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In ball-type robust universal hypothesis testing (UHT), the null hypothesis is a set of probability distributions constrained by a ball of radius r > 0 denoted B (P 0 , r) based on the cumulative density function of the nominal distribution P 0 . A major limitation is that this method is originally designed only for one-dimensional distributions. To overcome this limitation, this paper proposes a new method to deal with multidimensional samples. For this purpose, first of all, new bounds are defined in the multidimensional domain. Later, a new mathematical programming model based on the transformed region of B (P 0 , r) , namely empirical multidimensional robust UHT problem based on Kullback–Leibler divergence is proposed for ball-type robust UHT. The power of the new testing method combined with different types of bounds was then demonstrated by a computational study. This method fills the research gap by enabling ball-type robust UHT for multidimensional samples and is flexible in that it can be used with different type of bounds. [ABSTRACT FROM AUTHOR]

Self-oscillation enables continuous motion by transforming constant external stimuli into mechanical work, eliminating the necessity for supplementary control systems. This holds considerable promise in domains like actuators, wearable devices and biomedicine. In the current study, a novel suspended liquid crystal elastomer (LCEs) ball system consisting of a light-responsive hollow LCE ball and an air blower is constructed. Stable illumination allows for its continuous periodic oscillation. Drawing from the theoretical model in conjunction with the dynamic LCE model, the control equations for the system are established, and its dynamic motion characteristics are explored from theoretical viewpoint. The numerical calculations suggest that two motion patterns are present, i.e., hovering and self-oscillatory patterns. The critical conditions required to initiate the transition between two motion patterns are quantified for different system parameters. As evidenced by the outcomes, manipulating the light intensity, damping coefficient, contraction coefficient, air density, gravitational acceleration, bottom illumination zone height, characteristic coefficient and vertical wind speed at the blower outlet facilitates precise control over the motion patterns as well as the amplitude and frequency. With its simple structure, customizable dimensions, remote activation and active manipulation, this system may potentially change the design approach for energy harvesting, microsensors and aerial vehicles. [ABSTRACT FROM AUTHOR]

Introduction. Ellipsoids that approximate the half-ball in Rn (n≥2) and their volume is smaller than the volume of the ball can be used to construct algorithms for solving the problem of minimization of a convex (smooth or non-smooth) function, the problem of minimization of a convex function on a sphere, a general problem convex programming, saddle point problems of convex-concave functions and others. The speed of convergence of such algorithms will be determined by the ratio of the volume of the approximating ellipsoid to the volume of the ball. The purpose of the work is to describe properties of three ellipsoids for approximation of a n-dimensional half-ball, the volume reduction factor of which depends only on n - dimension of space. The first is the well-known ellipsoid of minimum volume, which is used in the classical Yudin-Nemirovsky-Shor ellipsoid method. It provides a minimum volume reduction factor and can be used if n≥2. If n=1, then the classical ellipsoid method replaces the dichotomy method. The other two ellipsoids are close to the minimum volume ellipsoid and at large n guarantee volume reduction coefficients close to the minimum. The results. It is shown that when n=1 the first approximate ellipsoid provides a coefficient of reduction of the segment length equal to 2–√2 ≈ 0.5858. The second approximate ellipsoid is new and the volume reduction factor for it is slightly larger than the factor for the first approximate ellipsoid. If n=1, then it provides a coefficient of reduction of the segment length equal to (√5–1)/2 ≈ 0.6180. For three ellipsoids, comparative results are given in terms of volume reduction coefficients (n=1/20) and the number of iterations for solving problems with relative accuracy 1e-10 (n=1/30). Conclusions. A new ellipsoid has been constructed to approximate the n-dimensional half-ball, which is close in volume to the minimal ellipsoid. The volume reduction factor of the proposed ellipsoid is approximated by an asymptotic formula 1–1/(2n)+1/n², which differs little from the formula 1–1/(2n) for an ellipsoid of minimum volume.

