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Abstract We compute the potential-graviton contribution to the scattering amplitude, the radial action, and the scattering angle of two extremal black holes in N $$ \mathcal{N} $$ = 8 supergravity at the fifth post-Minkowskian order and to next-to-leading order in a large mass expansion (first self-force order). Properties of classical unitarity cuts allow us to focus on the integration-by-parts reduction of planar integrals, while nonplanar integrals at this order are obtained from the planar ones by straightforward manipulations. We present the solution to the differential equations for all master integrals necessary to evaluate the classical scattering amplitudes of massive scalar particles at this order in all gravitational theories, in particular in N $$ \mathcal{N} $$ = 8 supergravity, and in general relativity. Despite the appearance of higher-weight generalized polylogarithms and elliptic functions in the solution to the differential equation for master integrals, the final supergravity answer is remarkably simple and contains only (harmonic) polylogarithmic functions up to weight 2. The systematic analysis of elliptic integrals discussed here, as well as the particular organization of boundary integrals in N $$ \mathcal{N} $$ = 8 observables are independent of supersymmetry and may have wider applications, including to aspects of collider physics.

Abstract We study the small-mass asymptotic behavior of so-called angular integrals, appearing in phase-space calculations in perturbative quantum field theory. For this purpose we utilize the strategy of expansion by regions, which is a universal method both for multiloop Feynman integrals and various parametric integrals. To apply the technique to angular integrals, we convert them into suitable parametric integral representations, which are accessible to existing automation tools. We use the code asy.m to reveal regions contributing to the asymptotic expansion of angular integrals. To evaluate the contributions of these regions in an epsilon expansion we apply the method of Mellin-Barnes representation. Our approach is checked against existing results on angular integrals revealing a connection between contributing regions and angular integrals constructed from an algebraic decomposition. We explicitly calculate the previously unknown asymptotics for angular integrals with three and four denominators and formulate a conjecture for the leading asymptotics and the pole part for a general number of denominators and masses.

Abstract We present analytical results for all master integrals for massless three-point functions, with one off-shell leg, at four loops. Our solutions were obtained using differential equations and direct integration techniques. We review the methods and provide additional details.

The objective of the current experimental study is to investigate influence of dissimilar welding between 316 L Austenitic and 202 Austenitic Stainless Steel. This is achieved through the utilization of Cold Metal Transfer (CMT) Welding in conjunction with the GTAW mode. Various welding approaches are employed, including the use of ER316L and ER309L fillers, as well as a no-filler (autogenous) welding technique. Microstructural observation shows martensitic formation in the interface region. The tensile test was conducted by using Universal Testing Machine for the weldment and found that ER316L filler (721 MPa) has higher strength than ER309L (672 MPa) and autogenous weld (528 MPa). Charpy impact test was used to determine toughness of the weldment and found that ER309L Filler weld has toughness (87 J) which is higher than ER316L filler weld (5 4 J) and autogenous weld (23 J). Vicker's hardness test shows that autogenous weld hardness (avg. 193.34 HV) which is highest than ER309L filler (avg.188 HV) and ER316L filler weld (avg. 184.67 HV). The intergranular corrosion test by double loop electrochemical potentiokinetic reactivation (DLEPR) test shows sensitization at highest degree for autogenous weld (18.25 %) than ER316L filler weld (9.22 %) and ER309L filler weld (7.28 %).

