This work aims to introduce a novel concept: the Riesz-Dunkl fractional derivatives, within the context of Dunkl type operators. A particularly noteworthy revelation is that when a specific parameter $\kappa$ equals zero, the Riesz-Dunkl fractional derivative smoothly reduces to both the well-known Riesz fractional derivative and the fractional second-order derivative. Furthermore, we introduce a new concept: the fractional Sobolev space. This space is defined and characterized using the versatile framework of the Dunkl transform.

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

The theory of fractional calculus extends the order of classical integer calculus from integer to non-integer. As a new engineering application tool, it has made many important research achievements in many fields, including image processing. This paper mainly studies the application of fractional calculus theory in image enhancement and denoising, including the basic theory of fractional calculus and its amplitude frequency characteristics, the application of fractional differential operator in image enhancement, and the application of fractional integral operator in image denoising. The experimental results show that the fractional calculus theory has more special advantages in image enhancement and denoising. Compared with the existing integer order image enhancement operators, the fractional differential operator can more effectively enhance the "weak edge" and "strong texture" details of the image. The fractional order integral image denoising operator can not only improve the signal-to-noise ratio of the image compared to traditional denoising methods, but also better preserve detailed information such as edges and textures of the image.

In this paper, we introduce two subclasses of analytic and Spirallike functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes .

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

In the paper, we develop some numerical schemes including finite difference scheme and finite volume scheme for the fractional Laplacian operator, and apply the resulted numerical schemes to solve some fractional diffusion equations. First, the fractional Laplacian operator can be characterized as the weak singular integral by a integral operator with zero boundary condition. Second, because of the solution of fractional diffusion equation is usually singular near the boundary, we apply finite difference scheme to discrete fractional Laplacian operator and fractional diffusion equation by fractional interpolation function. Moreover, it is find that the differential matrix of the above scheme is symmetric matrix, and strictly row-wise diagonally dominant in special fractional interpolation function. Third, we show finite volume scheme to discrete fractional diffusion equation by fractional interpolation function, and analyze the properties of differential matrix. Finally, the numerical experiments are given, and verify the correctness of theoretical results and the efficiency of the schemes.

In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow (OPF) problem and is called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution (DE) operator in a single algorithmic framework. Additionally, an adaptive method (AM) is proposed to update the number of solutions evolved by each DE operator based on both the diversity of population and quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering the intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results and thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%.

A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

This paper presents a new low-voltage versatile mixed-mode filter which uses a multi-ple-input/output differential difference transconductance amplifier (MIMO-DDTA). The multi-ple-input of the DDTA is realized using a multiple-input bulk-driven MOS transistor (MI-BD-MOST) technique to maintain a single differential pair, thereby achieving simple structure with minimal power consumption. In a single topology, the proposed filter can provide five standard filtering functions (low-pass, high-pass, band-pass, band-stop, and all-pass) in four modes: voltage (VM), current (CM), transadmittance (TAM), and transimpedance (TIM). This provides the full capability of a mixed mode filter (i.e., twenty filter functions). Moreover, the VM filter offers high-input and low-output impedances and the CM filter offers high-output impedance; therefore, no buffer circuit is needed. The natural frequency of all filtering functions can be electronically controlled by a setting current. The voltage supply is 0.5 V and for a 4 nA setting current, the power consumption of the filter was 281 nW. The filter is suitable for low-frequency biomedical and sensor applications that require extremely low supply voltages and nano-watt power consumption. For the VM low-pass filter, the dynamic range was 58.23 dB @ 1 % total harmonic distortion. The proposed filter was designed and simulated in the Cadence Virtuoso System Design Platform using the 0.18 µm TSMC CMOS technology.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.

In the present study, a mathematical model of non-steady partial differential equation from the process of oxygen mass transport in the human pulmonary circulation is proposed. Mathematical modelling of this kind of problems lead to a non-steady partial differential equation and for its numerical simulation, we have used finite differences. The aim of the process is the exact numerical analysis of the study, wherein consistency, stability and convergence is proposed. The necessity of doing the process is that, we would like to increase the order of numerical solution to a higher order scheme. An increment in the order of numerical solution makes the numerical simulation more accurate, also makes the numerical simulation being more complicated. In addition, the process of numerical analysis of the study in this order of solution needs more research work.

Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time are described. ARMA type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown.

