Integral Coefficients Research Articles

Rare decay t→cγγ via scalar leptoquark doublets

A calculation of the one-loop contribution to the rare three-body flavor changing neutral current top quark decay $t\to c\gamma\gamma$ is presented in the framework of models with one or more scalar leptoquark $SU(2)$ doublets with hypercharge $7/6$. Analytical expressions for the invariant amplitude of the generic decay $f_i\to f_j\gamma\gamma$, with $f_{i,j}$ a lepton or quark, are presented in terms of Passarino-Veltman integral coefficients, from which the amplitudes for the processes $t\to c\gamma\gamma$ and $\ell_i\to \ell_j\gamma\gamma$ follow easily. An analysis of the current constraints on the parameter space is presented in the scenario with only one scalar LQ doublet and bounds on the LQ couplings are obtained from the muon $g-2$ anomaly, the lepton flavor violating (LFV) decay $\tau\to \mu\gamma$ and extra constraints meant to avoid tension between theory predictions and experimental data. For a LQ with a mass in the range of $1$--$1.5$ TeVs, the estimate ${\rm Br}(t\to c\gamma\gamma)\sim 10^{-11}$--$10^{-12}$ is obtained for the largest allowed values of the LQ coupling constants, which means that this decay would be below the reach of future experimental measurements. We also consider an scenario with three scalar doublets, which was recently proposed to explain the lepton flavor universality violation anomalies in $B$ decays as well as the muon $g-2$ anomaly. Although this scenario allows large LQ couplings to the tau lepton and the $c$ and $t$ quarks, the branching ratio of the $t\to c\gamma\gamma$ decay is also of the order of $10^{-11}$--$10^{-12}$ for LQ masses of 1.7 TeV.

Analysis and Assessment of the State of Economic Security of the Sughd Region

The article proposed a method for assessing the level of economic security of the region, which relies on the study of the value of basic indicators, with the calculation of integral indicators. The development of methodological provisions for assessing the economic security of the region is relevant from the point of view of the need to make effective management decisions for the timely detection and elimination of possible dangers and threats, and to reduce the risks of economic security in the country and its regions.In recent years, economic security has undergone a number of major changes. Economic warfare and sovereignty have infiltrated strategic thinking and political discourse, along with free trade and attractiveness, which have so far been the main economic policies of most countries. The unprecedented polarization of global geopolitical relations and the increased stakes in technological superiority around new generations of telecommunications networks and data processing have been the catalyst for this paradigm shift . In this new situation, the strengths of the regional economy are also assets that can be used by large competing forces, oft en better equipped for this purpose.Bringing the basic indicators of the economic security of a particular region into a comparable form by normalizing them relative to the average values for all territories of the country. A rationing of basic indicators for assessing the state of economic security of the region is proposed. Economic security was assessed by calculating the integral coefficient, using the method of multivariate comparative analysis. To assess the economic security of the region, a group of indicators of macroeconomic development, social development, financial security, environmental security, personnel security was used, allowing to get an idea of economic security in general. It is proposed for each safety indicator to determine the best (reference) value, which is taken as a unit, then the indicators are compared for each safety component with the standard.

Design of 4UM-120D Electric Leafy Vegetable Harvester Cutter Height off the Ground Automatic Control System Based on Incremental PID

In this study, a 4UM-120D electric leafy vegetable harvester was employed as the research object. An automatic control system was created to maintain the cutter’s height above the ground within ±2% of the desired value. The intention was to reduce the operators’ work intensity while improving the leafy vegetable harvester’s working quality. The automatic control system for the cutter height from the ground was explained, along with its structure and operating philosophy. MATLAB was used to establish the two-phase hybrid stepper motor’s mathematical electrical equation and mechanical equation models. An analysis was carried out on the fundamentals and differences between position PID and incremental PID control algorithms. Utilizing incremental PID in combination, the control strategy for the harvester cutter height from the ground was built, and an automatic control system was produced under the corresponding control strategy. The stability, accuracy, and rapidity of the automatic control system of the cutter height from the ground under the incremental PID control strategy were analyzed by simulating different actual working conditions with MATLAB/Simulink and taking the steady-state transition time as the evaluation index. The test results show that when the deviation between the current value and the set value was greater than 2%—that is, when the harvester was in the condition of suddenly crossing the ditch or suddenly climbing the slope—the automatic control system based on the incremental PID control strategy had a good dynamic response performance and stability. This resulted in the automatic control function of the harvester cutter height off the ground being achieved. When the rotation angle PID control algorithm’s proportional coefficient is Kp = 4.665, the rotation speed PID control algorithm’s proportional coefficient is Kp = 5.65 and its integral coefficient is Ki = 3.86, and the current PID control algorithm’s proportional coefficient is Kp = 0.5455 and its integral coefficient is Ki = 30.4578. The harvester abruptly crossed a ditch while operating steadily, and the automatic control system’s steady-state transition time for the height of the cutter off the ground was 1.0811 s. The harvester abruptly climbed a slope while operating steadily, and the automatic control system’s steady-state transition time for the height of the cutter off the ground was 1.1185 s. Data from the field tests revealed a degree of reliability in the simulation test results. The study offered a strategy for raising the harvester quality for leafy vegetables while lowering the operator workload.