Aluminium alloys are indispensable in all manufacturing industries, particularly mechanical engineering. The objective of this study is to enhance the mechanical, wear, and corrosion properties of aluminium alloy AA5083 by incorporating nanoparticles as reinforcements, thereby creating hybrid aluminium nanocomposites. The base material utilised in this study was AA5083, with the reinforcement nanoparticles selected as Carbon nanotubes (CNTs) and Molybdenum disulfide (MoS2) at concentrations of 5 % and 3 % respectively. Nanocomposites were fabricated using the Powder Metallurgy (PM) technique, employing specific contrasting parameters including Ball mill speed (280, 320, 360, and 400 rpm), Mixing time (20, 30, 40, and 50 min), Compaction pressure (300, 350, 400, and 450 MPa), and Sintering time (2, 3, 4, and 5 h). The operating parameters of powder metallurgy were assessed using the Design of Experiments (DOE) L16 Orthogonal Array, and their corresponding outcomes were analyzed. The results revealed that there is a significant correlation between the mixing time and microhardness of the nanocomposites. The wear and corrosion reduction rates had a significant impact on the sintering time parameter. The present study determined that the highest recorded microhardness value was 136 VHN, while the lowest observed rates of wear and corrosion were 0.192 mm3/m and 0.00081 mm/year, respectively. Scanning electron microscopy (SEM) images clearly depicted the presence of various structural defects, such as pits, cracks, delamination, voids, and cusps, in the wear and corrosion samples that exhibited reduced strength.

This investigation deals with the microstructural and mechanical behaviours of friction stir processed (FSPed) commercially available pure magnesium with different tool profile geometry. The micro-level properties were assessed through in-situ micro-pillar compression which showed that FSPed material experienced significant plastic deformation and even re-distribution of residual oxide particles which was present in the cast magnesium together with grain refinement (from 3.4 μm to 2.6–2.7 μm). These changes in microstructure contributed to raise the compressive and yield strengths of the FSPed magnesium, up to 99 MPa and 94 MPa respectively, compared to 33 MPa of cast magnesium, when triangular tool profile was employed. Furthermore, the deformed material acquires ductile breakage with improved plasticity (micro-necking) irrespective of processing conditions, that is, either cast or friction stir processed.

We calculate the total Born cross section of the e+e−-pair production by an electron in the field of a nucleus (trident process) using the modern multiloop methods. For general energies we obtain the cross section in terms of converging power series. The threshold asymptotics and the high-energy asymptotics are obtained analytically. In particular, we obtain an additional contribution to the Racah formula due to the identity of the final electrons. Besides, our result for the leading term of the high-energy asymptotics reveals a typo in an old Racah paper.

Abstract We present the Sudakov form factor in full color N $$ \mathcal{N} $$ = 4 supersymmetric Yang- Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight.

Abstract We compute ε-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of transcendental weight nine. Our method is the glue-and-cut technique from Baikov and Chetyrkin, which proves extremely effective in that it determines all expansion coefficients to this order in terms of recursively one-loop integrals and only one further integral. We observe that our results are compatible with conjectures that predict π-dependent contributions.

Abstract We analytically evaluate the master integrals for the second type of planar contributions to the massive two-loop Bhabha scattering in QED using differential equations with canonical bases. We obtain results in terms of multiple polylogarithms for all the master integrals but one, for which we derive a compact result in terms of elliptic multiple polylogarithms. As a byproduct, we also provide a compact analytic result in terms of elliptic multiple polylogarithms for an integral belonging to the first family of planar Bhabha integrals, whose computation in terms of polylogarithms was addressed previously in the literature.

This paper proposes two different approaches to studying resistive switching of oxide thin films using scratching probe nanolithography of atomic force microscopy (AFM). These approaches allow us to assess the effects of memristor size and top-contact thickness on resistive switching. For that purpose, we investigated scratching probe nanolithography regimes using the Taguchi method, which is known as a reliable method for improving the reliability of the result. The AFM parameters, including normal load, scratch distance, probe speed, and probe direction, are optimized on the photoresist thin film by the Taguchi method. As a result, the pinholes with diameter ranged from 25.4 ± 2.2 nm to 85.1 ± 6.3 nm, and the groove array with a depth of 40.5 ± 3.7 nm and a roughness at the bottom of less than a few nanometers was formed. Then, based on the Si/TiN/ZnO/photoresist structures, we fabricated and investigated memristors with different spot sizes and TiN top contact thickness. As a result, the HRS/LRS ratio, USET, and ILRS are well controlled for a memristor size from 27 nm to 83 nm and ranged from ~8 to ~128, from 1.4 ± 0.1 V to 1.8 ± 0.2 V, and from (1.7 ± 0.2) × 10−10 A to (4.2 ± 0.6) × 10−9 A, respectively. Furthermore, the HRS/LRS ratio and USET are well controlled at a TiN top contact thickness from 8.3 ± 1.1 nm to 32.4 ± 4.2 nm and ranged from ~22 to ~188 and from 1.15 ± 0.05 V to 1.62 ± 0.06 V, respectively. The results can be used in the engineering and manufacturing of memristive structures for neuromorphic applications of brain-inspired artificial intelligence systems.