Shot hardening is investigated, and the stress–strain state of parts after shot hardening is determined. The contact interaction when a ball is pushed into an elastic half-space is analyzed. [ABSTRACT FROM AUTHOR]

The introduction of innovative approaches in the last decade has taken on a new form and character. Analyzing various methods of innovative development in sports and its impact on sports results, as a factor that improves the effectiveness of the educational and training process in the preparation of athletes of various qualifications and their physical fitness, it can be confidently noted that it is necessary to choose the right innovative path of development in health-saving technologies. Introduction of innovations in table tennis as one of the areas of innovation, through the use of new materials for the manufacture of playing and training uniforms, equipment, floor coverings in halls and the use of various robots in the educational and training process leads to an increase in students’ athletic skills and an improvement in the effectiveness of the training process.

This paper presents a synthetic dataset of labeled game situations in recordings of federated handball and basketball matches played in Galicia, Spain. The dataset consists of synthetic data generated from real video frames, including 308,805 labeled handball frames and 56,578 labeled basketball frames extracted from 2105 handball and 383 basketball 5-s video clips.Experts manually labeled the video clips based on the respective sports, while the individual frames were automatically labeled using computer vision and machine learning techniques. The dataset encompasses seven classes of game situations: left attack, left counterattack, left penalty, right attack, right counterattack, right penalty, and timeout. In basketball, the penalty class refers to the free throws attempted by players after they have been fouled by an opposing player.Each frame in the dataset is assigned to one of these classes, considering the game situation and specific context. Importantly, the dataset does not contain actual video frames; instead, it provides a synthetic, normalized representation of each frame in JSON format. This tabular data includes player, referee, and ball positions on a normalized field, player and referee velocities, and key regions on the court. Positions of players, referees, and the ball were automatically inferred in each frame by an object detector, followed by a tracking step to detect object positions across frames and compute the velocity vectors. Finally, the obtained coordinates underwent normalization through a perspective transformation, ensuring that the data remained unaffected by variations in camera configurations across different arenas and camera setups. We refer to this standardized coordinate space as the 'unified space'.The dataset holds significant potential for reuse in various domains related to sports analytics and machine learning research. It can serve as a valuable resource for researchers, coaches, and sports enthusiasts, contributing to improvements in player performance, game strategies, match retransmissions, and sports-related technologies.

With the constant advancement of electronic science and technology, accurate failure analysis has become crucial to meeting stringent quality standards in surface mount (SMT) products. Reflow soldering is commonly used in the SMT industry due to its efficiency and low failure rate. However, visual inspection is limited, especially for ball grid array (BGA) joints, requiring X-ray techniques for complete, non-destructive analysis. Although X-ray image analysis algorithms have been employed to improve defect detection, some still need to meet quality requirements, resulting in additional manual inspections. The high dimensionality and variations in X-ray images present additional challenges for detection algorithms. This study proposes a new computer-assisted inspection approach to accurately detect flaws in solder joints of SMD components using an X-ray scanning system. This approach aims to improve image interpretation and reduce workload manual. X-ray technology applied to BGA seeks to improve the accuracy of image analysis, enabling the detection of various faults, such as BGA ball connections, interconnections on printed circuit boards, and filling faults. [ABSTRACT FROM AUTHOR]

This article presents a comprehensive dataset of labeled game situations obtained from multiple professional handball matches, which corresponds to the research paper entitled “PlayNet: Real-time Handball Play Classification with Kalman Embeddings and Neural Networks” [1]. The dataset encompasses approximately 11 hours of footage from five handball games played in two different arenas, resulting in around 1 million data frames. Each frame has been meticulously labeled using seven distinct game situation classes (left and right attacks, left and right transitions, left and right penalties, and timeouts). Notably, the dataset does not contain video frames, but provides a synthetic normalized representation of each frame. This representation includes information about player, referee, and ball positions, as well as player and referee velocities, for every labeled game situation. We obtained said details automatically by using an object detector to infer the positions of players, referees, and the ball in each frame. After tracking the detected agent positions across frames, the extracted coordinates underwent normalization through a “bird's eye” perspective transform, ensuring that the data remained unaffected by variations in camera configurations across different arenas. Finally, a Kalman filter was applied to improve the robustness of player positions and derive their velocities. The labeling process was performed by domain experts employing a custom system designed to annotate game situations, considering the play type and its contextual setting. In conclusion, researchers can utilize this dataset for several purposes: game analysis, automated broadcasting, or game summarization. Furthermore, this dataset can contribute to a broader understanding of the relationship between player dynamics and game situations, shedding light on the level of granularity required for accurately classifying them.

