Universal Formula Research Articles

Synchronization dynamics of phase oscillators with generic adaptive coupling

Adaptive coupling schemes among interacting elements are ubiquitous in real systems ranging from physics and chemistry to neuroscience and have attracted much attention in recent years. Here, we extend the Kuramoto model by considering a particular adaptive scheme in a system of globally coupled oscillators. The homogeneous coupling is correlated with the global coherence of the population that is weighted by the generic nonlinear feedback function of the amplitude of the order parameter. The studied model is analytically tractable that generalizes the theory of Kuramoto for synchronization transition. We develop a mean-field theory by establishing the self-consistent equation describing the stationary dynamics in the thermodynamic limit. Importantly, the Landau damping effect, which turns out to be far more generic, is revealed in the framework of the linear stability analysis of the resonant pole theory. Furthermore, the relaxation rate of the order parameter in the subcritical region is obtained from a universal formula. Our study can deepen the understanding of synchronization transitions and other related collective dynamics in networked oscillators with adaptive interaction schemes.

Posterior Corneal Asphericity and the Refractive Outcome after Combined Phacovitrectomy

We assessed the correlation of posterior corneal asphericity and the refractive prediction error of the SRK-T and Barrett II Universal formulas for eyes following phacovitrectomy with peeling of the internal limiting membrane (ILM). We retrospectively analyzed 41 eyes of 41 patients following a combined phacovitrectomy with ILM peeling. Surgeries were performed by one fellowship-trained vitreoretinal surgeon between 2016 and 2021. Of the 41 patients, 41 eyes were included, with all having at least 1 month of postoperative data. Of the 41 eyes, 19 eyes were female (46%) and 22 were male (54%). The average age of the study population was 77.5 ± 10.7 years. The mean axial length (AL) was 22.7 ± 4.6 mm and the mean anterior chamber depth (ACD) was 3 ± 0.8 mm. The mean posterior Q value was - 0.29 ± 0.27. The mean absolute error (MAE) values 1-month postoperatively for the SRK-T and Barrett II Universal formulas were 0.73 and 0.65, respectively. Regression analysis yielded a significant correlation between posterior corneal asphericity and SRK-T MAE (r = 0.35, R2 = 0.12, p < 0.05) only. Posterior corneal surface asphericity is correlated to the refractive error of the SRK-T formula for eyes following phacovitrectomy.

Many-body coupled oscillator system with quadratic non-linearity

The present work investigates a system of N, one-dimensional classical coupled anharmonic oscillators with quadratic repulsive and linear attractive forces.Theoretical studies started on the basis of the Fourier transform of dynamical equations, to which both statistical and variational methods were applied. A new approach is proposed to obtain the frequency distribution using periodic test functions.Numerical calculations were carried out for N = 1, 2, 20, 100, which revealed a distribution of frequencies with non-zero broadening. The analytical and calculated results showed agreement, both pointing to a universal formula for the average period, as a function of non-linearity, the number of oscillators, and an amplitude factor.

Randomized double-blind pilot study of universal, species abundant, multiallergen subcutaneous immunotherapy for moderate-severe allergic rhinitis

BackgroundAllergic rhinitis affects approximately 10% to 20% of people living in industrialized nations leading to significant morbidity and large health care expenditures. Individualized high-dose, single-species allergen immunotherapy has been found to be effective in treating allergic rhinitis but can be associated with significant risks including anaphylaxis. Few studies have evaluated the safety and efficacy of universal low-dose multiallergen immunotherapy (MAIT). ObjectiveTo determine the efficacy and safety of a universal MAIT formula for the treatment of allergic rhinitis. MethodsPatients with moderate-severe perennial and seasonal allergic rhinitis were randomized in a double-blind, placebo-controlled fashion to receive a novel, subcutaneous MAIT regimen containing a unique mixture of more than 150 aeroallergens, including several cross-reactive species. All patients received the exact same universal immunotherapy formula regardless of which specific skin tests were positive. Primary outcome measures at 8 and 12 weeks of therapy included validated clinical assessments, total nasal sinus score and mini-rhinoconjunctivitis quality of life questionnaire, and the use of rescue medications. ResultsA total of 31 patients (n = 31) were randomized to receive MAIT vs placebo. By week 12, MAIT resulted in a −4.6 (−58%) decrease in the combined total nasal sinus score and rescue medication score (daily combined score) compared with −1.5 (−20%) for placebo (P = .04). Likewise, MAIT resulted in a decrease in the mini-rhinoconjunctivitis quality of life questionnaire score of −34.9 (−68%) compared with −17 (−42%) for the placebo (P = .04). Mild adverse events were uncommon and with similar frequency among the groups. ConclusionA novel, universal, and high-species abundant MAIT formula was well tolerated and resulted in significant improvement in symptoms of moderate-severe allergic rhinitis. The results of this pilot study should be considered preliminary, pending further randomized clinical trials.

