It is a popular paradoxical exercise to show that the infinite sum of positive integer numbers is equal to -1/12, sometimes called the Ramanujan sum. Here we propose a qualitative approach, much like that of a physicist, to show how the value -1/12 can make sense and, in fact, appears in certain physical quantities where this type of summation is involved. At the light of two physical examples, taken respectively from condensed matter -- the Landau diamagnetism -- and quantum electrodynamics -- the Casimir effect -- that illustrate this strange sum, we present a systematic way to extract this Ramanujan term from the infinity.
Las condicionales del español con la estructura cond + imperfecto de subjuntivo + condicional simple de indicativo evidencian la aparición de la flexión condicional en la prótasis, contrario a lo establecido en el español estándar. Además, de acuerdo con Lavandera (1984) y De Granda (1998), la diferencia entre grado de realidad podría motivar la aparición de dicha flexión de condicional en prótasis. Así, se busca vincular el grado de realidad con la aparición de la flexión de condicional simple de indicativo en la prótasis. A partir de lo propuesto por Thompson, Longacre y Hwang (2007) sobre grados de realidad, la Gramática de Construcciones (Hoffman y Trousdale, 2013), así como las investigaciones de Lavandera (1984) y De Granda (1998), se pone a prueba esa variable con cuestionarios escritos1.
Diptarka Chakraborty, Gunjan Kumar, Kuldeep S. Meel
We consider the problem of estimating the support size of a distribution $D$. Our investigations are pursued through the lens of distribution testing and seek to understand the power of conditional sampling (denoted as COND), wherein one is allowed to query the given distribution conditioned on an arbitrary subset $S$. The primary contribution of this work is to introduce a new approach to lower bounds for the COND model that relies on using powerful tools from information theory and communication complexity. Our approach allows us to obtain surprisingly strong lower bounds for the COND model and its extensions. 1) We bridge the longstanding gap between the upper ($O(\log \log n + \frac{1}{\epsilon^2})$) and the lower bound $\Omega(\sqrt{\log \log n})$ for COND model by providing a nearly matching lower bound. Surprisingly, we show that even if we get to know the actual probabilities along with COND samples, still $\Omega(\log \log n + \frac{1}{\epsilon^2 \log (1/\epsilon)})$ queries are necessary. 2) We obtain the first non-trivial lower bound for COND equipped with an additional oracle that reveals the conditional probabilities of the samples (to the best of our knowledge, this subsumes all of the models previously studied): in particular, we demonstrate that $\Omega(\log \log \log n + \frac{1}{\epsilon^2 \log (1/\epsilon)})$ queries are necessary.
The mathematical foundation of quantum mechanics is built on linear algebra, while the application of nonlinear operators can lead to outstanding discoveries under some circumstances. In this Letter, we propose a model of square-root higher-order Weyl semimetal (SHOWS) by inheriting features from its parent Hamiltonians. It is found that the SHOWS hosts both "Fermi-arc" surface and hinge states that connect the projection of the Weyl points. We theoretically construct and experimentally observe the exotic SHOWS state in three-dimensional (3D) stacked electric circuits with honeycomb-kagome hybridizations and double-helix interlayer couplings. Our results open the door for realizing the square-root topology in 3D solid-state platforms.
The purpose of this note is to clarify the solution of the non-local Peierls Boltzmann equation found by Hua and Lindsay (Phys. Rev. B 102, 104310 (2020)). They used methods of Cepellotti and Marzari. The response function "thermal distributor" is discussed. The new, "non-Fourier" term $\vec{B}$ [$\vec{J}_{\rm th}=-κ\vec{\nabla}T +\vec{B}]$ that occurs in non-local situations, gives rise also to a new term in the thermal distributor.
Hypoxia is a typical hallmark in several disease conditions, particularly in solid tumors. Thus, hypoxia-responsive nanocarriers that may specifically deliver and release payload under hypoxic cond...
Jacob Centala, Cameron Pogorel, Scott W Pummill
et al.
