is a single or double arm technique more advantageous in triple jumping triple jumpers employ either an asymmetrical single arm action or symmetrical double arm action in the takeoff of each phase of the jump this study investigated which technique is more beneficial in each phase using computer simulation kinematic data were obtained from an entire triple jump using a vicon automatic motion capture system a planar 13 segment torque driven subject specific computer simulation model was evaluated by varying torque generator activation timings using a genetic algorithm in order to match performance data the matching produced a close agreement between simulation and performance with differences of 3 8 2 7 and 3 1 for the hop step and jump phases respectively each phase was optimised for jump distance and an increase in jump distance beyond the matched simulations of 3 3 11 1 and 8 2 was obtained for the hop step and jump respectively the optimised technique used symmetrical shoulder flexion whereas the triple jumper had used an asymmetrical arm technique this arm action put the leg extensors into slower concentric conditions allowing greater extensor torques to be produced the main increases in work came at the joints of the stance leg but the largest increases in angular impulse came at the shoulder joints indicating the importance of both measures when assessing the impact of individual joint actions on changes in technique possible benefits of the double arm technique include cushioning the stance leg during impact raising the centre of mass of the body at takeoff facilitating an increase in kinetic energy at takeoff allowing a re orientation of the body during flight

on extension of isometries between unit spheres of l γ type space and a banach space e abstract in this paper we study the isometric extension problem between the unit spheres of l type space and a banach space e we prove that every surjective isometry between the unit spheres s l and s e can be extended to be a linear isometry of l onto e moreover we study this problem between c and a banach space and also get an affirmative answer

effect of arm swing direction on forward and backward jump performance this study quantified and compared how the directional differences in arm swing affected mechanical and physiological parameters during forward and backward jumping seven subjects maximally performed three types of forward and backward squat jumps no arm swing fj bj forward arm swing fjf bjf and backward arm swing fjb bjb from a force platform all performances were captured with a 3 d motion capture system electromyograms emgs of the lower extremity muscles were obtained variables were calculated by combining kinematic and kinetic data the jump displacement and center of mass velocity at take off were significantly larger in fjf than in fj or fjb and larger in bjb than in bj or bjf suggesting that the best performance was obtained by employing the same arm swing direction as a given jump direction the total work by three lower and two upper extremity joints was significantly larger in fjf than in fj or fjb and larger in bjb than in bj or bjf for the lower extremity joints hip work was the greatest in fjf and bjb the integrated emg of the biceps femoris when the hip power was produced was significantly larger in fjf and bjb than under other conditions these results suggest that if the arm swing direction is the same as a given jump direction the activation level of the hip extensor is greater to counter large loads which make the hip joint flex during the push off phase which result in increased hip extension torque power and work

isometries on unit sphere of lβn in this paper we characterize isometries between unit spheres of f space furthermore we study the isometric extension problem on such kind of metric linear spaces

characterizations on mazur ulam theorem abstract we consider the area preserving 2 isometries in linear 2 normed spaces in chu 2007 10 the mazur ulam theorem was proved in linear 2 normed spaces with the assumption of the collinearity preserving in this article we prove the mazur ulam theorem for the interior preserving mappings in linear 2 normed spaces recently amyari sadeghi 16 in non archimedean 2 normed spaces the mazur ulam theorem was proved under the condition of strict convexity in this paper we also prove the theorem on non archimedean 2 normed spaces over a linear ordered non archimedean field without the strict convexity assumption

properties of isometric mappings abstract some relations between isometry and linearity are examined in particular generalizations of the mazur ulam theorem and open problems are discussed

characterizations on isometries in linear n normed spaces abstract let f x y be a weak n isometry in linear n normed spaces in this paper we prove that if f satisfies some conditions then f is an n isometry

the aleksandrov problem in linear 2 normed spaces we introduce the concept of 2 isometry which is suitable to represent the notion of area preserving mappings in linear 2 normed spaces and then we obtain some results for the aleksandrov problem in linear 2 normed spaces

the problem of isometric extension in the unit sphere of the space sp α abstract in this paper we present an isometric extension from the unit sphere of a subspace of s p to the whole space s p we obtain that the lamperti isometric mapping of the unit sphere s s p into itself can be extended to an isometry on the whole space s p

inequalities for distances between points and distance preserving mappings abstract in this paper we generalize the short diagonals lemma by proving a new inequality for distances between six points moreover we apply this inequality to a partial solution to the aleksandrov rassias problem

on the generalizations of the mazur ulam isometric theorem abstract this paper contains several generalizations of the mazur ulam isometric theorem in f spaces which are not assumed to be locally bounded let x and y be two real f spaces and let x be locally pseudoconvex or midpoint bounded assume that a operator t maps x onto y in a locally 1 2i isometric manner for all i 0 n then t is affine in addition we give the sufficient conditions of a mapping between two topological vector spaces being affine

an inequality for distances between 2n points and the aleksandrov rassias problem in this paper we introduce an inequality for distances between every two points among the given 2n points and apply this inequality to a partial solution of the aleksandrov rassias problem which was first posed by th m rassias

on the aleksandrov problem in linear n normed spaces the aim of this article is to generalize the aleksandrov problem to the case of linear n normed spaces

