Pseudopotentials, tight-binding models, and k p theory have stood for many years as the standard techniques for computing electronic states in crystalline solids. Here, we present the first new method in decades, which we call atomistic k . p theory. In its usual formulation, k . p theory has the advantage of depending on parameters that are directly related to experimentally measured quantities, however, it is insensitive to the locations of individual atoms, We construct an atomistic k . p theory by defining envelope functions on a grid matching the crystal lattice, The model parameters are matrix elements which arc obtained from experimental results or ab natio wave functions in a simple way. This is in contrast to the other atomistic approaches in which parameters are fit to reproduce a desired dispersion and are not expressible in terms of fundamental quantities. This fitting is often very difficult. We illustrate our method by constructing a four-band atomistic model for a diamond/zinchlende crystal and show that it is equivalent to the sp(3) tight-binding model. We can thus directly derive the parameters in the sp(3) tight-binding model from experimental data, We then take the atomistic limit of the widely used eight-hand Kane model and compute the hand structures for all III V semiconductors not containing nitrogen or boron using parameters fit to experimental data. Our new approach extends k . p theory to problems in which atomistic precision is required, such as impurities, alloys, polytypes, and interfaces. It also provides a new approach to multiscale modeling by allowing continuum and atomistic k . p models to he combined in the same system, (C) 2015 AIP Publishing LLC
In this work, we investigate the production of the -resonance in the reaction within an effective Lagrangian approach. Especially, we explore the exchange considering two kinds of couplings and the exchange contributions. It is found that the angular distribution of the final K-0 and the spin state of the produced are sensitive to the production mechanisms and the characters can be used to distinguish the mechanisms of this reaction.
We present a model of K(-)p one-hadron-exchange potential. The hadrons being exchanged include sigma, rho, omega, Lambda and Sigma. The potential's parameters are determined by fitting to experimental data of K(-)p scattering, which are the spin-averaged differential cross sections. The energies being considered are between 51 MeV and 884 MeV. We calculate K(-)p scattering on a three-dimensional basis. The set of fitted parameters consists of cut-off parameters for the hadron form factors, sigma mass, and coupling constants
Du, Julia Q. D.
Liu, Edward Y. S.
Zhao, Jack C. D.
We present a unified approach to establish infinite families of congruences for p(k)(n) for arbitrary positive integer k, where p(k)(n) is given by the kth power of the Euler product Pi(infinity)(n=3D1) (1 - q(n))(k) =3D Sigma(infinity)(n=3D0) p(k)(n)q(n). For l is an element of {2, 3, 5, 7,13}, define xi(l) to be the least positive integer such that 24 vertical bar(l(2) - 1)xi(l) and delta(l)(m, k) the least non-negative integer satisfying 24 xi(-1)(l)delta(l)(m, k) (math) -k (mod l(m)). Using the Atkin U-operator, we find that the generating function of p(xi lk)(l(2 alpha)n + delta(l)(2 alpha, k)) (respectively, p(xi lk)(l(2 alpha+1)n + delta(l)(2 alpha + 2, k))) can be expressed as the product of an integral linear combination of modular functions on Gamma(0)(l) and Pi(infinity)(n=3D1) (1 - q(n))(xi lk) (respectively, Pi(infinity)(n=3D1) (1 - q(ln))(xi lk)) for any k > 0 and alpha >=3D 0. By investigating the properties of the modular equations of the lth order under the Atkin U-operator, we obtain that these generating functions are determined by some linear recurring sequences. Utilizing the periodicity of these linear recurring sequences modulo m, we are led to infinite families of congruences for p(xi lk)(n) modulo any m >=3D 2 with (m, l) =3D 1 and periodic relations between the values of p(xi lk)(n) modulo powers of l. As applications, infinite families of congruences for many partition functions such as l-core partition functions, the partition function and Andrews' spt-function are easily obtained.
This article describes and analyzes all existing algorithms for computing x =3D a(-1) omod pk THORN for a prime p, and also introduces a new algorithm based on the exact solution of linear equations using p-adic expansions. The algorithm starts with the initial value c =3D a(-1) omod pTHORN and iteratively computes the digits of the inverse x =3D a(-1) omod pk THORN in base p. The mod 2 version of the algorithm is more efficient than all existing algorithms for small values of k. Moreover, it stands out as being the only one that works for any p, any k, and digit-by-digit. While the new algorithm is asymptotically worse off, it requires the minimal number of arithmetic operations (just a single addition) per step, as compared to all existing algorithms.