Continuous K-theory and cohomology of rigid spaces

We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely valued field, its continuous K-groups vanish in degrees below the negative of the dimension. Likewise, the cohomology groups vanish in degrees above the dimension. The main result provides the existence of an isomorphism between the lowest possibly non-vanishing continuous K-group and the highest possibly non-vanishing cohomology group with integral coefficients. A key role in the proof is played by a comparison between cohomology groups of an admissible Zariski-Riemann space with respect to different topologies; namely, the rh-topology which is related to K-theory as well as the Zariski topology whereon the cohomology groups in question rely.

Modeling and Operating Time Optimization of Layer Melt Crystallization and Sweating Processes

Improving the separation efficiency of the layer melt crystallization process is a key but difficult task. Herein, a comprehensive model involving both crystallization and sweating was proposed and used to optimize the operating time of crystallization and sweating processes. The crystallization process was modeled based on the relationship between differential and integral distribution coefficients under a constant layer growth rate. For the sweating process, an empirical sweating equation was employed to govern the sweating model, the parameters of which were determined experimentally using P-xylene as the model substance. The separation efficiency was then optimized by minimizing the operating time at a given product purity and yield. A sensitivity analysis showed that the crystallization and sweating times nonlinearly increase with increasing yield. After the yield exceeds 0.65, an increasing crystallization time is the dominant factor in improving the separation efficiency, while the sweating time and ratio even slightly decrease. The total operating time at low yield is U-shaped with the layer growth rate. The optimal layer growth rate decreases with increasing yield. This model provides guidance for determining the optimal operating parameters of layer melt crystallization and sweating processes.

Adaptive PI control of ultrasonic motor using iterative learning methods

PI (proportional integral) controller is widely utilized in ultrasonic motor control systems. However, PI controllers which use fixed parameters is often difficult to ensure that the control performance meets the expectations. Based on the idea of iterative learning control (ILC), a new online adaptive adjustment method for PI control parameters is proposed. Simple P (proportional) type and PD (proportional differential) type iterative learning controllers are designed to adjust the proportional and integral coefficients of PI controller online. Using this method, the coefficients of PI controller are adaptively adjusted with the change of motor characteristics to ensure the control performance meets expectations. This method can improve the nonlinear expression ability of the controller, so that its input–output relationship can better match the characteristics of the controlled object, thereby improving the control performance. Results of comparative experiments indicate the validity of the proposed control strategy.

The Role of Expectations on Exchange Rate Determination in Indonesia

There are two purposes of this paper. Firstly, it deals with expectation formation. Secondly, it will be tested whether the expectation has a significant role in determining the current exchange rate in the case of Indonesian currency against the US dollar and Euro. This research will compare two kinds of expectation formation. Firstly, the expectation built from the fundamental economy is known as rational expectation formation. Secondly, the expectation formulated from past time series information, the Auto Regressive Moving Average (ARMA) model, is utilized. The steps to prove the role of expectation are stationary process, degree of integration, co-integration, and U-Theil's Inequality Coefficient Test (UTIC). It is found that both kinds of expectation formation have essential roles in determining the current exchange rate in Indonesia. However, according to UTIC criteria, a rational expectation better explains both current exchange rate movements.

Damage Evolution and Integrity Assessment of Jointed Rock Mass Based on Synthetic Rock Mass Approach

The integrity coefficient Kv of bed rock is one of the important approaches to evaluate the stability of engineering rock mass, but this parameter is difficult in frequent field tests. The integrity coefficient is the quantitative index for evaluating the complete deformation of rock mass, while the damage variable represents the level of damage of the jointed rock mass, and both have similar physical meanings and represent the degree of deterioration of surrounding rock. Damage variables and damage constitutive models were constructed based on Weibull distribution damage model and Synthetic Rock Mass (SRM) model. The relationship between damage variables and numerical calculation and damage constitutive curves of different weathered granite rocks in Hongtuzhang tunnel was calculated. A new method for evaluating integrity coefficient of rock mass is proposed.

