Fourth Power Research Articles

Fourth power mean values of one kind special Kloosterman's sum

<abstract><p>The main purpose of this article is using the analytic methods and properties of classical Gauss sums to study the calculating problem of fourth power mean values of one kind special Kloosterman's sum, and give a sharp asymptotic formula for it. At the same time, the paper also provides a new and effective method for the study of related power mean value problems.</p></abstract>

On the fourth power mean of one special two-term exponential sums

<abstract><p>The main purpose of this paper is using the elementary methods and the number of the solutions of some congruence equations to study the calculating problem of the fourth power mean of one special two-term exponential sums, and give an exact calculating formula for it.</p></abstract>

On two-term exponential sums and their mean values

<abstract><p>The mean value problems of exponential sums play a very important role in the research of analytic number theory, and many famous number theory problems are closely related to them. The main purpose of this paper is using some elementary methods and the number of the solutions of the congruence equations to study the calculating problem of some fourth power means of two-term exponential sums, and give exact calculating formulae and asymptotic formula for them.</p></abstract>

The generalized Kloosterman's sums and its fourth power mean

<abstract><p>The main purpose of this article is to study the calculating problem of one kind fourth power mean of the generalized Kloosterman's sums and provide an accurate calculating formula for it utilizing analytical methods and character sums' properties. Simultaneously, the work also provides a fresh and valuable approach for researching the related power mean problem.</p></abstract>

On the sixth power mean values of a generalized two-term exponential sums

<abstract><p>This paper examines the evaluations of sixth power mean values of a generalized two-term exponential sums. In the case $ p\equiv 3\bmod 4 $, we try to establish two precise formulas by applying the properties of character sums and the number of the solutions of relevant congruence equations modulo an odd prime $ p $.</p></abstract>

Many-body interactions between curvature-inducing membrane inclusions with arbitrary cross-sections.

By means of a multipolar expansion, we study analytically and numerically the interaction, in tensionless membranes, between multiple identical curvature-inducing membrane inclusions having arbitrary cross sections but uniform small detachment angles. In particular, for N circular inclusions forming regular polygons, we obtain analytical expressions for the total asymptotic interaction, up to N = 6, and we numerically compute the different multi-body contributions at arbitrary separations. We find that the latter are comparable to the sum of the two-body contributions. For N = 5 inclusions, the analytical asymptotic interaction scales as the inverse sixth power of the nearest neighbors distance d, weaker than the d-4 power for N ≠ 5. The analytical interactions are always repulsive and in good agreement with the numerical results. In the case of noncircular cross sections, we consider the case of two identical inclusions having a given number of equally shaped lobes. Depending on the number of lobes and their amplitude, we find that the interaction is asymptotically either repulsive as d-4 or attractive as d-2, and always repulsive at short distances. We also characterize how the interaction depends on the inclusion rotation angles in the membrane plane.

The sixth power mean of one kind generalized two-term exponential sums and their asymptotic properties

<abstract><p>The main aim of this article is using the elementary method and the number of the solutions of some congruence equations modulo an odd prime $ p $, to study the calculating problem of the sixth power mean of one kind generalized two-term exponential sums, and give a sharp asymptotic formula for it.</p></abstract>

Comparison of Methods for Emissivity Influence Suppression on Thermographic Data

Emissivity is a crucial parameter for a quantitative thermography measurement. It influences measured temperature using an infrared camera. Typically, the emissivity is handled by infrared camera software but often for more complex tasks—e.g., setting and controlling the emissivity of individual pixels—a custom-made solution must be created. This can be especially beneficial for active thermography measurement and dynamic building inspection by infrared thermography as many surfaces of interest with different emissivity occur in thermographic data. In literature, one technique for suppressing emissivity occurs most often—the technique used by infrared camera manufacturers. Nonetheless, two other techniques are marginally mentioned. The most complex technique is the one used by infrared camera manufacturers, which allows many parameters to be set, but it is difficult to incorporate it into own solution. In contrast, the second one can be adapted easily, and it uses the relationship between emissivity and the fourth power of temperatures. The third one is a scarcely used technique that occurs for some active thermography measurements, in which a thermographic sequence in counts is divided by a frame when temperature equilibrium is reached. The main goal of this article is to compare these individual techniques from the point of view of the accuracy and possibility of use. The experiment showed that all three methods can be successfully used for the suppression of emissivity influence.

The Role of Bladder Neck Injection in the Quest for Continence

The Role of Bladder Neck Injection in the Quest for Continence

INTELLIGENT TECHNOLOGIES IN AGRO-INDUSTRY COMPLEX IN THE WORLD

Most of the results achieved using AI technologies are superior to humans: in 1997, a computer beat the then world chess champion, and more recently, in 2016, other computers beat the world's best go and poker players. Computers prove or help prove mathematical theorems; knowledge is generated automatically, based on machine learning methods, and with the help of large data sets, the size of which is calculated in terabytes (from the 10th to the 12th power) and even petabytes (to the 10th to the 15th power).

