Related Formulas Research Articles

Determination of the concentration of heavy metals in infused teas and their assessment of potential health risk in Kashan, Iran

ABSTRACT Tea was known as one popular and power-consuming beverage. The purpose of the current study was to determine the concentration of heavy metals in infused tea consumed in Kashan City. This cross-sectional study was carried out on 29brands of dry tea purchased from Kashan city stores. The samples were placed under acidic digestion based on the cited method in the standard method. Measuring heavy metals such as chromium, cadmium, copper, nickel, lead, arsenic, zinc, and iron was performed through ICP-OES device.SPSS16 and Excel software was used to evaluate the statistical parameters. The evaluation carcinogenic risk was performed using related formula. The obtaining results indicated that mean concentration of heavy metals in infused black tea were related to iron, zinc, copper, lead, nickel, chromium, cadmium, arsenic which was equal to 0.819 ± 0.139, 0.419 ± 0.314, 0.173 ± 0.107, 0.125 ± 0.103, 0.097 ± 0.078, 0.059 ± 0.061, 0.045 ± 0.064, 0 mg/kg, respectively. According to their associated potential health risk assessment, HQ of some heavy metals including Cd, Pb, Cr, Ni, Cu, Zn, Fe and As was 0.642, 0.51, 0.2806, 0.0692, 0.0618, 0.0199, 0.0167 and 0 mg/kg-day and THQ or HI was upper than one(1.601).The results of the present study revealed that the concentration of copper, zinc and arsenic metals in all samples of infused tea was considered standard, but the concentration of lead, chromium, cadmium and nickel elements in some samples and the concentration of iron in all studied samples exceeded the maximum permissible limit presented by Iran National Standard and WHO. In addition, risk assessment analysis indicated that the consumption of the studied black tea on average(1 litre per day) had no adverse effect on the health of tea consumers.so, continuous monitoring of the concentration of heavy metals in black tea samples is essential.

Simplified calculation of fire resistant temperature for cold-formed steel load-bearing composite walls

The research on the fire resistance design of cold-formed steel (CFS) load-bearing composite walls, as the main vertical load-bearing and space-dividing components of the CFS structure, has received widespread attention. The purpose of this article is to propose a formula for calculating the fire resistant temperature of CFS composite walls in order to simplify the design method. Three different configurations for composite wall lined with gypsum plasterboards which commonly used were chosen as research objects. According to the temperature-rise rule and heat transfer mechanism, the temperature-rise curves at hot flange of the studs were obtained. Then a heat transfer model was established with considering both the heat conduction and cavity radiation where obtained temperature load was applied at hot flange of the stud to calculate the temperature distribution of the wall cross-section. The improved heat transfer model not only considered the effect of cavity radiation, but also simulated the direct exposure of the stud to high temperature due to the falling-off or losing of insulation for sheathed board. Then the heat transfer calculation results were imported into a simplified mechanical model for thermal–mechanical coupling numerical simulation. Integrity, insulation, and the load bearing capacity of the stud cross section were taken as the comprehensive consideration criteria for composite wall failure. The temperature at hot flange of the stud was defined as fire resistant temperature when the composite wall damaged. Finally, load ratio and fire resistance temperature related calculation formulas were fitted from the results of transient thermal–mechanical coupling simulation with varying load ratios. The comparison of fire resistance temperature between fitting formula and fire test results verified the applicability of the proposed fire resistance temperature calculation formula. Compared with the fire resistance temperature calculation formulas in the existing literature, the calculation formula proposed in this paper was more accurate and reasonable.

Relative Trace Formula for Compact Quotient and Pseudo-Coefficients for Relative Discrete Series

Abstract We introduce the notion of relative pseudo-coefficient for relative discrete series representations of real spherical homogeneous spaces of reductive groups. We prove that $K$-finite relative pseudo-coefficient does not exist for semisimple symmetric spaces of type $G_{\mathbb{C}}/G_{\mathbb{R}}$, where $K$ is a maximal compact subgroup of $G_{\mathbb{C}}$, and construct strong relative pseudo-coefficients for some hyperbolic spaces. We establish a toy model for the relative trace formula of H. Jacquet for compact discrete quotient $\Gamma \backslash G$. This allows us to prove that a relative discrete series representation, which admits strong pseudo-coefficients with sufficiently small support, occurs in the spectral decomposition of $L^2(\Gamma \backslash G)$ with a nonzero period.

