Isometric Immersions of Lightlike Warped Product Manifolds

In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.

Eccentric exercise-induced muscle weakness abolishes sex differences in fatigability during sustained submaximal isometric contractions

Background:Females are typically less fatigable than males during sustained isometric contractions at lower isometric contraction intensities.This sex difference in fatigability becomes more variable during higher intensity isometric and dynamic contractions.While less fatiguing than isometric or concentric contractions,eccentric contractions induce greater and longer lasting impairments in force production.However,it is not clear how muscle weakness influences fatigability in males and females during sustained isometric contractions.Methods:We investigated the effects of eccentric exercise-induced muscle weakness on time to task failure(TTF)during a sustained submaximal isometric contraction in young(18-30 years)healthy males(n=9)and females(n=10).Participants performed a sustained isometric contraction of the dorsiflexors at 35°plantar flexion by matching a 30%maximal voluntary contraction(MVC)torque target until task failure(i.e.,falling below 5%of their target torque for>2 s).The same sustained isometric contraction was repeated 30 min after 150 maximal eccentric contractions.Agonist and antagonist activation were assessed using surface electromyography over the tibialis anterior and soleus muscles,respectively.Results:Males were~41%stronger than females.Following eccentric exercise both males and females experienced an~20%decline in maximal voliuntary contraction torque.TTF was-34%longer in females than males prior to eccentic exercise-induced muscle weakness.However,following eccentric exercise-induced muscle weakness,this sex-related difference was abolished,with both groups having an"45%shorter TTF.Notably,there was~100%greater antagonist activation in the female group during the sustained isometric contraction following exercise-induced weakness as compared to the males.Conclusion:This increase in antagonist activation disadvantaged females by decreasing their TTF,resulting in a blunting of their typical fatigability advantage over males.

Hemodynamic Fetal Response to Maternal Isometric Exercise in Pregnant Patients with Hypertension

Objective: to evaluate the maternal-fetal hemodynamic response with Doppler in pregnant women with chronic arterial hypertension and preeclampsia submitted to controlled isometric activity. Methods: experimental study comparing 50 healthy and 26 hypertensive and 24 preeclamptic pregnant women, from 26 to 36 weeks of gestational age, submitted to isometric contraction with handgrip dynamometer. Maternal hemodynamic parameters (systolic and diastolic blood pressure;heart rate;uterine arteries Doppler) and fetal (heart rate;umbilical artery, middle cerebral and venous duct Doppler) were evaluated before, during and post-isometry. Results: in preeclampsia were observed higher values of blood pressure and uterine artery indexes in all times;middle cerebral artery indexes in the pre and post-isometry;and of maternal heart rate post-isometry. In hypertensive women, systolic blood pressure is increased all the times, with indexes of the right uterine and middle cerebral arteries higher in pre-isometry;middle cerebral and umbilical arteries greater during isometry;and maternal heart rate and umbilical artery indexes bigger after isometry. Conclusion: blood pressure is higher in preeclamptic and hypertension women. The right uterine artery has more resistance in preeclampsia, with a significant decrease in pre to isometry in hypertensive and preeclamptic women;and increased in contraction to post-isometry in healthy and hypertensive women. The left uterine artery increases resistance post-isometry in all groups. The fetal hemodynamic parameters did not show significant differences when comparing the before, during and post-isometry.

Hemodynamic Fetal Response to Maternal Isometric Exercise in Pregnant Patients with Diabetes

Background: Studies on physical activity during pregnancy and its impact on mother and fetus are still limited. International protocols consider only aerobic exercise and fail to provide information about other modalities such as isometric exercise. Isometric exercise promotes cardiorespiratory resistance and muscle strengthening, but it is rarely tested on pregnant women because it increases maternal blood pressure and can subsequently affect placental circulation. Objectives: To assess the fetal response by use of Doppler study in diabetes pregnant women submitted to isometric exercise. Methods: A cross-sectional experimental study was conducted on 25 diabetes pregnant women with gestational age between 26 and 36 weeks. The patients were submitted to isometric handgrip, and data were collected from the mother (blood pressure, heart rate and Doppler velocimetry for the uterine arteries) and from the fetus (heart rate, Doppler velocimetry for the umbilical artery, middle cerebral artery and ductus venosus). All variables were collected before, during and after the isometric handgrip. Results: There was a significant reduction in the pulsatilityindex (average values pre 0.77 ± 0.30, trans 0.65 ± 0.22, and post 0.75 ± 0.22, with p = 0.001), resistance index (average values pre 0.49 ± 0.12, trans 0.44 ± 0.10, and post 0.48 ± 0.90, with p =

L(Ω,μ) CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES OF AM-SPACES

This article presents a novel method to prove that： let E be an AM-space and if dim E ≥ 3, then there does not exist any odd subtractive.isometric mapping from the unit sphere S（E） into S[L（Ω, μ）]. In particular, there does not exist any real linear isometry from E into L（Ω, μ）.