This article is a big picture of how electrical noise or conducted Electromagnetic Interference (EMI) is generated and mitigated in power converters. It gives an overview of what EMI in power converters is – from generation through to conduction and mitigation. It is meant to cover the complete subject as a summary so that the reader will have an outline of how to control conducted EMI by design (where possible) and how to mitigate by filtering. A clear distinction is made between Differential Mode (DM) and Common Mode (CM) EMI generation and mitigation. By using a boost converter as an example the trade-offs for DM noise control are discussed. It is shown how CM EMI is generated in a boost converter using the concept of the “Imbalance Difference Model” (IDM). Practical measurements for an in-line power filter is given showing the effect of the filter on the total EMI of a boost converter. Measurements for the CM current produced due to the imbalance difference for different values of the boost conductor are also shown. The main contribution of this study is linking CM noise generation to DM EMI. It is shown that CM noise is a direct consequence of DM noise (although circuit imbalance and coupling to a common ground also play a role). This paper will be useful to designers seeking the “bigger picture” of how EMI is generated in power converters and what can be done to mitigate the noise.

Among colours, the green has the most sensitivity in human vision so that green defects on displays can be effortlessly perceived by a photopic eye with the most intensity in the wavelength 555 nm of the spectrum. With the market moving forward to high resolution, displays can have resolutions of 10 million pixels. Therefore, the task detects the appearance the panel using ultra-high resolutions in TFT-LCD. The machine vision associated with reflective chromaticity spectrometer quantises the defects are explored, such as blackening and whitening. The result shows the significant phenomena to recognize the non-uniformity film-related chromatic tendency. In contrast, the quantitative assessment illuminates that the chromaticity CIE xyY at 0.001 is a just noticeable difference (JND) and detects even more sensitivity. Moreover, an optical device associated with a 198 Hg discharge lamp calibrates the spectrometer accuracy.

The aim of this document is to provide practical guidance on the choice of target difference used in the sample size calculation of a randomised controlled trial (RCT). Guidance is provided with a definitive trial, one that seeks to provide a useful answer, in mind and not those of a more exploratory nature. The term “target difference” is taken throughout to refer to the difference that is used in the sample size calculation (the one that the study formally “targets”). Please see the glossary for definitions and clarification with regards other relevant concepts. In order to address the specification of the target difference, it is appropriate, and to some degree necessary, to touch on related statistical aspects of conducting a sample size calculation. Generally the discussion of other aspects and more technical details is kept to a minimum, with more technical aspects covered in the appendices and referencing of relevant sources provided for further reading.The main body of this guidance assumes a standard RCT design is used; formally, this can be described as a two-arm parallel-group superiority trial. Most RCTs test for superiority of the interventions, that is, whether or not one of the interventions is superior to the other (See Box 1 for a formal definition of superiority, and of the two most common alternative approaches). Some common alternative trial designs are considered in Appendix 3. Additionally, it is assumed in the main body of the text that the conventional (Neyman-Pearson) approach to the sample size calculation of an RCT is being used. Other approaches (Bayesian, precision and value of information) are briefly considered in Appendix 2 with reference to the specification of the target difference.

Taste signaling is a complex process that is linked to obesity and its associated metabolic syndromes. The sweet taste is mediated through a heterodimeric G protein coupled receptor (GPRC) in a species-specific manner and at multi-tissue specific levels. The sweet receptor recognizes a large number of ligands with structural and functional diversities to modulate different amplitudes of downstream signaling pathway(s). The human sweet-taste receptor has been extremely difficult to study by biophysical methods due to inadequate methods for producing large homogeneous quantities of the taste-receptor protein and a lack of reliable in vitro assays to precisely measure productive ligand binding modes leading to activity upon their interactions with the receptor protein. We report a multimodal high throughput assays to monitor ligand binding, receptor stability and conformational changes to model the molecular interactions between ligand-receptor. We applied saturation transfer difference nuclear magnetic resonance spectroscopy (STD-NMR) complemented by differential scanning calorimetry (DSC), circular dichroism (CD) spectroscopy, and intrinsic fluorescence spectroscopy (IF) to characterize binding interactions. Our method using complementary NMR and biophysical analysis is advantageous to study the mechanism of ligand binding and signaling processes in other GPCRs.