Development of hybrid ECC columns subjected to concentric and eccentric loading

In recent years, significant attention has been given in previous studies to improve the performance of structural members. It would be useful to further improve in this approach. This study was undertaken in order to investigate the structural behaviour of newly developed Engineering Cementitious Composites (ECC) columns subjected to concentric and eccentric loading. These columns were experimentally formulated using a hybridization of steel and polypropylene fibers. Two ratios were adopted for the steel fibres 0.5% and 1%, whilst the polypropylene fibre was kept constant at a ratio of 0.5% for all of the ECC columns. The eccentric loads were applied at two eccentricities: small (h/6) and large (5 h/12). The effect of slenderness ratio was taken into consideration at two values; 6 and 8. A comparison was also made with the behaviour of self-compacted concrete and traditional ECC columns containing either steel or polypropylene fibres. The vertical and lateral deformations as well as the maximum load at failure were noted. Amendments were performed on some of the related formulas suggested by the code of practice.The results obtained showed that the hybrid ECC columns exhibited higher load carrying capacities when compared with those of both self-compacted concrete and traditional ECC columns. The percentage increase reached 30%. The hybrid ECC column samples containing 1% steel fibre did not show a signification difference in the load-deformation behaviour when it compared with that containing 0.5% steel fibre. The values of eccentricity and slenderness ratio governed the global behaviour of the tested columns. The predicted load carrying capacities of the ECC columns using the existing code formulas need a magnification factor in case of concentric test, and to take into account the fibres ratio when calculating the area of steel reinforcement for eccentric loading.

Study on quality standard of fried Vaccariae Semen standard decoction

According to the preparation principle of standard decoction of Chinese herbal medicines, fourteen batches of fried Vaccariae Semen decoction were prepared in this study and the quality research was carried out to establish a quality evaluation method for the standard decoction of fried Vaccariae Semen. The contents of vaccarin were determined, and its transfer rate from decoction piece to standard decoction was calculated. The extract rate and pH value were measured, and HPLC fingerprint method was established for analysis. The results of the 14 batches of samples revealed that the transfer rates of vaccarin were between 58.98%-93.94%; the extract rates were between 8.67%-17.83%, and the pH values were between 5.55-6.44. Moreover, 9 common chromatographic peaks were identified in fingerprints analysis. The similarities of the 14 batches of samples were analyzed and compared, and the results showed that the similarities were all higher than 0.96. In this study, the preparation process for fried Vaccariae Semen standard decoction was standard, with high similarities in fingerprint. A convenient and reliable method of comprehensive quality evaluation was established in this study, with a high precision, stability and repeatability, which can provide a reference for the quality control of fried Vaccariae Semen standard decoction, dispensing granule and related Chinese classical formulas(decoction).

Supersymmetric phases of 4d mathcal{N} = 4 SYM at large N

We find a family of complex saddle-points at large N of the matrix model for the superconformal index of SU(N ) mathcal{N} = 4 super Yang-Mills theory on S3× S1 with one chemical potential τ . The saddle-point configurations are labelled by points (m, n) on the lattice Λτ = ℤτ + ℤ with gcd(m, n) = 1. The eigenvalues at a given saddle are uniformly distributed along a string winding (m, n) times along the (A, B) cycles of the torus ℂ/Λτ . The action of the matrix model extended to the torus is closely related to the Bloch-Wigner elliptic dilogarithm, and the related Bloch formula allows us to calculate the action at the saddle-points in terms of real-analytic Eisenstein series. The actions of (0, 1) and (1, 0) agree with that of pure AdS5 and the supersymmetric AdS5 black hole, respectively. The black hole saddle dominates the canonical ensemble when τ is close to the origin, and there are new saddles that dominate when τ approaches rational points. The extension of the action in terms of modular forms leads to a simple treatment of the Cardy-like limit τ → 0.