Dynamic Characteristics Analysis of Magnetic Levitation Rotor Considering Unbalanced Magnetic Pull

The working principle of the motor can cause unbalanced magnetic pull (UMP) between stator and rotor unavoidably. Previous research about nonlinear vibration excited by UMP was focused on the rotor supported by traditional mechanical bearings or gas bearings. However, the magnetic levitation rotor is particular due to the low rigidity provided by the active magnetic bearing (AMB). UMP amplifies rotor vibration in the resonant zone and further excites the nonlinear electromagnetic force, thus producing different vibration phenomena. The paper calculates rotor orbit, spectra analysis, and time-history plot with numerical methods and studies the influence of the rotation speed, eccentricity, key control parameters, and UMP on rotor dynamics in detail. Results illustrate displacement response spectra of the magnetic levitation rotor are quite different from previous research results. The appearing frequency components are inducted by universal formulas in this paper. Furthermore, research shows a slight adjustment of the control parameters affect significantly harmonic components and vibration characteristics. The research results have practical reference significance for fault diagnosis, feature recognition, and controller optimization of the AMB-rotor system.

Costs of IPO in Poland

Theoretical background: Entering the stock market is an important moment in the development of a company. However, whether the timing of the decision is determined by capital needs or driven by attractive market conditions is debated in literature studies. On the other hand, neither in financial theory nor in practice there is a single universal formula, the use of which would enable the determination of the most favourable capital structure for a given company, reconciling both the optimum profitability of its own capitals and a reasonable scale of risk. The decisions regarding the selection of sources of financing depend on several factors. There is no question the cost of capital is an important criterion used by companies when deciding on a financing decision. In the case of initial public offers (IPO), the total costs consist of directand indirect costs. This study fills a specific gap in the literature due to the lack of such analyses based on data coming from the Polish market especially in the context of the type of IPO and market conditions. Purpose of the article: The purpose of this article is to present the results of a study on the costs of IPO conducted on the Warsaw Stock Exchange (WSE) between 2005 and 2020. Research methods: The hypotheses were verified using the statistical analysis and an econometric linear regression. Analysis covers 249 companies debuting on the WSE between 2005 and 2020. Information on the costs of the analysed offers was obtained from the companies’ current reports published after the completion of the share subscription. Main findings: The analysis confirmed that indirect cost of the offer are higher than direct costs. Although the average total costs of the offer are highest in the case of the issuance of new shares but they are not statistically significant. Furthermore, the higher the value of the offer, the lower its total cost. The interest rates affect the total cost of IPO but the total offer costs may not be directly explained by the activity on the IPOs market. The results of the analysis indicate that the explainability of the estimated model is the biggest for the direct costs. There is also a significant difference between the years with the highest and the lowest total costs of the offer.