Centala, J, Pogorel, C, Pummill, SW, and Malek, MH. Listening to fast-tempo music delays the onset of neuromuscular fatigue. J Strength Cond Res XX(X): 000-000, 2019-Studies determining the effect of music on physical performance have primarily focused on outcomes such as running time to exhaustion, blood lactate, or maximal oxygen uptake. The electromyographic fatigue threshold (EMGFT) is determined through a single incremental test and operationally defined as the highest exercise intensity that can be sustained indefinitely without an increase in EMG activity of the working muscle. To date, no studies have examined the role of fast-tempo music on EMGFT. The purpose of this investigation, therefore, was to determine whether fast-tempo music attenuates neuromuscular fatigue as measured by the EMGFT. We hypothesized that listening to fast-tempo music during exercise would increase the estimated EMGFT compared with the control condition. Secondarily, we hypothesized that maximal power output would also increase as a result of listening to fast-tempo music during the exercise workbout. Ten healthy college-aged men (mean ± SEM: age, 25.3 ± 0.8 years [range from 22 to 31 years]; body mass, 78.3 ± 1.8 kg; height: 1.77 ± 0.02 m) visited the laboratory on 2 occasions separated by 7 days. The EMGFT was determined from an incremental single-leg knee-extensor ergometer for each visit. In a randomized order, subjects either listened to music or no music for the 2 visits. All music was presented as instrumentals and randomized with a tempo ranging between 137 and 160 b·min. The results indicated that listening to fast-tempo music during exercise increased maximal power output (No Music: 48 ± 4; Music: 54 ± 3 W; p = 0.02) and EMGFT (No Music: 27 ± 3; Music: 34 ± 4 W; p = 0.008). There were, however, no significant mean differences between the 2 conditions (no music vs. music) for absolute and relative end-exercise heart rate as well as end-exercise rating of perceived exertion for the exercised leg. These findings suggest that listening to fast-tempo music increased overall exercise tolerance as well as the neuromuscular fatigue threshold. The results are applicable to both sport and rehabilitative settings.
Ryan M. Curtis, R. Huggins, David P. Looney
et al.
Abstract Curtis, RM, Huggins, RA, Looney, DP, West, CA, Fortunati, A, Fontaine, GJ, and Casa, DJ. Match demands of National Collegiate Athletic Association Division I men's soccer. J Strength Cond Res 32(10): 2907–2917, 2018—This study aimed to profile positional movement characteristics of National Collegiate Athletic Association (NCAA) Division I male soccer players. Eighteen Division I male soccer players were monitored using global positioning systems, inertial movement, and heart rate (HR) technology during 24 matches over a full competitive season (N = 235 observations). Positional groups were classified as either a forward (F), center midfielder (CM), wide midfielder (WM), or defender (D). Movement was profiled by locomotor (walking [0–7.19 km·h−1], jogging [7.20–14.39 km·h−1], running [14.40–21.59 km·h−1], and sprinting [>21.6 km·h−1]), and acceleration/deceleration characteristics (low intensity [0–1.99 m·s2], moderate intensity [2–3.99 m·s2], and high intensity [>4 m·s2]). Players averaged distances of 9,367 ± 2,149 m per match at speeds of 91 ± 20 m·min−1 and physiological intensities of 78 ± 8 %HRmax. Center midfielder demonstrated the highest average speeds (97 ± 20 m·min−1) and covered the most distance (9,941 ± 2,140 m). Wide midfielder accumulated the most sprint distance (391 ± 145 m) and high-intensity accelerations (129 ± 30 n)/decelerations (96 ± 24 n). Several practically meaningful differences exist between positions for internal and external load metrics. Match loads seen in NCAA Division I soccer vary from reports of professional soccer; however, the effects of match regulation, structure, and congestion, which are unique to NCAA soccer, require further investigation. Physical and physiological load monitoring of NCAA soccer may aid coaches and practitioners in the periodization of training programs leading up to and during a competitive soccer season. These data speak to the necessity for examining both internal and external loads by position.