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We have taken a class on an isoperimetric problem for lower secondary school students who have high motivation to mathematics. In this paper, we have considered the lesson plan on an isoperimetric problem for the students and decided the goal of this class is to prove the theorem as below. 'A polygon which has the biggest area with same constant perimeter is a regular polygon.' After the class on an isoperimetric problem, we have realized the goal of isoperimetric problem for lower secondary school students will be suitable and have recognized strongly the mathematical experiments will be an important impact for this class.

A ring $R$ is said to be left $p$-injective if, for any principal left ideal $I$ of $R$, any left $R$-homomorphism $I$ into $R$ extends to one of $R$ into itself. In this note left nonsingular left $p$-injective rings are characterized using their maximal left rings of quotients and the structure of semiprime left $p$-injective rings of bounded index is investigated.

This paper proposes a design method of transmissions for underactuated mechanisms. This transmission consists of active and passive gear trains that align a series of gears over several joints. The transmission has no kinematic singular point that restricts the workspace. Thus, arbitrary joint-connected motions of the underactuated mechanisms can be designed by combining the gear trains. We investigate the kinematics and statics of underactuated mechanisms to find a transmission matrix that realizes the desired connected motions and adaptive grasps. We also develop a method to design gear trains that corresponds to the transmission matrix. We extend this design method with stepped gears and belt–gear mechanisms to increase the design flexibility. The proposed method was experimentally validated using the two- and three-jointed mechanisms.

Let R be a semiperfect ring and [M ] be the set of right ideals of the form eR for some primitive idempotent e and the ideal 0. Then the set [M ] is closed under multiplication if and only if R is a finite direct sum of matrix rings over some local ring.

Background There is little information on the association of sarcopenia with physical activity in elderly cardiac patients. This study determined differences in physical activity and cutoff values for physical activity according to the presence or absence of sarcopenia in elderly male cardiac patients. Methods and results Sixty-seven consecutive men aged ≥65 years with cardiac disease were enrolled. We defined sarcopenia using the European Working Group on Sarcopenia in Older People algorithm. Patients were divided into the sarcopenia group ( n =25) and the non-sarcopenia group ( n =42). In the patients with and without sarcopenia of physical activities were evaluated to determine cutoff values of physical activity. Results After adjusting for patient characteristics, both the average daily number of steps (3361.43±793.23 vs. 5991.55±583.57 steps, P =0.021) and the average daily energy expenditure of physical activity (71.84±22.19 vs. 154.57±16.18kcal, P =0.009) were significantly lower in the sarcopenia versus non-sarcopenia group. Receiver-operating characteristic analysis identified a cutoff value for steps of physical activity of 3551.80steps/day for 1 week, with a sensitivity of 0.73 and 1-specificity of 0.44 and a cutoff value for energy expenditure of physical activity of 85.17kcal/day for 1 week, with a sensitivity of 0.73 and 1-specificity of 0.27. Conclusions Physical activity in the male cardiac patients with sarcopenia was significantly lower than that in those without sarcopenia. The cutoff values reported here may be useful values to aid in the identification of elderly male cardiac patients with sarcopenia.

Little information exists on the relation between respiratory muscle strength such as maximum inspiratory muscle pressure (MIP) and sarcopenia in elderly cardiac patients. The present study aimed to determine the differences in MIP, and cutoff values for MIP according to sarcopenia in elderly cardiac patients. We enrolled 63 consecutive elderly male patients aged ≥65 years with cardiac disease in this cross-sectional study. Sarcopenia was defined based on the European Working Group on Sarcopenia in Older People algorithm, and, accordingly, the patients were divided into two groups: the sarcopenia group (n = 24) and non-sarcopenia group (n = 39). The prevalence of sarcopenia in cardiac patients and MIP in the patients with and without sarcopenia were assessed to determine cutoff values of MIP. After adjustment for body mass index, the MIP in the sarcopenia group was significantly lower than that in the non-sarcopenia group (54.7 ± 36.8 cmH2O; 95 % CI 42.5–72.6 vs. 80.7 ± 34.7 cmH2O; 95 % CI 69.5–92.0; F = 4.89, p = 0.029). A receiver-operating characteristic curve analysis of patients with and without sarcopenia identified a cutoff value for MIP of 55.6 cmH2O, with a sensitivity of 0.76, 1-specificity of 0.37, and AUC of 0.70 (95 % CI 0.56–0.83; p = 0.01) in the study patients. Compared with elderly cardiac patients without sarcopenia, MIP in those with sarcopenia may be negatively affected. The MIP cutoff value reported here may be a useful minimum target value for identifying elderly male cardiac patients with sarcopenia.