a fixed point approach to the stability of isometries in this paper we apply a fixed point theorem to the proof of hyers ulam rassias stability property for isometries from a normed space into a banach space in which the parallelogram law holds

tauberian theorems for power series methods applied to double sequences abstract we discuss the relations between power series methods weighted mean methods and ordinary convergence for double sequences in particular we study tauberian theorems for methods being products of the related one dimensional summability methods

on relations between weighted mean and power series methods of summability soit p n une suite de nombres non negatifs avec p 0 0 et p n k 0 n p k p x n 0 p u x n pour 0 x 1 soit s n une suite de nombres reels on etudie le lien entre la methode de sommabilite en moyenne carree et la methode de serie de puissances

isometries mazur ulam theorem and aleksandrov problem for non archimedean normed spaces abstract we study isometries between normed spaces over a non archimedean valued field k we show the failure of a mazur ulam theorem in the framework of non archimedean spaces considering aleksandrov problem we prove that a surjective lipschitz map e e with the strong distance one preserving property where e is a finite dimensional normed space is an isometry if and only if k is locally compact we prove also that every isometry e e for finite dimensional e is surjective if and only if k is spherically complete and card k is finite

mappings of conservative distances and the mazur ulam theorem abstract let x and y be two real hilbert spaces with the dimension of x greater than 1 several cases about the aleksandrov rassias problem for t x y preserving two or three distances are presented and geometric interpretations of these cases are also given

mappings of conservative distances in linear n normed spaces abstract the aim of this article is to generalize the mazur ulam theorem to the case of linear n normed spaces

equimodular and linearity in modular spaces abstract in this paper the concept of equimodular is introduced it contains several generalizations of mazur ulam s isometric theorem in modular spaces let x and y be two real modular spaces and x with 1 midpoint shrinking whose modular x satisfies the 2 condition assume that an operator t maps x onto y in an 2 ti equimodular manner for all i 0 n where ti is a null sequence of nonnegative reals with the property that t0 1 t1 1 2 and ti ti 1 2ti for i 2 then t is affine

understanding how an arm swing enhances performance in the vertical jump this investigation was conducted to examine the various theories that have been proposed to explain the enhancement of jumping performance when using an arm swing compared to when no arm swing is used twenty adult males were asked to perform a series of maximal vertical jumps while using an arm swing and again while holding their arms by their sides force motion and electromyographical data were recorded during each performance participants jumped higher 0 086 m in the arm swing compared to the no arm swing condition and was due to increased height 28 and velocity 72 of the center of mass at take off the increased height at take off was due to the elevation of the arm segments the increased velocity of take off stemmed from a complex series of events which allowed the arms to build up energy early in the jump and transfer it to the rest of the body during the later stages of the jump this energy came from the shoulder and elbow joints as well as from extra work done at the hip this energy was used to i increase the kinetic and potential energy of the arms at take off ii store and release energy from the muscles and tendons around the ankle knee and hip joint and iii pull on the body through an upward force acting on the trunk at the shoulder it was concluded that none of the prevailing theories exclusively explains the enhanced performance in the arm swing jump but rather the enhanced performance is based on several mechanisms operating together

tauberian conditions under which the original convergence of double sequences follows from the statistical convergence of their weighted means abstract in this paper we introduce a new type of slow oscillation and slow decrease conditions we prove that these or their variants are tauberian conditions from s m n s t s to s m n s we also prove that they are tauberian conditions from t m n 11 s t s to s m n s where t m n 11 are the weighted means of the double sequence s m n m n 0 our results not only generalize well known results but also solve the conjecture of moricz posed in f moricz tauberian theorems for double sequences that are statistically summable c 1 1 j math anal appl 286 2003 340 350

asymptotic properties of isometries abstract in this paper we prove two theorems on the local stability of isometries in connection with e p isometries these theorems reveal that a large class of e p isometries defined on various restricted domains are stable

complementary spaces and multipliers of double fourier series for functions of bounded variation complementary spaces for fourier series were introduced by g goes and generalized by m tynnov in this paper we investigate a notion of complementary space for double fourier series of functions of bounded variation various applications are given

on the mazur ulam problem in linear 2 normed spaces abstract we study the notion of 2 isometry which is suitable to represent the concept of area preserving mapping in linear 2 normed spaces and then prove the mazur ulam problem in linear 2 normed spaces

isomorphisms between unital c algebras abstract it is shown that every almost linear bijection h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all unitaries u a all y a and n 0 1 2 and that almost linear continuous bijection h a b of a unital c algebra a of real rank zero onto a unital c algebra b is a c algebra isomorphism when h 2 n u y h 2 n u h y for all u v a v v v 1 v is invertible all y a and n 0 1 2 assume that x and y are left normed modules over a unital c algebra a it is shown that every surjective isometry t x y satisfying t 0 0 and t u x u t x for all x x and all unitaries u a is an a linear isomorphism this is applied to investigate c algebra isomorphisms between unital c algebras

tauberian theorems for jp summability abstract we prove tauberian theorems for jp summability methods of power series type with respect to ordinary convergence under a o tauberian condition on the underlying sequence our tauberian conclusion is valid for all jp methods relaxing the tauberian assumption to a o type condition a related result is shown for methods with moderate weight sequences

on extension of isometries and approximate isometries between unit spheres article history received 10 april 2008 available online 19 november 2008 submitted by j bastero