The investigation on the issue of damage diagnosis based on strain modal parameters is conducted in this paper using simply supported wooden Beams as the study's object. First, ABAQUS is utilized to create finite element models of intact wooden beams as well as wooden beams with varying degrees of damage and perform modal analyses on them. Next, damage identification studies are conducted on the wooden beam structure using various strain modal parameters (strain mode strain modal difference, strain modal curvature difference), the timber beam damage identification test then yields the modal parameters of timber beams under various damage situations, and the test findings are contrasted with those of the numerical simulation. The outcomes demonstrate that the damage identification of the test data using the three types of damage identification indexes is consistent with the results of the numerical simulation; the three types of damage identification indexes can locate the damage to timber beams, but the identification effect of the indexes is different, the best-recognized metric is the strain mode curvature difference; the next best is the strain mode difference, and the worst is the strain modes. The study's findings can serve as a guide for future damage detection on wood beams.

The opioid crisis in the United States has had devastating effects on communities across the country, leading many states to pass legislation that limits the prescription of opioid medications in an effort to reduce the number of overdose deaths. This study evaluates the impact of two categories of PDMP and Pill Mill regulations on the supply of opioid prescriptions at the level of dispensers and distributors (excluding manufacturers) using ARCOS data. The study uses a difference-in-difference method with a two-way fixed design to analyze the data. The study finds that both of the regulations are associated with reductions in the volume of opioid distribution. However, the study reveals that these regulations may have unintended consequences, such as shifting the distribution of controlled substances to neighboring states. For example, in Tennessee, the implementation of Operational PDMP regulations reduces in-state distribution of opioid drugs by 3.36% (95% CI, 2.37 to 4.3), while the out-of-state distribution to Georgia, which did not have effective PDMP regulations in place, increases by 16.93% (95% CI, 16.42 to 17.44). Our studies emphasize that policymakers should consider the potential for unintended distribution shifts of opioid drugs to neighboring states with laxer regulations as well as varying impacts on different dispenser types.

Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, because the necessary mathematical tools have only just began to be developed.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

As a behavior of bilingual individuals and an indispensable part of bilingual speech, code-switching has been investigated by many researchers. However, there are many variables influencing code-switching, and each variable has the potential to be a confounding variable. Among these variables is the gender; however, whether there are significant gender differences and what are the gender differences in code-switching remains unknown for Mandarin Mandarin-English child bilinguals, as previous literature diverse on the existence of gender differences. Therefore, this paper seeks potential code-switching and distribution of code-switching by quantitative analysis of speech data in Singapore Bilingual Corpus. The results indicate that gender differences are significant in the amount of intra code-switching. However, neither considerable gender difference is observed in the amount of inter nor the code-switching related environment.

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

This paper compares the finite sample performance of three non-parametric threshold estimators via Monte Carlo method. Our results show that the finite sample performance of the three estimators is not robust to the relative position of the threshold level along the distribution of threshold variable, especially when a structural change occurs at the tail part of the distribution.

The pollution caused by nitrogen dioxide is a major environmental problem in China. This study introduces a new type of atmospheric trace gas remote-sensing instrument, an airborne fiber imaging spectrometer. This spectrometer has a spectral range of 300–410 nm and works in push-broom mode with a 30° field of view on a flight path. Flight experiments were conducted on December 30, 2022 and January 5, 2023, covering heavily polluted areas of east of Beijing and Tangshan. This equipment obtained the density distribution of NO2 over the flight area. The results showed that pollution was mainly concentrated in the Caofeidian area and at the power station in the north, and the main source of pollution was anthropogenic. Satellite and airborne data near the pollution points were compared, and the two datasets showed a positive correlation with a correlation coefficient of 0.78 and 0.7, on the two days, respectively. This study demonstrates the capability of an airborne fiber imaging spectrometer for NO2 regional emission remote sensing and identifying the pollution points.

This research presents a solution to the problem of planning the optimum area for economic crops by developed mathematical models and developed an algorithm to solve the problem of planning the optimum area by considered economic value for the maximize profit of farmers. The data were collected from farmers in 8 provinces in the northeastern region of Thailand. The 3 economic crops studied were rice, cassava and sugarcane. The solving problem methods were 1) Created mathematical models and solved the problems with Lingo V.11. 2) Improved Differential Evolution algorithms (I-DE) to solve the problems, which had 3 local search methods included (Swap, Cyclic Move and K-variable moves). The results of this study showed that in the small and medium problems instances, Lingo V.11 and DE provided equal profit outcome but DE was faster but in the large size of test instances DE generated better solution than that of Lingo v.11 when Lingo simulation time is set to 250 hours and DE simulation time has set to maximum 21.82 minutes. 2) Comparing DE and I-DE , I-DE outperforms DE in finding the better solution for all size of test instances (small, medium and large).

