attention can be oriented to and sustained at a location or reoriented in space to allow processing at other locations—critical in an ever-changing environment. Numerous studies have investigated attentional orienting in time and space, but little is known about the spatiotemporal dynamics of attentional reorienting. Here we explicitly manipulated attentional reorienting using a cuing procedure in a two- alternative forced-choice orientation-discrimination task. We interrogated attentional distribution by flashing two probe stimuli with various delays between the precue and target stimuli. Then we used the probabilities that both probes and neither probe were correctly reported to solve a second-degree equation, which estimates the report probability at each probe location. We demonstrated that attention reorients periodically at ~4 Hz (theta) between the two stimulus locations. We further characterized the processing dynamics at each stimulus location, and demonstrated that attention samples each location periodically at ;11 Hz (alpha). Finally, simulations support our findings and show that this method is sufficiently powered, making it a valuable tool for studying the spatiotemporal dynamics of attention