The definitions of stored gravitational energy are given. The value of the limited gravitational energy of two massive mutually nonpenetrating balls is calculated. It is established that the stored gravitational energy is always positive. A formula is presented for the maximum possible gravitational energy of two massive balls, which can be used to estimate the energy of the merger of space objects, in particular, gaseous, dusty, and plasma, as well as for ballistic calculations of space flights. [ABSTRACT FROM AUTHOR]

The assessment of technical skill is crucial in the training children in mini basketball, given the significance of ball-related abilities. To verify the present of specific criteria, a set of tests was employed in an experiment conducted as part of this research. The focus was on evaluating tests designed to assess technical skills involving the ball in mini basketball. The objective of this assessments was to provide coaches with valuable insights into the current motor skills of participating children aged 10 to 11 (n = 42). The data collected during the research underwent analysis through descriptive statistical methods. Descriptive statistics for all monitored variables are expressed through SV and SD values. To examine the reliability of the tests for the assessment of technical skills in mini basketball, the intraclass correlation coefficient ICC with a confidence interval (IP 95%) was used. Oneway analysis of variance (ANOVA) and Tukey's post hoc test were used to determine any potential differences between the given measurements in the aforementioned tests. The data obtained in this experiment based on the ICC indicate a high reliability of certain tests. All of these are direct variables for assessing the technical skills of young basketball players acceptable for creating valid and efficient testing protocols. The value of these results is reflected in the fact that the current literature lacks any data on the assessment of the reliability of all these tests assessing the technical skills of basketball players. The main limitation of this experiment is the small number of participants. It should be conducted on a larger sample, whereas the reliability of the tests should be examined with both younger and older children. [ABSTRACT FROM AUTHOR]

Abstract Acute subdural hematoma is a frequent complication of high-energy head injuries. Herein, we report an unusual case of this condition that occurred in a young footballer after he head-balled a football. A 37-year-old footballer, during a match, jumped and gave a head shot on the ball. Upon landing, he felt severe headaches forcing him out of the stadium. About 4 h later, he lost consciousness and went into a coma. After resuscitation, he remained clouded, with cephalalgia and had left hemiparesis. The performed brain scan revealed an acute right fronto-parietal subdural hematoma and the patient benefited from craniotomy surgery in our department with simple postoperative suites. The authors, after a brief discussion of the biomechanics of this serious condition, ask all the actors of this very popular sport, to consider the possibility of occurrence of this condition in players.

The surfaces of the mechanical parts involved in friction processes are made using different processing methods. Each of these processing methods leads to a certain profile of the asperities of the generated surfaces. When such surfaces are subjected to friction processes, it is possible to produce a change in time in the magnitude of the friction coefficient. For experimental research, the outer cylindrical surfaces of some steel test samples were generated using various machining methods such as turning, grinding, ball and diamond burnishing, and vibroburnishing. Later, using a device adapted to a lathe, experimental tests were carried out following the time variation of the value of the friction coefficient under conditions of dry friction and lubricated friction, respectively. The results of the experimental tests were processed mathematically, being determined by empirical mathematical models that highlight the influence of the final processing methods of the surface, the presence of the lubricant, and the test duration on the variation of the friction coefficient. It was found that first, there is an increase over time in the values of the friction coefficient, and then the values of this coefficient stabilize at certain values. The increase in the coefficient of friction until reaching the stabilization value takes place in a proportion of approximately 148–305%. [ABSTRACT FROM AUTHOR]

We present a numerical approach for computing attractive-repulsive power law equilibrium measures in arbitrary dimension. We prove new recurrence relationships for radial Jacobi polynomials on d-dimensional ball domains, providing a substantial generalization of the work started in Gutleb et al. (Math Comput 9:2247–2281, 2022) for the one-dimensional case based on recurrence relationships of Riesz potentials on arbitrary dimensional balls. Among the attractive features of the numerical method are good efficiency due to recursively generated banded and approximately banded Riesz potential operators and computational complexity independent of the dimension d, in stark constrast to the widely used particle swarm simulation approaches for these problems which scale catastrophically with the dimension. We present several numerical experiments to showcase the accuracy and applicability of the method and discuss how our method compares with alternative numerical approaches and conjectured analytical solutions which exist for certain special cases. Finally, we discuss how our method can be used to explore the analytically poorly understood gap formation boundary to spherical shell support. [ABSTRACT FROM AUTHOR]

