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The nucleon has been used as a laboratory to investigate its own spin structure and quantum chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the confinement regime of the theory to its asymptotic freedom regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov–Drell–Hearn, Bjorken and Burkhardt–Cottingham). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher-twist contributions have been examined through the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT.

The moments $〈r^m〉$ of the spherical three-parameter Fermi distribution (3pF) are presented for $m=1$ to 8 as a function of the parameter $w$, the half-density radius $c$ and the diffuseness parameter $a$ through the introduced parameter $\beta =\pi a/c$, which can be applied to study the neutron skin in neutron rich nuclei. The general expression of the moment can be written as the combination of integrals $I_n(k,w)$ with $k=c/a$. The errors of the analytic moments $〈r^m〉$ are estimated with the typical values of the parameters in 3pF compared with the numerical results.

A theoretical comparison has been made for some calcium isotopes (${}_{20}$Ca) which are even–even nuclei and have the atomic mass (Z = 20) with its previous experimental data. Theoretical calculations of some ${}_{20}$Ca isotopes (A = 42, 44, 46, 48, 50, 52) adopted by the shell model theory were performed to calculate the transition rate B(E2), theoretical intrinsic quadruple moments ($Q_{0\mathrm{\text{Th}}})$ and theoretical deformation parameters (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were calculated by two methods by using different effective interactions for each isotope such as, su3fp, fpbm, fprkb, fpd6, kb3. Through code NuShellX@MSU, the single-body density matrix was calculated. The effects of the core polarization were neglected by adopting various effective charges that were employed, effective charges of conventional (Con-E), effective charges of standard (St-E) and effective charges of Bohr and Mottelson (B-M-E) which were calculated. The theoretical values of the B(E2)_Th, the $Q_{0\mathrm{\text{Th}}}$ and the (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$ were then compared with the previous experimental data where values of the transition rate B(E2)_Th, theoretical intrinsic quadrupole moments $Q_{0\mathrm{\text{Th}}}$ and theoretical deformation parameter (${\beta }_2$, $\delta {)}_{\mathrm{\text{Th}}}$, using the fpbm, the fpd6 and the kb3 interactions were the best.

Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight into some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e., the Bjorken, Burkhardt–Cottingham, Gerasimov–Drell–Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The higher-twist contributions have been examined through the evolution of these moments as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low-energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation theory calculations agree reasonably well with the first moment of the spin structure function g₁ at low momentum transfer of 0.05–0.1 GeV² but fail to reproduce some of the higher moments, noticeably, the neutron data in the case of the generalized polarizability δ_LT. The Burkhardt–Cottingham sum rule has been verified with good accuracy in a wide range of Q² assuming that no singular behavior of the structure functions is present at very high excitation energies.

The cello suites of Johann Sebastian Bach exhibit several types of power-law scaling, the best examples of which can be considered fractal in nature. This article examines scaling with respect to the characteristics of melodic interval and its derivative, melodic moment. A new and effective method for pitch-related analysis is described and then applied to a selection of the 36 pieces that comprise the six cello suites.

A new type of iterated function systems is constructed based on different weights, and it is proved that this type of iterated function systems generates a class of bivariate continuous functions whose graphs are the fractal interpolation surfaces passing through the given interpolation points. Considering the influences of the fractal interpolation functions on different weights and basic functions, we give the corresponding error estimation formula. Finally, the calculation formula for the integral moments of this class of bivariate fractal interpolation functions is given.

Signature verification is one of the important methodologies for personnel identification. Because of its wide applications to security practices quite a number of signature verification techniques associated with various features have been proposed. The features utilized in a signature verification system directly affect the performance of the system. In this paper, we review a variety of recently proposed features of signatures and present two new features. Each of these features is examined to evaluate its performance for Chinese signature verification. Then we choose and combine the features that establish good verification rates. As a result, we propose an off-line Chinese signature verification system based on this combination of features. The experimental results show that the proposed system achieves a good performance in term of verification rate.