Дослідження технологічної придатності тракторів для роботи у складі комбінованих машинно-тракторних агрегатів

Goal. Determination of structural and techno­logical conditions of suitability of tractors with advanced technological properties for work as part of combined machine-tractor units. Methods. The basic methods of the theory of construction and operation of agricultural tractors are used. Theoretical calculations of the system of obtained analytical dependencies were carried out on a personal computer in the Mathcad 15 software environment. Results. The possibility and effectiveness of the use of the front hinged mechanism, front and rear power take-off shafts, reversibility of the transmission of the control post and other structural and technological elements of tractors for their potential suitability for work as part of combined machine-tractor units are analyzed. Conclusions. The developed integral coefficient of efficiency of the extended technological properties of wheeled power tools can serve as a quantitative assessment of their technological suitability for functioning as part of combined machine-tractor units. First of all, this applies to those that are arranged according to the «push-pull» construction scheme. Calculations of the obtained system of analytical dependencies established that, according to its technological properties, the domestic row-row tractor KhTZ-16131 potentially has the highest integral index of technological suitability, the value of which reaches the mark of 0.63. This is 12,5 – 57,5% more compared to the values of the same indicator for such power tools of a similar purpose, such as MTZ-1523, LTZ-155 and Fendt 711 Vario (Germany).

Research on borehole repair model and working parameters optimization of self-propelled rotary excavator

The collapse or plugging of gas extraction borehole can result in partial or complete failure of the extraction function, affecting the efficiency of gas extraction and increasing project costs. The integrated friction coefficient k indicates the resistance of the borehole repair system per unit length. The current repairing methods are mainly self-propelled and rotary drilling technology, which ignores the influence of drilling angle and return water flow on integrated friction coefficient k. In this paper, wellbore repair model based on Newton’s variable mass law is established. The relationship between repair length and hydraulic parameters, wellbore parameters and pipeline parameters is derived. The system resistance test experiment is carried out to clarify the influence of well length, angle, backwater and movement speed on the integrated friction coefficient k. Main conclusions are as follows: the integral friction coefficient k is the key parameter of the repair model, the system resistance increases linearly with the increase of drilling repair distance. Backwater exerts backward thrust on the front end of the drill bit and the high-pressure hose, resulting in an increase in the integrated friction coefficient k, the increase of drilling angle and jet pressure can lead to the increase of backwater flow and the increase of integral friction coefficient k. The improved repair model can more accurately predict the maximum repair distance of self-propelled and rotary drill bits. At the repair distance of 104.7 m, the error between the repair value and the experimental value is 5.7 m, which verifies the feasibility of the application of drilling repair in self-propelled and rotary drilling technology.

Energy Transfer Efficiency Based Nonlinear Ultrasonic Testing Technique for Debonding Defects of Aluminum Alloy Foam Sandwich Panels

In order to improve the accuracy of detection results of debonding defects of aluminum alloy thin plate, the nonlinear ultrasonic technology is used to detect the simulated defect samples, aiming at problems such as near surface blind region caused by the interaction of incident wave, reflected wave and even second harmonic wave in a short time due to the small thickness of thin plates. An integral method based on energy transfer efficiency is proposed to calculate the nonlinear ultrasonic coefficient to characterize the debonding defects of thin plates. A series of simulated debonding defects of different sizes were made using aluminum alloy plates with four thicknesses of 1 mm, 2 mm, 3 mm and 10 mm. By comparing the traditional nonlinear coefficient with the integral nonlinear coefficient proposed in this paper, it is verified that both methods can quantitatively characterize the size of debonding defects. The nonlinear ultrasonic testing technology based on energy transfer efficiency has higher testing accuracy for thin plates.

Sensorless Control Method of High-Speed Permanent Magnet Synchronous Motor Based on Discrete Current Error

When the Surface-Mounted Permanent Magnet Synchronous Motor (SPMSM) is in the condition of high-speed and low carrier-wave ratio, the performance of sensorless control is more affected by digital control delay, parameter inaccuracy, and other factors. This paper presents a sensorless control method based on the static error between the discrete d-axis current and the corresponding reference value. If there is no error in position angle, the discrete d-axis current should have no static error approximately. In addition, the static error of the d-axis current is related to the speed, so the PI controller with a variable proportional integral coefficient is used to ensure a stable error compensation performance in a wide speed range. The proposed method can accurately compensate the estimated rotor position of the motor under high-speed and low carrier ratio conditions and improve the accuracy of sensorless control. It provides an effective measure for the stable and reliable acceleration of electric vehicles and has specific practical significance for the development of electric vehicle control.

