High order Fuchsian equations for the square lattice Ising model: χ(6)\chi^{(6)}

This paper deals with $\tilde{\chi}^{(6)}$, the six-particle contribution to the magnetic susceptibility of the square lattice Ising model. We have generated, modulo a prime, series coefficients for $\tilde{\chi}^{(6)}$. The length of the series is sufficient to produce the corresponding Fuchsian linear differential equation (modulo a prime). We obtain the Fuchsian linear differential equation that annihilates the "depleted" series $\Phi^{(6)}=\tilde{\chi}^{(6)} - {2 \over 3} \tilde{\chi}^{(4)} + {2 \over 45} \tilde{\chi}^{(2)}$. The factorization of the corresponding differential operator is performed using a method of factorization modulo a prime introduced in a previous paper. The "depleted" differential operator is shown to have a structure similar to the corresponding operator for $\tilde{\chi}^{(5)}$. It splits into factors of smaller orders, with the left-most factor of order six being equivalent to the symmetric fifth power of the linear differential operator corresponding to the elliptic integral $E$. The right-most factor has a direct sum structure, and using series calculated modulo several primes, all the factors in the direct sum have been reconstructed in exact arithmetics.Comment: 23 page

The Ising model and Special Geometries

We show that the globally nilpotent G-operators corresponding to the factors of the linear differential operators annihilating the multifold integrals $\chi^{(n)}$ of the magnetic susceptibility of the Ising model ($n \le 6$) are homomorphic to their adjoint. This property of being self-adjoint up to operator homomorphisms, is equivalent to the fact that their symmetric square, or their exterior square, have rational solutions. The differential Galois groups are in the special orthogonal, or symplectic, groups. This self-adjoint (up to operator equivalence) property means that the factor operators we already know to be Derived from Geometry, are special globally nilpotent operators: they correspond to "Special Geometries". Beyond the small order factor operators (occurring in the linear differential operators associated with $\chi^{(5)}$ and $\chi^{(6)}$), and, in particular, those associated with modular forms, we focus on the quite large order-twelve and order-23 operators. We show that the order-twelve operator has an exterior square which annihilates a rational solution. Then, its differential Galois group is in the symplectic group $Sp(12, \mathbb{C})$. The order-23 operator is shown to factorize in an order-two operator and an order-21 operator. The symmetric square of this order-21 operator has a rational solution. Its differential Galois group is, thus, in the orthogonal group $SO(21, \mathbb{C})$.Comment: 33 page

Mekanik olarak sentezlenen NiTi + Zn tozlarının karakterizasyonu ve sinterlenelebilirliğinin araştırılması

In this study; prealloyed NiTi powders and ball mills with 2%, 4%, 6%, 8% and 10% Zn powder ratios were subjected to mechanical milling for 60 minutes. The milled NiTi + Zn powder mixtures were pressed under 750 MPa pressurize and then sintered at 1000 degrees C for 60 minutes. In order to determine the microstructural changes in the samples which were milled, pressed and then sintered samples; SEM, EDS, DSC and XRD analyses were applied, respectively. Changes in powder morphology were observed, depending of the increasing Zn content in the NiTi + Zn powder mixtures and it was determined that the powders containing 10% Zn completely covered the surface of the NiTi powders in a homogeneous manner after milling.Zn content in the micro structure also provided the alloy to be sintered at low temperatures by completely filling the gaps and pores after the sintering process at 1000 degrees C for 60 min. In addition, a homogenous and smooth microstructure was obtained with NiTi + 10Zn% content

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

The Beta Ansatz: A Tale of Two Complex Structures

Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi-Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d’enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstraß elliptic functions. We present a counter example to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges

Towards the system-wide implementation of the International Classification of Functioning, Disability, and Health in routine clinical practice: Empirical findings of a pilot study from Mainland China

