Function G1 Research Articles

The role of semi inclusive DIS data in determining polarized PDFs

A new combined NLO QCD analysis of the polarized inclusive and semi-inclusive DIS data is presented. In contrast to previous combined analyses, the 1/Q2 terms (kinematic –target mass corrections, and dynamic – higher twist corrections) in the expression for the nucleon spin structure function g1 are taken into account. The new COMPASS data are included in the analysis. The impact of the semi-inclusive (SIDIS) data on the polarized parton densities (PDFs) and on the higher twist corrections is demonstrated. The incompatibility of the polarized strange quark density obtained from DIS and from SIDIS data is discussed.

MOMENTS OF SPIN STRUCTURE FUNCTIONS: SUM RULES AND POLARIZABILITIES

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 δLT. 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.

Berezin Transform, Mellin Transform and Toeplitz Operators

We consider functions of the form \({f_1\bar g_1+h}\) in the range of the Berezin transform B, where f1 and g1 are holomorphic on the unit disk \({\mathbb D}\), and h is either harmonic or of the form \({f_2\bar g_2}\) for some holomorphic functions f2 and g2 on \({\mathbb D}\). First, by using the Mellin transform, we complement Ahern’s Theorem (Ahern in J Funct Anal 215:206–216, 2004) by proving that if \({u\in L^1}\) and B(u) is harmonic, then u is harmonic. Secondly, we extend Ahern’s Theorem when h is harmonic, and give very precise relations between f1 and f2, g1 and g2 when \({h=f_2\bar g_2}\) and g2(z) = zn with n ≥ 1. Finally, some applications of our results to the theory of Toeplitz operators are discussed.

EVOLUTION OF UNDERSTANDING POLARIZED DIS: FROM LARGE TO SMALL x

The standard theoretical description of Polarized DIS is based on the use of the DGLAP evolution equations. This approach controls the Q2 -evolution of the DIS structure functions but cannot describe the x -evolution and therefore should not be used at small x. We complement this approach, accounting for the x-evolution of the spin structure function g1 in the leading logarithmic approximation.

NON-UNIVERSALITY AND EVOLUTION OF THE SIVERS FUNCTION

We examine the large-x QCD evolution of the twist-three gluonic-pole strength defining an effective T -odd Sivers function, where evolution of the T -even transverse-spin DIS structure function g2 is multiplicative. The result corresponds to a colour-factor modified spin-averaged twist-two evolution.

Some remarks on methods of QCD analysis of polarized DIS data

The results on polarized parton densities obtained using different methods of QCD analysis of the present polarized DIS data are discussed. Their dependence on the method used in the analysis, accounting or not for the kinematic and dynamic 1=Q 2 corrections to spin structure function g1, is demonstrated. It is pointed out that the precise data in the preasymptotic region require a more careful matching of the QCD predictions to the data in this region in order to determine the polarized parton densities correctly.

Absence of Inflammatory Response from Upper Airway Epithelial Cells after X Irradiation

Radiotherapy of head and neck tumors causes adverse reactions in normal tissue, especially mucositis. The dose- and time-dependent response of upper airway cells to X radiation should be analyzed in terms of the pro-inflammatory potential. Immortalized BEAS-2B lung epithelial cells were treated with 2, 5 and 8 Gy. Out of 1232 genes, those that were transcribed differentially after 2, 6 and 24 h were assigned to biological themes according to the Gene Ontology Consortium. Enrichment of differentially regulated gene clusters was determined with GOTree ( http://bioinfo.vanderbilt.edu/gotm ). Eleven cytokines were measured in culture supernatants. The cell cycle response up to 24 h and induction of apoptosis up to 4 days after exposure were determined by flow cytometry. A significant dose- and time-dependent gene activation was observed for the categories response to DNA damage, oxidative stress, cell cycle arrest and cell death/apoptosis but not for immune/inflammatory response. This correlated with functional G(2) arrest and apoptosis. Pro-inflammatory cytokines accumulated in supernatants of control cells but not of X-irradiated cells. The complex gene expression pattern of X-irradiated airway epithelial cells is accompanied by cell cycle arrest and induction of apoptosis. In vivo, this may impair the epithelial barrier. mRNA and protein expression suggest at most an indirect contribution of epithelial cells to early radiogenic mucositis.

Phase II study of a 3-weekly liposome-encapsulated doxorubicin/docetaxel/pegfligrastrim in combination with weekly trastuzumab as primary treatment in HER2 positive early stage breast cancer patients (II-IIIa). GEICAM 2003-03 study.