In this article we investigate: conditions under which a primitive idempotent in a ring is central; the set of right ideals eR where e is a primitive idempotent in a ring R; the set of primitive idempotent ideals of a ring; and idempotent elements in the ring of matrices.

The contents of the lectures and the learner’s reaction in the pre master’s course in a mathematical domain are reported here. Two contents in the lectures are designed, the area of a circle and an isoperimetric problem. All learners were middle school students and have got high motivation for mathematics. Although the learners know the formula of the area of a circle well, they have little experiences which make them realize that the formula does really hold. In the first lecture, an argument − to compare the areas of inscribed regular polygons with the one of a unit circle, whose idea comes to the usual measure theory in the future, was explained. Through the process of calculating the areas of various kind of inscribed regular polygons to a unit circle, the learners appreciated that the area of a unit circle is really equal to π and convinced themselves of the fact. In the latter lecture, they have considered an isoperimetric problem and showed that the equilateral triangle has the largest area among the triangles with constant perimeter. Although a few mathematical concepts and treatments have been required to follow the procedure of the arguments, they overcame these difficulties eagerly and recognized two contents of mathematics in the pre master’s course. Through the program in the pre master’s course in a mathematical domain, we noticed that learners with high motivation for mathematics study many advanced contents extensively and extend their interests for themselves only with the help of introducing well−suited orientations and with the proper support to give some necessary concepts.

Background and aims: Maximum phonation time (MPT), which is related to respiratory function, is widely used to evaluate maximum vocal capabilities, because its use is non-invasive, quick, and inexpensive. We aimed to examine differences in MPT by age, following recovery phase II cardiac rehabilitation (CR). Methods: This longitudinal observational study assessed 50 consecutive cardiac patients who were divided into the middle-aged group (

Background: Health utility, which can be assessed by several preference-based utility measures, is an important measure in the analysis of cost effectiveness in health care. We aimed to examine differences in health utility by age following recovery phase II cardiac rehabilitation (CR). Methods: This longitudinal observational study assessed 62 consecutive cardiac surgery patients who were divided into a middle-aged group (

Handgrip strength (HS) and knee extensor muscle strength (KEMS) showed a negative correlation with the Disabilities of the Arm, Shoulder, and Hand (DASH) score at one month following cardiac surgery. We performed a longitudinal study to examine changes in HS/KEMS and DASH score during phase II cardiac rehabilitation (CR) in patients after cardiac surgery. We measured and assessed HS, KEMS, and DASH score in 41 consecutive patients at one and three months following cardiac surgery and examined the relation between these factors at three months following cardiac surgery. Wilcoxon signed-rank test and Spearman correlation coefficients were used to analyze the results. Finally, 26 patients (63.2 years, 73.1% male) were analyzed. There were significant differences from one month to three months following cardiac surgery in HS (26.78 &plusmn, 8.26 to 31.35 &plusmn, 9.41 kgf, p &lt, 0.001), KEMS (1.53 &plusmn, 0.42 to 1.72 &plusmn, 0.46 Nm/kg, p = 0.001), and DASH score (14.76 &plusmn, 12.58 to 7.62 &plusmn, 9.29, p &lt, 0.001). DASH score correlated negatively with HS (r = &minus, 0.41, p = 0.01) but not with KEMS (r = &minus, 0.32, p = 0.09) after three months of phase II CR. Although HS, KEMS, and DASH scores changed significantly from one to three months following cardiac surgery during phase II CR, only HS correlated negatively with DASH score at three months following cardiac surgery.