ISOMETRIC APPROXIMATION FROM 2-DIM BANACH SPACE INTO L^1[0,1]

In this paper, some characterizations of isometric operators and ε-isometric opertors from 2-dim Banach Space E2 into L1[0, 1] are given, where E2 denotes a Banach Spacewhose unit ball is the union of a polygon C and the region enclosd by C in the plane. Also,the answer for IAP(Isometric Approximation Problem) on B(E2,L1 [0, 1]) is obtained.

THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE S[e(Γ)] TO THE UNIT SPHERE S(E)

This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.

Efficacy of Slow Reversal Hold and Isometrics in Improving Muscle Strength, Increasing Range of Motion, and Reducing Pain in Patients with Osteoarthritis of Knee

Osteoarthritis of knee is a common problem in the elderly population worldwide. Physical therapy has been shown to be useful in decreasing pain and increasing mobility in this population. The aim of this study was to study the effectiveness of slow reversal hold and isometric exercise techniques in reducing pain, increasing muscle strength, and increasing range of motion for knee flexion in patients with osteoarthritis of knee. The other aim of this study was to compare the relative effectiveness of these two interventions. 60 subjects participated in this study and were randomly assigned either to the slow reversal hold group (n = 30) or, to the isometrics exercise group (n = 30). All subjects performed their respective exercises for 3 weeks. Pain scores using the visual analog scale, muscle strength using manual muscle testing of quadriceps and hamstrings, and range of motion (ROM) for knee flexion using a goniometer were recorded both pre-treatment and post-treatment for both left and right knees. Both the interventions showed a significant decrease in pain scores, an increase in muscle strength, as well as an increase in the ROM. However, ROM was significantly increased in the slow reversal hold group as compared to the isometrics group in both knees. It was concluded that both exercise techniques could be useful in patients with osteoarthritis of knee for decreasing pain and increasing muscle strength. Slow reversal hold technique might be a better technique than isometrics for increasing ROM for knee flexion.

sEMG Feature Analysis on Forearm Muscle Fatigue During Isometric Contractions

In order to detect and assess the muscle fatigue state with the surface electromyography(sEMG) characteristic parameters,this paper carried out a series of isometric contraction experiments to induce the fatigue on the forearm muscles from four subjects,and recorded the sEMG signals of the flexor carpi ulnaris.sEMG's median frequency(MDF) and mean frequency(MF) were extracted by short term Fourier transform(STFT),and the root mean square(RMS) of wavelet coefficients in the frequency band of 5—45 Hz was obtained by continuous wavelet transform(CWT).The results demonstrate that both MDF and MF show downward trends within 1 min; however,RMS shows an upward trend within the same time.The three parameters are closely correlated with absolute values of mean correlation coefficients greater than 0.8.It is suggested that the three parameters above can be used as reliable indicators to evaluate the level of muscle fatigue during isometric contractions.

Study of CNC Grinding Machining Method About Isometric Polygon Profile

The formed principle and CNC grinding machining method of isometric polygonal profile are studied deeply and systematically. Equation about section curve of isometric polygon profile is set up by means of geometric principle. With the use of differential geometry theory, the curve is proved to be with geometric feature of convex curve. It is referred to as Isometric Polygonal Curve (IPC), because that is a kind of convex curve on which the distance between any parallel tangent lines is equal. Isometric Polygonal Profile (IPP) or Isometric Polygonal Cone Profile (IPCP) or Isometric Polygonal Topless Cone (IPTC) is formed with the IPC and straight line as generating curve. But the machining and measuring of the IPCP are so inconvenient that it has little value. Keeping in mind the characteristic of the IPP and IPTC, this paper puts forward the program method of CNC grinding machining. Isometric polygonal profile connection is a kind of polygonal profile connection. It has the superiority over keys (prismatic key & spline etc), and can be suit for the situations such as high rotative velocity, large torque, high precision, and small fixed room and vibration. Nowadays, some countries such as America, Russia, German and Switzerland applied CNC machining to the machining of polygon surface coupling parts, which makes their applications in machine productions such as motor engine, heavy machine increase day by day. But reports about concrete machining technology of isometric polygonal profile and programming of CNC machining program are very few. CNC grinding of the IPP and IPTC is one kind of the precision machining technology. It is of great importance to the popularization of the IPP and IPTC connection. From the forming mechanism, we can see that the machining and measuring of the IPP and IPTC are convenient, and therefore they have the value of the popularization. But the machining and measuring of the IPCP are so inconvenient that it has little value. In the programming the CNC grinding of the IPP and IPTC, it is more reasonable to calculate the coordinate of node according to the approaching method of equal error arc. According to the method of CNC grinding mentioned above to design the grinding machine, the structure is simple and of economical and practical.

