Academic literature on the topic 'Distribution of the number of rejections'

Broadband light intensity modulators are useful in a number of applications. It has been reported that by making a multilayer stack having a random thickness/index distribution an excellent broadband reflector is obtained.1 If dynamic materials, i.e, electro-optic, nonlinear-optic materials are used to construct the device, a broadband light modulator is obtained. The light modulation is achieved by varying the applied external field if electro-optic materials are used. If nonlinear-optic material is used the device is self-modulating. The configuration chosen for analysis consists of alternating layers of two different electro-optic materials and two transparent surface electrode layers. The thickness distribution is completely random. In the transmission state the indices of the two materials are equal. When an external field is applied a difference in refractive index between adjacent layers is created through the electro-optic effect. This results in a reflection of incident light over a broadband of wavelengths. The characteristics of the rejection band depend on the random distribution profile and the maximum index difference achievable. Results based on computer simulations are presented.

This paper investigates a multiprocessor queueing system in which each incoming task requires a variable number of service nodes, reflecting the diverse resource demands found in modern parallel computing environments. By modelling the task arrival and service processes using Poisson and exponential distributions, the system’s behaviour is analyzed through differentialdifference equations that govern the steady-state probabilities. The research provides a comprehensive solution for determining the probability of different numbers of tasks being serviced, considering both the acceptance and rejection of tasks based on system capacity. The derived results offer valuable insights into optimizing system performance in terms of throughput, task completion, and resource utilization for multiprocessor systems.

Teaching disciplines involving mathematical modeling, simulation, statistics and data analysis can be approached in an attractive manner for students (from specialization such as Informatics) if the teacher appeals to visual programming environments. For statistical modeling and simulation, programming skills allow implementation of Windows applications with user friendly interface, with graphical representations and easy to interpret results. The objective of this paper is to present the facilities of a modern visual programming environment (Microsoft Visual C#), for teaching in an attractive way applications for generating random variables, statistical indicators calculation or empirical probabilities calculation. As a case study is presented the development of an application that models a real-life problem. It is considered that the time (in years) of operation for an equipment has a negative exponential distribution of parameter lambda. We are interested in mean time of functioning and the probability that an equipment will function properly after a number of years. In a first step, using visual components, graphical interface of the application is built. Using methods for generating random variables (inverse method or rejection method) there are simulated functioning times with a negative exponential distribution. Some statistical indicators, such as mean or variance are calculated and the probability of various events are calculated empirically by approximation with frequency. Values obtained through modeling and simulation are compared with theoretical values (mean, frequency, percentile). The research concludes that a visual programming environment has tools that allow a programmer implementation of more complex applications than those generally made using a specialized software for statistical analysis.

Abstract The ability to combine energy sources with intermittent performance with more consistent form of power is crucial for increasing the penetration of renewable energy sources in the electricity and heat generation sector. In this scenario, district heating networks are a promising solution but, to benefit the most from this technology, control tools must be developed with the objective of optimizing the heating load to each of the buildings in the network, while rejecting external disturbances. One of the main challenges for control design and verification is the limited access to data and experimental platforms. In addition, real systems are subjected to a large number of exogenous inputs and tests repeatability for benchmarking is a challenge. To overcome this limitation, a scaled experimental set up has been developed. This paper discusses the design of the experimental setup of a simple heat distribution network as well as the derivation, calibration and validation of a simulation model. Simulation results show that the model error in predicting temperature is always below 1 %.