Abstract We compute the two-loop mixed QCD-Electroweak (QCD-EW) corrections to the production of a Higgs boson and a gluon in gluon fusion through a loop of light quarks. The relevant four-point functions with internal massive propagators are expressed as multiple polylogarithms with algebraic arguments. We perform the calculation by integration over Feynman parameters and, independently, by the method of differential equations. We compute the two independent helicity amplitudes for the process and we find that they are both finite. Moreover, we observe a weight drop when all gluons have the same helicity. We also provide a simplified expression for the all-plus helicity amplitude, which is optimised for fast and reliable numerical evaluation in the physical region.

Abstract We compute all master integrals for massless three-loop four-particle scattering amplitudes required for processes like di-jet or di-photon production at the LHC. We present our result in terms of a Laurent expansion of the integrals in the dimensional regulator up to 8th power, with coefficients expressed in terms of harmonic polylogarithms. As a basis of master integrals we choose integrals with integrands that only have logarithmic poles — called dlog forms. This choice greatly facilitates the subsequent computation via the method of differential equations. We detail how this basis is obtained via an improved algorithm originally developed by one of the authors. We provide a public implementation of this algorithm. We explain how the algorithm is naturally applied in the context of unitarity. In addition, we classify our dlog forms according to their soft and collinear properties.

The creation of sustainable power sources for wearable electronics and self-powered systems is a promising direction of modern electronics. At the moment, a search for functional materials with high values of piezoelectric coefficient and elasticity, as well as non-toxicity, is underway to generate such power sources. In this paper, nitrogen-doped carbon nanotubes (N-CNTs) are considered as a functional material for a piezoelectric nanogenerator capable of converting nanoscale deformations into electrical energy. The effect of defectiveness and of geometric and mechanical parameters of N-CNTs on the current generated during their deformation is studied. It was established that the piezoelectric response of N-CNTs increased nonlinearly with an increase in the Young’s modulus and the aspect ratio of the length to diameter of the nanotube and, on the contrary, decreased with an increase in defectiveness not caused by the incorporation of nitrogen atoms. The advantages of using N-CNT to create energy-efficient piezoelectric nanogenerators are shown.

Abstract We analytically compute the four-loop QCD corrections for the colour structure (d F abcd )2 to the massless non-singlet quark form factor. The computation involves non-trivial non-planar integral families which have master integrals in the top sector. We compute the master integrals by introducing a second mass scale and solving differential equations with respect to the ratio of the two scales. We present details of our calculational procedure. Analytical results for the cusp and collinear anomalous dimensions, and the finite part of the form factor are presented. We also provide analytic results for all master integrals expanded up to weight eight.

Abstract We discuss the status of expansion by regions, i.e. a well-known strategy to obtain an expansion of a given multiloop Feynman integral in a given limit where some kinematic invariants and/or masses have certain scaling measured in powers of a given small parameter. Using the Lee–Pomeransky parametric representation, we formulate the corresponding prescriptions in a simple geometrical language and make a conjecture that they hold even in a much more general case. We prove this conjecture in some partial cases.