Abstract Abstract #5117 Objective: To assess the safety and efficacy of Myocet (M), Docetaxel (T), Trastuzumab (H) with prophylactic Pegfilgrastrim (N) as neoadjuvant chemotherapy in operable breast cancer patients (pts). The primary efficacy end point was pathologic complete response in the breast. Methods: Eligible pts had pathologically confirmed stage II or IIIA untreated breast cancer and HER2 overexpression determined by FISH in a central laboratory. M 50 mg/m2 and T 60 mg/m2 were given on day 1 and N on day 2 every 3 weeks for 6 cycles (Cy); H (4mg/Kgr loading dose, then 2 mg/Kgr/week) was given intravenously for 17 weeks, recommended dose in a phase I study (Proc ASCO 2007,25:596s Abstr.# 11.032). After all chemotherapy was completed, clinical responses were assessed. After surgery, pathological responses were evaluated using the Miller Payne scoring scale (MPSS). Results: 59 pts have been evaluated. Median age was 47.6 years (range 24-71) and median clinical tumour size 47.5 mm (range, 10-80). 19 pts (32.2%) presented with stage IIIA disease and 40 pts (67.8%) with stage II, 36 pts (61.0%) were premenopausal; 50 pts (84.8%) had histological grade 2-3 tumours; and 29 (49.2%) were ER-PgR-negative. All the pts received M and T 6 Cy with medium relative doses intense of 98.9% and 99.1% respectively. Objective clinical response rate was 84.7% (CI: 75.5-93.9) with 31 (52.5%) complete responses and 19 (32.2%) partial responses. 42 pts (71.2%) underwent conservative surgery, 17 pts (28.8%) achieved a pathological complete response in breast (Grade 5 in MPSS), of these, 16 pts (27.1%) achieved a pathological complete response in breast and axilar (Grade 5A+Grade 5D). Main grades (G) toxicities during MTHN treatment: leucopenia G3/4 was present in 18 pts (30.5%); neutropenia G3/4 in 17 pts (28.8%); febrile neutropenia G3 in 3 pts (5.1%); diarrhea G3 was present in 3 pts (5.1%); G2 rash in 2 pts (3.4%); G3 asthenia in 5 pts (8.5%) and stomatitis G3 in 1 pt (1.7%). 8 pts (13.6%) experienced asymptomatic and reversible cardiac left ventricular function G2. Conclusions: Concomitant administration of M plus THN is highly effective and active regimen with little toxicity in pts with HER2+ and early stage breast cancer. Citation Information: Cancer Res 2009;69(2 Suppl):Abstract nr 5117.

Gaussian core model phase diagram and pair correlations in high Euclidean dimensions

The physical properties of a classical many-particle system with interactions given by a repulsive Gaussian pair potential are extended to arbitrarily high Euclidean dimensions. The goals of this paper are to characterize the behavior of the pair correlation function g(2) in various density regimes and to understand the phase properties of the Gaussian core model (GCM) as parametrized by dimension d. To this end, we explore the fluid (dilute and dense) and crystalline solid phases. For the dilute regime of the fluid phase, a cluster expansion of g(2) in reciprocal temperature beta is presented, the coefficients of which may be evaluated analytically due to the nature of the Gaussian potential. We present preliminary results concerning the convergence properties of this expansion. The analytical cluster expansion is related to numerical approximations for g(2) in the dense fluid regime by utilizing hypernetted chain, Percus-Yevick, and mean-field closures to the Ornstein-Zernike equation. Based on the results of these comparisons, we provide evidence in support of a decorrelation principle for the GCM in high Euclidean dimensions. In the solid phase, we consider the behavior of the freezing temperature T(f)(rho) in the limit rho-->+infinity and show T(f)(rho)-->0 in this limit for any d via a collective coordinate argument. Duality relations with respect to the energies of a lattice and its dual are then discussed, and these relations aid in the Maxwell double-tangent construction of phase coexistence regions between dual lattices based on lattice summation energies. The results from this analysis are used to draw conclusions about the ground-state structures of the GCM for a given dimension.

A new simple asymmetric hysteresis operator and its application to inverse control of piezoelectric actuators

Piezoelectric actuators (PEAs) are commonly used as micropositioning devices due to their high resolution, high stiffness, and fast frequency response. Because piezoceramic materials are ferroelectric, they fundamentally exhibit hysteresis behavior in their response to an applied electric field. The positioning precision can be significantly reduced due to nonlinear hysteresis effects when PEAs are used in relatively long range applications. This paper describes a new, precise, and simple asymmetric hysteresis operator dedicated to PEAs. The complex hysteretic transfer characteristic has been considered in a purely phenomenological way, without taking into account the underlying physics. This operator is based on two curves. The first curve corresponds to the main ascending branch and is modeled by the function f1. The second curve corresponds to the main reversal branch and is modeled by the function g2. The functions f(1) and g(2) are two very simple hyperbola functions with only three parameters. Particular ascending and reversal branches are deduced from appropriate translations of f(1) and g(2). The efficiency and precision of the proposed approach is demonstrated, in practice, by a real-time inverse feed-forward controller for piezoelectric actuators. Advantages and drawbacks of the proposed approach compared with classical hysteresis operators are discussed.