The problem under research is of particular importance for the family and society because we can say, without fear of being subjective, that the socialization of children, i.e. their preparation to live in society, is a very topical problem precisely by ignoring its systematic and conscious approach at the level of society , especially in the context where puberty is the period when sports activities are of vital importance for socialization. At this stage of life, the child is sensitive to cognitive and moral development, he assumes different roles, learns that he is different from others and, above all, learns to build relationships with others. The purpose of the research. Establishing the socio-affective climate of the groups of students subject to research aims to identify the level of socialization and relationship among students, existing relationships at the group level, socialization, communication and relationship. The group interaction took place during swimming training, through the school curriculum Research method: sociometric test Sociometric testing reveals relevant aspects regarding the relationship of the student and the group as a whole. In order to know the level of socialization, empathy and mutual relations between adolescent students who practice swimming, the sociometric test was applied to the experimental group and the control group (50 students from the I.C. Vissarion Titu Theoretical High School, age level 13 , 14 years). The sociometric study has a triple orientation in the present research: 1. The teacher-coach's knowledge of the relationships within the group; 2. Students' identification of their own positions within the group; 3. Improving relationships and the psychosocial climate of the group through specific actions (socialization program in school camps The sociometric test was applied to students in the period 01.02-01.03.2023. the test was applied to both research groups. The results of the sociometric test were transposed into the sociometric matrices. For each group of pubertal age students (from the 8th grade of the I.C. Vissarion Titu Theoretical High School, age level 13-14), a matrix was created. This allowed the creation of a table with double entry, in which the subjects were numbered on the first line and column, in order to preserve the confidentiality of the data, respectively the names of the students, each student received a code name, the experimental group no. I-A1 - A25 and control group no. II- B1 - B30 (Appendices no. 4 and 5), and the data from the tests were recorded one by one in the sociometric matrix, thus reflecting the place of each member within the group. The resulting matrix shows that the highest score of positive attractions, namely 13, is obtained by A5 which has only 2 rejections, followed by A 16 and A24 with an attraction score of 12 and 2 rejections. Then, A8 and A11 stand out, each with a score of 9 in the election chapter. As I mentioned, in the center of the group is A5, chosen by 6 members of the group: A1, A2, A9, A12, A14 and A18, followed by A2, with 5 choices: A3, A10, A12, A16, A5. The following group members A 4, A10, A1, A19 have 4 choices each, followed by those with three choices: A1, A13, A14, A17, A 20. In the "chapter" rejections, the situation is as follows: A3 and A23 are each rejected by 6 members of the group, A 3 by A2, A5, A8, A14, A 21, A23 and A23 is rejected by A2, A3, A15, A18, A20, A24. We have also identified that A3 did not register any choice and so did A23. At the opposite pole, the fewest rejections were recorded by A4, A13, A16, one rejection each. From the analysis of the existing data, it appears that there are a number of 9 mutual choices: A1 with A19, A1 with A21, A4 with A24, A8 with A17, A8 with A20, A11 with A14, A13 with A 22, A14 with A21, A15 with A19 . At the same time, 4 mutual rejections were also identified: A3 with A23, A3 with A5, A6 with A25, A14 with A8. According to the matrix of the experimental group, within this group there are 2 subjects who did not register any attraction from the other members of the group, only registered rejections, they are A3, 0 choices and 6 rejections and A 23 0 choices and 6 rejections. The recorded results and the sociometric matrix show us that the subjects in the experimental group is not cohesive, there is no close relationship and communication between the group members. Lack of cohesion can lead to difficulties in communication, collaboration and achieving common goals. In the case of the second group subject to research, group no. II B (B1-B25), the results highlight the subjects with the highest score in positive choices are B5 and B15 registering an ISP index of 0.33, but those who have recorded the most positive choices are, B5 preferred by 8 members of the group: B1, B2, B7, B9, B12, B14, B19, B22, followed by B8 with 6 positive choices from the following members: B3, B5, B6, B10, B17, B21, and B16 registered 5 positive choices: B4, B7, B14, B15, B24. There were also 9 mutual positive choices, distributed as follows: B1-B2, B2-B12, B1-B5, B8-B10, B8-B17, B10-B13, B16-B24, B15-B19, B21-B1 . We note that B1 has reciprocal relationships with B2 and B5, and B8 with B10 and B17. In the case of group II B, the control group, all group members received choices and rejections. For example, there were subjects who chose but were rejected by the chosen: B2-B3, B-B3, B4-B25, B11-B4, B15-B4, B5-B12, B5-B19, B9-B24, B12-B20, B1-B19, B5-B19, B18-B20. In the rejection chapter, the highest negative score of 0.25 was recorded by A3 and A16, the most rejections are recorded by B3 with 5 rejections from the subjects: B2, B4, B5, B8, B25, followed by B15 all with 5 rejections obtained from: B1, B9, B12, B21, B23, then B25 also with 5 rejections from the following subjects: B4, B7, B16, B17, B19. The fewest rejections, respectively 1 each, were recorded by the following subjects: B1, B7, B9, B16, B24. The analysis of the results of the sociometric test applied to the two groups of adolescent students who practice swimming, groups I A and II B, brings to the fore a low degree of cohesion among the group members. Studying the indices of preferential status for group I, we find that the psychological value of preferential time "popular" registered three members, who were preferred by a certain subject. The preferential status index for the psychosocial value of the "popular" type fell within the value of 0.50 - 0.45. For the second group the psychological value of preferential time "popular" recorded two members, who were preferred by a certain subject. The preferential status index for the psychosocial value of the "popular" type fell to the value of 0.33. Within the "accept" preferential type psychosocial value, the first group, I, recorded 9 members, and the second group recorded 10 members, "accept" preferential status indices in group I A ranged from 0.25 -0 .04, compared to group II B where the preferential status index is between 0.25 and 0.08. The psychosocial value of the "marginalized" preferential type highlights the fact that the subjects of group I fall within the range of -0.45 and -0.08, and those of group II within the range of -0.33 and -0.04. Group I registered 11 "marginalized" subjects and group II 10 marginalized. The results of the initial testing show that the two research groups are relatively homogeneous. Studying the sociograms below, we notice that subjects A5, A16, A24 and B5, B15 are "popular" in the group of subjects, being placed in the center of the sociogram. Less integrated, registered under the chapter "accepted" are subjects A2, A4, A6, A7, A8, A10, A13, A22 and B1, B4, B6, B7, B8, B10, B11, B12, B21, B24. At the same time, the "marginalized" are highlighted A1, A3, A9, A11, A12, A14, A15, A18, A21, A23, A25 and in group II B2, B3, B9, B14, B16, B17 B18, B19, B20, B23 , B25, Indifferences are: A17, A19, A20 and B11, B13 B18.imageFigure 1. Sociogram of group I AimageFigure 2. Sociogram of group II BConclusions. By examining the sociogram, we gained useful information about how group members interact, who are the leaders, and who are the more socially isolated. This information is useful for us to develop strategies to strengthen relationships and improve group dynamics. According to the research results we recommend the following: - The coach can offer the children exercises and games to help them improve their verbal and non-verbal communication skills. - Encouraging children to participate in team games and cooperative activities.

