on structure sensitivity of degree based topological indices one of the general requirements for any topological index ti is that similar molecules have near lying ti values which is referred to as smoothness curiously however smoothness of topological indices was until now never examined and never quantified we now propose a pertinent mathematical model for this property and undertake a comparative study of the structure sensitivity of 12 degree based topological indices by using trees

note on the energy of regular graphs abstract for a simple graph g the energy e g is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix a g let n m respectively be the number of vertices and edges of g one well known inequality is that e g 1 n 1 2 m 1 where 1 is the spectral radius if g is k regular we have e g k k n 1 n k denote e 0 k k n 1 n k balakrishnan r balakrishnan the energy of a graph linear algebra appl 387 2004 287 295 proved that for each 0 there exist infinitely many n for each of which there exists a k regular graph g of order n with k n 1 and e g e 0 and proposed an open problem that given a positive integer n 3 and 0 does there exist a k regular graph g of order n such that e g e 0 1 in this paper we show that for each 0 there exist infinitely many such n that e g e 0 1 moreover we construct another class of simpler graphs which also supports the first assertion that e g e 0

kinetic analysis of the lower limbs during walking what information can be gained from a three dimensional model kinetic analyses joint moments powers and work of the lower limbs were performed during normal walking to determine what further information can be gained from a three dimensional model over planar models it was to be determined whether characteristic moment and power profiles exist in the frontal and transverse planes across subjects and how much work was performed in these planes kinetic profiles from nine subjects were derived using a three dimensional inverse dynamics model of the lower limbs and power profiles were then calculated by a dot product of the angular velocities and joint moments resolved in a global reference system characteristic joint moment profiles across subjects were found for the hip knee and ankle joints in all planes except for the ankle frontal moment as expected the major portion of work was performed in the plane of progression since the goal of locomotion is to support the body against gravity while generating movements which propel the body forward however the results also showed that substantial work was done in the frontal plane by the hip during walking 23 of the total work at that joint the characteristic joint profiles suggest defined motor patterns and functional roles in the frontal and transverse planes kinetic analysis in three dimensions is necessary particularly if the hip joint is being examined as a substantial amount of work was done in the frontal plane of the hip to control the pelvis and trunk against gravitational forces

validation of net joint loads calculated by inverse dynamics in case of complex movements application to balance recovery movements the joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation however even if this process is theoretically simple many sources of errors may lead to huge inaccuracies in the results moreover a direct comparison with in vivo measured loads or with gold standard values from literature is only possible for very specific studies therefore assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required this paper presents a simple method to evaluate both 1 the consistency of the results obtained by inverse dynamics 2 the influence of possible modifications in the inverse dynamic hypotheses this technique concerns recursive calculation performed on full kinematic chains and consists in evaluating the loads obtained by two different recursive strategies it has been applied to complex 3d whole body movements of balance recovery a recursive newton euler procedure was used to compute the net joint loads two models were used to represent the subject bodies considering or not the upper body as a unique rigid segment the inertial parameters of the body segments were estimated from two different sets of scaling equations de leva p 1996 adjustments to zatsiorsky suleyanov s segment inertia parameters journal of biomechanics 29 1223 1230 dumas r cheze l verriest j p 2006b adjustments to mcconville et al and young et al body segment inertial parameters journal of biomechanics in press using this comparison technique it has been shown that for the balance recovery motions investigated 1 the use of the scaling equations proposed by dumas et al instead of those proposed by de leva improves the consistency of the results average relative influence up to 30 for the transversal moment 2 the arm motions dynamically influence the recovery motion in a non negligible way average relative influence up to 15 and 30 for the longitudinal force and the transversal moment respectively