On the reciprocal sum of the fourth power of Fibonacci numbers

Abstract Let f n {f}_{n} be the n n th Fibonacci number with f 1 = f 2 = 1 {f}_{1}={f}_{2}=1 . Recently, the exact values of ∑ k = n ∞ 1 f k s − 1 ⌊{\left({\sum }_{k=n}^{\infty }\frac{1}{{f}_{k}^{s}}\right)}^{-1}⌋ have been obtained only for s = 1 , 2 s=1,2 , where ⌊ x ⌋ \lfloor x\rfloor is the floor function. It has been an open problem for s ≥ 3 s\ge 3 . In this article, we consider the case of s = 4 s=4 and show that ∑ k = n ∞ 1 f k 4 − 1 = f n 4 − f n − 1 4 + 2 ( − 1 ) n 5 f 2 n − 1 − n + 2 5 , ⌊{\left(\mathop{\sum }\limits_{k=n}^{\infty }\frac{1}{{f}_{k}^{4}}\right)}^{-1}⌋={f}_{n}^{4}-{f}_{n-1}^{4}+\frac{2{\left(-1)}^{n}}{5}{f}_{2n-1}-\left\{\frac{n+2}{5}\right\}, where { x } ≔ x − ⌊ x ⌋ \left\{x\right\}:= x-\lfloor x\rfloor .

A New Voltage-Multiplier-Based Power Converter Configuration Suitable for Renewable Energy Sources and Sustainability Applications

The sustainability of new-generation energy sources has become one of the most critical challenges in recent years as renewable energy sources (RESs) rapidly replace old fossil sources. Integration between RESs and the grid should be completed through power electronics converters and optimized control techniques. RESs have many advantages, such as having increased reliability and sustainability, being environmentally friendly, and having cheaper maintenance costs and more reasonable energy prices. Photovoltaic (PV) panels are among the most popular RESs. A PV array’s generated voltage level is unsuitable for direct load or grid connection and has to be enhanced via a DC-DC boost converter. After that, an inverter should be used to change the generated DC voltage to AC voltage for the grid or loads. In order to reach higher voltage gains, different structures have been proposed in the literature, such as cascaded converters, non-isolated converters (including transformers), and positive- and negative-voltage-lift Luo converters. These converters have some disadvantages, such as including a large number of semiconductor devices and inductors, heavy and bulky structures, and the need for intermediate converters to convert DC to AC voltage and vice versa. Besides the efficiency and high DC voltage gain feature, to achieve more reliability and sustainability and a longer lifetime of the PV source, the current drawn from these sources should be as ripple-free as possible. This study considers all these details by presenting a novel DC-DC power boost converter. The steady-state analysis, simulation, and test results are presented. The most important features of the proposed converter include the lack of need for a transformer, intermediate inverter, rectifier converters, and bulky and heavy components, while still ensuring that high voltage gains and high efficiencies are possible. Simulation results showed that for duty ratios from D = 0.05 to D = 0.15 for the switch S3, the gain of the converter was 22, 35, and 70 times greater than the input voltage, respectively. The desired 200 VDC and 400 VDC voltages for the output nodes were obtained using 12 VDC as the input voltage with and without the switched-capacitor cell, respectively. A limited number of the voltages between −47 and 12 V dropped across the inductors, and a reversed voltage from −12 to −48 V was reported for the power diodes. Additionally, an efficiency close to 96.88% was obtained for the proposed converter. According to the experimental results, a voltage close to 198 VDC was obtained with a 12 VDC input voltage source without using the switched-capacitor cell. A current with a maximum of 7 A was reported for the output diode, and more than 96% efficiency was reported. The results showed that the primary source of the power losses was the semiconductors, and the switching losses made up around 69% and 88% of the total losses for the switches and diodes, respectively. The present topology has three power switches. Two of the switches are activated and deactivated simultaneously. The third switch is activated or deactivated in reverse with the other switches. The results showed that for short-duty ratios such as 0.5 for switches S1 and S2 and 0.35 for switch S3, DC voltage gains close to 35 were obtained theoretically. The generated voltage could be doubled by applying fourth and fifth power switches by making a switched-capacitor-based topology. All of these details are illustrated in this study in detail. The proposed circuit was set up and tested in a laboratory environment. The test results confirm the simulation and theoretical analysis.

