Coefficients A2 Research Articles

Influence of Age and Sex on Stability Indicators of the Right-Left Hemodynamic Balance of Skin Microcirculation in Symmetrical Areas of the Human Head.

Indicators (markers) of microcirculation stability (MCR) of the skin in symmetric areas of the head were studied in young (18-19-years-old) and elderly (60-80-years-old) male and female subjects. We performed synchronous MCR measurements of symmetrical areas of the head using laser Doppler flowmetry in 40 healthy volunteers (10 men and 10 women in each age group). Numerical values of stability markers (T1, T2, and ζ) and indicators of the right-left hemodynamic balance of the MCR (regression coefficients a1, a2, b1, b2) were obtained using the previously developed computational and experimental methods. The coefficients a2 and b2 that determine the contribution of the right MCR bed to the right-left hemodynamic balance were higher in elderly men than in young men, while in young and elderly women, no significant differences in the values of these coefficients were revealed. In young men, coefficients a2 and b2 were lower than in young women, while in elderly subjects, the sex differences in these coefficients were leveled. Young men have lower stability markers than women, while in elderly subjects, these stability markers were similar in men and women. No significant age and sex differences in the level of perfusion of the symmetrical temporal regions were found. The results attest to low stability of MCR in young men in comparison with young women and similar stability in old age, which, apparently, can be explained by the influence of sex hormones on the regulation of human cardiovascular functions.

Subclasses of Bi-Univalent Functions Connected with Caputo-Type Fractional Derivatives Based upon Lucas Polynomial

In the current paper, we introduce new subclasses of analytic and bi-univalent functions involving Caputo-type fractional derivatives subordinating to the Lucas polynomial. Furthermore, we find non-sharp estimates on the first two Taylor–Maclaurin coefficients a2 and a3 for functions in these subclasses. Using the values of a2 and a3, we determined Fekete–Szegő inequality for functions in these subclasses. Moreover, we pointed out some more subclasses by fixing the parameters involved in Lucas polynomial and stated the estimates and Fekete–Szegő inequality results without proof.

Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function

Let Scos* denote the class of normalized analytic functions f in the open unit disk D satisfying the subordination zf′(z)f(z)≺cosz. In the first result of this article, we find the sharp upper bounds for the initial coefficients a3, a4 and a5 and the sharp upper bound for module of the Hankel determinant |H2,3(f)| for the functions from the class Scos*. The next section deals with the sharp upper bounds of the logarithmic coefficients γ3 and γ4. Then, in addition, we found the sharp upper bound for H2,2Ff/2. To obtain these results we utilized the very useful and appropriate Lemma 2.4 of N.E. Cho et al. [Filomat 34(6) (2020), 2061–2072], which gave a most accurate description for the first five coefficients of the functions from the Carathéodory’s functions class, and provided a technique for finding the maximum value of a three-variable function on a closed cuboid. All the maximum found values were checked by using MAPLE™ 2016 computer software, and we also found the extremal functions in each case. All of our most recent results are the best ones and give sharp versions of those recently published in [Hacet. J. Math. Stat. 52, 596–618, 2023].

Mathematical modeling and flow thermodynamics study of borosilicate glass melt after external addition of Cr2O3

This article uses a high-temperature sintering imaging instrument to test the flowability of borosilicate glass melt doped with Cr2O3, and establishes a mathematical model for high-temperature glass melt spreading. Discuss the glass melt from a thermodynamic perspective by combining model interpretation with experimental characterization. The results indicate that the thermodynamic judgment formula for high-temperature flow spreading of borosilicate glass is: Q≥ρ[A0exp(−T/k0)+S0]−M·δ[A0exp(−T/k0)+S0]1/2. To improve the high-temperature flow ability of borosilicate glass, it is necessary to increase the spreading activation energy Q. On the other hand, it is necessary to reduce the spreading coefficients A0、 k0 and S0. As a refractory metal oxide and active oxide, Cr2O3 plays a role in reducing the spreading coefficient of glass systems.

Theoretical studies and anharmonic effect analysis on the reaction mechanism of 3-methyl-1-butanol with OH radical

The mechanism of hydrogen abstraction in the reaction of 3-methyl-1-butanol with an OH radical was investigated by quantum chemical calculations. The total reaction consists of five channels (R1–R5), with channel R3 having the lowest energy barrier (5.4 kcal·mol−1) and channel R4 having the highest energy barrier (13.2 kcal·mol−1). All channels are exothermic reactions with lower energy barriers. Thermodynamic parameters, including constant pressure molar heat capacity CPo, enthalpy of formation ΔfHo, and entropy So, for all reactants and products, were researched using the CBS-QB3 level across a temperature scale of 298–5000 K. The harmonic and anharmonic rate constants of all reaction channels were calculated at the CCSD(T)/6-311++G(d,p) level for a temperature range of 223–4000 K. Throughout the temperature range, except for R2, the harmonic rate constant of all reaction channels is consistently higher than the anharmonic one, and it can be seen from the results that the anharmonic effect is significant and cannot be ignored. Meanwhile, the polynomial coefficients a1–a7 for the thermodynamic parameters and the polynomial coefficients A, n, and E for the kinetic parameters were fitted using the principle of least squares.