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

Developing new energy is critical to China's green and low-carbon development. And the New Energy Demonstration City Policy (NEDCP) is a vital innovation policy that inspires the development of new energy. Is the NEDCP facilitating green and low-carbon development, if so, how? Employing unbalanced panel data from 2003 to 2017, the impact of NEDCP on green and low-carbon development was studied by using the "difference in difference" (DID) model. We find that this policy can take significantly role. After various robustness tests, our results are still valid. According to the heterogeneity analysis, non-resource and non-old industrial base cities have a greater positive impact from this policy. The mechanism analysis denotes that the positive policy effect works through upgrading the industrial structure and stimulating urban innovation. The substantial empirical evidence presented in this article supports the continued promotion and implementation of new energy demonstration cities.

We discuss a remote sensing system that is used to simultaneously detect range-resolved differential absorption LIDAR (light detection and ranging; DIAL) signals and integrated path DIAL signals (IP-DIAL) from aerosol targets for ranges up to 22 km. The DIAL/IP-DIAL frequency converter consists of an OPO pumped at 1064 nm to produce light at 1.6 μm and operates at 100 Hz pulse repetition frequency. The probe light is free space coupled to a movable platform that contains one transmitter and two receiver telescopes. Hybrid photon counting/current systems increase the dynamic range for detection by two orders of magnitude. Range resolved and column integrated dry-air CO2 and CH4 mixing ratios are obtained from line shape fits of CO2 and CH4 centered at 1602.2 nm and 1645.5 nm, respectively and measured at 10 different frequencies over ≈ 1.5 cm-1 bandwidth. The signal-to-noise ratios (SNR) of the IP-DIAL returns from cloud aerosols approach 1000:1 and the uncertainties in the mixing ratios weighted according to the integrated counts over the cloud segments range from 0.1 % to 1 %. The range averaged DIAL mixing ratios are in good agreement with the IP-DIAL mixing ratios at the 1 % to 2 % level for both CO2 and CH4. These results can serve as a validation method for future active and passive satellite observational systems.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

The importance of various markers such as sclerostin, Dickkopf-1 (DKK-1), Irisin, receptor activator of NF-kB ligand (RANKL), and Vitamin D have been well studied in bone metabolism. Additionally, inflammatory cytokines such as tumor necrosis factor-alpha (TNF-α) and Interleukine-6 (IL-6) have been identified to hinder muscle protein synthesis, leading to the loss of muscle and strength. However, a research gap exists in the understanding their role in muscle function and physical activity. Therefore, this study aims to explore the serum levels of sclerostin, DKK-1, irisin, IL-6, RANKL, Vitamin D, and TNF-α and assess their relationships with upper and lower body strength in young adults. In this study, 38 college-aged students 18-23 years participated and completed the protocols. The participants’ lower and upper body strength were assessed by the vertical jump test (Just Jump, Probotic, AL) with a Tendo FitroDyne (Tendo Sports Machines, Trencin, Slovak Republic) and handgrip (HG) dynamometry (Takei Scientific Instruments, Yashiroda, Japan), respectively. Fasting morning blood samples were analyzed for serum levels of the biomarkers by ELISA. The results indicate significant sex differences in sclerostin, DKK-1, irisin, and vitamin D levels (p<0.05). Furthermore, a positive association was observed between sclerostin, DKK-1, and vitamin D, with lower body muscle performance variables (p<0.05). Conversely, a significant negative correlation was observed between TNF-α and upper-body muscle performance variables (p<0.05). The results suggest that these markers may have a distinct effect on muscle performance, underscoring the need for further investigation to elucidate the concept of muscle-bone crosstalk.

Background/Aim: Rapid onset of facial ptosis can impact physical appearance and compromise the outcomes of facelift procedures. The level of vitamin D has a potential correlation with collagen formation and its deficiency with inflammatory processes that affect the breakdown of hyaluronic acid. This study aims to investigate the potential relationship between accentuated facial ptosis in women and low levels of vitamin D. Furthermore, it aims to explore preventive measures or strategies to slow down facial ptosis and enhance the longevity of facelift results. Materials and Methods: The study was focused on monitoring the vitamin D levels in women and men with advanced facial ptosis and comparing them with a control group. Results: Notably, a direct association between gender and serum vitamin D levels was observed, indicating less sustainable outcomes in women. Conclusion: Women face additional challenges in the aging process due to hormonal shifts after menopause or premenopausal, which are associated with osteoporosis and lower vitamin D levels.