A rock mechanics calculation model for identifying bed separation position and analyzing overburden breakage in mining

During coal seam mining, the overlying rock can deform, break, and produce a large number of fractures, including horizontal and vertical fractures; the horizontal fractures are also known as bed separation. A bed separation water disaster (BSWD) is a destructive release of roof water, and preventing BSWDs requires accurate location of bed separation positions. A calculation model for overburden deformation and fracture analysis during mining is therefore needed. First, the deformation and breakage area of overlying rock above an active mining face were reduced to a triangular overburden deformation area (TODA), based on the results of similar material simulation experiments. Second, the hierarchy comparison merging method (HCMM) was proposed to analyze the combination and separation of rock layers in the overlying strata. The triangular calculation model (TCM), which can be used to identify bed separation locations and analyze overlying strata breakage, was then obtained by combining TODA with HCMM, and the discriminant principle and related calculation formulas of the model were given. Finally, the model was applied and validated using a mining case, showing that the TCM is a practical tool for analyzing bed separation position and overburden breakage during mining.

Study on the service life prediction of freeze–thaw damaged concrete with high permeability and inorganic crystal waterproof agent additions based on ultrasonic velocity

Based on a rapid freeze–thaw test of inner-doped silicon-ash concrete specimens that were coated using three different externally coated inorganic coating methods, ultrasonic wave velocity and dynamic elastic modulus measurements were employed. The characteristics of the ultrasonic wave velocity attenuation and dynamic elastic modulus of the concrete utilizing three types of inorganic coating methods under the effect of freeze–thaw cycles were analysed. Based on the theory of damage mechanics and the evolution equation for freeze–thaw or corrosion damaged concrete, the damage evolution equations of the relative dynamic elastic modulus for three types of inorganic coated concrete were verified by a large amount of experimental data under the action of a single freeze–thaw factor. According to the relative dynamic elastic modulus formula, based on the ultrasonic wave velocity of Ababneh, the relative ultrasonic velocity was determined to be 0.7746 when the relative dynamic elastic modulus was 0.60. The equivalent freeze–thaw damage model of the ultrasonic wave velocity of the concrete was established, the concept of relative ultrasonic wave velocity was proposed, the relative dynamic elastic modulus method was verified, and the relative P-wave velocity and relative shear wave velocity of Ababneh for the three types of concrete under the effect of freeze–thaw cycles was determined for service life prediction. The above three methods can accurately predict the service life of concrete. Ultimately, the service life of concrete materials in different mix proportions and use areas will be able to be predicted using ultrasonic non-destructive testing in the future.

The Quantum Corrections on Kerr-Newman Black Hole Thermodynamics by the Generalized Uncertainty Principle

By the generalized uncertainty principle, the quantum corrections on Kerr-Newman black hole thermodynamics is studied. Using the modified quantum uncertainty of particles near the event horizon, the relationship between the temperature and the horizon radius for the general stationary black hole is given. Then, to ensure the relational formula having the basic physics meaning, the critical state with Planck temperature for the black hole is obtained. In addition, considering the quantum gravity effects and using the first law of black hole thermodynamics, the entropy of the charged rotating black hole is calculated and the quantum corrections including the logarithmic item to the Bekenstein-Hawking entropy are obtained. Also, in the context of the generalized uncertainty principle, the thermal capacity of Kerr-Newman black hole is obtained. Letting the thermal capacity equal zero, the black hole radiation remnant with Planck temperature is derived. It is found that, for Kerr-Newman black hole, the remnant state is consistent with the critical state. Such, using the generalized uncertainty principle, the temperature divergence at the last stage of evaporation in the traditional Kerr-Newman black hole thermodynamics is removed.

Besov norms of the continuous wavelet transform in variable Lebesgue space

In this paper, the continuous wavelet transform is studied in variable $$L^{p(\cdot )}$$ spaces. Parseval relation and Reconstruction formula for the continuous wavelet transform in variable $$L^{p(\cdot )} $$ spaces are derived. The characterization of variable Besov spaces associated with the continuous wavelet transform is also presented.

Statistical Processing and Correlations Between Concentrations of Some Atmospheric Pollutants in Suceava and Botosani Counties

The abundance of some pollutants from the air depend on the geographic area, the human activities intensity, the climate, the season and even on the hour within a day. The nitrogen oxides are the most abundant and most dangerous toxic species from the air, and these emissions are tightly connected to human polluting activities. Therefore, in our work, the first part is assigned for a wide literature search concerning the incidence of the keywords �nitrogen oxide� and searching the connections with other significant related terms and formulas, investigated by the researches worldwide. Then, a statistic approach was applied trying to correlate the values of the concentration in air of nitrogen monoxide, nitrogen dioxide, carbon monoxide, sulfur dioxide, benzene and particulate matter PM10, all of these being generated to a large extent from the exhaust gases from different automotives. The data were collected from the official site of the National Network of Air Quality Monitoring from Romania, and processed by statistical methods, using specific software and methods, in order to find significant differences between the pollutants concentrations values in two neighbor counties (Suceava and Botosani), with relatively similar climate conditions, but different social wealth. The findings of these statistical processing indicate that the PM10 values do not present significant differences between the two locations, neither the time within a day, while the other parameters exhibit distinctions between the values of the other pollutants concentrations in different seasons (summer and winter) and hourly intervals within a day (night, morning, afternoon and evening).