Aging related changes in cardiovascular system in healthy female population: photoplethysmography method and DFA analysis

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): Ministry of Science Technological Development and Innovation Background The cardiovascular system undergoes dynamic changes during the biological aging in humans, leading to chronic cardiovascular and cerebrovascular diseases. Purpose Developing the novel method for non-invasive monitoring of age induced changes in arterial vessels. Methodology The pilot study was performed on 58 women, in good health, non-smokers, between the ages of 20 and 70, divided into three age groups. All subjects underwent arterial blood pressure measurement using a photoplethysmography sensor. Recordings were performed in left carotid artery and the left index finger area. Arterial blood flow waveform was then analyzed using DFA analysis, calculating the values of the scalar coefficients α1 and α2. Based on the waveform time interval shift between the standing and supine positions, the pulse wave velocity (PWV) ratio was determined. Results Systolic and diastolic arterial pressure showed a slight linear increase with the age, but without significant difference between the three age categories (p > 0.5). Also, the PWV ratio between the supine and standing positions did not show a statistically significant increase between the age groups. Only scalar coefficients ratio α1/α2 demonstrated a significant difference in value between all age categories. Conclusion In subjects included in this pilot study, only the scalar coefficients ratio varied significantly with the age, indicating the occurrence of structural changes in the cardiovascular system caused by biological aging.

Effects of Fatigue Parameters on Fatigue Crack Growth Rate of Pipe Steels and Girth Weld

Abstract Oil and gas pipeline steels and welds are subjected to a wide variety of cyclic loadings: internal pressure variation, pulsation of gas pressure resulting from the cyclic operation of a reciprocating compressor at a gas compressor station, internal flow-induced vibration resulting from the turbulent flow within the pipe, vortex-induced vibration of a free-spanning section exposed to air (wind) for aboveground pipelines or water for water-crossing pipelines, and cyclic thermal stresses developed by significant changes in temperature due to seasonal changes or changes in operating temperatures. These cyclic loadings are very variable and complex. Considering the fatigue situations, a better understanding of the effects of fatigue test parameters on fatigue behaviors of pipeline steels and welds is required. Hence, in this study, the influences of fatigue test parameters on the Paris law coefficients were studied for pipeline steels and welds. It was analyzed for pipe steels of X65∼X100 and a girth weld of X70. Influences of material strength, crack orientation relative to the pipe axis, and frequency in the range of 1∼30 Hz were insignificant. It was found that the coefficients a1 and b2 of the m-ln(C) relationships linearly relied on the load ratio. The constants (α1, β1, α2, and β2) of these linear relationships between R-ratio and a1 (and b2) were determined for pipe steels.

Coefficient Bounds for a Certain Subclass of Bi-Univalent Functions Associated with Lucas-Balancing Polynomials

In this paper, we introduce a new subclass of bi-univalent functions defined using Lucas-Balancing polynomials. For functions in each of these bi-univalent function subclasses, we derive estimates for the Taylor–Maclaurin coefficients a2 and a3 and address the Fekete–Szegö functional problems for functions belonging to this new subclass. We demonstrate that several new results can be derived by specializing the parameters in our main findings. The results obtained from this study will enrich the theoretical foundation of this field and open new avenues for mathematical inquiry and application.

Analytic Functions Related to a Balloon-Shaped Domain

One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions X defined in the new domain, including the sharp estimates for the coefficients a2,a3, and a4, and for three second-order and third-order Hankel determinants, H2,1X,H2,2X, and H3,1X. The optimality of each obtained estimate is given as well.

Applications of Shell-like Curves Connected with Fibonacci Numbers

We introduce a new subclass JΣη,δ,μ(p˜) of bi-univalent functions, defined by shell-like curves connected with Fibonacci numbers. Our main results in this paper include estimates of the Taylor–Maclaurin coefficients a2 and a3 for functions in this subclass, as well as solutions to Fekete–Szegö functional problems. We also show novel outcomes resulting from the specialization of the parameters used in our main results.

Spectral invariants of the magnetic Dirichlet-to-Neumann map on Riemannian manifolds

This paper is devoted to investigating the heat trace asymptotic expansion associated with the magnetic Steklov problem on a smooth compact Riemannian manifold (Ω, g) with smooth boundary ∂Ω. By computing the full symbol of the magnetic Dirichlet-to-Neumann map M, we establish an effective procedure, by which we can calculate all the coefficients a0, a1, …, an−1 of the asymptotic expansion. In particular, we explicitly give the first four coefficients a0, a1, a2, and a3. They are spectral invariants, which provide precise information concerning the volume and curvatures of the boundary ∂Ω and some physical quantities.

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q-Calculus

In this investigation, the q-difference operator and the Sălăgean q-differential operator are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine the general Taylor–Maclaurin coefficient of the functions in this class using the Faber polynomial method. We demonstrate the unpredictable behaviour of initial coefficients a2, a3 and investigate the Fekete–Szegő problem a3−a22 for the subclasses of bi-close-to-convex functions. To highlight the connections between existing knowledge and new research, certain known and unknown corollaries are also highlighted.