Optimization of Magnetohydrodynamics parameters on the velocity profile and temperature distribution of incompressible fluid flow on a porous channel was evaluated. The fluid flow was considered to be unsteady, incompressible and flowing in 2-D in porous channel. The effects of magnetic parameter, Darcy’s number and fluid pressure on velocity profiles, and the effect of variable viscosity and Eckert number on temperature distribution in incompressible fluid flow were determined. The flow was considered to be in a channel running along the x-axis on which the magnetic field exist and finally along the y-axis on the porous part of the channel. The resulting model equations were solved by Finite Difference Method (FDM) in MATLAB software. Analysis of results indicated that increasing Darcy’s number and fluid pressure leads to increase in fluid velocity profile, while increasing magnetic parameter decreases fluid velocity profile. Also, it was observed that increase in both Eckert number and fluid viscosity lead to increase in temperature distribution. Optimization in temperature was achieved by increasing the magnetic field while viscosity was optimized by increasing the length of the porous part of the channel. This study will helpful to contribute alternative equations and methodology to engineering and in factories where getting the MHD parameters optimally is the main objective, particularly on temperature, velocity and pressure.

Cancer diseases lead to the second-highest death rate all over the world. The dynamics of invasion of cancer cells into the human body tissues and metastasis are the main causes of death in patients with cancer. This study deals with theoretical investigation of the dynamics of invasion of cancer cells for tumour growths in human body tissues using discretized Cahn-Hilliard, concentration and reaction-diffusion equations which were solved by Finite Difference Method with the aid of MATLAB computer software. A Crank-Nicolson numerical scheme was developed for the discretized model equations. The numerical result obtained was used to describe the dynamics of cancer invasion of tissues with respect to cancer cells density on tumour growth, turbulence and mobility and equilibrium between charge and discharge of cancer cells. The results of the study provide new insights into combating cancer disease by providing mitigating and intervention measures to this major health problem.

We employ another approach to quantize electromagnetic fields in the coordinate space, instead of the mode (or Fourier) space, such that local features of photons can be efficiently, physically, and more intuitively described. To do this, coordinate-ladder operators are defined from mode-ladder operators via the unitary transformation of systems involved in arbitrary inhomogeneous dielectric media. Then, one can expand electromagnetic field operators through the coordinate-ladder operators weighted by non-orthogonal and spatially-localized bases, which are propagators of initial quantum electromagnetic (complex-valued) field operators. Here, we call them QEM-CV-propagators. However, there are no general closed form solutions available for them. This inspires us to develop a quantum finite-difference time-domain (Q-FDTD) scheme to numerically time evolve QEM-CV-propagators. In order to check the validity of the proposed Q-FDTD scheme, we perform computer simulations to observe the Hong-Ou-Mandel effect resulting from the destructive interference of two photons in a 50/50 quantum beam splitter.

In this paper, we study the dynamics of following system of nonlinear difference equations x_n+1 = x_n-1y_n - 1, y_n+1 = y_n-1z_n - 1, z_n+1 = z_n-1x_n - 1. Especially we investigate the periodicity, boundedness and stability of related system of difference equations.

In this paper, we investigate the equilibrium points of following a system of difference equations x_n+1 = x_n 2y_n−1, y _n+1 = y_n 2x_n−1. We also study the asymptotic stability of related system of difference equations. Further we examine the periodic solutions of related system with period two. Additionally, we find out the invariant interval and periodic cycles of related system of difference equations.

A finite-difference approach with non-uniform meshes was presented for simulating magnetotelluric responses in 2D structures. We presented the formulation of this scheme and gave some sights into its successful implementation, and compared finite-difference solution with known numerical results and simple analytical solutions. First, a homogeneous half-space model was tested and the finite-difference approach can provide very good accuracy for 2D magnetotelluric modeling. Then we compared to the analytical solutions for the two-layered model, the relative errors of the apparent resistivity and the impedance phase were both increased when the frequency was increased. In the end, we compare our finite-difference simulation results with COMMEMI 2D-0 model with the finite-element solutions. Both results are in close agreement to each other. These comparisons confirm the validity and reliability of our finite-difference algorithm.