Impact of thermal radiation on turbine blades with film cooling structures

With increasing temperature in front of turbine blades, the impact of thermal radiation on the cooling of turbine blades continues to increase. Therefore, to ensure the long-term reliable operation of blades, the impact must be accurately evaluated. In this study, a method for separating the contribution of radiative heat flow from the total heat flow is proposed for turbine blades with different complex film-cooling structures. Here, the effect of the film hole angle on the proportion of the radiative heat flow was studied using parallel experiments and nonlinear regression methods, which allowed the radiative heat flow to be estimated with a high degree of accuracy. The method was verified by computational fluid dynamics (CFD) simulation data results showing that after considering the change in the physical properties of the boundary layer, the convective heat flow curve inclines upward along the wall temperature, and is no longer a linear function of the wall temperature. The radiative heat flow is driven by the 4th power of temperature, and the curve instead inclines downward. When the mainstream gas temperature was 1600 K, the radiant heat flow of the film cooling plate with a 30° hole angle accounted for up to 40 % of the total heat flow, with the 45° and 60° hole angles both accounting for more than 20 %. Future research must focus on the effect of thermal radiation in the heat transfer design of the blade.

Q-Supercongruences from squares of basic hypergeometric series

We give some new q-supercongruences on truncated forms of squares of basic hypergeometric series. Most of them are modulo the cube of a cyclotomic polynomial, and two of them are modulo the fourth power of a cyclotomic polynomial. The main ingredients of our proofs are the creative microscoping method, a lemma of El Bachraoui, and the Chinese remainder theorem for coprime polynomials. We also propose several related conjectures for further study.

Pathophysiology and pathogenic mechanisms of pulmonary hypertension: role of membrane receptors, ion channels, and Ca2+ signaling.

The pulmonary circulation is a low-resistance, low-pressure, and high-compliance system that allows the lungs to receive the entire cardiac output. Pulmonary arterial pressure is a function of cardiac output and pulmonary vascular resistance, and pulmonary vascular resistance is inversely proportional to the fourth power of the intraluminal radius of the pulmonary artery. Therefore, a very small decrease of the pulmonary vascular lumen diameter results in a significant increase in pulmonary vascular resistance and pulmonary arterial pressure. Pulmonary arterial hypertension is a fatal and progressive disease with poor prognosis. Regardless of the initial pathogenic triggers, sustained pulmonary vasoconstriction, concentric vascular remodeling, occlusive intimal lesions, in situ thrombosis, and vascular wall stiffening are the major and direct causes for elevated pulmonary vascular resistance in patients with pulmonary arterial hypertension and other forms of precapillary pulmonary hypertension. In this review, we aim to discuss the basic principles and physiological mechanisms involved in the regulation of lung vascular hemodynamics and pulmonary vascular function, the changes in the pulmonary vasculature that contribute to the increased vascular resistance and arterial pressure, and the pathogenic mechanisms involved in the development and progression of pulmonary hypertension. We focus on reviewing the pathogenic roles of membrane receptors, ion channels, and intracellular Ca2+ signaling in pulmonary vascular smooth muscle cells in the development and progression of pulmonary hypertension.

Control of Dy164 Bose-Einstein condensate phases and dynamics with dipolar anisotropy

We investigate the quench dynamics of quasi-one and two dimensional dipolar Bose-Einstein condensates (dBEC) of $^{164}$Dy atoms under the influence of a fast rotating magnetic field. The magnetic field thus controls both the magnitude and sign of the dipolar potential. We account for quantum fluctuations, critical to formation of exotic quantum droplet and supersolid phases in the extended Gross-Pitaevskii formalism, which includes the so-called Lee-Huang-Yang (LHY) correction. An analytical variational ansatz allows us to obtain the phase diagrams of the superfluid and droplet phases. The crossover from the superfluid to the supersolid phase and to single and droplet arrays is probed with particle number and dipolar interaction. The dipolar strength is tuned by rotating the magnetic field with subsequent effects on phase boundaries. Following interaction quenches across the aforementioned phases, we monitor the dynamical formation of supersolid clusters or droplet lattices. We include losses due to three-body recombination over the crossover regime, where the three-body recombination rate coefficient scales with the fourth power of the scattering length ($a_s$) or the dipole length ($a_{dd}$). For fixed values of the dimensionless parameter, $\epsilon_{dd} = a_{dd}/a_s$, tuning the dipolar anisotropy leads to an enhancement of the droplet lifetimes.

Burying small Pt nanoparticles in the TiO2 microsphere support to form visible light antenna-reactor photocatalysts.

