Eigenvalue bounds for a class of singular potentials in N dimensions

The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963] for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to N-dimensions. In particular a simple formula is derived which bounds the eigenvalues for the spiked harmonic oscillator potential V(x) = x^2 + lambda/x^alpha, alpha > 0, lambda > 0, and is valid for all discrete eigenvalues, arbitrary angular momentum ell, and spatial dimension N.Comment: 10 pages (plain tex with 2 ps figures). J.Phys.A:Math.Gen.(In Press

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision

Closed-form sums for some perturbation series involving associated Laguerre polynomials

Infinite series sum_{n=1}^infty {(alpha/2)_n / (n n!)}_1F_1(-n, gamma, x^2), where_1F_1(-n, gamma, x^2)={n!_(gamma)_n}L_n^(gamma-1)(x^2), appear in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic oscillator Hamiltonian H = -d^2/dx^2 + B x^2 + A/x^2 + lambda/x^alpha 0 0, A >= 0. It is proved that the series is convergent for all x > 0 and 2 gamma > alpha, where gamma = 1 + (1/2)sqrt(1+4A). Closed-form sums are presented for these series for the cases alpha = 2, 4, and 6. A general formula for finding the sum for alpha/2 = 2 + m, m = 0,1,2, ..., in terms of associated Laguerre polynomials, is also provided.Comment: 16 page

Memory of the Unjamming Transition during Cyclic Tiltings of a Granular Pile

Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phases description -strong and weak contact networks- for a granular system, as soon as it has approached the unjamming transition.Comment: 13 pages, 15 figures, soumis \`{a} Phys. Rev.

THE INFLUENCE OF SOCIAL MEDIA ON CONSUMERS PURCHASE DECISION: THE CASE OF QATAR

The consumer journey is highly influenced by social media as more people spent a significant portion of their time online. The increased understanding of how consumers make decisions has been widely studied and codified into models. Using the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) this study examines the extent of influence of social media marketing on consumer purchase decisions in Qatar and the challenges that could prevent the full utilization of social media marketing in Qatar. The study collected survey data from online users in Qatar based on a link shared on social media platforms. The results reveal the significant impact exerted by social media in molding consumer buying behaviors in Qatar. Although the nation has a high rate of social media participation, it lags behind worldwide trends in terms of online sales, indicating a notable discrepancy. Trust has a crucial role in influencing behavioral intentions, but perceived value also has a big influence on consumer choices. This research emphasizes the need for firms to customize marketing tactics to the distinctive social media environment in Qatar, recognizing the difficulties and possibilities inherent therein. The research provides detailed and valuable data that might be advantageous for companies, marketing professionals, and legislators that want to understand and improve Qatar's digital consumer ecosystem. It highlights the need of tailored marketing strategies that connect the online portrayal of a product or service with the actual number of sales. This involves resolving any differences that have been detected and making the most of the opportunities provided by social media to influence customer behavior

Biology of biomechanics: Finite Element Analysis of a Statically Determinate System to Rotate the Occlusal Plane for Correction of Skeletal Class III Openbite Malocclusion

Introduction In the absence of adequate animal or in-vitro models, the biomechanics of human malocclusion must be studied indirectly. Finite element analysis (FEA) is emerging as a clinical technology to assist in diagnosis, treatment planning, and retrospective analysis. The hypothesis tested is that instantaneous FEA can retrospectively simulate long-term mandibular arch retraction and occlusal plane rotation for the correction of a skeletal Class III malocclusion. Methods Seventeen published case reports were selected of patients treated with statically determinate mechanics using posterior mandible or infrazygomatic crest bone screw anchorage to retract the mandibular arch. Two-dimensional measurements were made for incisor and molar movements, mandibular arch rotation, and retraction relative to the maxillary arch. A patient with cone-beam computed tomography imaging was selected for a retrospective FEA. Results The mean age for the sample was 23.3 ± 3.3 years; there were 7 men and 10 women. Mean incisor movements were 3.35 ± 1.55 mm of retraction and 2.18 ± 2.51 mm of extrusion. Corresponding molar movements were retractions of 4.85 ± 1.78 mm and intrusions of 0.85 ± 2.22 mm. Retraction of the mandibular arch relative to the maxillary arch was 4.88 ± 1.41 mm. Mean posterior rotation of the mandibular arch was –5.76° ± 4.77° (counterclockwise). The mean treatment time (n = 16) was 36.2 ± 15.3 months. Bone screws in the posterior mandibular region were more efficient for intruding molars and decreasing the vertical dimension of the occlusion to close an open bite. The full-cusp, skeletal Class III patient selected for FEA was treated to an American Board of Orthodontics Cast-Radiograph Evaluation score of 24 points in about 36 months by en-masse retraction and posterior rotation of the mandibular arch: the bilateral load on the mandibular segment was about 200 cN. The mandibular arch was retracted by about 5 mm, posterior rotation was about 16.5°, and molar intrusion was about 3 mm. There was a 4° decrease in the mandibular plane angle to close the skeletal open bite. Retrospective sequential iterations (FEA animation) simulated the clinical response, as documented with longitudinal cephalometrics. The level of periodontal ligament stress was relatively uniform (<5 kPa) for all teeth in the mandibular arch segment. Conclusions En-masse retraction of the mandibular arch is efficient for conservatively treating a skeletal Class III malocclusion. Posterior mandibular anchorage causes intrusion of the molars to close the vertical dimension of the occlusion and the mandibular plane angle. Instantaneous FEA as modeled here could be used to reasonably predict the clinical results of an applied load

Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Synthesis of high-T_g hole-transporting polymers with different redox potentials and their performance in organic two-layer LEDs

Organic hole transport materials are used in organic LEDs, where they substantially improve device performance if placed as a hole transport layer (HTL) between the anode and the electroluminescent layer (EL). Soluble polymeric hole transport materials with high glass transition temperatures are of particular interest, because they allow for efficient device fabrication through spin casting of the HTL, and high glass transition temperatures have been found to improve thermal and long-term stability of the device. The redox potential of the hole transport material determines the facility of charge injection at the anode/HTL and the HTL/EL interfaces, thus affecting the overall device efficiency. We have synthesized a series of soluble hole-transporting polymers with glass transition temperatures in the range of 130 degrees C to 150 degrees C. The synthetic method allows facile substitution of the hole transport functionality with electron-withdrawing and electron-donating groups, which permits tuning of the redox potential of the polymer. These polymers have been used as HTL in tow-layer devices ITO/HTL/Alq/Mg. The maximum external quantum efficiency increase, if the redox potential is changed to facilitate reduction of the hole transport material at the HTL/EL interface. Electron-deficient derivatives show higher external quantum efficiencies. The device stability, however, follows the opposite trend

Coherent states associated to the wavefunctions and the spectrum of the isotonic oscillator

Classes of coherent states are presented by replacing the labeling parameter $z$ of Klauder-Perelomov type coherent states by confluent hypergeometric functions with specific parameters. Temporally stable coherent states for the isotonic oscillator Hamiltonian are presented and these states are identified as a particular case of the so-called Mittag-Leffler coherent states.Comment: 12 page