Calculus, as a starting point to everyone's study of mathematics, was developed along with classical mechanics. Though not rigorously formulated, the intuition for differential form and infinitesimal motion makes calculus not hard to understand. And hence it does not require great effort to grasp the principles of classical mechanics. However, the situation becomes quite different when it comes to the quantum world. Given a particle system, what of interest is always the physical quantity of this system, such as energy, position, momentum, entropy, etc. But it is no longer straightforward.

Molecular studies regarding regulatory elements such as small ncRNAs and their mechanisms are poorly understood in infectious diseases. Tuberculosis is one of the oldest infectious diseases of humanity, and it is still a challenge to prevent and treat it. The control of the infection as well as its diagnosis are still complex, and treatments used are linked to several side effects. This study aimed to investigate miRNA’s expression profile to identify possible biomarkers for tuberculosis. We applied NGS techniques to investigate miRNA’s global expression profile from blood samples of infected patients with tuberculosis, their respective healthy physicians, and external healthy individuals as controls. Samples from 22 individuals run through a differential expression, target genes, gene set enrichment, and miRNA-gene network analysis. We observed 153 altered miRNAs, among which, only three DEmiRNAs (hsa-let-7g-5p, hsa-miR-486-3p and hsa-miR-4732-5p) were found between the investigated patients and their respective physicians. These DEmiRNAs are suggested to play an important role in granuloma regulation and their immune physiopathology. Our results propose that miRNAs may be involved in immune modulation, regulating the repertoire of genes expressed in the immune system’s cells. Our findings encourage the application of miRNAs as potential biomarkers for tuberculosis.

Agricultural activities are the second largest source of greenhouse gas emissions, and carbon emissions from agricultural land use (CEALU) have become a hot issue across the world. However, few scholars explored the impact of agricultural land policies on carbon emissions, such as the High-standard farmland construction(HSFC) in China.Thus，by relying on provincial panel data for China for the period 2005-2017, the effect of the high-standard basic farmland construction policy on carbon emissions from agricultural land use per unit area and its regional differences were quantitatively analyzed using the difference-in-difference (DID) model. The results showed that: 1) China's CEALU per unit area presented a fluctuating upward trend during the period 2005-2017, from 392.58 kg/ha to 457.72 kg/ha, with an average annual growth rate of 1.31%. 2) The high-standard farmland construction(HSFC) policy produced a significant carbon emission reduction effect in agricultural land use, and reduced the CEALU per unit area by 10.80% on average. With the promotion of this policy, its carbon emission reduction effect in agricultural land use presented an overall increasing trend. 3) The carbon emission reduction effect of the high-standard farmland construction policy in agricultural land use was significant in central China, but non-significant in eastern China and western China.

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

The sonification of data to communicate information to a user is a relatively new approach that established itself around the 1990s. To date many researchers design their individual sonification from scratch. There are no standards in sonification design and evaluation. But researchers and practitioners have formulated several requirements and established several methods. There is wide consensus that psychoaocustics could play an important role in the sonification design and evaluation phase. But this requires an adaption of psychoacoustic methods to the signal types and the requirements of sonification. In this method paper we present PAMPAS, a PsychoAcoustical Method for the Perceptual Analysis of multidimensional Sonification. A well-defined and well-established, efficient, reliable and replicable Just Noticeable Difference experiment using the Maximum Likelihood Procedure serves as the basis to achieve linearity of parameter mapping during the sonification design stage and to identify and quantify perceptual effects during the sonification evaluation stage, namely the perceptual resolution, hysteresis effects and perceptual interferences. The experiment results are universal scores from a standardized data space and a standardized procedure. These scores can serve to compare multiple sonification designs of a single researcher, or even between different research groups. The method can supplement other sonification design and evaluation methods from a perceptual viewpoint.

