Narrow Results

The main features of obtaining the asymptotic behavior of the electric structure function $A(p)$ at large values of the transmitted momentum are analyzed. The asymptotic behavior of the structure function $A(p)$ was determined to take into account the asymptotic behavior of the deuteron form factors and the original dipole approximation for the nucleon form factors. Asymptotic values of $A(p)$ were obtained for the nucleon–nucleon potential Reid93 and compared with the calculations for different nucleon form factor models and their approximations. In the broad momentum range up to 12.5 fm${}^{-1}$, the basic forms of the asymptotic behavior of the electric structure function are demonstrated and compared with the experimental data of the modern collaborations. As the analysis shows in most cases considered, the asymptotic for $A(p)$ is represented in the form of the power function $p^{-n}$.

The NuTeV experiment obtained high statistics samples of neutrino and antineutrino charged current events during the 1996-1997 Fermilab fixed target run. The experiment combines sign-selected neutrino and antineutrino beams and the upgraded CCFR iron-scintillator neutrino detector. A precision continuous calibration beam was used to determine the muon and hadron energy scales to a precision of 0.7% and 0.43% respectively. The structure functions F₂(x, Q²) and xF₃(x, Q²) obtained by fitting the y-dependence of the sum and the difference of the ν and differential cross sections are presented.

We present a model that realizes both resonance-Regge (Veneziano) and parton–hadron (Bloom–Gilman) duality. We first review the features of the Veneziano model and we discuss how parton–hadron duality appears in the Bloom–Gilman model. Then we review limitations of the Veneziano model, namely that the zero-width resonances in the Veneziano model violate unitarity and Mandelstam analyticity. We discuss how such problems are alleviated in models that construct dual amplitudes with Mandelstam analyticity (so-called DAMA models). We then introduce a modified DAMA model, and we discuss its properties. We present a pedagogical model for dual amplitudes and we construct the nucleon structure function F₂(x, Q²). We explicitly show that the resulting structure function realizes both Veneziano and Bloom–Gilman duality.

Transverse momentum dependent (TMD) parton distributions, also referred to as unintegrated parton distribution functions (UPDFs), are produced via the Kimber–Martin–Ryskin (KMR) prescription. The GJR08 set of parton distribution functions (PDFs) which are based on the valence-like distributions is used, at the leading order (LO) and the next-to-leading order (NLO) approximations, as inputs of the KMR formalism. The general and the relative behaviors of the generated TMD PDFs at LO and NLO and their ratios in a wide range of the transverse momentum values, i.e. $k_t^2=10$, $10^2$, $10^4$ and $10^8{\mathrm{\text{GeV}}}^2$ are investigated. It is shown that the properties of the parent valence-like PDFs are imprinted on the daughter TMD PDFs. Imposing the angular ordering constraint (AOC) leads to the dynamical variable limits on the integrals which in turn increase the contributions from the lower scales at lower $k_t^2$. The results are compared with our previous studies based on the MSTW2008 input PDFs and it is shown that the present calculation gives flatter TMD PDFs. Finally, a comparison of longitudinal structure function $(F_L)$ is made by using the produced TMD PDFs and those that were generated through the MSTW2008-LO PDF from our previous work and the corresponding data from H1 and ZEUS collaborations and a reasonable agreement is found.

The structure function of the vortex lattice of layered superconductor is calculated to one-loop order. Based on a phenomenological melting criterion concerning the Debye–Waller factor, we calculate the melting line of the vortex lattice, and compare our results to Monte Carlo simulation and experiment. We find that our results are in good agreement with the Monte Carlo results. Moreover, our analytic calculation of the melting line of BSCCO fits the experiment reasonably.

The neutron-to-proton ratio of the structure functions, , as well as the corresponding difference are obtained within a statistical quark model for the nucleon, where the quark energy levels are given by a central linear confining potential.

The quark exchange model and the full three-nucleon wave function in the configuration space are used to evaluate the role of Fermi motion on the structure functions (SFs) of helium-3 and tritium nuclei. The three-nucleon wave function is obtained from the solution of the Faddeev equations with the Malfliet–Tjon-type potential, by using the three-dimensional approach as a function of the magnitudes of the Jacobi momenta vectors and the angle between them. In this calculation, the initial valence quarks inputs are taken from the GRV's (Glück, Reya and Vogt) fitting procedure and the next-to-leading order (NLO) QCD calculation on , which give a very good fit to the available experimental data in the (x, Q²)-plane. The role of Fermi motion on the EMC ratio of the SFs of ³He and ³H nuclei are analyzed through the NLO expansion of the nuclear wave function in the coordinate space. A good agreement between the calculated EMC ratios, the corresponding experimental data and the theoretical results is found. Finally, the ratios of the SFs of the neutron to the proton (with the isospin symmetry assumption) with and without the Fermi motion effect, are also calculated, and they are compared with the available experimental data. Our results show that the roles of the Fermi motion in the framework of the quark exchange model for the calculations of the nuclear SFs are important.

The quark exchange formalism is formulated to calculate the quark momentum distribution in the iso-scalar Lithium nucleus. Then by boosting the nucleus to an infinite momentum frame, the Lithium structure function is evaluated at different nucleon "sizes", i.e., b = 0.7, 0.8, 0.9 and 1 fm and the Bjorken scale (x) values. It is shown that the Lithium structure function becomes narrower, and it is pushed to the smaller x values, as the nucleon size is increased. Similar to our previous works for three nucleon systems, the Lithium nucleus European muon collaboration (EMC) ratio decreases, as we increase the x and b values and it shows larger effect, with respect to the free nucleon and three nucleons iso-scalar nucleus. On the other hand, present calculation of the EMC ratio for Lithium nucleus shows a good agreement with the corresponding NMC data, which is available for 1.4 × 10^-4 ≤ x ≤ 0.65. Since the atomic number is still small (A = 6), in this work as usual, we ignore the possibility of simultaneous exchange of quarks between more than two nucleons, which can be important as one moves to the heavy nuclei. Although, according to Hen et al., in the neutron rich nuclei the protons have a greater probability than neutrons to have momentum greater than the Fermi momentum, the three-body contribution may be suppressed.