Background Daytime sleepiness can be assessed by the Epworth Sleepiness Scale (ESS), which is widely used in the field of sleep medicine as a subjective measure of a patient&rsquo, s sleepiness. Also, health utility assessed by the mean Short-Form Six-Dimension (SF-6D) score, one of several preference-based utility measures, is an important measure in health care. We aimed to examine age-related differences in daytime sleepiness and health utility and their relationship in patients 5 months after cardiac surgery. Methods, This cross-sectional study assessed 51 consecutive cardiac surgery patients who were divided into a middle-aged (&lt, 65 years, n = 29) and older-age group (&ge, 65 years, n = 22). The mean ESS and SF-6D utility scores were measured at 5 months after cardiac surgery and compared. In addition, the relationship between ESS and SF-6D utility scores were assessed. Results, There were no significant differences between the middle-aged and older-aged groups in either the mean ESS (5.14 &plusmn, 2.96 vs. 4.05 &plusmn, 3.23, p = 0.22) or SF-6D utility (0.72 &plusmn, 0.14 vs. 0.71 &plusmn, 0.10, p = 0.76) scores. However, there was a negative correlation between both values in all of the patients after cardiac surgery (r = &minus, 0.41, p = 0.003). Conclusions, Although there were no age-related differences in the ESS and SF-6D utility values between the two groups, there was a negative correlation between these values in all patients at 5 months after cardiac surgery. This suggested that sleepiness is associated with decreased utility scores in patients at 5 months after cardiac surgery.

Background: The Disabilities of the Arm, Shoulder, and Hand (DASH) questionnaire is a valid and reliable patient-reported outcome measure. DASH can be assessed by self-reported upper extremity disability and symptoms. We aimed to examine the relationship between the physiological outcome of muscle strength and the DASH score after cardiac surgery. Methods: This cross-sectional study assessed 50 consecutive cardiac patients that were undergoing cardiac surgery. Physiological outcomes of handgrip strength and knee extensor muscle strength and the DASH score were measured at one month after cardiac surgery and were assessed. Results were analyzed using Spearman correlation coefficients. Results: The final analysis comprised 43 patients (men: 32, women: 11; age: 62.1 ± 9.1 years; body mass index: 22.1 ± 4.7 kg/m2; left ventricular ejection fraction: 53.5 ± 13.7%). Respective handgrip strength, knee extensor muscle strength, and DASH score were 27.4 ± 8.3 kgf, 1.6 ± 0.4 Nm/kg, and 13.3 ± 12.3, respectively. The DASH score correlated negatively with handgrip strength (r = −0.38, p = 0.01) and with knee extensor muscle strength (r = −0.32, p = 0.04). Conclusion: Physiological outcomes of both handgrip strength and knee extensor muscle strength correlated negatively with the DASH score. The DASH score appears to be a valuable tool with which to assess cardiac patients with poor physiological outcomes, particularly handgrip strength as a measure of upper extremity function, which is probably easier to follow over time than lower extremity function after patients complete cardiac rehabilitation.

a Graduate School of Health Sciences, Kobe University, Kobe, Japan b Department of Rehabilitation Medicine, St. Marianna University School of Medicine Hospital, Kawasaki, Japan c Department of Physical Therapy, Tokushima Bunri University, Tokushima, Japan d Faculty of Sport Sciences, Waseda University, Tokorozawa, Japan e Division of Cardiology, St. Marianna University Toyoko Hospital, Kawasaki, Japan f Department of Cardiology, St. Marianna University Yokohama City Seibu Hospital, Yokohama, Japan g Department of Health and Exercise Science, Wake Forest University, Winston-Salem, NC, USA h Department of Orthopedic Surgery, St. Marianna University School of Medicine, Kawasaki, Japan i Division of Cardiology, Department of Internal Medicine, St. Marianna University School of Medicine, Kawasaki, Japan