Revenue diversification strategies of online news organisations: subscriptions and memberships

The funding model crisis for newspapers is a matter of public concern; and it is not only a business issue, but also a social and political one, as news organisations are considered to have an irreplaceable function in democratic systems. Technological and social changes have transformed the business model of news organisations so that, in a digital scenario with a strong competition for consumers’ attention, they have had to diversify their portfolio of income streams. In such a context, this study analyses the state of the diversification of revenue streams in the Spanish digital media market, using the available data from the total universe of digital media in the country. The article focusses on the two most common revenue streams related to user payment -subscriptions and memberships- and analyses the importance of four variables in this diversification of revenue strategies: their nature (digital native versus traditional), thematic scope (general versus specialised), territorial scope (local versus national), and the type of organisation that promotes it (traditional, new, or independent groups). The data obtained suggest that there are no universal formulae in the implementation of payment models for Spanish digital media. Specifically, there are significant differences in the revenue models between native and non-native digital media. Thus, payment strategies are more prevalent among non-native digital media than among native media. Furthermore, the non-native media that have opted for paid models tend to diversify their sources of income more than the non-native ones based on free model. Additionally, data show that paywalls and memberships are more usual among specialised non-native digital media and generalist native outlets. Also, payments are more often required by local and regional media than national outlets. From the ownership point of view, although the main Spanish media corporations are developing their revenue models, the pay-per-content model is also quite extended among organisations, associations, and foundations not linked with the traditional publishing groups. This study, due to its exhaustiveness, dimensions, and novelty, identifies in detail the current state of the implementation of the pay model for digital media in Spain, which can help and facilitate media managers in their decision-making.

Preformation probability and kinematics of cluster emission yielding Pb-daughters* *Supported by the Fundamental Research Grant Scheme (FRGS/1/2019/STG02/UNIMAP/02/2) from the Ministry of Education Malaysia stipulated with the Institute of Engineering Mathematics (IMK) of the Faculty of Applied and Human Sciences UniMAP as the beholder, Science and Engineering Research Board (SERB, CRG/2021/001229), FOSTECT Project (FOSTECT.2019B.04), FAPESP Project (2017/05660-0)

In the present study, the newly established preformation formula is applied for the first time to study the kinematics of the cluster emission from various radioactive nuclei, especially those that decay to the double shell closure Pb nucleus and its neighbors as daughters. The recently proposed universal cluster preformation formula has been established based on the concepts that underscore the influence of mass and charge asymmetry ( and ), cluster mass , and the Q-value, paving the way to quantify the energy contribution during preformation as well as during the tunneling process separately. The cluster-daughter interaction potential is obtained by folding the relativistic mean-field (RMF) densities with the recently developed microscopic R3Y using the NL and the phenomenological M3Y NN potentials to compare their adaptability. The penetration probabilities are calculated from the WKB approximation. With the inclusion of the new preformation probability , the predicted half-lives of the R3Y and M3Y interactions are in good agreement with the experimental data. Furthermore, a careful inspection reflects slight differences in the decay half-lives, which arise from their respective barrier properties. The for systems with double magic shell closure Pb daughter are found to be an order of higher than those with neighboring Pb daughter nuclei. By exploring the contributions of the decay energy, the recoil effect of the daughter nucleus is evaluated, in contrast to several other conjectures. Thus, the centrality of the -value in the decay process is demonstrated and redefined within the preformed cluster-decay model. Additionally, we have introduced a simple and intuitive set of criteria that governs the estimation of recoil energy in the cluster radioactivity.

The diagonal of the multiplihedra and the tensor product of A ∞ -morphisms

We define a cellular approximation for the diagonal of the Forcey–Loday realizations of the multiplihedra, and endow them with a compatible topological cellular operadic bimodule structure over the Loday realizations of the associahedra. This provides us with a model for topological and algebraic A ∞ -morphisms, as well as a universal and explicit formula for their tensor product. We study the monoidal properties of this newly defined tensor product and conclude by outlining several applications, notably in algebraic and symplectic topology.

Image formation by two plane mirrors

We revisit the problem of image formation of a point object by two plane mirrors meeting at a convex angle θ. Although a complete solution to the problem already exists in the literature, the simple formula is often assumed to be the universal formula that counts the number of images, irrespective of θ or the location of the object. A survey, involving both school students and teachers, shows that the simple formula in conjunction with rounding off to the closest integer(s) is still widely thought of as the correct way to count the number of images formed. In order to address this rampant misconception, we rederive the correct formula for an arbitrary mirror angle θ and arbitrary location of the object in an elementary way. The proof is easily communicable to high school students. We justify the formula using a physical setup and capturing real-life images. Finally, we provide a simulation written in an open source software GeoGebra as an additional visual aid in understanding the problem and its solution.