entropy bounds for dendrimers abstract many graph invariants have been used for the construction of entropy based measures to characterize the structure of complex networks when considering shannon entropy based graph measures there has been very little work to find their extremal values a reason for this might be the fact that shannon s entropy represents a multivariate function and all probability values are not equal to zero when considering graph entropies dehmer and kraus proved some extremal results for graph entropies which are based on information functionals and express some conjectures generated by numerical simulations to find extremal values of graph entropies dehmer and kraus discussed the extremal values of entropies for dendrimers in this paper we continue to study the extremal values of graph entropy for dendrimers which has most interesting applications in molecular structure networks and also in the pharmaceutical and biomedical area among all dendrimers with n vertices we obtain the extremal values of graph entropy based on different well known information functionals numerical experiments verifies our results

whole body inverse dynamics over a complete gait cycle based only on measured kinematics this paper presents a three dimensional 3d whole body multi segment model for inverse dynamics analysis over a complete gait cycle based only on measured kinematic data the sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data a new validated smooth transition assumption was used to solve the indeterminacy problem in the double support phase kinematic data is required for all major body segments and hence a whole body gait measurement protocol is presented finally sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results the model gave reasonably good estimates of sagittal plane ground forces and moment however the estimates in the other planes were less good which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment the errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters a digital filtering cut off frequency of 4 5 hz was found to produce the best results it was also shown that errors in the mass properties of body segments can play a crucial role with changes in properties sometimes having a disproportionate effect on the calculated ground reactions the implication of these results is that even when force plate data is available the estimated joint forces are likely to suffer from similar errors

second order randic index of fluoranthene type benzenoid systems fluoranthene type benzenoid system are polycyclic conjugated molecules consisting of two benzenoid fragments connected by two carbon carbon bonds so as to form a five membered ring fluoranthene type benzenoid system and its congeners are compounds which in view of their chemical and physical properties belong among benzenoid hydrocarbons let f denotes a fluoranthene type benzenoid system whose second order randic index is denoted by r2 f in this paper we give the expression of r2 f in terms of their inlet features and we find the minimal and maximal value of the second order randic index over the set of cata catacondensed fluoranthene type benzenoid systems and characterize their corresponding graphs

extremality of degree based graph entropies abstract many graph invariants have been used for the construction of entropy based measures to characterize the structure of complex networks based on shannon s entropy we study graph entropies which are based on vertex degrees by using so called information functionals when considering shannon entropy based graph measures there has been very little work to find their extremal values the main contribution of this paper is to prove some extremal values for the underlying graph entropy of certain families of graphs and to find the connection between the graph entropy and the sum of degree powers further conjectures to determine extremal values of graph entropies are given

the general connectivity indices of fluoranthene type benzenoid systems the general connectivity index r g of a graph g v e is defined as r g u v e g d u d v where u v is an edge of g du and dv denote the degrees of the vertices u and v respectively and 0 is an arbitrary real number in this paper we give the expressions for computing the general connectivity indices of fluoranthene type benzenoid systems and we determine the extremal values of r g in f benzenoid systems with h hexagons for some real number especially the extremal values of r g in cata catacondensed fluoranthene type benzenoid systems with h hexagons were studied

two sided tolerance limits for balanced random effects anova models in this article we derive two sided approximate content tolerance limits for multiway balanced random effects models we provide factors obtained from numerical integration that can be used to obtain content tolerance intervals we describe methods for extending the results to nested models and discuss the use of the tabled tolerance factors for exact intervals for simple random samples when we have an independent estimate of the variance we demonstrate the procedure with an experimental design used to evaluate the firing time precision in a high explosives system

effect of foot progression angle on hip joint moments during gait loosening has emerged as the most serious long term complication of total hip replacement and torsional loading of the femoral implant has been implicated as a possible cause in an effort to explore a strategy for minimizing this risk the following hypothesis was tested the foot progression angle has a significant effect on the resultant hip moments and particularly the internal external rotation moment during level walking twelve normal subjects performed a total of nine trials three in which they walked normally with the right foot pointing approximately straight ahead three in which they were told to walk with the foot internally rotated approximately 30 degrees and three in which the foot was externally rotated about 30 degrees the inverse dynamics approach was used to integrate the body segment parameter kinematic and force plate data and to solve for the resultant moment at the right hip joint in all three conditions foot straight foot in and foot out the subjects walked at the same average speed of 1 5 0 3 ms 1 for the flexion extension moment where the maximum flexion moment of 95 nm was in good agreement with other published data there was no significant difference between the three foot orientation conditions for the abduction adduction moment the foot straight condition exhibited the classic double peak pattern with a maximum abductor moment of 57 nm and there was no statistically significant difference between the three curves abstract truncated at 250 words

