Symmetry breaking in the self-consistent Kohn-Sham equations

The Kohn-Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and this solution is a uniform particle density. We show that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C$_{60}$ molecule.Comment: a few typos eliminate

Implementation of an enhanced recovery protocol for open and laparoscopic repair of ventral hernia

In the light of introduction of the concept of rapid recovery and the use of miniinvasive methods of treatment of postoperative ventral hernias, laparoscopic herniology attracts more and more attention of practical surgeons. This is due to virtually no wound complications, a reduction of the duration surgery and inpatient stay, which greatly improves social and labor adaptation. Objective. Evaluate the benefits of laparoscopic hernioplasty over the open one in the light of the concept of rapid recovery of ERAS – enhanced recovery after surgery. Materials and methods. For a comparative evaluation in the period from 2015 to 2017, 81 patients with postoperative ventral hernias were examined and surgically treated. According to the methods of hernioplasty, all patients were divided into two groups. The group 1 consisted of 38 (46.91 %) persons who underwent laparoscopic hernioplasty. The group 2 consisted of 43 (53.09 %) persons who underwent "open" allohernioplasty. The multimodal patient management program provided for common elements for both groups aimed at rapid recovery in the postoperative period. Results. The average duration of "open" hernioplasty was (143±25) min, laparoscopic – (98±14) min. The laparoscopic technique of hernioplasty does not require routine drainage of the abdominal cavity. When open allohernioplasty drainage was performed in 72 (69.20 %) cases. 5–6 hours after the surgery, using the "sublay" technique 66 (63.50 %), patients were able to take the vertical position and activate the motor activity within the hospital ward, the rest – during the first day. The postoperative stay in the stanionarium in the group of patients after the "open" hernioplasty was on average (7.98±1.36) days, after the laparoscopic operation – (2.63±1.28) days, respectively. Conclusions. Endovideo-surgical methods for the elimination of primary and postoperative ventral hernias are effective, safe, provide early mobilization of patients and their rapid labor and social adaptation due to a significant smaller number of early and late complications. Restrictions in the use of these treatments are considered to be hernia of a gigantic size, especially postoperative with pronounced joint process and severe concomitant diseases, in which the increase in intraabdominal pressure will be critical and will negatively affect the immediate results of surgical treatment

An edge index for the Quantum Spin-Hall effect

Quantum Spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the Quantum Hall systems where the charge conductance of the edge modes is quantized, the spin conductance is not and it remained an open problem to find the observable whose edge current is quantized. In this paper, we define a particular observable and the edge current corresponding to this observable. We show that this current is quantized and that the quantization is given by the index of a certain Fredholm operator. This provides a new topological invariant that is shown to take same values as the Spin-Chern number previously introduced in the literature. The result gives an effective tool for the investigation of the edge channels' structure in Quantum Spin-Hall systems. Based on a reasonable assumption, we also show that the edge conducting channels are not destroyed by a random edge.Comment: 4 pages, 3 figure

Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms

In this paper we study the problem of uniqueness of solutions to the Hartree and Hartree-Fock equations of atoms. We show, for example, that the Hartree-Fock ground state of a closed shell atom is unique provided the atomic number $Z$ is sufficiently large compared to the number $N$ of electrons. More specifically, a two-electron atom with atomic number $Z\geq 35$ has a unique Hartree-Fock ground state given by two orbitals with opposite spins and identical spatial wave functions. This statement is wrong for some $Z>1$, which exhibits a phase segregation.Comment: 18 page

Model for Quantitative Estimation of Functionality Influence on the Final Value of a Software Product

The gap between software development requirements and available resources of software developers continues to widen. This requires changes in the development and organization of software development. This study introduced a quantitative software development management methodology that estimates the relative importance and risk of functionality retention or abundance, which determines the final value of the software product. The final value of a software product is interpreted as a function of its requirements and functionalities, represented as a computational graph (called a software product graph). The software product graph allows the relative importance of functionalities to be estimated by calculating the corresponding partial derivatives of the value function. The risk of not implementing functionality was estimated by reducing the product's final value. This model was applied to two EU projects, CareHD and vINCI. In vINCI, functionalities with the most significant added value to the application are developed based on the implemented model, and those related to the least value are abandoned. Optimization was not implemented in the CareHD project, and proceeded as initially designed. Consequently, only 71% of the CareHD potential value was achieved. The proposed model enables rational management and organization of software product development with real-time quantitative evaluation of functionalities impacts and, assessment of the risks of omitting them without a significant impact. Quantitative evaluation of the impacts and risks of retention or abundance is possible based on the proposed algorithm, which is the core of the model. This model is a tool for the rational organization and development of software products