A Mineralogical Model for Thermal Transport Properties of Rocks: Verification for Low-Porosity, Crystalline Rocks at Ambient Conditions

AbstractThermal conductivity (K) describes the response of matter to temporal or spatial variations in temperature (T). To quantify the effect of varying mineralogy on heat transport of rocks, an accurate (±2%) contact-free heat transfer method was applied at ambient T to multiple sections from 33 different low porosity, continental, igneous and metamorphic rocks. Thermal diffusivity (Dheat) was measured using laser-flash analysis, which was previously used to construct our large mineralogical database and which mitigates spurious radiative transfer found in other techniques. These measurements constrain K, because K is the product of Dheat with the known (or calculable) properties of density and specific heat measured at constant pressure (P). Compositions, proportions, and orientations of minerals, plus rock density, average grain-size (L), and porosity were characterized for 61 sections from 29 silicate rocks plus 5 sections from 3 marbles. Our database was used to evaluate component summation (averaging) formulae that were recently developed by considering Fourier’s laws, and to quantify the dependence of K and/or Dheat on key rock descriptors. We found that: (1) phase proportions and compositions are the main cause of variations; (2) minor porosity and foliation have minor effects; and (3) within ~5%, isotropic rocks follow Dheat = ½{[Σ(fi/Di)]−1 + Σ(fiDi)} where fi is volumetric mineral fraction, analogous to the Voigt-Reuss-Hill average for elastic moduli. Using this formula predictively depends on the accuracy of fi and Di. Quartzo-feldspathic rocks can be described by a new formula that uses only quartz fraction and plagioclase composition. Combining our mineralogical model with a universal formula for Dheat(T) and a thermodynamic identity for K(P) accurately constrains conductive thermal transport for Earth’s low porosity, crystalline rock layers.

Navier-Stokes Solutions for Accelerating Pipe Flow—A Review of Analytical Models

This paper reviews analytical solutions for the accelerated flow of an incompressible Newtonian fluid in a pipeline. This problem can be solved in one of two ways according to the (1) imposed pressure gradient or (2) flow rate. Laminar accelerated flow solutions presented in a number of publications concern cases where the two driving mechanisms are described by simple mathematical functions: (a) impulsive change; (b) constant change; (c) ramp change, etc. The adoption of a more complex and realistic description of the pressure gradient or flow rate will be associated with a profound mathematical complexity of the final solution. This is particularly visible with the help of the universal formula derived by several researchers over the years and discussed in this paper. In addition to the solutions strictly defined for laminar flow, an interesting extension of this theory is the theory of underlying laminar flow for the analysis of turbulent accelerated pipe flows (TULF model developed by García García and Alvariño). The TULF model extends the Pai model developed more than 60 years ago, which has been previously used for steady flows only. The discussed solutions extend the theory of analytical solutions of simplified two-dimensional Navier–Stokes equations and can be used not only to study the behavior of liquids during accelerating pipe flow but they can also be used to test the accuracy of commercial CFD codes.

On the exactness of the universal backprojection formula for the spherical means Radon transform

The spherical means Radon transform is defined by the integral of a function f in over the sphere of radius r centered at a x, normalized by the area of the sphere. The problem of reconstructing f from the data where x belongs to a hypersurface and has important applications in modern imaging modalities, such as photo- and thermo- acoustic tomography. When Γ coincides with the boundary of a bounded (convex) domain , a function supported within Ω can be uniquely recovered from its spherical means known on Γ. We are interested in explicit inversion formulas for such a reconstruction. If , such formulas are only known for the case when Γ is an ellipsoid (or one of its partial cases). This gives rise to a question: can explicit inversion formulas be found for other closed hypersurfaces Γ? In this article we prove, for the so-called ‘universal backprojection inversion formulas’, that their extension to non-ellipsoidal domains Ω is impossible, and therefore ellipsoids constitute the largest class of closed convex hypersurfaces for which such formulas hold.