The problem of ideals of [formula omitted]: Beyond the exponent 3/2

The paper deals with the problem of ideals of H∞: describe increasing functions φ⩾0 such that for all bounded analytic functions f1,f2,…,fn,τ in the unit disc D the condition |τ(z)|⩽φ((∑|fk(z)|2)1/2)∀z∈D implies that τ belong to the ideal generated by f1,f2,…,fn, i.e. that there exist bounded analytic functions g1,g2,…,gn such that ∑k=1nfkgk=τ.

Comparison of Critical Exponents Determined by Rheology and Dynamic Light Scattering on Irreversible and Reversible Gelling Systems

AbstractSummary: The sol‐gel transition of a radical chain cross‐linking copoly‐merization system [N‐vinylcaprolactam/2‐hydroxylethyl methacrylate/allyl‐methacrylate] and various thermoreversible gelling systems (mixtures made of xanthan gum and locust bean gum as well as gelatin) have been studied using in‐situ time‐resolved dynamic light scattering (DLS) and in‐situ rheology. A critical dynamical behavior was observed near the sol‐gel transition, which is characterized by the presence of a power‐law spectra in the time‐intensity correlation function g2(t)−1 ∝ t−µ and in the low‐amplitude oscillatory shear experiment G′(ω) ∝ G″(ω) ∝ ωn. A comparison of the obtained critical dynamical exponents µ and n were made according to the theory by Doi and Onuki. This theory predicts a relation between these exponents, but up to now no detailed experimental comparison was done in the past. It was found that for all investigated systems n > µ.

Non-autonomous 2D Navier–Stokes System with Singularly Oscillating External Force and its Global Attractor

eρ g1 � x e , t � , x ∈ Ω R 2 , t ∈R,0 ρ 1. If the functions g 0(x, t) and g1 (z, t) are translation bounded in the corresponding spaces, then it is known that the global attractor A e is bounded in the space H, however, its normA e � H may be unbounded as e → 0+ since the magnitude of the external force is growing. Assuming that the function g1 (z, t) has a divergence represen- tation of the form g1 (z, t) = ∂z1 G1(z, t) + ∂z2 G2(z, t), z = (z1, z2) ∈ R 2 , where the functions G j (z, t) ∈ L b (R; Z ) (see Section 3), we prove that the global attractors A e of the N.-S. equations are uniformly bounded with respect to e :� A e � H C for all 0 <e 1. We also consider the "limiting" 2D N.-S. system with external force g0(x, t). We have found an estimate for the devia- tion of a solution u e (x, t) of the original N.-S. system from a solution u 0 (x, t) of the "limiting" N.-S. system with the same initial data. If the function g1 (z, t) admits the divergence representation, the functions g0(x, t) and g1 (z, t) are trans- lation compact in the corresponding spaces, and 0 ρ< 1, then we prove that the global attractors A e converges to the global attractor A 0 of the "limiting" system as e →0+ in the norm of H. In the last section, we present an estimate for the Hausdorff deviation of A e from A 0 of the form:distH (A e ,A 0 ) C(ρ)e 1−ρ in the case, when the global attractor A 0 is exponential (the Grashof number of the "limiting" 2D N.-S. system is small).

SPIN CONSTRAINTS ON REGGE PREDICTIONS AND PERTURBATIVE EVOLUTION IN HIGH ENERGY COLLISIONS

Two key issues in the application of perturbative QCD and Regge predictions to high energy processes are whether the hard and soft pomerons should be considered as two separate distinct exchanges and whether the Regge intercepts are Q2 independent or not. Models involving a distinct hard pomeron exchange predict much larger values for the LHC total cross-section. Here we argue that there is a polarized analogue of this issue in the isovector part of the spin structure function g1 and that the spin data appear to favour a distinct hard exchange.

Singlet structure function g1 at small x and small Q2

Explicit expressions for the singlet spin structure function g1 at small x and small Q2 are obtained with a total resummation of the leading logarithmic contributions. It is shown that g1 practically does not depend on x in this kinematic region. In contrast, it would be interesting to investigate its dependence on the invariant energy 2pq, because g1, being positive at small 2pq, can turn negative at greater values of this variable. The position of the turning point is sensitive to the ratio of the initial quark and gluon densities, so its experimental detection would enable one to estimate this ratio.