The outer race is an important component of the ball bearing that supports heavy load from the attached spindle shaft to the inner race via the bearing balls. The machinery that uses bearing for revolving the shaft, their performance depends on the internal surface condition of the outer-race. A typical outer-race of ball bearing (ORBB) of EN-31 steel has been considered to fine-finish its inner surface using the rotational magnetorheological honing (RMRH) in this work. In this research, the response surface methodology approach was used to find out the best finishing variables. From an initial surface roughness of 0.39 µm, a significant surface finish of 0.06 µm was reached after 40 min of RMRH finishing. Furthermore, the surface waviness on the finally finished surface is lessened to 0.08 µm from 0.38 µm on the traditionally honed interior surface of the ORBB, resulting in a substantial increase in straightness. In addition, a circularity test is carried out to see whether the finished surface's circularity has improved. The change in the surface appearance of the ORBB's interior surface is explored using a scanning electron microscope test done on its initial honed and finally finished surfaces using the RMRH technique. [ABSTRACT FROM AUTHOR]

Nonty p ho Ida L Salmonella is a major foodborne pathogen, with the highest percentages of Salmonella positive samples reported in broilers (14%), turkeys (7.4%), pigs (1.7%) and sheep (1.2%), as reported by EFSA annual report on zoonoses for 2023. For 2022 - 2023, three major foodborne outbreaks were reported, caused by serovars Mbandaka, Ball ST 3502 and Virchow ST16, which are not common, but due to the wide host range, that they invade and the food matrices from which they are isolated, they entered the top 20 most common Salmonella serovars. More than 99.5% of Isolates carry virulence factor Um encoded by 9 genes (fimA, C, D, F, H, L, W, YandZ). A large set of resistance genes have been identified in the genome of 5. Mbandaka, Virchow STI6 and Ball ST 3502 isolates. Avian Isolates contain the largest number of resistance determinants. It is necessary to implement molecular biological methods, with the aim of rapid diagnosis, taking adequate and timely measures and decisions related to the control and reduction of the spread of Salmonella. Surveillance should be expanded and hygiene control and disinfection measures should be strengthened at each stage of the agrifood chain, in order to be able to take adequate, timely and effective measures in case of possible detection of Salmonella serovars Mbandaka, Virchow and Ball in Bulgaria. [ABSTRACT FROM AUTHOR]

This study conducted a comprehensive experimental and numerical assessment to investigate the effect of plastic circular balls placed in the middle of a section of a reinforced concrete slab on strength, ductility, thermal, and acoustic performance. The ball diameter/slab thickness (D/H), grades of concrete, and longitudinal tensile reinforcement ratio (ρ) in the slab were selected as the main variables. The variation in thermal and acoustic performance depending upon the ball's diameter was investigated as well. The results showed that the slab's load-carrying capacity, ductility, and energy dissipation capacity did not differ if the D/H ratio did not exceed 0.4; however, significant decreases in these values were observed when the D/H ratio exceeded 0.4. Moreover, the increase in the concrete and reinforcement's strength had a negative effect on the slab with a D/H ratio of 0.8. The experimental results revealed that balled slabs are 3.15 times superior with respect to thermal conductivity and provide 1.38 times more insulation to absorb sound compared to non-balled slabs. In the numerical study of the slabs' thermal performance, the mean surface temperature and heat flux on the slab where the heat transfer takes place decreased as the ball diameter increased. As seen in acoustic models, the level at which the slabs absorbed sound varied depending upon both the diameter of the balls and the sound frequency. [ABSTRACT FROM AUTHOR]

Acute subdural hematoma is a frequent complication of high-energy head injuries. Herein, we report an unusual case of this condition that occurred in a young footballer after he head-balled a football. A 37-year-old footballer, during a match, jumped and gave a head shot on the ball. Upon landing, he felt severe headaches forcing him out of the stadium. About 4 h later, he lost consciousness and went into a coma. After resuscitation, he remained clouded, with cephalalgia and had left hemiparesis. The performed brain scan revealed an acute right fronto-parietal subdural hematoma and the patient benefited from craniotomy surgery in our department with simple postoperative suites. The authors, after a brief discussion of the biomechanics of this serious condition, ask all the actors of this very popular sport, to consider the possibility of occurrence of this condition in players. [ABSTRACT FROM AUTHOR]