This article presents the results of experimental studies of the impact of electrode material and the effect of nanoscale film thickness on the resistive switching in forming-free nanocrystalline ZnO films grown by pulsed laser deposition. It was demonstrated that the nanocrystalline ZnO film with TiN, Pt, ZnO:In, and ZnO:Pd bottom electrodes exhibits a nonlinear bipolar effect of forming-free resistive switching. The sample with Pt showed the highest resistance values RHRS and RLRS and the highest value of Uset = 2.7 ± 0.4 V. The samples with the ZnO:In and ZnO:Pd bottom electrode showed the lowest Uset and Ures values. An increase in the number of laser pulses from 1000 to 5000 was shown to lead to an increase in the thickness of the nanocrystalline ZnO film from 7.2 ± 2.5 nm to 53.6 ± 18.3 nm. The dependence of electrophysical parameters (electron concentration, electron mobility, and resistivity) on the thickness of the forming-free nanocrystalline ZnO film for the TiN/ZnO/W structure was investigated. The endurance test and homogeneity test for TiN/ZnO/W structures were performed. The structure Al2O3/TiN/ZnO/W with a nanocrystalline ZnO thickness 41.2 ± 9.7 nm was shown to be preferable for the manufacture of ReRAM and memristive neuromorphic systems due to the highest value of RHRS/RLRS = 2307.8 ± 166.4 and low values of Uset = 1.9 ± 0.2 V and Ures = −1.3 ± 0.5 V. It was demonstrated that the use of the TiN top electrode in the Al2O3/TiN/ZnO memristor structure allowed for the reduction in Uset and Ures and the increase in the RHRS/RLRS ratio. The results obtained can be used in the manufacturing of resistive-switching nanoscale devices for neuromorphic computing based on the forming-free nanocrystalline ZnO oxide films.

Abstract This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an ϵ-expansion series with numerical coefficients. The algorithm is based on using generalized power series expansions near singular points of the differential system, solving difference equations for the corresponding coefficients in these expansions and using matching to connect series expansions at two neighboring points. Here we use our algorithm and the corresponding code for our example of four-loop generalized sunset diagrams with three massive and tw massless propagators, in order to obtain new analytical results. We analytically evaluate the master integrals at threshold, p 2 = 9m 2, in an expansion in ϵ up to ϵ 1. With the help of our code, we obtain numerical results for the threshold master integrals in an ϵ-expansion with the accuracy of 6000 digits and then use the PSLQ algorithm to arrive at analytical values. Our basis of constants is build from bases of multiple polylogarithm values at sixth roots of unity.

Abstract We compute the three-loop QCD corrections to the massive quark form factors with external vector, axial-vector, scalar and pseudo-scalar currents. All corrections with closed loops of massless fermions are included. The non-fermionic part is computed in the large-N c limit, where only planar Feynman diagrams contribute.

Abstract We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ϵ.

Abstract We compute the three-loop QCD corrections to the massive quark-anti-quark-photon form factors F 1 and F 2 involving a closed loop of massless fermions. This subset is gauge invariant and contains both planar and non-planar contributions. We perform the reduction using FIRE and compute the master integrals with the help of differential equations. Our analytic results can be expressed in terms of Goncharov polylogarithms. We provide analytic results for all master integrals which are not present in the large-N c calculation considered in refs. [1, 2].

Abstract We compute the four-loop QCD corrections to the massless quark-anti-quark-photon form factor F q in the large-N c limit. From the pole part we extract analytic expressions for the corresponding cusp and collinear anomalous dimensions.