Decomposition formulas for the double hypergeometric functions G1 and G2

With the help of Burchnall and Chaundy operator method the Decomposition for Hypergeometric G1 (α; β1, β2; x, y), G2 (α1, α2, β1, β2; x, y) functions have been found. The obtained Decomposition consists of Hypergeometric of Appell’s functions. Further, the found decomposition is used for determination of Integral Representation such as Euler type of Hypergeometric G1 (α; β1, β2; x, y), G2 (α1, α2, β1, β2; x, y) functions.

Cubic elliptic functions

The function $$\displaylines{\displaystyle \Phi(\theta;q) = \theta + 3\sum_{k=1}^\infty\frac{\sin(2k\theta)q^k}{k(1+q^k+q^{2k})}}$$occurs in one of Ramanujan’s inversion formulas for elliptic integrals. In this article, a common generalization of the cubic elliptic functions $$\displaylines{g_1(\theta;q) = \frac{1}{6} + \sum_{k=1}^\infty \frac{q^k}{1+q^k+q^{2k}}\cos k\theta,\cr g_2(\theta;q) = \frac{1}{2} \frac{\sin \frac{\theta}{2}}{\sin \frac{3\theta}{2}} + \sum_{k=1}^\infty \frac{\chi_3(k)q^k}{1-q^k} \cos k\theta,} $$is given. The function g1 is the derivative of Ramanujan’s function Φ (after rescaling), and χ3(n) = 0, 1 or −1 according as n≡ 0, 1 or 2 (mod 3), respectively, and |q| < 1. Many properties of the common generalization, as well as the functions g1 and g2, are proved.

First experimental observation on different ionic states of isopropylthio ((CH 3) 2CHS) radical

A continuous beam of isopropylthio radical (CH3)2CHS was generated in the gas phase by the pyrolysis of isopropyl disulfide C3H7SSC3H7. The electronic structure of isopropylthio radical has been investigated by the in situ HeI photoelectron spectroscopy, in combination with density functional theory and G2 calculations. The first PE band at 8.95 eV with vibrational progression of 625 ± 60 cm−1 is designated as the X3A″ ground ionic state of (CH3)2CHS+, deriving from ionization of the electron from the SHOMO. Both photoelectron spectroscopy experiment and theoretical calculations provide evidence for the existence of different ionic states of isopropylthio radical for the first time.

Attractors of dissipative hyperbolic equations with singularly oscillating external forces

We study a uniform attractor $$\mathcal{A}^\varepsilon $$ for a dissipative wave equation in a bounded domain Ω ⋐ ℝn under the assumption that the external force singularly oscillates in time; more precisely, it is of the form g 0(x, t)+ e−α g 1 (x, t/e), x ∈ Ω, t ∈ ℝ, where α > 0, 0 < e ≤ 1. In E = H 0 1 × L 2, this equation has an absorbing set B e estimated as ‖B e‖ E ≤C 1+C 2e−α and, therefore, can increase without bound in the norm of E as e → 0+. Under certain additional constraints on the function g 1(x, z), x ∈ Ω, z ∈ ℝ, we prove that, for 0 < α ≤ α 0, the global attractors $$\mathcal{A}^\varepsilon $$ of such an equation are bounded in E, i.e., $$\parallel \mathcal{A}^\varepsilon \parallel _E \leqslant C_3 $$ , 0 < e ≤ 1. Along with the original equation, we consider a “limiting” wave equation with external force g 0(x, t) that also has a global attractor $$\mathcal{A}^0 $$ . For the case in which g 0(x, t) = g 0(x) and the global attractor $$\mathcal{A}^0 $$ of the limiting equation is exponential, it is established that, for 0 < α ≤ α 0, the Hausdorff distance satisfies the estimate $$dist_E (\mathcal{A}^\varepsilon ,\mathcal{A}^0 ) \leqslant C\varepsilon ^{\eta (\alpha )} $$ , where η(α) > 0. For η(α) and α 0, explicit formulas are given. We also study the nonautonomous case in which g 0 = g 0(x, t). It is assumed that sufficient conditions are satisfied for which the “limiting” nonautonomous equation has an exponential global attractor. In this case, we obtain upper bounds for the Hausdorff distance of the attractors $$\mathcal{A}^\varepsilon $$ from $$\mathcal{A}^0 $$ , similar to those given above.

SUM RULES AND MOMENTS OF THE NUCLEON SPIN STRUCTURE FUNCTIONS

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 δLT.