The mechanical behavior and buckling failure of sharp-notched 6061-T6 aluminum alloy tubes with different notch depths subjected to cyclic bending are experimentally and theoretically investigated. The experimental moment–curvature relationship exhibits an almost steady loop from the beginning of the first cycle. However, the ovalization–curvature relationship exhibits a symmetrical, increasing, and ratcheting behavior as the number of cycles increases. The six groups of tubes tested have different notch depths, from which two different trends can be observed from the relationship between the controlled curvature and the number of cycles required to ignite buckling. Finite element software ANSYS is used to simulate the moment–curvature and ovalization–curvature relationships. Additionally, a theoretical model is proposed for simulation of the controlled curvature-number of cycles concerning the initiation of buckling. Simulation results are compared with experimental test data, which shows generally good agreement.

The purpose of this study was to compare the ankle joint moments in different foot strike patterns during stair descent and to find a better strategy. Methods: Twenty young subjects participated in this study. Subjects performed two trials of descending stairs in rearfoot strike (RFS) and forefoot strike (FFS) strategies. Kinematic and kinetic data were measured by a motion capture system and force plates. Ankle joint moments, ground reaction forces, and moment arms in three planes of motion were calculated from the measured data. The root-mean-squared means of ankle joint moments, ground reaction forces, and moment arms were compared between different foot strike patterns for each phase of stair descent (weight acceptance, forward continuance, and controlled lowering). Results: In the weight acceptance phase, FFS showed greater ankle joint moments than RFS in all three (dorsi/plantar-flexion, inversion/eversion, and internal/external rotation) directions ($p<0.01$). In the forward continuance phase, FFS showed greater dorsi/plantar moments than RFS ($p<0.05$). In controlled lowering phase, FFS showed smaller dorsi/plantar moments than RFS ($p<0.01$). Discussion: The greater ankle joint moments of FFS in the weight acceptance phase were influenced by both the greater GRF magnitudes and greater moment arms. The greater dorsi/plantar moments of FFS in the forward continuance phase and the smaller dorsi/plantar moment of FFS in the controlled lowering phase were dominated by the greater moment arm and the smaller ground reaction force, respectively. RFS strategy resulted in smaller ankle joint moments in the majority of stair descent phases (weight acceptance and forward continuance), therefore, RFS would be a better strategy than FFS for stair descent in terms of ankle joint load.

Flat foot is the most common foot disorder that influences the alignment of the lower limb structure. It is controversial whether the use of foot insole influences kinetic and kinematic of the leg or not. Therefore, this study investigated the influence of foot insole on the gait performance in subjects with flat foot disorder.

A group of flat foot subject was recruited into this study (the number of subjects was 15). The motion of the leg joints was determined using the Qualysis motion analysis system. Moreover, the force applied on the lower limb was recorded by a Kistler force plate. The range of motion of the lower limb joints, the moments applied on the lower limb joints and force transmitted through the leg were the parameters used in this study. The difference between these parameters during walking with and without insole was evaluated using the paired $t$-test. Significant value was set at $p\le 0.05$.

There was no significant difference between the range of motion of ankle joint while walking with and without insole. However, the medial directed force applied on the leg decreased significantly $(p<0.05)$. The use of foot insole did not influence the moments transmitted through the hip and knee joints. The walking speed of the subjects improved while walking with foot insole.

Use of foot insole influenced the magnitude of the force applied on the leg and the adductor moment of ankle joint due to its influence on foot alignment. As the walking speed of the improved subjects follows the use of insole, it can be concluded that it may have a positive effects on the performance of flat foot subjects.

In this paper, the general procedure for obtaining the distribution for the superstatistics is presented. Besides, the new type of effective Boltzmann factor with non-vanishing $r$th moments for even $r$ is presented and some examples are discussed.