MORPHOLOGICAL RESPONSE TO IMPLANTATION OF A POLYPROPYLENE MESH WITH A PRF MEMBRANE IN PATIENTS WITH POSTOPERATIVE VENTRAL HERNIA AND UNDIFFERENTIATED CONNECTIVE TISSUE DYSPLASIA

Background. Current herniology promotes the widespread usage of mesh implants in the primary treatment and, especially, in the for postoperative ventral hernias. Objective. The aim of the research was to study the morphological response of the tissues of muscular aponeurotic layer to implantation of a polypropylene mesh with using PRF membrane-enriched platelets in the patients with postoperative ventral hernia and concomitant undifferentiated dysplasia of connective tissues. Methods. The research involved 98 patients with postoperative ventral hernia, who underwent retro-muscular alogernioplasty by the Sublay technique of implantation of ‘light’ meshes, and a ‘light’ polypropylene mesh (PPM) in combination with a platelet-rich fibrin (PRF) membrane. The patients were divided into experimental groups according to the presence of undifferentiated connective tissue dysplasia syndrome. Results. Microscopic studies carried out after the implantation of a polypropylene mesh with a PRF membrane has proved that structural changes in connective tissues are like those of a polypropylene mesh, but they are less significant. There was a leukocyte infiltration near the mesh material, but its area was small. The enlargement and blood filling of the vessels of microcirculatory channel was a manifestation of the increased vascularization of this area. Conclusions. The usage of a polypropylene mesh in combination with a PRF membrane in the surgical treatment of postoperative ventral hernias reduces inflammatory changes in the tissues significantly and increases the activation of fibroblasts and signs of collagen fibers around the mesh material that is relevant especially for the patients with connective tissue pathology

Changes of pro- inflammatory and anti-inflammatory interleukins in cases of implantation of polypropylene meshes of different types in implant hernioplasty

The use of polypropylene meshes in the treatment of ventral and postoperative ventral hernias is uncontroversial. Their use is accompanied by a significant inflammatory response in the implantation area, contributes to the formation of a dense connective tissue capsule and, as a result, leads to shrinkage of the mesh. The issue of postoperative exudative complications that complicate the postoperative course much is topical. Objective. The aim of the research was to conduct a comparative evaluation of the results of the use of ‘light’, ‘heavy’ polypropylene meshes, as well as the ‘light’ one in combination with the PRF membrane, based on the study of the state of systemic indices of cytokines in retro-muscular allohernioplasty in the patients with primary and postoperative ventral hernia. Materials and methods. The research was based on the examination of 165 patients, who underwent surgery for primary and postoperative ventral hernia with the implantation of ‘light’, ‘heavy’ polypropylene meshes, as well as the ‘light’ one in combination with the PRF membrane. The study of systemic indices of cytokines in the serum of peripheral blood were conducted. The ratio of pro-inflammatory and anti-inflammatory interleukins TNF-α, IL-8 and IL-4 as well as the content of serum immunoglobulin (Ig) A was determined before the surgery, on the first day after the surgery, and on the day of discharge from the hospital (7-9th day of the postoperative period), in order to evaluate the stage and course of the immune response to the implantation of different types of polypropylene meshes. Results. On the day of discharge from the hospital, a decrease in the level of pro-inflammatory and anti-inflammatory cytokines in the main group was evidenced in the patients, who underwent implantation of the ‘light’ mesh as well as in those, who underwent implantation of the ‘light’ one in combination with the PRF membrane. In the patients, who underwent ‘heavy’ mesh implantation, a statistically significant increase in IL-8 and IL-4 levels was proved on the day of discharge from the hospital (