Sets Of Different Numbers Research Articles

Dental pattern diversity in a military population and its usefulness for assessing the degree of certainty in dental identification

In forensic dentistry, the analysis of dental diversity forms the basis of probability calculations in dental identification. The present study aimed to contribute to the knowledge of dental diversity in a Spanish military population (considering isolated teeth, sets of different numbers of teeth, and combinations of teeth of forensic interest) and its implications for dental identification. A further aim was to compare the performance of three coding systems (detailed, generic, and binary) to assess dental pattern diversity. Dental diversity of a representative sample of the Spanish military population (3920 individuals aged between 18 and 55 years) was calculated according to a genetic (mitochondrial DNA) model in which diversity was defined as the likelihood that two randomly selected individuals in a sample would exhibit different patterns. By performing all pairwise comparisons of dental patterns in the dataset, the total number of matches was generated, and the diversity of dental patterns was then derived. First and third molars were the teeth that showed the highest levels of diversity, and a high diversity value (>0.99) was obtained with only 5 teeth (16, 36, 38, 46, and 48) when detailed coding was used. In addition, dental diversity in the full dentition and posterior teeth exceeded the threshold of 0.99 in all three coding systems. Although a very high diversity value (≥0.999) was only achieved with detailed coding, it should be noted that the generic coding system requires less time and skill to use, and can also provide high diversity values. Our findings show that further efforts should be made to establish large, periodically updated dental datasets of different populations in order to assess dental pattern diversity (without excluding third molars) based on empirical comparison, and to substantiate the certainty of dental identification.

Higher Length Necklaces from Lower Ones When the Absolute Value of the Difference of Two Adjacent Beads Belongs to a Set of Integers

A successive method of deriving the necklaces of higher lengths from the lower ones when the absolute difference of two adjacent beads (DBs) belongs to a specified set of numbers is developed. Some of them can be obtained in sequence; while others are obtained from even length to next even length, or odd length to next odd length. There are many possible necklaces for the same length. The technique is extended to DBs with different sets of numbers which include 1. Gluing method is developed which gives the higher length necklaces from lower ones by interconnecting two necklaces.

МОДЕЛИРОВАНИЕ ВОЗМОЖНЫХ СЛЕДСТВИЙ ФОРМИРОВАНИЯ ЧАСТИЦ СВИНЦА В ВИДЕ РАСКАТКИ ДО СОСТОЯНИЯ ПЛАСТИНЫ В ПРОЦЕССЕ ЕГО ОКИСЛЕНИЯ В ПРИСУТСТВИИ МЕХАНИЧЕСКИХ ВОЗДЕЙСТВИЙ НА ПОВЕРХНОСТЬ

Using lead loadings in the form of single plates with different weights and physical surfaces, as well as sets of different numbers of plates and approximately the same total mass during its oxidation in organic phases containing molecular iodine and hydrogen peroxide simultaneously and only hydrogen peroxide as an oxidizer, a simulation of the possible consequences of rolling lead particles with bulk shapes into thin plates under the influence of mechanical factors in the course of oxidative processes has been carried out. It was established that single plates under the selected conditions were consumed in accordance with zero-order macrokinetics and velocities which increased with increasing the plate mass and decreasing its physical surface. The same trend persists in sets of plates: the more plates in the set while maintaining the total mass, the worse the process proceeds. At the same time, each set corresponds to its own type of the macrokinetic curve of lead consumption in the range from auto-accelerated development with a transition to the stationary or wave mode to auto-delayed development with an exit to a very slow, stationary mode close to zero order. Consequently, the rolling of particles of bulk forms into plates during the process automatically leads to a slowdown in the passing, which cannot be eliminated by external influence.

Fatigue behavior and electromechanical properties of additively manufactured continuous wire polymer composites for structural health monitoring

AbstractThe fatigue behavior of continuous wire polymer composite (CWPC) fabricated by fused filament fabrication (FFF) was investigated. Four compositions were examined: polylactic acid (PLA), PLA with copper wire (Cu), thermoplastic polyurethane (TPU), and TPU with Cu wire. Residual properties were measured after different sets of number of cycles (102, 104, 105). Residual strengths were 89.7% and 70.5% of the ultimate tensile strength of the original material after 105 cycles for PLA CWPC and TPU CWPC, respectively. A one‐way analysis of variance (ANOVA) statistical tests showed insignificant changes in the residual strengths of PLA‐based materials after an increasing number of cycles and significant changes for the TPU‐based materials. CWPC electromechanical properties under fatigue test demonstrated reverse piezoresistance behavior. A strain‐controlled fatigue life analytical model was compared with the experimental results showing good agreement. This study demonstrates the applicability of FFF technique to print sensors with continuous integrated wire with tunable properties.

A Reliability and Comparative Analysis of the New Randomized King-Devick Test.