Interplay of Kelvin–Helmholtz instability with acoustics in a viscous potential flow

Among the hydrodynamic instabilities influencing the evolution, stabilization, and control of flows, the Kelvin–Helmholtz (KH) instability mode is a profound trigger to induce unsteadiness and turbulence—either within a single fluid, by means of a velocity shear, or along the interface of multiple fluids. This mechanism has been analytically studied by Funada and Joseph [“Viscous potential flow analysis of Kelvin–Helmholtz instability in a channel,” J. Fluid Mech. 445, 263 (2001)], for the surface separating two fluids within the approximation of inviscid and viscous potential flows. The present investigation extends the Funada–Joseph formulation to incorporate the effect of imposed acoustic waves on the system under consideration. Specifically, the KH–acoustic interaction is studied by employing a modification of the Bychkov approach [V. Bychkov, “Analytical scalings for flame interaction with sound waves,” Phys. Fluids 11, 3168 (1999)], which has been originally derived for the acoustic coupling to the combustion instability. The analytic formulae for the dispersion relations, growth rates, and neutral curves describing the perturbed interface of the KH instability/acoustic region are derived. Specifically, the limits for stable/unstable regimes as a function of hydrodynamic and acoustic parameters are identified. Two interacting modes are of particular interest: resonant and parametric modes, characterized by acoustic fields having the same frequency (resonant) and twice the frequency (parametric) of the instability oscillations. It is shown that while relatively weak acoustics provide a promising contribution to stabilize the KH instability, those of higher strength can excite the parametric instability. Overall, a comprehensive parametric study of the KH–acoustic coupling and stability limits shows that a global stability region may exist between that of the resonant and parametrically unstable regimes.

A frequency measurement method using rising-falling edge of square wave for increasing proton magnetometer precision

To improve the measurement precision of the proton magnetometer (PM), a multi-average multi-cycle frequency measurement (M-MFM) method using both rising and falling edge of square wave is proposed in this study. First, the M-MFM method using Rising-Falling edge of square wave is presented based on the multi-cycle frequency measurement (MFM) method, and the formula of frequency measurement is deduced. Then, the relative error of the proposed method is analyzed, and the proposed method is optimized by solving the minimum value of the relative error formula. Finally, the implementation process of the proposed method in STM32 is introduced. The experimental results of the frequency measurement demonstrate that the measurement precision for low SNR sine signals is significantly increased by the proposed method. The experimental results of the magnetic field measurement show that the sensitivity is about 0.11 nT/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> @0.25 Hz in the range of the geomagnetic field while the proposed method is adopted by the PM, which is better than that of the other methods and the commercial instruments.

Liquidity in Equity Markets – Definitions and Formulae

The purpose of this paper is to set up a clear definition of liquidity in equity markets and to develop a liquidity factor to measure liquidity, including its formula. We claim that four necessary elements in sum are sufficient to define the term liquidity. Its structure is determined by the relations between these elements. To specify our considerations, we will focus on the trading of equity products in their home market when defining liquidity and deriving its formula. However, our deliberations can be transferred equally to any other liquidity pool and to the other modules of the value chain. To underline our assumptions, we will start with some general remarks about definitions which we then apply to the term liquidity. In a next step we will develop a concept of liquidity: A general and abstract definition for the liquidity of equity markets. This is the basic starting point for the concretization and individualization of the term liquidity. It enables us to measure liquidity in concrete situations in the real world. Having reached the highest level of concretization and individualization we are now able to apply the liquidity factor λ as the measured ease to trade a certain stock. We end up with some working definitions which are core for the development and application of the formula. After these rather theoretical considerations we turn to the concrete calculation of the liquidity factor λ. We spend some thoughts on general aspects for the calculation of liquidity before we derive a concrete formula for its measurement. We analyze this liquidity factor from different angles and also take a look at related formulae before we conclude our paper with an outlook on further objects of investigation. As to the methodology of this paper we will pursue a deductive approach. We will start with some general rules on liquidity before we successively narrow the range under consideration until we draw our conclusions on liquidity for a certain stock under predefined premises. Nevertheless, the results we will obtain are equally applicable to other securities with other predefined premises: They are applicable to equity markets in general.