Non-Extendability of Special DIO 3-Tuples Involving Nonaganal Pyramidal Number

Abstract: This paper concerns with the construction of three distinct polynomials with integer coefficients (a1, a2, a3) such that the product of any two contribution of the set subtracted to their sum and improved by a non-zero integer (or a polynomial with integer coefficients) is a perfect square and this shows the non-extendability of Special Dio Quadruple

A New Comprehensive Subclass of Analytic Bi-Univalent Functions Related to Gegenbauer Polynomials

In the current study, we provide a novel qualitative new subclass of analytical and bi-univalent functions in the symmetry domain U defined by the use of Gegenbauer polynomials. We derive estimates for the Fekete–Szegö functional problems and the Taylor–Maclaurin coefficients a2 and a3 for the functions that belong to each of these new subclasses of the bi-univalent function classes. Some more results are revealed after concentrating on the parameters employed in our main results.

Jeffreys heat conduction in coupled semispaces subjected to interfacial heating

A Jeffreys heat conduction problem for coupled semispaces subjected to the action of an interfacial heat source was defined. An analytical solution of the problem was derived for a polynomial specific power of the heat source using the Laplace transform approach. The asymptotic and parametric analysis was performed for different ratios of thermal conductivities K1,2, thermal diffusivities k1,2, thermal relaxation times τ1,2 and coefficients α1,2 indicating the relative contribution of Fourier heat conduction. It was found that Jeffreys heat conduction results in continuous variation of the contact temperature, whilst its particular case — Cattaneo heat conduction — is accompanied by a step change of the contact temperature at the initial time. Another finding is that the initial heat partition occurs due to the ratio of K1α1/k1 and K2α2/k2 under Jeffreys heat conduction and due to the different ratio of K1/k1τ1 and K2/k2τ2 under Cattaneo heat conduction. The solution applicability was demonstrated on the simulation example of ultrashort laser pulse welding. The type of heat conduction was revealed to have qualitative and quantitative impacts on the contact temperature and heat fluxes.

Acoustic thermometer operating up to 11 m: uncertainty assessment and new values for Cramer coefficients around 40 kHz

The present article describes an acoustic thermometer to measure the average air temperature integrated along a path ranging from 1 m to 11 m. It is based on time-of-flight measurement of ultrasound pulses at frequencies close to 40 kHz. Several methods for the detection of arrival times were investigated, notably cross-correlation and cross-spectrum. The uncertainty of the instrument itself, independent of that of the Cramer equation has been estimated at between 0.13 K to 0.09 K for distances ranging from 3 m to 11 m respectively. In practice, an experimental comparison with Pt100 probes (uncertainty of 0.1 K) has shown that the estimated uncertainty levels are relatively compatible, although the linearity of the system does not appear to be very good. To solve this problem, appropriate values for the Cramer coefficients a0 and a1 for an acoustic frequency of about 40 kHz have been determined, which contributes to improved knowledge of this equation as a function of acoustic frequency.

Horadam Polynomials and a Class of Biunivalent Functions Defined by Ruscheweyh Operator

In this paper, we introduce and investigate a class of biunivalent functions, denoted by , that depends on the Ruscheweyh operator and defined by means of Horadam polynomials. For functions in this class, we derive the estimations for the initial Taylor–Maclaurin coefficients |a2| and |a3|. Moreover, we obtain the classical Fekete–Szegö inequality of functions belonging to this class.

An Application of Rabotnov Functions on Certain Subclasses of Bi-Univalent Functions

In this study, a new class RΣμ(x,γ,α,δ,β) of bi-univalent functions studied by means of Gegenbauer polynomials (GP) with Rabotnov functions is introduced. The coefficient of the Taylor coefficients a2 and a3 and Fekete-Szegö problems for functions belonging to RΣμ(x,γ,α,δ,β) have been derived as well. Furthermore, a variety of new results will appear by considering the parameters in the main results.

New Subclasses of Bi-Univalent Functions with Respect to the Symmetric Points Defined by Bernoulli Polynomials

In this paper, we introduce and investigate new subclasses of bi-univalent functions with respect to the symmetric points in U=z∈C:z<1 defined by Bernoulli polynomials. We obtain upper bounds for Taylor–Maclaurin coefficients a2,a3 and Fekete–Szegö inequalities a3−μa22 for these new subclasses.

Multipole Mixing Ratios of Gamma Rays From Ge 70 32 (p,nγ) As 70 33 Reaction Using the Constant Statistical Tensor Method (CST)

The δ-Multipole mixing ratios of  -transitions from levels of 70As populated in the Ge 70 32 (p,nγ) As 70 33 reaction are calculated by using the constant statistical tensor method (CST). This method has been used in other works [1-5] but only with pure transitions orwith transitions that can be considered as pure transitions. In our work, we used this method for mixed gamma -transitions in addition to pure gmma - transitions. The experimental angular distribution coefficients (a2) was used from previous work [6] in order to calculet δ-values.