complete solution to a problem on the maximal energy of unicyclic bipartite graphs abstract the energy of a simple graph g denoted by e g is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix denote by c n the cycle and p n 6 the unicyclic graph obtained by connecting a vertex of c 6 with a leaf of p n 6 caporossi et al conjectured that the unicyclic graph with maximal energy is p n 6 for n 8 12 14 and n 16 in hou et al 2002 y hou i gutman c woo unicyclic graphs with maximal energy linear algebra appl 356 2002 27 36 the authors proved that e p n 6 is maximal within the class of the unicyclic bipartite n vertex graphs differing from c n and they also claimed that the energies of c n and p n 6 is quasi order incomparable and left this as an open problem in this paper by utilizing the coulson integral formula and some knowledge of real analysis especially by employing certain combinatorial techniques we show that the energy of p n 6 is greater than that of c n for n 8 12 14 and n 16 which completely solves this open problem and partially solves the above conjecture

the general randic index of trees with given number of pendent vertices the general randic index of a graph g is defined as r g u v e g d u d v where d u denotes the degree of a vertex u in g and is a real number in this paper we determine the maximum general randic indices of trees and chemical trees with n vertices and k pendent vertices for 4 k n 2 3 and 0 0 where 0 0 5122 is the unique non zero root of the equation 6 4 20 9 10 12 16 5 24 0 the corresponding extremal graphs are also characterized

effects of asymmetric load carrying on the biomechanics of walking abstract the purpose of the study was to investigate the effects of an asymmetric sidepack carrying system on frontal plane joint moments of force in both lower extremities and in the l5 s1 joint during level walking ground reaction force data and frontal plane film records were obtained from five males performing three walking conditions 0 10 and 20 bodyweight loads in a sidepack supported by the left shoulder inverse dynamics were used to calculate the lower extremity moments during stance and a static model of the pelvis was used to calculate the l5 s1 moments during single support for each limb normal walking was characterized by symmetric kinetics between left and right limbs and around the l5 s1 joint the asymmetric loads produced unbalanced lateral trunk muscle dominance between left and right limb stance phases increased right hip and knee moments and decreased left hip and knee moments during normal walking the l5 s1 moment was dominant on the contralateral trunk side for both limbs the asymmetric loads applied to the left side caused a shift in l5 s1 moment dominance to the right side during left and right single support phases

the connectivity index of a weighted graph abstract let g be a simple graph and consider the m connectivity index m x g i 1 i n hellip i m 1 1 d i 1 d i m d i m 1 where i 1 i 2 i m 1 runs over all paths of length m in g and di denotes the degree of the vertex i we find upper bounds for m g using the eigenvalues of the laplacian matrix of an associated weighted graph the method provides also lower bounds for 1 g

improved factors for one sided tolerance limits for balanced one way anova random model abstract we investigate in this article various techniques for determining a tolerance limit such that the probability is that at least a proportion p of a population produced in batches exceeds that limit if the variance ratio is known one may obtain exact tolerance limits for settings where the variance ratio is not necessarily known we describe a procedure based on the satterthwaite approximation for obtaining conservative tolerance limits the factors based on the satterthwaite approximation are smaller than those obtained using the procedure of lemon 1977