Classical limit of quantum Borcherds-Bozec algebras

Let g be a Borcherds-Bozec algebra, U(g) be its universal enveloping algebra and Uq(g) be the corresponding quantum Borcherds-Bozec algebra. We show that the classical limit of Uq(g) is isomorphic to U(g) as Hopf algebras. Thus, Uq(g) can be regarded as a quantum deformation of U(g). We also provide explicit formulas for the commutation relations among the generators of Uq(g).

Bi-Periodic Pell Sequence

In this study, we introduce a new generalization of the Pell numbers which is called bi-periodic Pell sequences. We then proceed to find the Binet formula as well as the generating function for this sequence. The well-known Cassini, Catalan and the D’ocagne’s identities as well as some related binomial summation and sum formulas are also given. The convergence properties of the consecutive terms of this sequence is also examined.

The modified Camassa–Holm equation: Bäcklund transformation and nonlinear superposition formula**Dedicated to the memory of Jon Nimmo.

This paper is concerned with the modified Camassa–Holm equation and its Bäcklund transformation. With the aid of reciprocal transformation and the associated modified Camassa–Holm equation, a Bäcklund transformation, which involves both dependent and independent variables, is constructed for the modified Camassa–Holm equation. The related nonlinear superposition formula is worked out and applications of both Bäcklund transformation and nonlinear superposition formula are considered.

An Accurate Efficiency Calculation of Self-excited Induction Generator Including Effects of All Machine Parameters

In this paper an accurate method for efficiency calculation of self-excited induction generator (SEIG) at different operating conditions is proposed, considering the effect of stator and rotor iron core losses, stator and rotor circuits stray load losses, stator and rotor winding (copper) losses, mechanical losses, skin-effect losses, and skew-effect losses. The proposed procedure of efficiency calculation is based on the conventional machine tests such as no-load test, load test at variable supply voltage and temperature test without additional measurements. From these conventional tests, all the SEIG losses can be calculated accurately by their related formulas derived based on the SEIG equivalent circuit. The reduction of these losses causes an increase in the SEIG percentage efficiency, and this is a very important feature in electric energy saving by minimization of SEIG equivalent circuit components.

A Parameter Estimation Method of Shock Model Constructed with Phase-Type Distribution on the Condition of Interval Data

The phase-type distribution (also known as PH distribution) has mathematical properties of denseness and closure in calculation and is, therefore, widely used in shock model constructions describing occurrence time of a shock or its damage. However, in the case of samples with only interval data, modeling with PH distribution will cause decoupling issues in parameter estimation. Aiming at this problem, an approximate parameter estimation method based on building PH distribution with dynamic order is proposed. Firstly, the shock model established by PH distribution and the likelihood function under samples with only interval data are briefly introduced. Then, the principle and steps of the method are introduced in detail, and the derivation processes of some related formulas are also given. Finally, the performance of the algorithm is illustrated by a case with three different types of distributions.

Functorial transfer between relative trace formulas in rank 1

According to the Langlands functoriality conjecture, broadened to the setting of spherical varieties (of which reductive groups are special cases), a map between L -groups of spherical varieties should give rise to a functorial transfer of their local and automorphic spectra. The “beyond endoscopy” proposal predicts that this transfer will be realized as a comparison between limiting forms of the (relative) trace formulas of these spaces. In this paper, we establish the local transfer for the identity map between L -groups, for spherical affine homogeneous spaces X = H \ G whose dual group is SL 2 or PGL 2 (with G and H split). More precisely, we construct a transfer operator between orbital integrals for the ( X × X ) / G -relative trace formula, and orbital integrals for the Kuznetsov formula of PGL 2 or SL 2 . Besides the L -group, another invariant attached to X is a certain L -value, and the space of test measures for the Kuznetsov formula is enlarged to accommodate the given L -value. The transfer operator is given explicitly in terms of Fourier convolutions, making it suitable for a global comparison of trace formulas by the Poisson summation formula, hence for a uniform proof, in rank 1 , of the relations between periods of automorphic forms and special values of L -functions.