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This paper contains a proposal for a free, nonzero-rest-mass particle’s proper spacetime, determined exclusively by the particle’s rest mass m 0 and numbers. The approach defines proper time as de Broglie time, which is isomorphic to a sequence of natural numbers 1 , 2 , … , n that count de Broglie time units (h / c 2) (m 0 - 1) (see Ferber in Found Phys Lett 9:575, 1996). The approach is based on defining the spatial coordinate as proper following the constructive definition of positive and negative integers as all possible differences of ordered pairs of natural numbers multiplied by the Compton unit (h / c) (m 0 - 1) . The spatial and temporal coordinates that form the particle’s proper spacetime are constructed as Euclidean projections of the de Broglie time. The corresponding expression in the form of an energy-momentum relation reveals the existence, aside from the rest energy term m 0 c 2 , of an additional energy term of the same order of magnitude, which is related to large intervals of the m 0 -particle’s proper space. The relation of the numbers-based approach to the foundations of the special theory of relativity and of quantum mechanics is discussed. [ABSTRACT FROM AUTHOR]

Comment on: I Manca A, Cugusi L, Pomidori L, Felisatti M, Altavilla G, Zocca E, Zocca M, Bussu F, Dvir Z, Deriu F (2020) Listening to music while running alters ground reaction forces: a study of acute exposure to varying speed and loudness levels in young women and men. Future studies should spare no effort in enhancing the experimental control for instance by manipulating not only the music loudness but also the runners' step cadence (e.g., preferred I vs. i slightly increased/decreased), the music tempo and type (i.e., participant-chosen I vs. i researcher-dictated music choice, hard I vs. i soft), and whether it is delivered synchronously or asynchronously. [Extracted from the article]

Radiative lifetimes for 2≤v′≤44 rovibronic C1Σ+ state levels of NaRb and quenching collision cross-sections with Rb atoms have been directly measured in a thermal cell by detecting time resolved laser induced fluorescence after pulsed excitation. Many body multipartitioning theory was applied to calculate C1Σ+-X1Σ+ and C1Σ+-A1Σ+ transition dipole moments. The relevant ab initio matrix elements were converted to the C1Σ+ state radiative lifetimes. The strong spin-orbit A1Σ+∼ b3Π coupling effect on the total C → A transition probabilities and lifetimes of the C1Σ+ state is discussed. The measured radiative lifetimes show a decrease from 61 to 34 ns as the v′ values increase, the results being in good agreement with calculations. The averaged collisional quenching cross-section value σ=(3±1)×10-14 cm2 was determined for NaRb (C1Σ+) + Rb collisions from the Stern-Volmer plots. [ABSTRACT FROM AUTHOR]

We present a first detailed experimental study of the C(3)1Σ+ state of the NaRb molecule converging to the Na(3p) + Rb(5s) states of separated atoms. Two different high resolution spectroscopic methods have been applied: the Fourier transform spectroscopy of laser induced fluorescence and the V-type optical-optical double resonance polarization labeling spectroscopy. The entire data field for the C1Σ+ state of Na85Rb and Na87Rb consists of rovibrational levels with v'=0–64 and J'=4–123. The data were incorporated into a direct fit of a single potential energy curve to the level energies using the Inverted Perturbation Approach method. As the experimental data extend to the “shelf" region of the potential at large internuclear separations of 8.5 Å, the C state's suitability for photoassociation yielding cold heteronuclear NaRb is discussed. [ABSTRACT FROM AUTHOR]

We present a detailed experimental study of the D1Π state of the NaRb molecule by means of Fourier transform spectroscopy of laser induced fluorescence. The entire data field for the D1Π state of Na85Rb and Na87Rb consists of rovibrational levels with v′=0-39 and J′=1-200. The data were incorporated into a direct fit of a single potential energy curve to the level energies using the Inverted Perturbation Approach method. The D1Π state q factors , which describe the Λ-doubling, have been obtained in a wide range of rotational and vibrational quantum numbers. Analysis revealed several perturbation regions in the D1Π state. [ABSTRACT FROM AUTHOR]