The King-Devick (K-D) test is a rapid visual screening tool that can assess underlying brain trauma such as concussion via impairments in saccadic rhythm. A new tablet version of the K-D test using randomized numbers is now available, but reliability for this new version and comparison to the traditional K-D test has not yet been reported. Known for learning effects in the test, the aim of this study was to determine test-retest reliability and to compare performance of the new "randomized" version to the "traditional" K-D test version. We hypothesized that the "traditional" K-D test would show a greater rate of improvement with repeat application, compared with the "randomized" K-D test. Using a cross-sectional, repeated measures design in a healthy university student cohort (n = 96; age 21.6 ± 2.8 years; 49 women, 47 men), participants were required to complete the K-D test twice with a one-week break between testing sessions. Participants were randomly assigned into a "traditional" group, where they completed a test-retest of the established K-D protocol, using the same numbers; or the "randomized" group, where they completed test-retest protocol using 2 different sets of numbers. Reliability testing showed a strong intraclass correlation coefficient for both the "traditional" test group (control group; 0.95 [CI: 0.91-0.97]) and the "randomized test group" (0.97 [CI: 0.95-0.98]). However, contrary to our hypothesis, no differences were found between "traditional" and "randomized" groups for baseline (control: 42.5 seconds [CI: 40.2-44.9 s] vs randomized: 41.5 [38.7-44.4], P = 0.23) and repeated testing between groups (control: 40.0 seconds [37.9-42.1 s] vs randomized: 39.5 [36.9-42.0], P = 0.55), with both groups showing improved times with repeated testing (control: 2.1 seconds [CI: 1.1-3.2 seconds] and randomized: 1.9 seconds CI: [0.9-2.9 seconds], P < 0.001). The "randomized" version of the K-D test, using different sets of numbers, demonstrates good reliability that is comparable to the traditional K-D testing protocol that uses the same number sets. However, similar to the "traditional" K-D test, learning effects were also observed in the "randomized" test, suggesting that learning effects are not because of content memorization, but rather familiarity of the test. As a result, although either test format is suitable for sideline concussion screening or return to play decisions, comparison of data should be made to the individual's baseline rather than to normative data sets.

Simulation of Pedestrian Walking Through Angled-Corridors for Evacuation Behaviour Study

The effect of acute- and obtuse-angled-corridors on the evacuation behaviour is rarely studied. In the previous work, we have confirmed that corridor with less than 90° turning angle has negative impact to the pedestrians walking behaviour due to the tendency of the pedestrians to slow down their motion when approaching the turning of the corridor. This restrict the flow of walkers during high-density situation and cause congestion near that turning of the corridor. In this contribution, empirical data collected from previous experimental work is utilised to further study the effect of turning angle on the evacuation behaviour. The simulations of walking through angled-corridor were reproduced which reflects evacuation scenarios. Three different types of angled-corridor are taken into consideration (a 60°-, a 90°-, and a 135°-angled-corridors) with different sets of number of pedestrians (NOP: 60, 70, 80, 90 and 100). Three metrics of evacuation behaviour measurement are reported: (1) inflexion points, (2) escape time, and (3) interaction force. Inflexion point is used to evaluate the restriction flow occurred during the evacuation. From the results, the 60° angled-corridor contained the highest number of inflexion points. With the highest number of inflexion points, the escape time for the 60° angled-corridor is 14.8% to 24% longer compared to the other two types of angled-corridors. This shows that this kind of angled-corridor need to be avoided in the future design of walkways. On top of that, the 60° angled-corridor also gives the maximum interaction force with 213.75 N. This reconfirmed that the corridor with less than 90° turning angle is not suitable to be built as a walkway. This work is relevant to be studied due to its immediate applications in assessment of crowd safety for building egress.

An artificial neural network to model response of a radiotherapy beam monitoring system.

The integral quality monitor (IQM) is a real-time radiotherapy beam monitoring system, which consists of a spatially sensitive large-area ion chamber, mounted at the collimator of the linear accelerator (linac), and a calculation algorithm to predict the detector signal for each beam segment. By comparing the measured and predicted signals the system validates the beam delivery. The current commercial version of IQM uses an analytic method to predict the signal, which requires a semi-empirical approach to determine and optimize various calculation parameters. The process of developing the calculation model is complex and time consuming, and moreover, the model cannot be easily generalized across various beam delivery platforms with different combinations of beam energy, beam flattening, beam shaping elements, and Linac models. Therefore, as an alternative solution, we investigated the feasibility of developing a machine learning (ML) method, using an artificial neural network (ANN), to predict the ion chamber signal. In developing an ANN, it is not necessary to explicitly account for each of the elements of beam interactions with various structures in the beam path to the ion chamber. The ANN was designed with multilayer perceptron (MLP). The input layer consisted of multiple features, derived from the geometrical characteristics of beam segments. Gradient descent error backpropagation technique was used to train the ANN. The combined training dataset included 270 rectangular fields, and 801 clinical IMRT fields delivered using 6 MV beams on Varian TrueBeamTM and Elekta InfinityTM . Each of 12 different ANN configurations (3 different sets of input features×4 different sets of number of hidden nodes) was simulated 10 times with randomly selected 80% of data for training and the remaining data for validation. Artificial neural networks with one hidden layer, consisting of 10 nodes, and 10 input features provided optimum results. Once the feature sets were extracted, the time required for the network training was on the order of a few minutes, and the time required to perform an output calculation per field was only fraction of a second. More than 95% of clinical intensity-modulated radiation therapy (IMRT) segments were calculated within±3.0% modeling error for Varian Truebeam (90% and ±3.3% for Elekta Infinity). A total of 3320 volumetric-modulated arc therapy (VMAT) segments from Truebeam were calculated using the ANN trained with IMRT fields. More than 95% of the cumulative VMAT beam segments were within 3.6% modeling error, similar to the performance for IMRT segments. In general the modeling error was found to be inversely proportional to the size and intensity of the beam segment. A prototype ANN has been developed for predicting the signals of the IQM system, with substantially less efforts compared to the analytic model. The performance of the ANN was found to be at least equivalent to that of the analytic method, in terms of average and maximum error, for 6 MV beams on both Varian TrueBeam and Elekta Infinity platforms.