In this paper, the polarized neutron structure function $g_1^n$ in the ${}^3\mathrm{\text{He}}$ nucleus is investigated and an analytical solution based on the Laplace transform method for $g_1^n$ is presented. It is shown that the neutron spin structure function can be extracted directly from the polarized nuclear structure function of ${}^3\mathrm{\text{He}}$. The nuclear corrections due to the Fermi motion of the nucleons as well as the binding energy considerations are taken into account within the framework of the convolution approach and the polarized structure function of ${}^3\mathrm{\text{He}}$ nucleus is expressed in terms of the spin structure functions of nucleons and the light-cone momentum distribution of the constituent nucleons. Then, the numerical results for $g_1^n$ are compared with experimental data of the SMC and HERMES collaborations. We found that there is an overall good agreement between the theory and experiments.

In this work, we study the differential scattering cross-section (DSCS) in the first-order Born approximation. It is not difficult to show that the DSCS can be simplified in terms of the system response function. Also, the system response function has this property to be written in terms of the spectral function and the momentum distribution function in the impulse approximation (IA) scheme. Therefore, the DSCS in the IA scheme can be formulated in terms of the spectral function and the momentum distribution function. On the other hand, the DSCS for an electron off the ${}^4\mathrm{\text{He}}$ and ${}^{16}\mathrm{\text{O}}$ nuclei is calculated in the harmonic oscillator shell model. The obtained results are compared with the experimental data, too. The most important result derived from this study is that the calculated DSCS in terms of the spectral function has a high agreement with the experimental data at the low-energy transfer, while the obtained DSCS in terms of the momentum distribution function does not. Therefore, we conclude that the response of a many-fermion system to a probe particle in IA must be written in terms of the spectral function for getting accurate theoretical results in the field of collision. This is another important result of our study.

Scaling region identification is of great importance in calculating the fractal dimension of a rough surface profile. A new method used to identify the scaling region is presented to improve the calculation accuracy of fractal dimension. In this method, the second derivative of the double logarithmic curve is first calculated and the $K$-means algorithm method is adopted to identify the scaling region for the first time. Then the margin of error is reasonably set to get a possible scaling region. Finally, the $K$-means method is used again to obtain a more accurate scaling region. The effectiveness of the proposed method is compared with the existing methods. Both the simulation and experimental results show that the proposed method provides more precise results for extracting the scaling regions and leads to a higher calculation precision of fractal dimensions.

We used multifractals to analyze the Lebanese topography focusing on Mount Lebanon. The elevation data were obtained from NASA STRM Global Digital Elevation of Earth Land, spaced at 80m in the East-West direction, and at 90m in the North-South direction. After transforming the grid to be perpendicular and parallel to the range, we found anisotropic scaling from 500m to 10,000m, and it reflected the fact that the Lebanese topography was more correlated in the direction perpendicular to the mountain range, probably due to occurrence of valleys and ridges in that direction. We estimated the parameters of the Universal Multifractal (UM) model and found $\alpha =1.45$ and $c1=0.05$, consistent with values reported for topography. The UM parameter $H$ was found to be 0.72 across the range and 0.57 along the range, the latter value agrees with prior observations. However, the larger value across the range is consistent with the higher spatial correlation in that direction. We introduced a new expression for the 2D power spectral density, and we showed that it can decently capture the anisotropic scaling. We also generated multiple realizations and we showed that the generation of anisotropic scaling did not alter the underlying parameter values $\alpha$ and $c1$ of the UM model. We also proposed an approximate method for generating conditional simulations, and we showed that through a judicious selection of values, one may reproduce approximately the observed field values at the desired locations. We believe such an approach could be used to generate realistic simulations of fields that are time-invariants, such as topography and soil properties.

Inspection threshold is one of effective methods to reduce causes of misjudgement under imperfect inspection. Based on the Bayesian theory, the threshold is defined as the boundary between inspection and noninspection execution. However, the formulation of the true threshold is difficult under a general complex system. This paper proposes approximation methods to derive the maximum and the minimum inspection thresholds for a general system. A binary reliability theory is used for the derivation of the thresholds. Structure functions, minimal path and cut sets are used for the approximation. Finally, some numerical examples are given.

In this paper, we study structures and properties of Null scrolls. We define the (relative) invariants for Null scrolls by using a kind of standard equation. Using these (relative) invariants of Null scrolls, we give some new characterizations and classifications of Null scrolls and B-scrolls.

During the 1980s the structure–function relationship of nonsteroidal estrogens and antiestrogens using an a prolactin gene target in primary cultures of rat pituitary cells created basic models for the estrogen receptor (ER)–mediated modulation of estrogen-induced prolactin synthesis. However, the cloning and sequencing of the human ER, made possible by the creation of monoclonal antibodies to the ER, created a new dimension in our understanding of the mechanics of estrogen and antiestrogen action. Although the whole human ER has not been crystallized with ligands that binds to the ligand-binding domain (LBD), the crystallization and resolution of estrogen and antiestrogen LBD complexes are consistent and informative. Simply stated, an array of different complexes are formed with selective ER modulators (SERMs) and a pure antiestrogen causes considerable structural disruption of the LBD. This chapter tells the story of how the shape of the ligand–ER complex programs the interaction with coactivators for estrogen actions or becomes the signal for the destruction of the complex.

A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is presented. A natural approach to building coherent states associated to deformed algebras is then deduced.