The I >(1405) production in p + p collisions at 3.5 GeV and K--induced reactions is discussed. The shift of the measured spectral function of the I >(1405) in p + p reactions does not match either theoretical calculations for p + p reactions or experimental observation in previous K--induced reactions. New experiments with stopped and in-flight K (-) are needed to study this initial state more in detail. The state of the art of the analysis is discussed.
Huang, F.
Wang, A. C.
Wang, W. L.
Haberzettl, H.
Nakayama, K.
We use an effective Lagrangian approach in the tree-level approximation to analyze the high-precision cross-section data for reported by the CLAS Collaboration. Apart from the t-channel K, , exchanges, the s-channel nucleon (N) exchange, the u-channel , , exchanges, and the generalized contact current, we found that at least two nucleon resonances ('s) should be considered to well describe the high-precision cross-section data. One is the that is responsible for the shape of the angular distribution near the threshold via its interference with the t-channel K exchange, and the other could be one of the , , , and . The results for , T and P are predicated and it is pointed out that more data on these observables are needed to further pin down the resonance contents and their associated parameters in this reaction.
We propose a parametrization for interpreting some of the presently available data of the B-+/- -> K-+/- p (p) over bar decay, in particular those by the LHCb and Belle Collaborations. The model is inspired by the well-known current and transition contributions, usually assumed in this kind of decay. However, in the light of considerations as regards the dominant diagrams and final state interactions, we modify some parameters of the model, determining them by means of a best fit to the data. We show the results, which we discuss in some detail. Moreover, we give some predictions on other observables relative to the decays.
Let p(n, k) denote the number of partitions of n into parts less than or equal to k. We show several properties of this function modulo 2. First, we prove that for fixed positive integers k and m, p(n, k) is periodic modulo m. Using this, we are able to find lower and upper bounds for the number of odd values of the function for a fixed k.
In this paper, the goal is to reconstruct a tensor, i.e., a multi-dimensional array, when only subsets of its entries are observed. For well-posedness, the tensor is assumed to have a low-Tucker-rank structure. To estimate the underlying tensor from its partial observations, we first propose an estimator based on a newly defined balanced spectral (k, p)-support norm. To efficiently compute the estimator, we come up with a scalable algorithm for the minimization of the spectral (k, p)-support norm. Instead of directly solving the primal problem which involves full SVD in each iteration, the proposed algorithm benefits from the Lagrangian dual through minimizing the dual norm of the (k, p)-support norm which only computes the first k leading singular values and singular vectors in each iteration. To explore the statistical performance of the proposed estimator, upper bounds on the sample complexity and estimation error are then established. Simulation studies confirm that the error bounds can predict the scalable behavior of the estimation error. Experimental results on synthetic and real datasets demonstrate that the spectral (k, p)-support norm based method outperforms the nuclear norm based ones.
The foods in the diet contain a wide range of organic and inorganic compounds. Considering these from an elemental perspective, 5 so-called macroelements, calcium, potassium, sodium, phosphorus and chlorine, are contained in comparatively large quantities in foods compared to all other elements. This chapter attempts to review the importance of these dietary macroelements on oral health, and in particular their role in tooth loss, dental caries, erosive tooth wear and periodontal disease. Calcium and phosphate make up the bulk of the mineralized human tissues. Adequate intake of both is therefore of crucial importance in maintaining the health, function and retention of teeth and bones. Supplementation of the diet with calcium has also been shown to aid in maintaining and improving oral health. Several attempts have been made to lessen the erosive potential of beverages through calcium supplementation. Adequate calcium intake is also crucial for maintaining periodontal health. In many areas, however, the evidence is still emerging or controversial. Phosphate supplementation of the diet was once thought to decrease caries incidence, although studies in children were not successful. Furthermore, little attention has been paid to the other macroelements, highlighting the need for more well-controlled and comprehensive studies. =C2=A9 2020 S. Karger AG, Basel.