Human umbilical cord blood mononuclear cells (HUCBMCs) are used as the common or adjuvant therapy to treat about 80 different diseases. This is determined by high proliferative activity of cells, low immunogenicity and the possibility of selecting rare HLA types for transplants. In this regard, assessing the cellular material in protocols of immunopharmacology is relevant. Objective: to study the allergenic and immunotoxic effects of mononuclear cells of human umbilical cord-placental blood in the preclinical testing on animals. Materials and methods: 1. The study of type I hypersensitivity to HUCBMCs was carried out using a standard method for assessing bronchospasm in the trachea of male and female guinea pigs. Samples of tracheal sections were incubated in Ringer-Tyrode solution with concentration of mononuclear cell suspension 2.5 %, positive control – histamine hydrochloride. 2. Antibody detection to HUCBMCs was carried out on male mice of the CBAxC57B2/6 line using the complement fixation test (indication – absence of hemolysis of sheep erythrocytes). Mice were administrated single intravenous injection of cell material at 10, 50 and 100-fold the therapeutic dosage for humans (8.57∙107, 4.28∙108, 8.57∙108 cells/kg body weight (b.w.), respectively); blood for analysis was taken 21 days after the administration of the biomaterial. Positive control – serum from mice immunized with St. aureus. 3. A study of the phagocytic activity of neutrophils was carried out on male and female Wistar rats, which were administered a single intravenous injection of HUCBMCs at 10-fold therapeutic dosage. After 30 days, the phagocytic index and phagocytic number were studied using the ink test method and analyzing 600 cells for each group. The median, upper and lower quartiles (Me (C25-C75)) were calculated; hypotheses were compared using the Mann-Whitney U test. Results: we didn't detect anaphylactogenic activity and production of antibodies to cellular material after administration of HUCBMCs to animals. In female rats, the phagocytic activity of neutrophils increased statistically significantly (p = 0.004) relative to control animals (56.5 (53.8-60.8) and 44.0 (40.5-47.5), respectively); in male rats there was a tendency to increase phagocytic activity by 13 % (p = 0.054). The phagocytic index in all compared groups remained in the zone of fluctuations of standard values of 1.8 – 2.0. Conclusion: Human umbilical cord blood mononuclear cells do not have an anaphylactogenic, and at 100-fold at the therapeutic dosage (8.57∙108 cells/kg) an immunotoxic effect, but contribute to increase of phagocytic activity of neutrophils, which requires further preclinical and clinical trials of the effectiveness and safety of the use of biomaterial with high therapeutic potential.

We have experimentally studied the influence of pulsed laser deposition parameters on the morphological and electrophysical parameters of vanadium oxide films. It is shown that an increase in the number of laser pulses from 10,000 to 60,000 and an oxygen pressure from 3 × 10−4 Torr to 3 × 10−2 Torr makes it possible to form vanadium oxide films with a thickness from 22.3 ± 4.4 nm to 131.7 ± 14.4 nm, a surface roughness from 7.8 ± 1.1 nm to 37.1 ± 11.2 nm, electron concentration from (0.32 ± 0.07) × 1017 cm−3 to (42.64 ± 4.46) × 1017 cm−3, electron mobility from 0.25 ± 0.03 cm2/(V·s) to 7.12 ± 1.32 cm2/(V·s), and resistivity from 6.32 ± 2.21 Ω·cm to 723.74 ± 89.21 Ω·cm. The regimes at which vanadium oxide films with a thickness of 22.3 ± 4.4 nm, a roughness of 7.8 ± 1.1 nm, and a resistivity of 6.32 ± 2.21 Ω·cm are obtained for their potential use in the fabrication of ReRAM neuromorphic systems. It is shown that a 22.3 ± 4.4 nm thick vanadium oxide film has the bipolar effect of resistive switching. The resistance in the high state was (89.42 ± 32.37) × 106 Ω, the resistance in the low state was equal to (6.34 ± 2.34) × 103 Ω, and the ratio RHRS/RLRS was about 14,104. The results can be used in the manufacture of a new generation of micro- and nanoelectronics elements to create ReRAM of neuromorphic systems based on vanadium oxide thin films.

We experimentally investigated the effect of post-growth annealing on the morphological, structural, and electrophysical parameters of nanocrystalline ZnO films fabricated by pulsed laser deposition. The influence of post-growth annealing modes on the electroforming voltage and the resistive switching effect in ZnO nanocrystalline films is investigated. We demonstrated that nanocrystalline zinc oxide films, fabricated at certain regimes, show the electroforming-free resistive switching. It was shown, that the forming-free nanocrystalline ZnO film demonstrated a resistive switching effect and switched at a voltage 1.9 ± 0.2 V from 62.42 ± 6.47 (RHRS) to 0.83 ± 0.06 kΩ (RLRS). The influence of ZnO surface morphology on the resistive switching effect is experimentally investigated. It was shown, that the ZnO nanocrystalline film exhibits a stable resistive switching effect, which is weakly dependent on its nanoscale structure. The influence of technological parameters on the resistive switching effect in a forming-free ZnO nanocrystalline film is investigated. The results can be used for fabrication of new-generation micro- and nanoelectronics elements, including random resistive memory (ReRAM) elements for neuromorphic structures based on forming-free ZnO nanocrystalline films.