Integral assessment of non-specific lipid peroxidation reactions blood in adolescent girls of the Siberian ethnos

BACKGROUND: Integral parameters, in particular, the oxidative stress coefficient are informative and can be used both for evaluation of pathological conditions and compensatory-adaptive reactions of the organism.
 AIM: To investigate an integral coefficient the activity of nonspecific reactions of lipid peroxidation in adolescent girls of the Buryat, Evenki and Tofalar ethnic groups, as compared to the non-indigenous ethnic groups, by applying.
 METHODS: Total 190 adolescent girls (Buryats, Evenki and Tofalar, and nonindigenous population (for example of Russians)) living in the Irkutsk region were the objects of research. The survey was carried out in expeditionary conditions, in the territories of compact residence of ethnic groups. To calculate the integral coefficient (oxidative stress coefficient), spectrophotometry and fluorometry methods we implemented. The individual indicators: primary, secondary, and final products of lipid peroxidation as well as antioxidant defense components were measured.
 RESULTS: According to the obtained data, a lower content of diene conjugates (DC) (p 0.0001), ketodienes and conjugated trienes (KD and СT) (p=0.0003), -tocopherol (p 0.0001) with elevated levels of TBA-active products (p=0.0074) and superoxide dismutase activity (p=0.0008) in the Buryat ethnic girls group relative to similar parameters of girls in the non-ingenious population was observed. Girls of Tofalar ethnic group had higher values of DC (p=0.0009), with reduced values of KD and CT (p=0.0044) compared to the non-indigenous population. There were no differences among girls of the Evenk ethnic group relative to Russians. An integrative analysis of the state of nonspecific lipid peroxidation reactions using the coefficient showed no significant differences between the studied groups.
 CONCLUSION: The conducted study demonstrates certain changes in the lipid peroxidationantioxidant defence system, in the absence of changes in the total indicator among girls representing Siberian ethnic groups and the Russian population living next to them, which can be the basis for subsequent monitoring of their health status.

Structural changes in Ukraine’s electricity generation and their impact on the reduction of CO2 emissions

The purpose of the study is to assess the state of and structural changes in Ukraine’s electricity generation and their impact on the reduction of carbon dioxide (CO2) emissions. For the investigation, data from the International Energy Agency and the National Power Company Ukrenergo were used. The study analyzes the trends in Ukraine CO2 emissions by economic sector, the trends in the country’s electricity generation and electricity generation capacities, the structure of electricity generation capacities by type of flexibility and presents the calculations of the integral coefficients of structural changes in the electricity generation capacities and electricity generation by type of flexibility. The study also examines how the structure of the energy sector of Ukraine has changed in terms of electricity generation. For this purpose, the structure of the Ukrainian electricity generation capacities and electricity generation by generation type is considered and the integral coefficients of structural changes in the electricity capacities and electricity production by generation type are calculated. Based on the study results, it is determined that, over the considered period, the decrease in Ukraine’s electricity generation was more significant than the decrease in its generation capacities, which has led to a corresponding reduction in CO2 emissions in the country; the structural changes in the electric power industry of Ukraine were not adequate to the structural changes in the country’s economy, which has led to a shortage in flexible capacities but also resulted in the reduction of CO2 emissions due to a decline in electricity generation.

Enhancement of biogranules development using magnetized powder activated carbon.

Biogranulation has emerged as a viable alternative biological wastewater treatment approach because of its strong biodegradability potential, toxicity tolerance, and biomass retention features. However, this process requires a long duration for biogranules formation to occur. In this study, magnetic powder activated carbon (MPAC) was used as support material in a sequencing batch reactor to enhance biogranules development for wastewater treatment. Two parallel SBRs (designated R1 and R2) were used, with R1 serving as a control without the presence of MPAC whileR2 wasoperated with MPAC. The biodegradability capacity and biomass properties of MPAC biogranules were compared with a control system. The measured diameter of biogranules for R1 and R2 after 8weeks of maturation were 2.2mm and 3.4mm, respectively. The integrity coefficient of the biogranules in R2 was higher (8.3%) than that of R1 (13.4%), indicating that the addition of MPAC improved the structure of the biogranules in R2. The components of extracellular polymeric substances were also higher in R2 than in R1. Scanning electronic microscopy was able to examine the morphological structures of the biogranules which showed there were irregular formations compacted together. However, there were more cavities situated in R1 biogranules (without MPAC) when compared to R2 biogranules (with MPAC). Dye removal reached 65% and 83% in R1 and R2 in the post-development stage. This study demonstrates that the addition of MPAC could shorten and improve biogranules formation. MPAC acted as the support media for microbial growth during the biogranulation developmental process.