In this study, a design of Morlet wavelet neural networks (MWNNs) is presented to solve the prediction differential model (PDM) using the global approximation capability of genetic algorithm (GA) and local quick interior-point algorithm scheme (IPAS), i.e., MWNN-GAIPAS. The famous PDM is known as a variant of functional differential system that works as an opposite of the historical delay differential models. A fitness function is optimized using the mean square error by applying the GA-IPAS for solving the PDM. Three PDM examples have been presented numerically to check the authenticity of the MWNN-GAIPAS. For the perfection of the designed MWNN-GAIPAS, the comparability of the obtained results and exact results is performed. Moreover, the neuron analysis is performed by taking the 3, 10 and 20 number of neurons. The statistical observations have been performed to authenticate the reliability of the MWNN-GAIPAS for solving the PDM.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

Workplace bullying is a prevalent issue with a significant impact on employees’ mental health. This study aimed to explore the relationship between workplace bullying and the prevalence of depression with a particular focus on the role of gender. A total of 12,344 Korean employees aged 19–65 years were included in the study. They completed questionnaires including the Korean version of the Occupational Stress Scale, the Oldenburg Burnout Inventory, and the Center for Epidemiologic Studies Depression Scale (CES-D). A score of 16 or higher in CES-D indicated depression. The association between workplace bullying and depression was analyzed using logistic regression analyses. The average CES-D scores were higher for both male and female employees who experienced bullying than for those who did not (p &lt; 0.001). The association between the experience of workplace bullying and the prevalence of depression was statistically significant for both genders, with a stronger correlation observed among male employees (p for interaction &lt;0.001). Organizations are urged to address workplace bullying, particularly for male employees, through the implementation of anti-bullying strategies and policies, as well as the provision of mental health resources and support.

In this study, we have considered for numerical solution of a Poisson equation in a domain. we have presented a first and second order finite difference method for solving the system of the intial boundary value. We have presented the numerical solution of the Poisson equations in a two-dimensional finite region. Numerical Solution and exact solution for the presented method has been compared and the figures presented. The present error analysis tables demonstrate the efficiency of the method.

In public health literature the risk of death or disease associated with a dietary, environmental of behavioral factor is most commonly denoted by odds ratio (OR), hazard ratio (HR) or risk ratio (RR). The ratio indices have several desirable statistical properties. However, the most important question is whether there are some evolved innate norms of perception of risk that people use and what they are. We conducted a simple one question survey of 98 individuals with different age, sex, educational and professional backgrounds. The respondents were asked to judge the relative perceived risk of four different hypothetical habits for which data on the percentage of people affected by the disease with and without the habit was given. They were asked to rank the risks for the four habits. Results showed that the habits that had the highest difference between probability of acquiring the disease were ranked high on risk perception. The probability ratios did not affect risk perception significantly. Further age, sex, profession or formal training in statistics did not affect the response significantly. Even individuals that were formally trained to use OR and HR as risk indicators, preferred using probability differences over ratios for judging their own risk in the perceived context. This preliminary inquiry into intuitive statistical perception suggests that designing statistical indices based on people’s innate perception may be a better strategy than trying to train people to understand the indices designed by expert statisticians.

In this paper, we investigate the equilibrium points, stability of two equilibrium points, convergences of negative equilibrium point, periodic solutions, and existence of bounded or unbounded solutions of a system of nonlinear difference equations x_n+1 =x_n-1y_n - 1, y_n+1 = y_n-1x_n - 1 n = 0,1,..., where the initial values are real numbers. Additionally we present some numerical examples to verify our theoretical results.

The Internet use has become an integral part of daily life, adolescents are especially at a higher risk to develop problematic Internet use (PIU). Although one of the most well-known comorbid conditions of PIU is sleep disturbance, little is known about the sex disparity in this association. This school-based survey in students of grades 7-9 was conducted to estimate the prevalence of PIU and sleep disturbance among Chinese adolescents, to test the association between PIU and sleep disturbance, and to investigate the role of the child’s sex in this association. A two-stage stratified cluster sampling method was used to recruit participants, and a two-level logistic regression models were fitted. The mean Internet addiction test scores was 37.2 (SD: 13.2), and 15.5% (736) met the criteria for PIU. After adjusting for control variables, problematic Internet users were at a higher risk of sleep disturbance (adjusted odds ratio=2.41, 95% CI=2.07-3.19). Sex-stratified analyses also demonstrated that association was greater in girls than boys. In this respect, paying more attention to the sleep patterns of adolescents who report excessive Internet use is recommended, and this early identification may be of practical importance for schools, parents, and adolescents themselves.