Abstract The use of 4 mm thickness Mini-C(T) specimens for Master Curve evaluation is drawing attention as a possible alternative / supplemental surveillance test method to current Charpy-based approaches in on-going efforts to update JEAC4201[1]. Obtaining a “valid” To per ASTM E1921 [2] and JEAC4216 [3] is a challenge for the Mini-C(T) because its tests must be performed at a low temperature relative to To to stay below the plasticity limit (KJclimit) of the testing standards while remaining above another limit on minimum test temperature (To – 50 °C) imposed by the testing standards. Minimizing the number of censored data caused by the violation of the KJclimit requirement is important in practical surveillance testing applications, since only a limited number (e.g., 12) of specimens may be available. Therefore, finding the appropriate test temperature within the first few specimens tested is essential. In this paper, the authors develop a KJc test temperature selection algorithm to maximize the chance of obtaining an E1921 and JEAC4216-valid To value with 12 or fewer tests. By the combined consideration of rejecting fewer specimens for being conducted below the low-temperature limit and having fewer specimens censored due to excess plasticity, we assumed that the test temperature of the next specimen in a series could be identified as the intersection of the KJclimit curve and the 98% tolerance bound of the KJc distribution, which is determined from an estimate of To made using already tested specimens. The appropriateness of this assumption is confirmed by a series of Monte-Carlo calculations, which demonstrates that this approach produces a valid To by testing 12 Mini-C(T)s > 98 % of the time. The study validated this testing reliability for a realistic range of yield stress and To values for reactor pressure vessel steels.

This study presents the methodology for the KAPSARC Distribution Hosting Capacity Tool (KDHCT). This tool can support the future of renewable energy in Saudi Arabia. The use of distributed energy resources (DERs), such as solar panels, energy storage and electric vehicles (EVs), is expected to increase. The KDHCT evaluates how many of these assets a particular distribution system can accommodate. The number of DERs and the load that an electric distribution system can reliably accommodate without significant grid upgrades is called its hosting capacity (HC) (Abad, Ma, and Han 2019). HC analysis informs electricity customers and utilities about the best places and times to install DERs and EVs on any distribution system. Thus, utilities can avoid reliability problems and costly distribution system upgrades.