This article argues that 5th century BC Athenian vases show that the construction and contents of two medium-sized bags are distinct: phormiskoi were stiff, tightly woven bags that held knuckle-bones (astragaloi), whereas a second type, the name of which is not preserved, but might have been diktydia, were of flexible open net-like make and held small balls. The visual contexts for both types of bags are examined and are found to reinforce the distinction. The representations of the games played with small balls and astragaloi, especially the players actions, are also discussed, few and difficult to interpret though they are. Finally, note is taken of the role of astragaloi beyond the ludic and an image introduced that might show astragalomanteia in action.

This work presents research conducted to increase the level of safety and durability of the actuation mechanism of the screw jack - rotating nut. The study promotes the principle of competitive design by reducing the number of components in a mechanism without compromising the safety, maneuverability, and reliability of the product. The main focus of this study is a metal ball and two plungers housed in a metal box, which replace the functional role of other elements found in similar mechanisms. The calculations, determinations, and verifications in this work were performed using both classical analytical methods and modern calculation methods using the SolidWorks-Simulation program, applied to the components of the box, plungers, and metal ball. Both calculation methods yielded the same results, which fall within the permissible values of the required strength and safety limits. [ABSTRACT FROM AUTHOR]

The possibility of the use of directed crystallization for obtaining a graded structure in grinding balls from chromium white irons is assessed. The chemical composition of the iron is determined. The structure and the microhardness of the balls are studied after a heat treatment. Tests of the grinding balls are performed. Directed crystallization in metallic molds is used to provide a graded structure from the surface to the center of the balls. Preliminary modification with manganese also affects the formation of the structure. The structure of the surface layer in the radial direction is represented by austenitic dendrites and a quasi-eutectic based on (Cr, Fe)7C3 carbides and meets the principle of composite hardening making the balls highly abrasion-resistant. The core of the grinding balls consists of a dispersed spherulitic eutectic and base leading carbides of type M7C3, which raises the resistance of the balls to impact loads during service. [ABSTRACT FROM AUTHOR]

The paper discusses the solution of an interior-boundary value problem of one-dimensional time-fractional Cattaneotype heat conduction and its stress fields for a rigid ball. The interior value problem describes the dependence of the boundary conditions within the ball's inner plane at any instant with a prescribed temperature state, in contrast to the exterior value problem, which relates the known surface temperature to boundary conditions. A single-phase-lag equation with Caputo fractional derivatives is proposed to model the heat equation in a medium subjected to timedependent physical boundary conditions. The application of the finite spherical Hankel and Laplace transform technique to heat conduction is discussed. The influence of the fractional-order parameter and the relaxation time is examined on the temperature fields and their related stresses. The findings show that the slower the thermal wave, the bigger the fractional-order setting, and the higher the period of relaxation, the slower the heat flux propagates. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to constructing a measure of psychological disability for young football players under (19) years old, knowing the relationship between the measure of psychological disability and some of the basic skills of football players for youth under (19) years, and knowing the relationship between the measure of psychological disability and the fixed playing conditions of football players for youth under (19) years. The method chosen by the researcher must be suitable for solving a problem. Therefore, the researcher used the descriptive method. The research community is represented by the players of the Baghdad youth clubs teams for the Premier League under (19) years of football for the season (2021/2022), by (330) players representing Baghdad clubs, by (30) players for each club, and the researcher deliberately chose the community, and chose the youth category Under (19) years old, excluding the other categories, due to the clarity of the problem in this category and in a large way, which led to conducting the research. The research sample was divided into three groups: (the construction sample amounted to (110) players) who were subjected to special tests in constructing the psychological disability scale, and the percentage was (40%) of the parent community, (the sample of the reconnaissance experiment amounted to (6) players), and the percentage was (1.557). %) of the parent community, (the main experiment sample included (214) players), and the percentage was (57.441%) of the parent community, knowing that the research community was distributed randomly (lottery), and thus the percentage of the total sample from the research community is (100%) Where the researcher used all members of the community. Table 1 below shows the number of clubs and players for each club, the total number and the sample (construction, exploratory and main). One of the most important results reached by the researcher is that: The scale proved effective in measuring the psychological disability of the sample, the level of psychological disability is inversely related to the level of scoring, and the level of psychological disability is inversely related to the level of head butting. One of the most important recommendations recommended by the researchers is that: Using the scale to know the level of psychological disability and its impact on scoring and head-butting the ball, and psychological preparation and attention to age groups to reduce their level of psychological disability to qualify them for higher levels in the future. [ABSTRACT FROM AUTHOR]