By rational design and parameter engineering of the TiO2-Pt core-satellite construction, visible light absorption in small Pt nanoparticles (NPs) can be enhanced by nearly 100 times. The TiO2 microsphere support works as the optical antenna, giving rise to superior performance compared to conventional plasmonic nanoantennas. A crucial step is to bury the Pt NPs completely in the high refractive index TiO2 microsphere, because light absorption in the Pt NP approximately scales with the fourth power of the refractive index of its surrounding media. The proposed evaluation factor for light absorption enhancement in the Pt NPs at different positions is proved to be valid and useful. The physics modeling of the buried Pt NPs corresponds to the general case in practice where the surface of the TiO2 microsphere is naturally rough or a thin TiO2 coating is subsequently added. These results offer new avenues for directly transforming dielectric supported nonplasmonic catalytic transition metals into visible light photocatalysts.

Understanding chemical enhancements of surface-enhanced Raman scattering using a Raman bond model for extended systems.

In this work, we extend a previously developed Raman bond model to periodic slab systems for interpreting chemical enhancements of surface-enhanced Raman scattering (SERS). The Raman bond model interprets chemical enhancements as interatomic charge flow modulations termed Raman bonds. Here, we show that the Raman bond model offers a unified interpretation of chemical enhancements for localized and periodic systems. As a demonstration of the Raman bond model, we study model systems consisting of CO and pyridine molecules on Ag clusters and slabs. We find that for both localized and periodic systems, the dominant Raman bonds are distributed near the molecule-metal interface and, therefore, the chemical enhancements are determined by a common Raman bond pattern. The effects of surface coverage, thickness, and roughness on the chemical enhancements have been studied, which shows that decreasing surface coverage or creating surface roughness increases chemical enhancements. In both of these cases, the inter-fragment charge flow connectivity is improved due to more dynamic polarization at the interface. The chemical enhancement is shown to scale with the inter-fragment charge flow to the fourth power. Since the inter-fragment charge flow is determined by the charge transfer excitation energy, the Raman bond model is connected to the transition-based analysis of chemical enhancements. We also show that the SERS spectra of localized and periodic systems normalized by inter-fragment charge flows can be unified. In summary, the Raman bond model offers a unique framework for understanding SERS spectra in terms of Raman bond distributions and offers a connection between localized and periodic model systems of SERS studies.

Van der Waals–London interaction of atoms with pseudorelativistic kinetic energy

We consider a multiatomic system where the nuclei are assumed to be point charges at fixed positions. Particles interact via Coulomb potential and electrons have pseudo-relativistic kinetic energy. We prove the van der Waals-London law, which states that the interaction energy between neutral atoms decays as the sixth power of the distance $|D|$ between the atoms. We rigorously compute all the terms in the binding energy up to the order $|D|^{-9}$ with error term of order $\mathcal{O}(|D|^{-10})$ . As intermediate steps we prove exponential decay of eigenfunctions of multiparticle Schr\"odinger operators with permutation symmetry imposed by the Pauli principle and new estimates of the localization error.

The Role of Women-Journalists and Writers in the Development of Democracy and Culture in Australia (the end of the XIXth century – 70s of the XXth century)

The emancipation of Australian women in particular journalists and writers, who dedicated their lives to the development of culture of the fifth continent has been detected in this article. The goal of the article is to analyse the arrival of women – journalists, editors, publishers - in the print media and to determine their role in the formation and development of democracy and culture of the young state.
 As a result of the interdisciplinary research (combination of history, sociology, philology, culturology) new data on the role of women were obtained in the formation of democracy in Australia. This gives reason to affirm that this is the first study of this problem in Ukraine.
 New names of such outstanding Australian men – journalists, editors, publishers, writers as E.S. Hall, S. Bennet, H. Parks, G. Mott, C. Feilberg, W. Winn and women – L. Lawson, F. Baverstock, N. Palmer were introduced into scientific circulation. Significantly expanded and supplemented historical and cultural information about such outstanding women writers and journalists as M. Gilmore, E.F. Richardson, M. Franklin, K.S. Prichard, C. Stead, C. McCullough. Their life is investigated in the context of socio-historical development of Australia and world events that were reflected in their work. Great is their contribution to the antifascist struggle, to the defence of freedom and democratic values in Australia.
 The artistic value of the work of each of them is determined. The humanistic and realistic approach in creating their characters is clarified. It reflects the historical and socio-cultural development of Australia since the mid-XIX century to the 70-s of the XX century. It is proved that the history of periodicals and the development of literature on the fifth continent is the story of extraordinary talented women, in whose destinies the history of the development of the fourth power and the literature of Australia is reflected. The stages of The Bulletin magazine’s existence, the reasons for its closure and its influence on formation of Australian national literature are analysed.
 The practical value of the work lies in the fact that it brings new data to academic courses such as “The History of Australia”, “The Print Media of Australia”, “The Literature of Australia”.
 It is proved than women writers and journalists of Australia enriched Australian literature with bright original works and also made a significant contribution to its culture and democracy.