translational and rotational joint power terms in a six degree of freedom model of the normal ankle complex abstract we hypothesized that defining joint power jp merely on the basis of joint rotations ignores important translational power terms and may not adequately represent the energy flow profile for a given muscle group a novel six degree of freedom 6 dof model of the ankle complex was implemented accounting for previously ignored joint translations as well as traditional rotations foot and shank kinematic and kinetic data were collected over a stride cycle on five male and five female adults walking five trials each at 0 69 statures s 1 during intra subject analyses ensemble averages were calculated n 5 for jp associated with each dof and for related velocity and force moment data translational joint velocities typically peaked below 10 of the mean walking velocity the largest peak in jp occurred for the rotational dof associated with dorsi planter flexion 360 w the next largest peak in jp was for the vertical translational dof and was nearly 10 of the predominant peak positive work during push off was significantly less p 0 05 for the 6 dof model 27 9 j than for either 1 or 3 dof rotational models 30 3 and 29 9 j respectively negative work during early stance was significantly less for the 6 dof model 10 3 j than for either the 1 or 3 dof models 13 1 and 12 6 j respectively inter subject analyses n 50 were conducted for jp data only with similar results we conclude that translational jp terms are of practical importance in mechanical energy studies and may be of particular concern when evaluating energy storing prostheses when summing total power at several joints and when studying pathologies that disturb joint geometry

a three dimensional kinematic and dynamic model of the lower limb a model describing the kinematics and dynamics of the lower limb is presented the lower limb is modeled as a sequence of four rigid links connected by three universal rotary joints representing the hip knee and ankle joints each joint is modeled as a sequence of three single axis rotational joints thus ascribing to the lower limb a total of 12 degrees of freedom a method is described to measure the gait variables so that all nine angles can be computed based on the positions of nine markers placed on the subject during a gait study the gait variables are then used in an iterative newton euler formulation to compute the moments exerted about the axes of each joint during gait

adjustments to mcconville et al and young et al body segment inertial parameters body segment inertial parameters bsips are important data in biomechanics they are usually estimated from predictive equations reported in the literature however most of the predictive equations are ambiguously applicable in the conventional 3d segment coordinate systems scss also the predictive equations reported in the literature all include two assumptions the centre of mass and the proximal and distal endpoints are assumed to be aligned and the inertia tensor is assumed to be principal in the segment axes these predictive equations restraining both position of the centre of mass and orientation of the principal axes of inertia become restrictive when computing 3d inverse dynamics when analyzing the influence of bsip estimations on joint forces and moments and when evaluating personalized 3d bsips obtained from medical imaging in the current study the extensive data from mcconville et al 1980 anthropometric relationships of body and body segment moments of inertia afamrl tr 80 119 aerospace medical research laboratory wright patterson air force base dayton ohio and from young et al 1983 anthropometric and mass distribution characteristics of the adults female technical report afamrl tr 80 119 faa civil aeromedical institute oklaoma city oklaoma are adjusted in order to correspond to joint centres and to conventional segment axes in this way scaling equations are obtained for both males and females that provide bsips which are directly applicable in the conventional scss and do not restrain the position of the centre of mass and the orientation of the principal axes these adjusted scaling equations may be useful for researchers who wish to use appropriate 3d bsips for posture and movement analysis

a model of foot placement during gait foot placement is known to affect balance during gait however how foot placements are chosen is unknown objectives of this research were to analyze swing trajectories of the foot during gait with respect to the pelvis and to propose a model of foot placement control which provides a stable base of support effects of gait speed and vision on this model of foot placement were then examined foot trajectories were analyzed using spherical coordinates referenced to the pelvis termed the pelvic spherical coordinates pscs a model was developed based on this coordinate system which predicts foot placement in terms of position and velocity with respect to the pelvis it is proposed that foot placements are chosen to minimize the sum of psc coordinates of the stance and swing feet foot velocity at heel contact is proposed to minimize the sum of the psc stance and swing angular velocities experimental data were collected to test this model during walking trials of different speeds both with and without vision results showed that sums of stance and swing feet pscs were very close to zero at heel contact supporting the positional control hypothesis sums of psc velocities however were not zero at heel contact rather individual swing leg psc velocities were zero at heel contact suggesting independent swing leg velocity control vision did not have an effect on position or velocity variables at heel contact gait speed did have an effect particularly on psc velocities at heel contact abstract truncated at 250 words