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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.

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.

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.

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.

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 (

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: 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.

We consider a ring whose left modules of finite length are semisimple and prove some results on such a ring. We also consider when such a ring is a left V-ring.

We continue the study of the right finite intersection property under a weaker condition on annihilators, introducing the concept of generalized right finite intersection property (simply, generalized right FIP). We observe the structure of rings with the generalized right FIP and examine the generalized right FIP for various kinds of basic extensions of rings with the property. We show that the generalized right FIP does not go up to polynomial rings, and that the 2-by-2 full matrix ring over a domain has the generalized right FIP. In the process, we also obtain an equivalent condition for which a nonzero polynomial, over the ring of integers modulo n ≥ 2, is a non-zero-divisor.

Anderson-Smith (1) studied weakly prime ideals for a com- mutative ring with identity. Blair-Tsutsui (2) studied the structure of a ring in which every ideal is prime. In this paper we investigate the struc- ture of rings, not necessarily commutative, in which all ideals are weakly prime. condition for a ring to have such property is given and several examples to support given propositions are constructed. We then further investigate commutative rings in which every ideal is weakly prime and the structure of such rings under assumptions that generalize commutativity of rings. At the end, we consider the structure of rings in which every right ideal is weakly prime. Definitions and general results

Let R be a semisimple Artinian ring with a partial action α of ℤ on R, and let R[x; α] be the partial skew polynomial ring. By the classification of the set E of all minimal central idempotents in R into three different types, a complete description of the prime radical of R[x; α] is given. Moreover, it is shown that any nonzero prime ideal of R[x; α] is maximal and is either principal or idempotent. In the case where α is of finite type, it is shown that R[x; α] is a semiprime hereditary ring.

〔目的〕浴槽移乗動作を模した側方またぎ動作能力測定が臨床応用可能であるかを明らかにするため，その信頼性を検討した。〔対象〕要介護高齢者50名を対象とし，有している主な疾患により対象者を3群に分け各群について検者内信頼性を，各群から抽出した対象者に対して検者間信頼性を検討した。〔方法〕浴槽の縁を模した障害物を側方からまたぐことができる最大の高さを，手すりを使用する条件，使用しない条件ごとに調査した。信頼性の検討にはκ係数を用いた。〔結果〕各群の検者内信頼性は，手すりを使用する条件において0.64～0.82，手すりを使用しない条件において0.54～0.72であった。検者間信頼性は，手すりを使用する条件でκ＝0.64，使用しない条件でκ＝0.54を示した。κ係数はModerate～Almost perfectの一致度と解釈された。〔結語〕本測定は臨床応用可能なテストと考えられた。

〔目的〕5つの運動機能検査を用いて運動能力に関する自己認識が適切に行えているかどうかの評価（以下適切度）を実施し，転倒との関連について検討した。〔対象〕デイサービス利用高齢者76名とした。〔方法〕日常動作に関連が深い5つの運動機能検査（Functional reach test，立ち上がりテスト，またぎテスト，台昇降テスト，最大歩幅テスト）について対象者自身による予測値と実測値を測定した。得られた予測値と実測値の一致の程度をもとに適切度を評価し，適切評価群と不適切評価群の2群に分類して転倒との関連について検討した。〔結果〕「立ち上がりテスト」と「またぎテスト」に基づく評価では，不適切評価群の転倒経験者の割合が適切評価群のそれに比して有意に多い結果を示した。また，5つの運動機能検査の適切度を総合して判断した評価（以下5P適切度）においても同様の結果を示した。さらに転倒予測指標としての感度と特異度の検討では，単一検査の適切度に比して複合検査による5P適切度の方が感度ならびに特異度ともに比較的良好な値を示した。〔結語〕本研究で用いた運動能力に関する自己認識評価は転倒予測として臨床応用できる可能性があり，単一検査の適切度よりも複合的な適切度を用いる方がより転倒予測精度を向上できる可能性が示唆された。

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.

New characteristic properties of left GPGV-rings are given. It is shown that if R is a left GPGV-ring, then for any nonzero element a in R, there is a positive integer n such that an≠ 0 and (RaR+ l(an))⊕ L=R for some left ideal L contained in Soc (RR). As a corollary of this result, we are able to give a positive answer to a question raised by Yue Chi Ming.

Let k be a positive integer. The structure of rings all of whose ideals are n-primary for some positive integer n ≤ k is studied, and several examples of such rings are constructed. Rings all of whose nonzero ideals are n-primary for some positive integer n ≤ k is also considered.

We consider countable rings with ascending chain con- dition on right annihilators. We determine the structure of a count- able right p-injective Baer ring, a countable semiprime quasi-Baer ring and a countable quasi-Baer biregular ring.

We investigate a ring R with the property that for every right R-module M and every ideal I of R the annihilator of I in M is a direct summand of M, and determine conditions under which such a ring is semisimple Artinian.

We give some characterisations of rings R whose modules with composition series are all cyclic. In particular, we prove that all left R-modules of finite length are cyclic if and only if R has no nonzero Artinian factor rings.

We study the structure of rings R with the property that, for every right R-module M and an ideal I of R, the annihilator of I in M is a direct summand of M.

Large quantities of Prevotella nigrescens ATCC 25261 (P. nigrescens) cells adhere to hydroxyapatite (HA) treated with extract from Porphyromonas gingivalis 381 (Pg-Ext), but not to HA coated with human serum albumin (HSA) or human serum globulin (HSG). The duration of HA treatment with Pg-Ext and several other conditions were tested to determine the factors causing Pg-Ext to promote P. nigrescens cell adhesion. Pg-Ext adsorbed rapidly to HA in less than 5 min. The maximum adherence of P. nigrescens cells to HA was observed after treatment of HSA and HSG and then retreatment of HA with Pg-Ext. It was found that Pg-Ext heated at 80°C for 30 min did not lose its propensity to promote attachment of P. nigrescens to HA and that it also remained stable at 4°C for at least 6 days. The trypsin-like enzyme activity of Pg-Ext was also measured, with BAPNA as the substrate and commercially purchased trypsin as the standard, and was approximately 0.12 units/mg. These data suggest that the presence of Pg-Ext is one of the essential factors responsible for P. nigrescens cell attachment to apatitic surfaces, and that with its trypsin-like activity, Pg-Ext may be considered an extremely important substance for the establishment of P. nigrescens in the periodontal pocket and the development of periodontal disease. (J. Oral Sci. 45, 99-106, 2003)

Let R be a ring and let R[x] denote the polynomial ring over R. We study relations between the set of annihilators in R and the set of annihilators in R[x].

Little is known about differences in the risk of poor nutritional status as assessed by the Geriatric Nutritional Risk Index (GNRI) in relation to physical performance in elderly female cardiac inpatients. The present study aimed to determine both differences in physical performance based on the GNRI and physical performance cut-off values according to the GNRI in elderly female cardiac inpatients. We enrolled 105 consecutive female Japanese inpatients aged ≥65 years (mean age, 74.6 years) with cardiac disease in this cross-sectional study. We divided the patients into two groups according to GNRI: high-GNRI group (≥92 points) (n = 71) and low-GNRI group (