The proliferation of technology and communication has resulted in increased digitalisation that includes digital payments. This study is aimed at unravelling the relationship between awareness of individuals about the digital payment system and customer satisfaction with digital payments. Two models were developed in this study. First model considers awareness → usage pattern → customer satisfaction. Second model considers usage pattern → customer satisfaction → perception of digital payments. These two alternative models were tested by collecting data from 507 respondents in southern India was analysed using the structural equation modelling. The results indicate that usage pattern acted as a mediator between awareness and satisfaction, and satisfaction acted as a mediator between usage pattern and consumers' perception of digital payments. The implications for theory and practice are discussed.

Aim/Purpose: This study seeks to present a learning model of discrete mathematics elements, elucidate the content of teaching, and validate the effectiveness of this learning in a digital education context. Background: Teaching discrete mathematics in the realm of digital education poses challenges, particularly in crafting the optimal model, content, tools, and methods tailored for aspiring computer science teachers. The study draws from both a comprehensive review of relevant literature and the synthesis of the authors’ pedagogical experiences. Methodology: The research utilized a system-activity approach and aligned with the State Educational Standard. It further integrated the theory of continuous education as its psychological and pedagogical foundation. Contribution: A unique model for instructing discrete mathematics elements to future computer science educators has been proposed. This model is underpinned by informative, technological, and personal competencies, intertwined with the mathematical bedrock of computer science. Findings: The study revealed the importance of holistic teaching of discrete mathematics elements for computer science teacher aspirants in line with the Informatics educational programs. An elective course, “Elements of Discrete Mathematics in Computer Science”, comprising three modules, was outlined. Practical examples spotlighting elements of mathematical logic and graph theory of discrete mathematics in programming and computer science were showcased. Recommendations for Practitioners: Future computer science educators should deeply integrate discrete mathematics elements in their teaching methodologies, especially when aligning with professional disciplines of the Informatics educational program. Recommendation for Researchers: Further exploration is recommended on the seamless integration of discrete mathematics elements in diverse computer science curricula, optimizing for varied learning outcomes and student profiles. Impact on Society: Enhancing the quality of teaching discrete mathematics to future computer science teachers can lead to better-educated professionals, driving advancements in the tech industry and contributing to societal progress. Future Research: There is scope to explore the wider applications of the discrete mathematics elements model in varied computer science sub-disciplines, and its adaptability across different educational frameworks.

The traditional numerical simulation method of financial fluctuation cycle does not focus on the study of non-linear financial fluctuation but has problems such as high numerical simulation error and long time. To solve this problem, this paper introduces the non-linear equation of motion to optimise the numerical simulation method of financial fluctuation cycle. A comprehensive analysis of the components of the financial market, the establishment of a financial market network model and the acquisition of relevant financial data under the support of the model. Based on the collection of financial data, set up financial volatility index, measuring cycle, the financial wobbles, to establish the non-linear equations of motion, the financial wobbles, the influence factors of the financial volatility cycle as variables in the equation of motion, through the analysis of different influence factors under the action of financial volatility cycle change rule, it is concluded that the final financial fluctuation cycle, the results of numerical simulation. The simulation results show that, compared with the traditional method, the numerical simulation of the proposed method has high precision, low error and short time, which provides relatively accurate reference data for the stable development of regional economy.

How should the NIOSH lifting equation be used?

Washington – In an effort to prevent work-related musculoskeletal disorders, NIOSH has released a mobile app based on the Revised NIOSH Lifting Equation, an internationally recognized standard for safe manual lifting.

This study proposes an operation optimization framework for impurity-free recycling of spent lithium-ion batteries. Using a hybrid population balance equation integrated with a data-driven condition classifier, the study firstly identifies the optimal batch and semi-batch operation conditions that significantly reduce the operation time with 100% purity of product; detailed guidelines are given for industrial applications.

This study introduces an alternative method to the Takagi–Taupin equations for investigating the dark-field X-ray microscopy (DFXM) of deformed crystals. In scenarios where dynamical diffraction cannot be disregarded, it is essential to assess the potential inaccuracies of data interpretation based on the kinematic diffraction theory. Unlike the Takagi–Taupin equations, this new method utilizes an exact dispersion relation, and a previously developed finite difference scheme with minor modifications is used for the numerical implementation. The numerical implementation has been validated by calculating the diffraction of a diamond crystal with three components, wherein dynamical diffraction is applicable to the first component and kinematic diffraction pertains to the remaining two. The numerical convergence is tested using diffraction intensities. In addition, the DFXM image of a diamond crystal containing a stacking fault is calculated using the new method and compared with the experimental result. The new method is also applied to calculate the DFXM image of a twisted diamond crystal, which clearly shows a result different from those obtained using the Takagi–Taupin equations.

The Takagi–Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source Python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.

The general equation of the δ direct methods is established and applied in its difference form to the definition of one of the two residuals that constitute the SMAR phasing algorithm. These two residuals use the absolute value of ρ and/or the zero conversion of negative Fourier ripples (≥50% of the unit-cell volume). Alternatively, when solved for ρ, the general equation provides a simple derivation of the already known δM tangent formula.