Perinatal pathologies and foremost perinatal central nervous system injury are attended with delayed neurosomatic disorders frequently leading to disability. The success of realisation of individual compensation potential of every child depends on dynamics analysis of patient's condition on every survey stage, personalized choice of necessary and sufficient methods of polysystemic diseases correction. The contemporary view on ethiology and pathogenesis of main perinatal pathologies are presented in this review, main mechanisms of its development are also revealed. Recent non-invasive diagnostic technique allow to perform correction of vital signs and prevent cascade reactions of neuronal apoptosis. The sanogenetic importance of some therapeutic interventions (therapeutic hypothermia, erythropoietin, caffeine) is established in early neonatal period. The role of implementation of external factors causing epigenetic effects is clear: optimal nutrition, correction of intestinal microbiota, sensory and motional stimulation. The abilitation success depends largely on successive team activity of specialists and their collaboration with the family. Methods of multifactorial statistical analysis allow not only to prognosticate the outcomes of perinatal affection, but also to create effective mathematical models for personalized choice of facilitation measures.

The paper assesses the current state and development trends of the social service system. The authors presented the current scheme of the system of social services in Russia and determined that it includes the budgetary, non-profit and commercial sectors. In particular, it is shown that the dominant sector providing social services is the public sector. However, despite the dominant role of the public sector in the provision of social services, in recent years there has been a tendency towards an increasing role of the sector of non-profit (non-budget) and commercial organizations, which have different principles of pricing for social services. For a more complete description and development trends of the social services system in the Russian Federation, the authors determined the most important indicators characterizing the functioning of the social service system and the provision of social services to the population. For a quantitative assessment, a regression model of the dependence of these indicators was created. Analysis of the data in the table shows that, on average, over the past 3 years, the number of recipients of social services in the stationary form of social services has de-creased by 2% per year, while in the form of social services at home it has grown by 0.25% per year. The authors determined, that in the future, the demand for inpatient social services will be within the range of recent years, which should not increase the load on the system.

Background: Patient registries help to obtain relevant information about the peculiarities of certain diseases, as well as the safety and effectiveness of different medical technologies. Moreover, it allows conducting a continuous monitoring in a studied group. Objective: to analyze the effectiveness and safety of a long-term target therapy with Omalizumab (more than 4 years) in children with severe persistent uncontrolled asthma based on the electronic clinical cases database (registry). Methods. The outcomes of the treatment were evaluated based on the data from the registry of patients with severe uncontrolled asthma. Time period: November 2007- March 2018. The main goal of the research was to identify the number of patients who achieved the disease control (20 points С-АСТ-test in children aged 6–11 years or 25 points АСТ-test in children aged 12–17 years) at least in one of the time points — in 4; 6; 12 or 48 months. Results. The results of the treatment of 26 children were analyzed (males — 73%), median age — 17 years. The posology of Omalizumab was 75 to 600 mg, median (Me) 300 mg [225; 375]. Asthma control test (ACT) before the start of the treatment was 14 points (Me 14 [12; 17,5], in 48 mo — 21 points (Me 22 [20; 24]; p=0,0017). The decrease of the amount of the daily therapy was demonstrated. The median dose of the ICS (fluticasone) was 575 mcg/day (Me 500 [437,5; 750]) before the start of the treatment, in 48 mo — 492 mcg/day (Me 500 [250; 562,5]; p=0,066). The decrease of the number of exacerbations and the use of SABA from 12 (Me 10,5 [9,75; 13,25]) to 0,8 times/month (Me [1; 0;1]) was observed after 4 years of treatment (р=0,000). No adverse events were observed. Conclusions. Long-term therapy with Omalizumab increases the disease control in children with severe persistent asthma. The registry as a continuous monitoring tool enables to conduct a complex evaluation of the effectiveness and safety of the treatment.