Development of Arithmetical Thinking: Evaluation of Subject Matter Knowledge of Pre-Service Teachers in Order to Design the Appropriate Course

One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.

Q(&amp;#8730;m)Q Under the Action of PSL&lt;sub&gt;2&lt;/sub&gt;(Z)&amp;#8745; [x, y:x&lt;sup&gt;2&lt;/sup&gt; = y&lt;sup&gt;6&lt;/sup&gt; = 1

This study is concerned with the natural action (as Möbius transformations) of some subgroups of $PGL_2 (Ζ)$ on the elements of quadratic number field over the rational numbers. We start with two groups- the full modular group $G = PSL_2 (Ζ)$ and another group of Möbius transformations $M = \langle x, y : x^2 = y^6 = 1\rangle$. We consider different sets of numbers with fixed discriminants in the quadratic field and look at structure of the orbits orbits of the actions of $G , M , G ∩ M$ and their subgroups on these sets. The results of earlier studies on the number of orbits and the properties of elements belonging to them are extended by similar results related to the new twist connected to the group M which has nontrivial intersection with G and opens a possibility to look at orbits which were not computed in earlier studies.

The mathematical relationship between the number of events in which people are injured and the number of people injured.

In this paper the mathematical relationship between the number of times people sustained injuries and the number of people injured is discussed. The number of injury-causing events in a population will be larger than the number of people injured as people can be injured on more than one occasion. The Poisson distribution is used as a way to study the relationship between the two different sets of numbers. A practical example is given of injuries sustained while running. From this it seems that injury proneness needs to be considered in studying those who were injured on more than one occasion while running during the past year.

Five studies of subjective equivalence

Subjects set intervals around various numerical values to indicate the ranges within which they would regard unaided subjective judgments of those values as being essentially correct. This was done for five different sets of numbers: historical dates, proportions, people's ages, seriousness of diseases and life events, and the money values of inheritances and gifts. In some cases the interval breadths were determined by the magnitudes of the numbers involved; in other cases they were determined by task characteristics; and in yet other cases they were determined by both magnitudes and task characteristics but in very intuitively reasonable ways. Ties between this research and studies of subjective judgments of variances and of credible intervals, as well as lexicographic choice, are examined and various implications of this line of research are explored.

An Integer Construction Problem

1. The problem. With the digits 1, 2, 3, 4 express the consecutive integers from 1 upwards as far as possible: each of the four digits being used once, and only once, in the expression of each number. The puzzle quoted above from Ball* is illustrative of a common type of mathematical recreation: a numerical construction problem. A set of numbers is given (with possibly a fixed number of repetitions for each of the numbers); certain numerical operations are allowed to be performed on these numbers; and some or all of the resulting numbers are required to be found. In the puzzle quoted above, an answer is that, if only the operations of addition, subtraction, and multiplication on the integers 1, 2, 3, 4 (each integer being used exactly once) are allowed, then all integers from 1 through 28, as well as 30, 32, and 36, but no others, can be constructed. A proof of this statement is found in Section 6. If other operations are allowed, then it may be expected that different sets of numbers may be constructed; Ball gives several examples of this. In this paper, an explicit expression is determined for a specific integer, namely the largest possible integer, constructible from a given set of positive integers, using only the operations of addition, subtraction, and multiplication. Use of the specific properties of a system of notation for integers is not allowed.

On the Spectrum of Neutral Helium

Silberstein's formula for the lines of neutral helium.- As objections to the validity of the formula ν=4N (I/n12-I/m12+I/n22-I/m22) it is pointed out that the ionizing potential computed by means of this formula does not agnee with that given by experiments; that no definite principle of selection has been given to indicate observable lines; that there is no arrangement of lines as regards series relationship, division into singlet and doublet systems, or of intensities. The difference between the actual and the calculated frequencies is shown to be the same as that to be expected on the assumption that the coincidences are purely accidental; and the same frequencies can be obtained with different sets of numbers.