The multiple-sets split feasibility problem (MSSFP) requires finding a point closet to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. Motivated by the ball-relaxed projection algorithm proposed by Yu et al. for the split feasibility problem (SFP), in this paper, we introduce ball-relaxed projection algorithms for solving the MSSFP. Instead of the level sets or half-spaces, our algorithms require computing the orthogonal projections onto closed balls. We establish weak and strong convergence of the proposed algorithms to a solution of the MSSFP. Finally, we provide preliminary numerical experiments to show the efficiency and the implementation of our method. [ABSTRACT FROM AUTHOR]

Since nonlinear systems are difficult to analyze but play a critical role in control theory, the construction of an appropriate controller is essential. A robust controller should be capable of dealing with abruwpt changes, uncertainty, disturbances, and other nonlinearities in the system. An accurate control system for nonlinear and unstable ball and beam system is essential, moreover it presents a significant challenge to be controlled by engineers and researchers. The ball and beam problem can be solved by using a controller that would monitor the ball position in the system. The ball and beam system is a very popular system due to its semplicity to be understood and the control techniques that can be studied over it. The system has been built in many ways before some easier and some more effective ones. This system in an openloop setting is inseparably nonlinear and unstable but with the appropriate steps it can stabilize its response. Physical laws are used to conduct the ball and beam system theoretical analysis. System mathematical modeling is presented clearly and simulations together with their analysis will be done by using MATLAB software. It will be necessary to use mathematical modeling, which will include linearization of the model. The performance of each controller will be evaluated and compared. Two different controllers are used in this work. [ABSTRACT FROM AUTHOR]

This paper reports on research that explored the experiences of secondary Physical Education Teacher Education (PETE) professionals' simultaneous negotiation and implementation of the new Curriculum for Wales (CfW) Health and Well‐Being (HWB) Area of Learning and Experience (AoLE) and policies focused on the transformation of Initial Teacher Education (ITE) in Wales. The study was an exploratory case study of PETE professionals working within one university's ITE programme. Data were generated through documentary analysis of PETE and ITE programme materials and semi‐structured interviews with staff involved in programme management and delivery. Data analysis employed Ball and colleagues' conceptualisation of policy actors and contexts to critically examine the varied policy positions that PETE professionals adopt in navigating and negotiating enactment of the HWB AoLE within their ITE provision. Attention is drawn to the significance of historical and culturally situated dimensions of secondary physical education and PETE in Wales, and significant changes to the professional culture of ITE, in shaping PETE educators' engagement with the HWB AoLE. The paper concludes by contending that ITE institutions in Wales need to further consider how PETE (and other) educators can be actively supported to engage in sophisticated policy work within their institutions and across policy and professional networks. [ABSTRACT FROM AUTHOR]

A device is proposed for determining the pressure in a joint based on an interference fit. Its sensitive element consists of balls located between the contacting surfaces. Two types of contact interaction between the balls and the components of the joint are considered: elastoplastic deformation of the balls; and elastoplastic deformation of the parts. The pressure in shaft–bush contact is determined from the deformation. [ABSTRACT FROM AUTHOR]

The purpose of this report is to walk readers through the conceptual design development of an autonomous transporter that carries a golf ball and shoots it as far as possible. High and low-level design requirements are outlined to discuss intended functionality of the transporter. Preliminary design concepts are presented. An Objective Tree and a Pairwise Comparison Chart are then used to select the best concept based on desired qualities. CAD models of the chosen design are shown. Preliminary calculations for the drive and launch systems are formed and discussed to prove the robot’s ability to succeed at accomplishing the proposed task.