Again earning a spot among the top 100 organizations in the midmarket financial software reselling sector

Homeowners are increasingly paying attention to improving their indoor air quality, and dehumidification is a big part of the IAQ equation.

Regression equations for estimating premorbid intelligence.

Orbit equation and orbital precession General Relativity explains gravity as Space-Time curvature and orbits of planets as geodesics of curved Space-Time. However, this concept is extremely hard to understand and geodesics hard to compute. If we can find an analytical orbit equation for planets like Newtonian orbit equation, relativistic gravity will become intuitive and straightforward...

Ole Løseth Elvetun and Bjørn Fredrik Nielsen
Math. Comp. 93 (), 2811-2836.
Abstract, references and article information

Katherine Baker, Lehel Banjai and Mariya Ptashnyk
Math. Comp. 93 (), 2711-2743.
Abstract, references and article information

Constantin Carle and Marlis Hochbruck
Math. Comp. 93 (), 2611-2641.
Abstract, references and article information

Buyang Li, Zongze Yang and Zhi Zhou
Math. Comp. 93 (), 2557-2586.
Abstract, references and article information

Yinji Li, Zhiwei Wang and Xiangyu Zhou
Trans. Amer. Math. Soc. 377 (), 5947-5992.
Abstract, references and article information

Ning Jiang, Yi-Long Luo and Shaojun Tang
Trans. Amer. Math. Soc. 377 (), 5323-5359.
Abstract, references and article information

Lauri Hitruhin and Sauli Lindberg
Proc. Amer. Math. Soc. 152 (), 5265-5278.
Abstract, references and article information

Anh Tuan Nguyen, Tómas Caraballo and Nguyen Huy Tuan
Proc. Amer. Math. Soc. 152 (), 5175-5189.
Abstract, references and article information

Simão Correia
Proc. Amer. Math. Soc. 152 (), 5117-5136.
Abstract, references and article information

Roland Donninger
Bull. Amer. Math. Soc. 61 (), 659-685.
Abstract, references and article information

Alin Bostan, Xavier Caruso and Julien Roques
Bull. Amer. Math. Soc. 61 (), 609-658.
Abstract, references and article information

National Bureau of Economic Research

While the Mahayuti is popular among the upper castes, Marathas, and those who are economically well-off, the MVA seems to be the first choice among Muslims, Buddhists, Adivasis, and farmers.

New York, NY : Routledge, 2016.

New York, N.Y. : Springer Science, 2007

New York : Springer, [2005]

New York : Routledge, 2020

New York, NY : Routledge/Taylor & Francis Group, 2016

From the early 2000s, sustainability has emerged as a central policy-making consideration as climate change and population growth have heightened concerns about already-stretched natural resources.

From the early 2000s, sustainability has emerged as a central policy-making consideration as climate change and population growth have heightened concerns about already-stretched natural resources.

Webinar: Andreas Schleicher, Director of the OECD Directorate for Education and Skills, presents the findings of Equations and Inequalities - Making Mathematics Accessible to All

The generalized Darwin–Hamilton equations [Wuttke (2014). Acta Cryst. A70, 429–440] describe multiple Bragg reflection from a thick, ideally imperfect crystal. These equations are simplified by making full use of energy conservation, and it is demonstrated that the conventional two-ray Darwin–Hamilton equations are obtained as a first-order approximation. Then an efficient numeric solution method is presented, based on a transfer matrix for discretized directional distribution functions and on spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially if the detector only covers a finite solid angle.

To describe multiple Bragg reflection from a thick, ideally imperfect crystal, the transport equations are reformulated in three-dimensional phase space and solved by spectral collocation in the depth coordinate. Example solutions illustrate the orientational spread of multiply reflected rays and the distortion of rocking curves, especially for finite detectors.

With consumer outlets being shut, fashion brands and retailers have taken an enormous hit to their bottom line and cash reserves. But the worst hit were the factory workers, of which almost 85% are women, who typically earn below living wages and do not accumulate any savings.

A taper equation and associated tables are presented for red alder (Alnus rubra Bong.) trees grown in plantations. The data were gathered from variable-density experimental plantations throughout the Pacific Northwest. Diameter inside bark along the stem was fitted to a variable exponent model form by using generalized nonlinear least squares and a first-order continuous autoregressive process. A number of parameterizations of the exponent were examined in a preliminary analysis, and the most appropriate form was determined. This was achieved by examining alternative models across geographic locations and silvicultural treatments on the basis of their ability to behave well outside the range of the modeling data by using an independent evaluation data set from across the region and a model validation procedure. Incorporating three easily measured tree variables--diameter at breast height, total tree height, and crown ratio--provided the best fit among location and treatment. This taper equation can be used to estimate diameter inside bark anywhere along the stem, inside bark volume of the entire stem to any top height diameter, and merchantable height and volume between any two points along the stem (i.e., individual log volumes). The flexibility of the model allows for accurate volume predictions across a range of operational stand conditions and management activities and is therefore an improvement over previously published red alder volume and taper equations.