Objective: The aims of this study were to evaluate the feasibility of using the International Classification of Functioning, Disability and Health (ICF) Generic Set in routine clinical practice, and of creating a functioning score based on it, and, subsequently, to examine its sensitivity to change.Methods: In this prospective cohort study, data from 761 adult inpatients from 21 Chinese hospitals were analysed. Each patient was assessed at admission and discharge. Feasibility was evaluated by analysing mean assessment time. The Rasch model was used to create a metric of functioning. Sensitivity to change was analysed with mixed-effects regression and by calculating standardized effect size based on Cohen's f2.Results: Mean duration of assessment was 5.3 min, with a significant decrease between admission and discharge. After removal of the item remunerative employment, the remaining ICF Generic Set categories fitted the Rasch model well. With a mean improvement in functioning of 12.1(95% confidence interval (95% CI):11.5-12.6), this metric proved sensitive to change, both in terms of statistical significance (p < 0.001) and standardized effect size (Cohen's f2=2.35).Discussion: The ICF Generic Set is feasible for use in routine clinical practice and is promising to serve as the basis for the development of a functioning score that is sensitive to change.Chinese Mainland Affairs Offic

Symphytum Species: A Comprehensive Review on Chemical Composition, Food Applications and Phytopharmacology

Symphytum species belongs to the Boraginaceae family and have been used for centuries for bone breakages, sprains and rheumatism, liver problems, gastritis, ulcers, skin problems, joint pain and contusions, wounds, gout, hematomas and thrombophlebitis. Considering the innumerable potentialities of the Symphytum species and their widespread use in the world, it is extremely important to provide data compiling the available literature to identify the areas of intense research and the main gaps in order to design future studies. The present review aims at summarizing the main data on the therapeutic indications of the Symphytum species based on the current evidence, also emphasizing data on both the e cacy and adverse e ects. The present review was carried out by consulting PubMed (Medline), Web of Science, Embase, Scopus, Cochrane Database, Science Direct and Google Scholar (as a search engine) databases to retrieve the most updated articles on this topic. All articles were carefully analyzed by the authors to assess their strengths and weaknesses, and to select the most useful ones for the purpose of review, prioritizing articles published from 1956 to 2018. The pharmacological e ects of the Symphytum species are attributed to several chemical compounds, among them allantoin, phenolic compounds, glycopeptides, polysaccharides and some toxic pyrrolizidine alkaloids. Not less important to highlight are the risks associated with its use. In fact, there is increasing consumption of over-the-counter drugs, which when associated with conventional drugs can cause serious and even fatal adverse events. Although clinical trials sustain the folk topical application of Symphytum species in musculoskeletal and blunt injuries, with minor adverse e ects, its antimicrobial potency was still poorly investigated. Further studies are needed to assess the antimicrobial spectrum of Symphytum species and to characterize the active molecules both in vitro and in vivo

Prospects for progress on health inequalities in England in the post-primary care trust era : professional views on challenges, risks and opportunities

Background - Addressing health inequalities remains a prominent policy objective of the current UK government, but current NHS reforms involve a significant shift in roles and responsibilities. Clinicians are now placed at the heart of healthcare commissioning through which significant inequalities in access, uptake and impact of healthcare services must be addressed. Questions arise as to whether these new arrangements will help or hinder progress on health inequalities. This paper explores the perspectives of experienced healthcare professionals working within the commissioning arena; many of whom are likely to remain key actors in this unfolding scenario. Methods - Semi-structured interviews were conducted with 42 professionals involved with health and social care commissioning at national and local levels. These included representatives from the Department of Health, Primary Care Trusts, Strategic Health Authorities, Local Authorities, and third sector organisations. Results - In general, respondents lamented the lack of progress on health inequalities during the PCT commissioning era, where strong policy had not resulted in measurable improvements. However, there was concern that GP-led commissioning will fare little better, particularly in a time of reduced spending. Specific concerns centred on: reduced commitment to a health inequalities agenda; inadequate skills and loss of expertise; and weakened partnership working and engagement. There were more mixed opinions as to whether GP commissioners would be better able than their predecessors to challenge large provider trusts and shift spend towards prevention and early intervention, and whether GPs’ clinical experience would support commissioning action on inequalities. Though largely pessimistic, respondents highlighted some opportunities, including the potential for greater accountability of healthcare commissioners to the public and more influential needs assessments via emergent Health & Wellbeing Boards. Conclusions - There is doubt about the ability of GP commissioners to take clearer action on health inequalities than PCTs have historically achieved. Key actors expect the contribution from commissioning to address health inequalities to become even more piecemeal in the new arrangements, as it will be dependent upon the interest and agency of particular individuals within the new commissioning groups to engage and influence a wider range of stakeholders.</p