Simulation of the neck growth of non-isometric biosphere during initial sintering

Because powders are mostly non-isometric during the sintering process, copper powders were chosen to study the effects of four material transport mechanisms, including surface diffusion, grain-boundary diffusion, volume diffusion, and multi-couplings. These material transport mechanisms were studied with respect to sintering neck growth of a non-isometric biosphere during initial sintering. The evolution of the neck growth in the four transport mechanisms was simulated by Visual C＋＋ as well based on the model of different particles. The results show that the increase of the sintering temperature, both the grain-boundary diffusion and volume diffusion play primary roles in neck growth, while surface diffusion gradually becomes the secondary mechanism. Both the sintered neck and the shrinkage of the two centers increase with increasing temperature by means of the coupling diffusion mechanism. The radius of the sintering neck decreased, and the shrinkage rate of the two centers increased with an increase of the diameter ratio of the two spheres.

ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS

In this paper, we consider the infinitesimal I- and Il-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Euclidean space. At the same time, we generalize some classical results in E-3 Go the submanifolds immersed in a space form of constant curvature.

The diagnostic value of the shoulder rotator cuff muscles’ isometric force testing

The most prevalent group of disorders of human shoulder is related to the muscles of the rotator cuff. In order to develop a mechanical method for rotator cuff muscles’ evaluation, we hypothesized that measurement of the isometric force generated by the individual muscle of the rotator cuff might detect the variations, which are characteristic to the different disorders of rotator cuff muscles in adults. The isometric force of supraspinatus, infraspinatus and subscapularis muscles were measured in patients with rotator cuff tears, calcific tendinitis and subacromial impingement syndrome, 30 patients with each disorder, and compared to the normal values from our previous study. Torque of the force was calculated and normalized to lean body mass. The profiles of the mean torque-time curves of each group were compared statistically. We found the expected significantly lower profiles of the torque-time curves of all the tested rotator cuff muscles in comparison to the normal values. The best resolution between the curves of different study groups was found in the testing of the infraspinatus muscles. Therefore the previously unrecognized variations of rotator cuff muscles’ isometric strength build up patterns in the common disorders involving the rotator cuff muscles were revealed. The presented data might be a basis for the future development of a simple mechanical diagnostic method for identification of the abnormal patterns of muscle isometric strength in patients with rotator cuff muscles’ pathology.

ON THE ISOMETRIC ISOMORPHISM OF PROBABILISTIC METRIC SPACES

There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM space (E, F) is isometrically isomorphic to a generating space of quasi-metric family (E', d(r), r is an element of (0, 1)). This paper establishes the connection between the two kinds of isometric isomorphism.

ASYMPTOTICALLY ISOMETRIC COPIES OF l_P (1≤P<∞) AND c_0 IN BANACH SPACES

Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l^1, then X contains complemented asymptotically isometric copies of l^1. Every infinite dimensional closed subspace of l1. contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X^＊ contains asymptotically isometric copies of lp （1 〈 p 〈∞）. Then there exists a quotient space of X which is asymptotically isometric to lq （1/p ＋ 1/q=1）. Complemented asymptotically isometric copies of co in K（X, Y） and W（X, Y） are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of co, it has to contain complemented asymptotically isometric copies of co.

The Effect of Isometric and Isotonic Exercises of Lower Limbs Extensor Sling on Static and Dynamic Balance in Basketball Players with Patellofemoral Pain

Background: Patellofemoral Pain Syndrome (PFPS) is one of the most common conditions among athletes. Although there are various causes for this condition, reduced balance is the problem most frequently expressed by these patients. The aim of the present study was to examine the effect of Extensor Muscle Sling Isometric and Isotonic (EMSII) exercises of lower limbs on female basketball players suffering from PFPS. Method: A total of 30 participants, all female basketball players suffering from PFPS, with an average age of 20 - 30 years, were divided into two isometric/isotonic and control experimental groups. Eight weeks of isometric and isotonic exercises were recommended to the participants with a focus on EMSII exercises of lower limbs in two four-week phases. The control group received no specific exercise program. Pre-test and post-test included the use of Stork balance test (SBT) and Y Balance tests (YBT) to assess the static and dynamic balance, respectively. Results: After eight weeks of performing separate isometric and isotonic exercises on the mentioned muscles, and according to the results of the pre-test, a significant increase was observed in the results of both static and dynamic balance tests (P Conclusion: EMSII exercises of lower limbs showed a significant effect on the increased balance. Recommended exercises can be suggested according to the type of exercises as a factor for increasing static and dynamic balance.