A gradient-analysis-based model and grid-based map are presented that use the potential vegetation zone as the object of the model. Several new variables are presented that describe the environmental gradients of the landscape at different scales. Boundary algorithms are conceptualized, and then defined, that describe the environmental boundaries between vegetation zones on the Olympic Peninsula, Washington, USA.

One proves the existence and uniqueness of a generalized (mild) solution for the nonlinear Fokker--Planck equation (FPE) egin{align*} &u_t-Delta (eta(u))+{mathrm{ div}}(D(x)b(u)u)=0, quad tgeq0, xinmathbb{R}^d, d e2, \ &u(0,cdot)=u_0,mbox{in }mathbb{R}^d, end{align*} where $u_0in L^1(mathbb{R}^d)$, $etain C^2(mathbb{R})$ is a nondecreasing function, $bin C^1$, bounded, $bgeq 0$, $Din(L^2cap L^infty)(mathbb{R}^d;mathbb{R}^d)$ with ${ m div}, Din L^infty(mathbb{R}^d)$, and ${ m div},Dgeq0$, $eta$ strictly increasing, if $b$ is not constant. Moreover, $t o u(t,u_0)$ is a semigroup of contractions in $L^1(mathbb{R}^d)$, which leaves invariant the set of probability density functions in $mathbb{R}^d$. If ${ m div},Dgeq0$, $eta'(r)geq a|r|^{alpha-1}$, and $|eta(r)|leq C r^alpha$, $alphageq1,$ $alpha>frac{d-2}d$, $dgeq3$, then $|u(t)|_{L^infty}le Ct^{-frac d{d+(alpha-1)d}} |u_0|^{frac2{2+(m-1)d}},$ $t>0$, and the existence extends to initial data $u_0$ in the space $mathcal{M}_b$ of bounded measures in $mathbb{R}^d$. The solution map $mumapsto S(t)mu$, $tgeq0$, is a Lipschitz contractions on $mathcal{M}_b$ and weakly continuous in $tin[0,infty)$. As a consequence for arbitrary initial laws, we obtain weak solutions to a class of McKean-Vlasov SDEs with coefficients which have singular dependence on the time marginal laws.

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give some new results for the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.

It is well-known that a celebrated J"{o}rgens-Calabi-Pogorelov theorem for Monge-Amp`ere equations states that any classical (viscosity) convex solution of $det(D^2u)=1$ in $mathbb{R}^n$ must be a quadratic polynomial. Therefore, it is an interesting topic to study the existence and uniqueness theorem of such fully nonlinear partial differential equations' Dirichlet problems on exterior domains with suitable asymptotic conditions at infinity. As a continuation of the works of Caffarelli-Li for Monge-Amp`ere equation and of Bao-Li-Li for $k$-Hessian equations, this paper is devoted to the solvability of the exterior Dirichlet problem of Hessian quotient equations $sigma_k(lambda(D^2u))/sigma_l(lambda(D^2u))=1$ for any $1leq l<kleq n$ in all dimensions $ngeq 2$. By introducing the concept of generalized symmetric subsolutions and then using the Perron's method, we establish the existence theorem for viscosity solutions, with prescribed asymptotic behavior which is close to some quadratic polynomial at infinity.

Connections between set theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and twisted algebras and we derive the associated defining algebra relations for $R$-matrices being Baxterized solutions of the $A$-type Hecke algebra ${cal H}_N(q=1)$. We show in the case of the reflection algebra that there exists a "boundary" finite sub-algebra for some special choice of "boundary" elements of the $B$-type Hecke algebra ${cal B}_N(q=1, Q)$. We also show the key proposition that the associated double row transfer matrix is essentially expressed in terms of the elements of the $B$-type Hecke algebra. This is one of the fundamental results of this investigation together with the proof of the duality between the boundary finite subalgebra and the $B$-type Hecke algebra. These are universal statements that largely generalize previous relevant findings, and also allow the investigation of the symmetries of the double row transfer matrix.

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of the fluid and as such determines the variable part of a time changing domain (that is hence a part of the solution) containing the fluid. The uniqueness result is a consequence of a stability estimate where the difference of two solutions is estimated by the distance of the initial values and outer forces. For that we introduce a methodology that overcomes the problem that the two (variable in time) domains of the fluid velocities and pressures are not the same. The estimate holds under the assumption that one of the two weak solutions possesses some additional higher regularity. The additional regularity is exclusively requested for the velocity of one of the solutions resembling the celebrated Ladyzhenskaya-Prodi-Serrin conditions in the framework of variable domains.

In this work we consider the initial-value problem associated with a coupled system of generalized Korteweg-de Vries equations. We present a relationship between the best constant for a Gagliardo-Nirenberg type inequality and a criterion for the existence of global solutions in the energy space. We prove that such a constant is directly related to the existence problem of solitary-wave solutions with minimal mass, the so called ground state solutions. To guarantee the existence of ground states we use a variational method.

We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot-Savart kernel and the same common noise. The approximation happens by sending the number of particles $N$ to infinity and the regularization $epsilon$ in the Biot-Savart kernel to $0$, as a suitable function of $N$.