The aim of this investigation is to study the ferromagnetism and magnetic properties of LiMgP HH with double impurities, namely $C$-2$p$ and (Fe and Ni)-3$p$, connected to LiMg${}_{0.95}$Fe${}_{0.05}$P${}_{0.95}$C${}_{0.05}$ and LiMg${}_{0.95}$Ni${}_{0.05}$P${}_{0.95}$C${}_{0.05,}$respectively. To achieve this, we perform KKR-CPA combined with GGA. The ferromagnetic stability of LiMg₀P${}_{0.95}$C${}_{0.05}$is observed, where C-2$p$ is set on the spin-down of $E$${}_F$ connected to the half metallicity. In the case of LiMg${}_{0.95}$Fe${}_{0.05}$P alloy, the Fe-3$d$ states show a variation in the exchange splitting ($t_2^{+}$,$t_2^{-}$) with respect to the spin-up ${}^{(\uparrow )}$ and spin-down ${}^{(\downarrow )}$. The Fe-3$d$ states are located around the $E$${}_F$ and exhibit half-metallic characteristic. Similarly, the LiMg${}_{0.95}$Ni${}_{0.05}$P alloy also exhibits half metallic characteristic. The co-doped LiMg${}_{0.95}$Fe${}_{0.05}$P${}_{0.05}$C${}_{0.05}$ and LiMg${}_{0.95}$Ni${}_{0.05}$P${}_{0.95}$C${}_{0.05}$ alloys predict an improvement in magnetic properties due to the presence of carbon, resulting in hybridization between C-2$p$ and Fe-3$d$ in the valence band (VB) maximum and conduction band (CB) minimum on the minority states. Similarly, in the case of LiMg${}_{0.95}$Ni${}_{0.05}$P${}_{0.95}$C${}_{0.05}$, hybridization occurs between C-2$p$ and Ni-3$d$ below $E$${}_F$ in the minority states, within the range of (−0.2 to 0 Ry) in the VB.

The blended wing body (BWB) is the hottest one of the aerodynamic shapes of next generation airliner because of its' high lift-drag ratio, but there are still some flaws that cut down its aerodynamical performance. One of the most harmful flaws is the low efficiency of elevator and direction rudder, this makes the BWB hard to be controlled. In this paper, we proposed a new control method to solve this problem by morphing wing—that is, to control the BWB only by changing its wing shape but without any rudder. The pitching moments, rolling moments and yawing moments are plotted versus the parameters section and the wing shape in figures and are discussed in the paper. The result shows that the morphing wing can control the moments of BWB more precisely and in wider range. The pitching moments, rolling moments and yawing moments increases or decreases linearly or almost linearly, with the value of the selected parameters. These results show that using morphing wing is an excellent aerodynamic control way for a BWB craft.

We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups $\mathrm{\text{O(N)}}$, $\mathrm{\text{U(N)}}$ and $\mathrm{\text{Sp(2N)}}$. For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle.

Some aspects of long surface waves are considered. Special attention is focused on the existence of conservation laws for this physical system and related problems.

The nucleon spin structure has been an active, exciting and intriguing subject of interest for the last three decades. Recent experimental data on nucleon spin structure at low to intermediate momentum transfers provide new information in the confinement regime and the transition region from the confinement regime to the asymptotic freedom regime. New insight is gained by exploring moments of spin structure functions and their corresponding sum rules (i.e. the generalized Gerasimov-Drell-Hearn, Burkhardt-Cottingham and Bjorken). The Burkhardt-Cottingham sum rule is verified to good accuracy. The spin structure moments data are compared with Chiral Perturbation Theory calculations at low momentum transfers. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g₁ at momentum transfer of 0.05 to 0.1 GeV² but fail to reproduce the neutron data in the case of the generalized polarizability δ_LT (the δ_LT puzzle). New data have been taken on the neutron (³He), the proton and the deuteron at very low Q² down to 0.02 GeV². They will provide benchmark tests of Chiral dynamics in the kinematic region where the Chiral Perturbation theory is expected to work.

In practice, it is not likely that enough data about the failure behavior can be collected to use the probability for reliability analyzing. In some cases, the information we have about the functioning of components and systems is not based on statistics, but is of a linguistic nature. Very often the reliability of the system is presented in a form of the mean time to failure (MTTF) or comparative MTTFs. In order to use this reliability measure for further computations the new models have to be developed. A theory of imprecise probabilities might be a basis for reliability analyzing when we have such the incomplete information about reliability behavior of systems. The basic tool for computing new reliability measures is the natural extension which can be regarded as a linear optimization problem. The reliability of series, parallel, cold standby, m-out-of-n and simple repairable systems is provided by using the natural extension. The chapter may be viewed as an attempt to generalize the classical reliability theory based on the probabilistic models and to study the basic properties and advantages of the new reliability models.

This paper proposes a new approximation formula for pricing average options under Heston's stochastic volatility model. When using the formula based on the Gram-Charlier expansion, it is necessary to know any moments of an averaged underlying asset price. We try to derive an analytical solution of the moments under the Heston model. There are two key points of the derivation: One of them is to repeatedly apply change of a certain measure. Another is to sequentially solve a system of ordinary differential equations. Moreover, numerical examples support the accuracy of the proposed average option pricing formula.