Low back pain(LPB)is a common and impactful health concern globally,affecting individuals across various demographics and imposing a significant burden on the health care system.Nonspecific chronic LBP(NCLBP),charac-t...Low back pain(LPB)is a common and impactful health concern globally,affecting individuals across various demographics and imposing a significant burden on the health care system.Nonspecific chronic LBP(NCLBP),charac-terized as pain lasting over 12 weeks without an identifiable cause,leads to notable functional limitations and reduced quality of life.Traditional rehabil-itation programs,often focusing on dynamic exercises for lumbar strengthening,typically do not target the deep stabilizing muscles crucial for lumbar support and effective recovery.Multi-angular isometric lumbar exercise(MAILE)offers a low-impact method for strengthening lumbar stabilizers through multi-angular isometric contractions,reducing risks from dynamic movements.This article examines MAILE’s potential in addressing motor control dysfunctions in NCLBP,highlighting studies on lumbar muscle activation,core stability,and isometric exercises.The article explores the prevalence and socioeconomic impact of NCLBP in the Middle East,highlighting the need for affordable treatment options in areas like Qatar and Saudi Arabia.This article aims to validate the efficacy of MAILE in reducing pain,enhancing mobility,and improving lumbar stability,offering a valuable option for NCLBP management.Future research should focus on large-scale clinical trials to substantiate these findings and guide clinical practice.展开更多
The short communication discusses the interrelationships of loxodromes,isometric latitudes and the normal aspect of Mercator projection.It is shown that by applying the isometric latitude,a very simple equation of the...The short communication discusses the interrelationships of loxodromes,isometric latitudes and the normal aspect of Mercator projection.It is shown that by applying the isometric latitude,a very simple equation of the loxodrome on the sphere is reached.The consequence of this is that the isometric latitude can be defined using the generalized longitude,and not only using the latitude,as was common until now.Generalized longitude is the longitude defined for every real number;modulo 2πof generalized and usual longitude are congruent.Since the image of the loxodrome in the plane of the Mercator projection is a straight line,the isometric latitude can also be defined using this projection.Finally,a new definition of theMercator projection is given,according to which it is a normal aspect cylindrical projection in which the images of the loxodromes on the sphere are straight lines in the plane of the projection that,together with the images of the meridians in the projection,form equal angles,as do the loxodromes with the meridians on the sphere.The short communication provides additional knowledge to all those who are interested in the theory of maps in navigation and have a piece of requisite mathematical knowledge,as well as an interest in map projections.It will be useful for teachers and students studying cartography and GIS,navigation or applied mathematics.展开更多
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 ...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.展开更多
K hler流形间的全纯等距嵌入问题是多复变领域的热点问题之一。单项式多面体是Hartogs三角形的非平凡推广,研究其与复欧氏空间是否具有公共子流形是有意义的。借助Nash函数的性质及二维单项式多面体的Bergman核函数,得到具有Bergman度...K hler流形间的全纯等距嵌入问题是多复变领域的热点问题之一。单项式多面体是Hartogs三角形的非平凡推广,研究其与复欧氏空间是否具有公共子流形是有意义的。借助Nash函数的性质及二维单项式多面体的Bergman核函数,得到具有Bergman度量的二维单项式多面体与具有平坦度量的复欧氏空间不存在公共的K hler子流形,即二维单项式多面体与复欧氏空间是不相关的。展开更多
文摘Low back pain(LPB)is a common and impactful health concern globally,affecting individuals across various demographics and imposing a significant burden on the health care system.Nonspecific chronic LBP(NCLBP),charac-terized as pain lasting over 12 weeks without an identifiable cause,leads to notable functional limitations and reduced quality of life.Traditional rehabil-itation programs,often focusing on dynamic exercises for lumbar strengthening,typically do not target the deep stabilizing muscles crucial for lumbar support and effective recovery.Multi-angular isometric lumbar exercise(MAILE)offers a low-impact method for strengthening lumbar stabilizers through multi-angular isometric contractions,reducing risks from dynamic movements.This article examines MAILE’s potential in addressing motor control dysfunctions in NCLBP,highlighting studies on lumbar muscle activation,core stability,and isometric exercises.The article explores the prevalence and socioeconomic impact of NCLBP in the Middle East,highlighting the need for affordable treatment options in areas like Qatar and Saudi Arabia.This article aims to validate the efficacy of MAILE in reducing pain,enhancing mobility,and improving lumbar stability,offering a valuable option for NCLBP management.Future research should focus on large-scale clinical trials to substantiate these findings and guide clinical practice.
文摘The short communication discusses the interrelationships of loxodromes,isometric latitudes and the normal aspect of Mercator projection.It is shown that by applying the isometric latitude,a very simple equation of the loxodrome on the sphere is reached.The consequence of this is that the isometric latitude can be defined using the generalized longitude,and not only using the latitude,as was common until now.Generalized longitude is the longitude defined for every real number;modulo 2πof generalized and usual longitude are congruent.Since the image of the loxodrome in the plane of the Mercator projection is a straight line,the isometric latitude can also be defined using this projection.Finally,a new definition of theMercator projection is given,according to which it is a normal aspect cylindrical projection in which the images of the loxodromes on the sphere are straight lines in the plane of the projection that,together with the images of the meridians in the projection,form equal angles,as do the loxodromes with the meridians on the sphere.The short communication provides additional knowledge to all those who are interested in the theory of maps in navigation and have a piece of requisite mathematical knowledge,as well as an interest in map projections.It will be useful for teachers and students studying cartography and GIS,navigation or applied mathematics.
文摘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.