Let $B$ be a Euclidean ball in ${\mathbb R}^n$ and let $C(B)$ be a space of continuos functions $f:B\to{\mathbb R}$ with the uniform norm $\|f\|_{C(B)}:=\max_{x\in B}|f(x)|.$ By $\Pi_1\left({\mathbb R}^n\right)$ we mean a set of polynomials of degree $\leq 1$, i.e., a set of linear functions upon ${\mathbb R}^n$. The interpolation projector $P:C(B)\to \Pi_1({\mathbb R}^n)$ with the nodes $x^{(j)}\in B$ is defined by the equalities $Pf\left(x^{(j)}\right)=f\left(x^{(j)}\right)$, $j=1,\ldots, n+1$.The norm of $P$ as an operator from $C(B)$ to $C(B)$ can be calculated by the formula $\|P\|_B=\max_{x\in B}\sum |\lambda_j(x)|.$ Here $\lambda_j$ are the basic Lagrange polynomials corresponding to the $n$-dimensional nondegenerate simplex $S$ with the vertices $x^{(j)}$. Let $P^\prime$ be a projector having the nodes in the vertices of a regular simplex inscribed into the ball. We describe the points $y\in B$ with the property $\|P^\prime\|_B=\sum |\lambda_j(y)|$. Also we formulate some geometric conjecture which implies that $\|P^\prime\|_B$ is equal to the minimal norm of an interpolation projector with nodes in $B$. We prove that this conjecture holds true at least for $n=1,2,3,4$.

In the Romanian Principalities, society balls were held between 1st of January and Lent. Everyone was eager to revel in this joyful period to the full. The prosperous upper classes and those less well-to-do all made preparations and saved substantial amounts of money for this purpose. Satirists found balls to be a rich source of inspiration for their humorous writings. N. T. Orășanu, I. C. Fundescu, Iorgu Caragiale and his brilliant nephew, Ion Luca Cargiale, wrote about them with great perception and wit in contemporary periodicals.

In an infinite-dimensional real Hilbert space setting, we introduce a new self-adaptive inertial Halpern-type projection algorithm for solving multiple-sets split feasibility problem assuming that the involved convex subsets are level subsets of strongly convex functions by approximating the original convex subsets by a sequence of closed balls instead of half-spaces. Since the projection onto the closed ball has a closed form, the proposed algorithm is hence easy to implement. Moreover, we construct a new self-adaptive stepsize that is bounded away from zero and is independent of the operator norm. Under some mild assumptions and without the usual Lipschitz’s continuity of the gradient operator assumption, we establish and prove a strong convergence of the sequence generated by the proposed algorithm. Several numerical illustrations indicate that the proposed algorithm is computationally efficient and competes well with some existing algorithms in the literature. The proposed method is an improvement and generalization of many results in the literature. [ABSTRACT FROM AUTHOR]

Copyright of Gymnasium: Scientific Journal of Education, Sports & Health is the property of Alma Mater and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bitnuaa Movement is the property of Academic Center Levinsky-Wingate and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We establish short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. So far, such results were only known in simple cases where explicit formulae are available, i.e., for sets as half-line, interval and their products. Presented asymptotics may be considered as a complement or a generalization of the famous "principle of not feeling the boundary" in case of a ball. Following the metaphor, the principle reveals when the process does not feel the boundary, while we describe what happens when it starts feeling the boundary. [ABSTRACT FROM AUTHOR]

The aim of this research was to identify new ways to attract and stimulate the body to maintain the capacity of the physical effort of the operational staff within the professional structures for emergency situations, namely military firefighters using the game of basketball. The study was carried out on duty and had as subjects about 30 military personnel, to which a set of strength exercises performed on the specific equipment of the basketball game was applied. The military personnel involved were fully equipped with personal protective equipment consisting of nomex water protection suit, intervention boots/boots, seat belt, safety helmet, protective gloves, hood, flashlight and compressed air respirator. After going through the motor circuit made and carried out on the unit's plateau, as well as when the weather conditions are unfavorable or in the cold season, respectively in the car garage, we can say that the staff on duty keeps their motor capacity at normal parameters to meet happy ending to the missions entrusted to you by the game of basketball. In this case, we can say that the exercises and circuits designed, as well as the conditions in which they were performed, can maintain the optimal level of physical training for military firefighters.