Universal formula for the density of states with continuous symmetry

We consider a $d$-dimensional unitary conformal field theory with a compact Lie group global symmetry $G$ and show that, at high temperature $T$ and on a compact Cauchy surface, the probability of a randomly chosen state being in an irreducible unitary representation $R$ of $G$ is proportional to $(\mathrm{dim}\text{ }R{)}^{2}\mathrm{exp}[\ensuremath{-}{c}_{2}(R)/(b{T}^{d\ensuremath{-}1})]$. We use the spurion analysis to derive this formula and relate the constant $b$ to a domain wall tension. We also verify it for free field theories and holographic conformal field theories and compute $b$ in these cases. This generalizes the result in 2109.03838 that the probability is proportional to $(\mathrm{dim}R{)}^{2}$ when $G$ is a finite group. As a byproduct of this analysis, we clarify thermodynamical properties of black holes with non-Abelian hair in anti--de Sitter space.

Design of controls for ISS and Integral ISS Stabilization of Multistable State Periodic Systems

This paper is devoted to the construction of continuous and periodic controllers for ISS or iISS stabilization of a class of multistable state periodic systems. For this purpose, the concepts of practical ISS-, ISS- and iISS-control Leonov functions are introduced. Then, it is proven that the existence of these functions is a sufficient condition to ensure that the system under study is ISS- or iISS stabilizable, and explicit feedback control laws can be obtained by means of a mild adaptation of Sontag's universal formula. The proposed method is illustrated by the design of an excitation controller for a synchronous generator ensuring ISS of the closed-loop system.

УНИВЕРСАЛЬНАЯ ФОРМУЛА ДЛЯ ОЦЕНКИ ПРЕДЕЛОВ ПРОЧНОСТИ МОРСКОГО ЛЬДА НА СЖАТИЕ И ИЗГИБ ДЛЯ ТЕРМОДИНАМИЧЕСКИХ РАСЧЕТОВ

Thermodynamic modeling of the ice cover of freezing seas is carried out according to their hydrometeorological conditions. It is an important tool in assessing the evolution of the main ice parameters. However, the calculation of the ice strength properties is currently complicated by a need to introduce additional full-scale parameters. A new universal formula that is devoid of this drawback was developed for assessing the main strength properties of ice. The results of a comparison of calculations performed according to the formula and methods from the main regulatory documents are presented. A comparison of the calculations based on the formula with field measurements was provided and showed a high accuracy of the average ice strength values estimated using the proposed formula.

РАСЧЁТ ЭЛЕКТРИЧЕСКИХ РЕЖИМОВ СИСТЕМ ЭЛЕКТРОСНАБЖЕНИЯ

When solving the issues of creation and improvement of power supply systems, calculations of steady-state modes are the most common. Since power supply systems contain nonlinear elements, their steady state mode is described by nonlinear equations. Solving such equations is possible only by iterative methods, which is associated with the problem of convergence of the iterative process. The proposed method calculations of steady-state modes are the most common in solving the issues of creation and improvement of power supply systems, and the algorithms implementing it are relatively easy to program and provide the necessary speed and accuracy of calculations. They are designed to solve a number of practical problems related to the design and operation of complex closed power supply systems. Due to a number of features of electrical systems, which are inherent in the power supply systems of the agricultural and forestry complex, the convergence of the iterative process may be delayed and even not provided. In this regard, the authors proposed a direct calculation method with cyclic correction of the initial information for each cycle in order to take into account the nonlinearity of the elements of the electrical system. The proposed method is based on universal calculation formulas for determining eigenand mutual resistances, which are obtained as a result of transformation and solution of nodal equations

A Universal Formula for Evaluating the Compressive and Flexural Strength of Sea Ice at Thermodynamic Calculations

A Universal Formula for Evaluating the Compressive and Flexural Strength of Sea Ice at Thermodynamic Calculations

Синтез профілю зубчатих коліс малошумного шестеренного насоса з низькою пульсацією