The integral Picard groups of low-degree Hurwitz spaces

We compute the Picard groups with integral coefficients of the Hurwitz stacks parametrizing degree 4 and 5 covers of \(\mathbb {P}^1\). As a consequence, we also determine the integral Picard groups of the Hurwitz stacks parametrizing simply branched covers. For simple branching, the Picard groups are finite, with order depending on the genus.

Proportion of modular forms with transcendental zeros for general levels

Let $\Gamma$ be a congruence subgroup such that $\Gamma_{1}(N)\subset\Gamma\subset\Gamma_{0}(N)$ for some positive integer $N$. For a positive integer $k$, let $M_{k,\mathbf{Z}}(\Gamma)$ be the set of modular forms of weight $k$ on $\Gamma$ with integral Fourier coefficients. Let $R_{k}(\Gamma)$ be the set of common zeros in the upper half plane $\mathbf{H}$ of all the modular forms of weight $k$ on $\Gamma$. In this note, we prove that the density of modular forms in $M_{k,\mathbf{Z}}(\Gamma)$ with an algebraic zero $z \notin R_{k}(\Gamma)$ is zero.

Model-Free Adaptive Control of Hydrometallurgy Cascade Gold Leaching Process with Input Constraints.

Hydrometallurgy technology can directly deal with low grade and complex materials, improve the comprehensive utilization rate of resources, and effectively adapt to the demand of low carbon and cleaner production. A series of cascade continuous stirred tank reactors are usually applied in the gold leaching industrial process. The equations of leaching process mechanism model are mainly composed of gold conservation, cyanide ion conservation, and kinetic reaction rate equations. The derivation of the theoretical model involves many unknown parameters and some ideal assumptions, which leads to difficulty and imprecision in establishing the accurate mechanism model of the leaching process. Imprecise mechanism models limit the application of model-based control algorithms in the leaching process. Due to the constraints and limitations of the input variables in the cascade leaching process, a novel model-free adaptive control algorithm based on compact form dynamic linearization with integration (ICFDL-MFAC) control factor is first constructed. The constraints between input variables is realized by setting the initial value of the input to the pseudo-gradient and the weight of the integral coefficient. The proposed pure data-driven ICFDL-MFAC algorithm has anti-integral saturation ability and can achieve faster control rate and higher control precision. This control strategy can effectively improve the utilization efficiency of sodium cyanide and reduce environmental pollution. The consistent stability of the proposed control algorithm is also analyzed and proved. Compared with the existing model-free control algorithms, the merit and practicability of the control algorithm are verified by the practical leaching industrial process test. The proposed model-free control strategy has advantages of strong adaptive ability, robustness, and practicability. The MFAC algorithm can also be easily applied to control the multi-input multi-output of other industrial processes.

Derivation of an elastic shell model of order as tends to infinity

Starting from three-dimensional linear elasticity and performing the dimensional reduction by integration over the thickness, we derive a general form of the areal strain energy density for elastic shells. To obtain the new constitutive model, we do not approximate the deformation fields as polynomials in the thickness coordinate, but rather we keep all terms in the thickness-wise series expansions. As a result, we deduce the explicit form of the shell strain energy density in which the constitutive coefficients are expressed as integrals depending on the thickness h and on the initial curvature. Then, to obtain the shell model of order , we expand the integral coefficients in the strain energy function as power series of h and truncate them to the power . In the case , we recover the classical strain energy density for combined bending and stretching of linear shells, which leads to the Koiter model. Finally, we prove that the proposed shell strain energy function is coercive for any , as well as for the general case .

The cohomology of $$C_2$$-surfaces with $${\underline{{\mathbb {Z}}}}$$-coefficients

Let $$C_2$$ denote the cyclic group of order 2. We compute the $$RO(C_2)$$ -graded cohomology of all $$C_2$$ -surfaces with constant integral coefficients. We show when the action is nonfree, the answer depends only on the genus, the orientability of the underlying surface, the number of isolated fixed points, the number of fixed circles with trivial normal bundles, and the number of fixed circles with nontrivial normal bundles. When the action on the surface is free, we show the answer depends only on the genus, the orientability of the underlying surface, whether or not the action preserves the orientation, and one other invariant.