Fetal Hemodynamic Response to Maternal Isometric Exercise

Background: Studies on physical activity during pregnancy and its impact on mother and fetus are still limited. International protocols consider only aerobic exercise and fail to provide information about other modalities such as isometric exercise. Isometric exercise promotes cardiorespiratory resistance and muscle strengthening, but it is rarely tested on pregnant women because it increases maternal blood pressure and can subsequently affect placental circulation. Objective: To evaluate maternal and fetal response of low-risk pregnant women undergoing isometric testing through a Doppler velocimetry study. Methodology: A cross-sectional, experimental study was performed on 46 healthy pregnant women (gestational age between 26 and 36 weeks) who underwent isometric testing. This testing was performed using a handgrip dynamometer to measure maternal and fetal hemodynamic parameters before, during, and after isometric testing. Results: There was a significant increase in systolic blood pressure (BP;pre-isometrics 113.13 ± 9.92 mmHg, during isometrics 117.13 ± 10.24 mmHg, and post-isometrics 112.43 ± 9.87 mmHg, p 0.001) and heart rate (HR;pre-isometrics 87.52 ± 14.10 bpm, during isometrics 97.61 ± 14.83 bpm, and post-isometrics 85.13 ± 13.24 bpm, p 0.001). There were significant decreases in the pulsatility index (PI;pre-isometrics 0.63 ± 0.15, during isometrics 0.56 ± 0.15, and post-isometrics 0.65 ± 0.17, p = 0.001), resistance index (RI;pre-isometrics 0.44 ± 0.08, during isometrics 0.40 ± 0.07, and post-isometrics 0.45 ± 0.08, p = 0.001), and systolic/diastolic (S/D) ratio (pre-isometrics 1.81 ± 0.26, during isometrics 1.69 ± 0.24, and post-isometrics 1.85 ± 0.29, p 0.001) of the left uterine artery (UA). These results showed significant changes only during the isometric exercise, and not between the pre- and post-isometric exercises. There were no significant differences in fetal parameters when the results before, during, and after the isometric test were compared. Conclusion: Isometric testing had no repercussions for fetal hemodynamics in healthy low-risk pregnant women.

Reliability of Power Spectral Analysis of Surface Electromyogram Recorded during Sustained Vastus Medialis Isometric Contraction in Assessment of Muscle Fatigability

The aim of this study was to determine the within-day and between-days reliability of surface electromyographic (EMG) power spectral analysis in assessing fatigability of the vastus medialis (VM) muscle during knee and hip flexion under constant load application. The subjects were 13 healthy adult men free of knee abnormalities. Surface EMG was recorded from vastus medialis obliquus (VMO) and vastus medialis longus (VML) during sustained isometric contractions at 60% of maximal voluntary contraction until exhaustion on the leg press machine (static leg press test). Linear regression analysis was applied to median frequency (MF) time series to calculate initial MF and MF slope. For VMO and VML, the initial MF showed moderate to high reliability, while the MF slope showed high reliability (Intraclass correlation coefficient (ICC) = initial MF: 0.63 - 0.92, MF slope: 0.70 - 0.86). The results demonstrated that spectral analysis of surface EMG recording during isometric VM muscle contraction has high within-day and between-days reliability in the assessment of fatigability of the VMO and VML.

Effects of Facial Isometric Exercise on Antioxidant Capacity

Background: Facial isometric exercise is a static contraction of facial muscles without any visible movement in the angle of the joints. To examine the effects of facial isometric exercise on subjective stress and oxidative stress/antioxidant capacity. Methods: In this study, we included 13 participants (6 males, 7 females;average age, 44.8 ± 19.6 years;age range: 20 - 74 years) who were exposed to constant temperature and humidity in a room. Fifteen minutes after entering the room, the force was measured before and after facial isometric exercise of the target muscles: upper lip levator, small zygomatic, large zygomatic, levator animus, laughing, buccal, muzzle, mental, temporal, masseter, and cervical muscles), and further evaluated by comparing the facial isometric exercise group and control (non-facial isometric exercise) group (crossover test). Results: Subjective stress significantly improved by 8.7 ± 16.3 in the facial isometric exercise group, and no significant difference in oxidative stress level was observed in both the groups. However, the antioxidant capacity significantly increased by 126.8 ± 168.1 μmol/l in the facial isometric exercise group. Conclusion: The results of this study suggest that facial isometric exercise is an exercise therapy that can provide mental stability and antiaging effects due to improvement in subjective stress and biological antioxidant potential.

ε-isometric Approximation Problem

In this paper, some problems for isometric approximation are discussed. It is shown that an almost isometry from the unit ball of C(X) into the unit ball of C(Y) is near to an isometry. We also give a counterexample to this problem on the unit ball of l1.