Maximum gait speed and physical activity (PA) relate to mortality and morbidity, but little is known about gender-related differences in these factors in elderly hospitalized cardiac inpatients. This study aimed to determine differences in maximum gait speed and daily measured PA based on sex and the relationship between these measures in elderly cardiac inpatients.A consecutive 268 elderly Japanese cardiac inpatients (mean age, 73.3 years) were enrolled and divided by sex into female (n = 75, 28%) and male (n = 193, 72%) groups. Patient characteristics and maximum gait speed, average step count, and PA energy expenditure (PAEE) in kilocalorie per day for 2 days assessed by accelerometer were compared between groups.Gait speed correlated positively with in-hospital PA measured by average daily step count (r = 0.46, P < 0.001) and average daily PAEE (r = 0.47, P < 0.001) in all patients. After adjustment for left ventricular ejection fraction, step counts and PAEE were significantly lower in females than males (2651.35 ± 1889.92 vs 4037.33 ± 1866.81 steps, P < 0.001; 52.74 ± 51.98 vs 99.33 ± 51.40 kcal, P < 0.001), respectively.Maximum gait speed was slower and PA lower in elderly female versus male inpatients. Minimum gait speed and step count values in this study might be minimum target values for elderly male and female Japanese cardiac inpatients.

This study aimed to determine the relation between the regression slope relating minute ventilation to carbon dioxide output (V˙E/V˙CO2 slope) and maximum phonation time (MPT), and the MPT required to attain a threshold value for V˙E/V˙CO2 slope of ≤34 in chronic heart failure (CHF) patients. This cross-sectional study enrolled 115 CHF patients (mean age, 54.5 years; men, 84.9%). V˙E/V˙CO2 slope was assessed during cardiopulmonary exercise testing (CPX). Thereafter, patients were divided into 2 groups according to exercise capacity: V˙E/V˙CO2 slope ≤34 (V˙E/V˙CO2 ≤34 group, n = 81) and V˙E/V˙CO2 slope >34 (V˙E/V˙CO2 >34 group, n = 34). For MPT measurements, all patients produced a sustained vowel/a:/ for as long as possible during respiratory effort from the seated position. All subjects showed significant negative correlation between V˙E/V˙CO2 slope and MPT (r = −0.51, P 34 group (21.4 ± 6.4 vs 17.4 ± 4.3 s, F = 7.4, P = 0.007). The appropriate MPT cut-off value for identifying a V˙E/V˙CO2 slope ≤34 was 18.12 seconds. An MPT value of 18.12 seconds may be a useful target value for identifying CHF patients with a V˙E/V˙CO2 slope ≤34 and for risk management in these patients.

The property of having a finite number of orbits under the regular action has been used to study properties of rings and algebras. For example, in ring theory, Yasuyuki Hirano was able to use this property to show that rings with finitely many orbits under the regular action can be decomposed as direct sum of uniserial rings and a finite ring. In this thesis, we study modules under the regular action. More precisely, if R is a unital ring and M is a left(right) R-module, we describe all modules M that have finitely many orbits under the regular action. Along the way, we give a (new) module theoretical proof to the theorem of Yasuyuki Hirano on the classification of rings with finitely many orbits under the regular action which was proven using using methods from ring theory. Our charaterization of modules with finitely many orbits under the regular action shows a connection between algebras with finitely many submodules and distributive modules. A particular algebra that is of interest to us is the incidence algebra of a finite poset. Incidence algebras were originally introduced in the 1960’s by Gian-Carlo Rota as a way to study combinatorial problems but it became apparent later on that such algebras were an interesting object to study in their own right. They include ring theoretical examples such as the product of copies of a ring R and the upper triangular matrices over R. Robert B. Feinberg in his work on incidence algebras developed an internal characterization of incidence algebras of lower finite quasi-ordered sets. For example, he showed that an associative unital complete topological algebra Λ over a field k, where k has the discrete topology, is isomorphic to an incidence algebra if and only if 1. Λ has a faithful unital left module M with a distributive lattice of submodules. Fur