Bayesian Propositional Logic

We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w , where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w , for all w, and give some formal properties of it.National Science Centre, Poland, numbers of grants: 2015/19/B/HS1/02478, 2015/19/N/HS1/02401

A Note on Invariant Random Variables

In this paper we present a simple theory, based on the notion of group action on a set, which explains why processes of throwing random sets of points and throwing random lines are similar up to the second moment of counting functions connected with them. We also discuss other applications of this method and show how to calculate higher moments using the group acting on a set

On the Dynamics of Systems of Urns

In this paper we present an analysis of some generalization of the classic urn and balls model. In our model each urn has a fixed capacity and initially is filled with white balls. Black balls are added to the system of connected urns and gradually displace white balls. We show a general form of formulas for the expected numbers of black balls in a given urn and we analyze some special cases (parallel and serial configurations). We are mainly interested in a counterpart of the Coupon Collector Problem for the model considered. The primary motivation for our research is the formal analysis of the mix networks (introduced by D. Chaum) and its immunity to so-called flooding (blending) attacks

On the Dynamics of Systems of Urns

In this paper we present an analysis of some generalization of the classic urn and balls model. In our model each urn has a fixed capacity and initially is filled with white balls. Black balls are added to the system of connected urns and gradually displace white balls. We show a general form of formulas for the expected numbers of black balls in a given urn and we analyze some special cases (parallel and serial configurations). We are mainly interested in a counterpart of the Coupon Collector Problem for the model considered. The primary motivation for our research is the formal analysis of the mix networks (introduced by D. Chaum) and its immunity to so-called flooding (blending) attacks

Kinetics and Dynamics of the Stiff and Flexible Tines with the Duckfoot and the Coulter after Impact with Stones Embedded in Compacted Soil. Part II

The kinetics and dynamics of the stiff and flexible tines with the duckfoot and the coulter after impact with stones embedded in compacted soil were examined. The beak of the duckfoot was positioned in the axis of the row of stones embedded in the soil at the depth of stones thickness. The coulter covered the stone or impact the edge of the stone halfway along its length. The tools worked at a speed of 0.83–2.22 m·s−1 and a working depth of 0.05–0.10 m. The results of specific parameters were compared to the response of the tools to loads in soil without stones. For both soil conditions, the kinetics of the flexible tine was 24 times more reactive, and the dynamic loads were two times lower than for the stiff tine. The responses of both tines were suppressed along with the working depth because of the more favorable place of impact of the duckfoot beak with the stone. Along with the working speed, for a stiff tine, the specific accelerations decreased significantly, by ten times, and the specific forces increased slightly, by 1.6 times. Among the two systems of setting the coulter, the impact of the cutting edge of the coulter with the stone in the middle of its length was more unfavorable than the work of the coulter covering the stone

Effect of Stone Impacts on Various Ground Engaging Tools (Flexible/Stiff Tines and Coulter): Part I

Analysis of the state of knowledge showed a gap in the description of tool–stone feedback. Therefore, the aim of this study was to investigate tool–stone interactions. Spherical-like silicate stones were hit by stiff and flexible tines with a duckfoot or a coulter. The tools worked with various parameters in the depth range of 0.05–0.10 m and a speed of 0.83–2.22 m·s–1. The characteristics of stone movement were specific to the type of tool and were described by the Numerical Stone Movement Scale developed for the purpose of the research. After the impact with the stiff tine, the stones were thrown the greatest distance of 0.26–1.08 m, and these distances were strongly dependent on the working speed and slightly dependent on the working depth. Large vibrations of the flexible tine and the location of the contact point of the tine in relation to the centre of the stone thickness contributed to the random behaviour of stones that were slightly moved, rotated or displaced. The specific work required to remove the stone reflected the distance travelled by the stone as well as the specific force which largely contributed to increasing the differences in this work between both tines

A new hoe share design for weed control: measurements of soil movement and draught forces during operation

This research introduces a new share design (L-share) that reduces the undesired random soil movement, providing a more controlled disturbance of the upper soil layer. Purpose: The aim of this study was to evaluate draught forces and soil movements when operating the new share. Materials and Methods: Experiments were conducted in a laboratory set-up using a soil bin with a fine loamy soil texture. The soil was compacted to a bulk density of 1500 kg m−3, with a penetration index of 486 kPa and a mean water content of 10%. The cultivation depths were 30, 50 and 70 mm and the operation speeds were 0.84, 1.67 and 2.31 m s−1. Cubes were used to measure soil movement by recording the displacement from their initial positions. The soil surface and furrow profile were measured by using a 2D laser range scanner. Results: The results showed that increasing operation speed and cultivation depths generally increased draught forces and soil movement. Changing the cultivation depth from 30 to 50 mm resulted in a 63% greater longitudinal force (Fx), and 71% greater Fx when increasing the cultivation depth from 50 to 70 mm. Conclusion: The study showed that the new L-share mounted on a modified spring tine only causes minor soil movement and thereby minimising the undesirable soil movement