Low-noise gear pumps with non-involute gear profiles, which have undeniable advantages over pumps with involute gear profiles (low noise characteristics, low pressure and volumetric pulsation, inseparability of gear contact), have not gained wide popularity due to difficulties in designing and manufacturing the working profiles of the gears. Companies manufacturing low-noise pumps provide only promotional information, while information about the meshing geometry, profile, and manufacturing technology is practically absent. The aim of the research is to obtain universal formulas for calculating the complex sinusoidal profile of gears for low-noise pumps. This will allow designing sinusoidal meshings with different input parameters (number of teeth, center distance, etc.). Additionally, for the helical sinusoidal meshing, it is necessary to derive a formula for determining the minimum tooth helix angle that ensures inseparability of contact in the meshing. Several stages are involved in obtaining the universal formulas. In the first stage, the construction of a base sinusoidal curve is performed. The obtained profile is not mutually enveloping, meaning that when positioning the gears at the center distance and forming the meshing, there is interference of curves. Hence the need for forming a unified profile where both gears have identical profiles and can be processed by the same tool. In the second stage, the generation of the conjugate gear profile is performed as an enveloping family of circular sine waves, by rolling a dividing circle of the sine wave around the generating circle of the formed gear. Segments of this profile will be further involved in forming the final gear profile. In the third stage, the circular sine wave and its enveloping positions are overlaid to a common center of coordinates. As a result, the conjugate profile points lying on the dividing circle are formed. The unification of the gear profile is achieved by removing certain sections of the curve within the dedendum and addendum, while the remaining sections that have a common tangent at the end points of the conjugation form the final gear profile. As a result of the conducted research, a mathematical apparatus has been developed that allows building gear tooth profiles for low-noise gear pumps with arbitrary geometric parameters and number of teeth. The minimum value of the tooth helix angle required to ensure contact inseparability and absence of clearances has been determined.

ІНФОРМАЦІЙНА ТЕХНОЛОГІЯ ОЦІНКИ ЯКОСТІ ЗНАНЬ ФАХІВЦІВ В ІТ-ГАЛУЗІ

Urgency of the research. The topic of the research is the quality of the specialist's training and knowledge. The sources do not have a single definition of the terms "quality of specialist training" and "quality of specialist knowledge", but theyall mean general "quality". The quality of a specialist means that they have properties that allow them to perform their professional work in accordance with their specialty, to be an active citizen, to constantly improve their qualifications and, if necessary, to change their profession.Target setting. In the modern IT labor market, there are many areas, such as UX/UI designers, Front-End, Back-End specialists, network specialists and cyber security specialists. In Ukraine, there are more than 212 thousand IEs working in the field of IT. In 2021, the increase in the number of IEs increased by 16%. Currently, the growth in the number of IEs has decreased compared to 2018-2020. Ukraine has many CTEAs related to IT, including computer programming, informatization consulting, data processing, publishing of computer games and other software.Actual scientific researches and issues analysis. In his research, P.I. Kanivets defined the quality of a specialist as a setof properties and characteristics that defines them as a specialist of a certain profession and specialty. The skills of a specialist can be divided into technical and communication skills, and they are determined by the level of productivity and the ability to do a job well. In the field of IT, there are many different levels of technical specialists with different levels of knowledge, skills and experi-ence. Differences between levels determine the ability to solve various problems and the ability to learn and improve oneself.Uninvestigated parts of generalmatters defining. There are general skills that IT professionals need, but there are also many other skills that have different levels of value depending on the position. At the moment, there is no universal way to automatically detect the level of specialists' skills, which concerns both "hard skills" (technical skills) and "soft skills" (inter-personal skills).The research objective. The purpose of the work is to study the general skills and abilities of an IT specialist and an attempt to derive a universal formula for calculating the reference model of the competencies of an IT specialist. The statement of basic materials. In particular, a methodology has been developed that allows to assess the compliance of the level of training of graduates with the requirements of vacant positions in the design department. A survey of managers and leading employees of UX/UI design departments from various organizations was also conducted in order to determine the most important qualities of employees in UI/UX design.Conclusions. On the basis of the opinion of the heads of the IT industry, the dominant professionally significant and personal qualities necessary for specialists to successfully implement professional activities in the field of UX design wereidentified.Based on the requirements of the reference competency model of an IT specialist, a methodology that allows to assess the level of training of candidates for the position with the requirements of IT department managers, as well as to provide assistance in supporting decision-making when choosing the most suitable employee has been created.