The ground state Xof NaCs was studied by laser induced fluorescence Fourier-transform spectroscopy. An accurate potential energy curve was derived from more than 5000 transitions. This potential reproduces the experimental observations within their uncertainties ofcm-1 and covers about 99.97% of the potential well depth. Few vibrational levels of the shallow state abelow the atomic ground state asymptote were observed. The identification is mainly done by the observed and quantitatively interpreted molecular hyperfine structure applying atomic parameters of the ground states of Na and Cs. An estimated potential curve for ais reported which can be used together with that of Xfor coupled channel calculations of cold collisions between Na and Cs. An example is given. [ABSTRACT FROM AUTHOR]

It has been postulated that the adaptations of lower extremity function exhibited by anterior cruciate ligament (ACL) deficient and post-ACL surgical patients represent early accommodations to the loss of ACL function after injury so that excessive anterior displacement of the tibia is prevented. Prior studies have suggested that compensation patterns in ACL deficient and post-ACL surgical subjects may affect joint moments of the knee as well as the hip. However, the variance in knee and hip forces between ACL deficient, post-surgical ACL and uninjured groups has not been clearly elucidated. The purpose of this study was to assess hip:knee extensor torque ratios relative to anterior tibia shear in pre-surgical-ACL deficient, post-surgical and uninjured subjects. Measurements of hip and knee joint moments and anterior tibia shear were recorded from 45 injured and uninjured subjects (21 men, 24 women) during lower extremity, variable resistance exercise. Anterior tibia shear was computed by decomposing joint moments and reaction forces according to a model derived from cadaver knee dissections and radiography, in combination, to estimate the tibio-femoral compressive and shear forces generated by the patellar tendon at various angles throughout the knee joint range. Three groups of subjects were studied: recently injured ACL deficient pre-surgical subjects who were scheduled for immediate surgery (PRE; n=15); post-surgical subjects who had undergone ACL reconstructive surgery at least 1 year prior to testing (POST; n=15); and uninjured controls (CON; n=15). All PRE and POST subjects had a normal contralateral limb. Tests were conducted under six conditions: 1 and 1.5 Hz cadence and maximal speed at 33% and 50% one repetition maximum resistance. The results revealed that the hip:knee ratios were significantly greater for the post-ACL surgical group than the PRE and CON groups (P < 0.01; P < 0.03). There were significant negative correlations between the hip extensor:knee extensor torque ratios and maximal anterior tibia shear. across all groups. The hip:knee extensor torque ratio increased with decreased anterior tibia shear in all groups with significant correlations ranging from -0.55 to -0.88 (P < 0.01) for the injured limbs of PRE and POST groups, and -0.64 to -0.78; (P < 0.01) for the CON group. The highest overall correlations were found for the post-surgical subjects. The results revealed that anterior tibia shear declined significantly with speed (P < 0.01) in all groups. However, the converse was true for the hip:knee extensor torque ratio across speeds. The ratio increased significantly with speed (P < 0.001) for all groups at the 33% and 50% resistances. The results suggest (1) that post-ACL surgical subjects appear to accommodate to ACL substitution by using hip extensors to a significantly greater extent than the uninjured controls in closed-chain lower extremity exercise; (2) that the hip:knee extensor torque ratio is significantly related to the magnitude of anterior tibia shear; and (3) that the anterior tibia shear is significantly reduced as speed increases in closed-chain lower extremity exercise. [ABSTRACT FROM AUTHOR]

In two experiments we explore the relationship of gaze control to quiet stance and lunge in elite ballet dancers, ACL-deficient and normal controls. In order to maintain postural stability, all direct their gaze straight ahead at appropriate moments in order to maintain alignment of the centre of gravity over the functional centre of pressure (CoP). Not surprisingly, the elite ballet dancers were better at establishing a line of gaze forward at appropriate moments while the other groups were less likely to use this gaze control strategy. The ballet dancers appeared to use a visual straight ahead (VSA), which was a line of gaze horizontal to the base of support that momentarily stabilized their body for current and future actions. Surprisingly, they employed a more variable CoP, while the normal controls and ACL-deficient adopted a CoP distributed over a narrower and less dynamic base of support even while the gaze tracked a more variable pattern in space. In the lunge forward to return, the results were similar, with the exception the ballet dancers were more adept at returning their gaze to the VSA at appropriate moments while the ACL deficient had greater difficulty. These results are discussed within Bernstein’s notion of “freezing, freeing, and exploiting” the degrees of freedom of an action, in terms of both the control of the gaze and posture. [ABSTRACT FROM AUTHOR]