Antiangiogenic therapy (AAT) is an indirect oncological modality which is aimed at disruption of cancer cells nutrient supply. Invasive tumors have been shown to possess inherent resistant to this treatment, while compactly growing benign tumors react to it by shrinkage. It is generally accepted that AAT by itself is not curative. This study presents a mathematical model of non-invasive tumor growth with physiologically justified account of alteration of microvasculature and biomechanical aspects during tumor growth and AAT. In untreated setting the model reproduces tumor growth with saturation, where the maximum tumor volume depends on the level of angiogenesis. The outcomes of simulations of AAT depend on the tumor size at the moment of treatment initiation. If it is close to the stable size of avascular tumor grown in absence of angiogenesis, then the tumor is rapidly stabilized by AAT. Treatment of large tumors is accompanied by displacement of normal tissue due to the tumor shrinkage. During it, microvasculature undergoes distortion which degree depends on the displacement distance. As it affects tumor nutrient supply, the stable size of a tumor that undergoes AAT negatively correlates with its size at the beginning of treatment. For sufficiently large initial tumors, the long-term survival of tumor cells is compromised by competition with normal cells for severely limited inflow of nutrients, which makes AAT effectively curative.

In this work, the analytical treatment of Fourth order pd equations has been discussed with the variational iteration algorithm with an auxiliary parameter. The technique has the capability of reducing the size of computational work and easily overcomes the difficulty of the perturbation method or Adomian polynomials. Comparison with the classic variational iteration algorithm- is carried out, showing that the modification is more efficient and reliable.

Background: By using outcome prediction scores, it is possible to distinguish between good and poor performers with cochlear implants (CI) after CI implantation. The reasons for poor performance, despite good basic conditions, can be manifold. On the one hand, the postoperative fitting may be inadequate; on the other, neurophysiological disease processes may impair speech understanding with a CI. These disease processes are not yet fully understood. In acoustics, it is known that the auditory brainstem responses (ABR) and their latencies and amplitudes allow differential diagnosis based on reference values for normal-hearing individuals. The aim of this study was to provide reference values for electrically evoked brainstem responses (EABRs) in terms of rate-dependent latencies and amplitudes. Methods: 20 experienced adult CI recipients with a predicted and measured good postoperative word recognition score were recruited from the clinic’s patient pool. In the same stimulation mode and intensity we measured latencies and interpeak-latencies of EABRs and electrically evoked compound action potentials (ECAPs). With a defined supra-threshold stimulation intensity above the individual ECAP threshold, we applied stimulation at several rates between 11 and 91 stimuli per second. Results: We found rate dependences for EABR latency t3 and t5 in the order of 0.19 ms and 0.37 ms respectively, while ECAP was not affected by rate. Correspondingly, the interpeak intervalls’ rate dependences for t5-t1, t5-t3 and t3-t1 were of the order of 0.37 ms, 0.18 ms and 0.19 ms. Comparing the EABR amplitudes between the stimulation rates 11/s and 81/s, we found that at 81/s the amplitudes were significantly reduced down: to 73% for A3 and 81% for A5. These rate dependences of latency and amplitude in EABR have characteristics comparable to those of acoustic ABR. Conclusions: These data may serve to provide reference values for EABR and ECAP latencies, interpeak intervals and amplitudes with respect to stimulation rate. Altered response patterns of ECAPs and EABRs to normalised stimulation modes could be used in the future to describe and classify neuropathological processes in a better-differentiated way.

The core reasoning task for datalog engines is materialization, the evaluation of a datalog program over a database alongside its phys- ical incorporation into the database itself. The de-facto method of computing it, is through the recursive application of inference rules. Due to it being a costly operation, it is a must for datalog engines to provide incremental materialization, that is, to adjust the computation to new data, instead of restarting from scratch. One of the major caveats, is that deleting data is notoriously more involved than adding, since one has to take into account all possible data that has been entailed from what is being deleted. Differential Dataflow is a computational model that provides efficient incremen- tal maintenance, notoriously with equal performance between ad- ditions and deletions, and work distribution, of iterative dataflows. In this paper we investigate the performance of materialization with three reference datalog implementations, out of which one is built on top of a lightweight relational engine, and the two others are differential-dataflow and non-differential versions of the same rewrite algorithm, with the same optimizations.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

This study aims to implement a SSDBI (single-stage differential boost inverter, SSDBI) applying in a single-stage BESS (battery energy storage system, BESS) topology, which can supply power from lower voltage battery module to AC load. Compared with the common two-stage topology, which has a two-stage converter and higher voltage battery module array, the single-stage topology can reduce the number of cells and components, and improve the power density. In addition, a modified SPWM control was proposed to reduce the control complexity of the SSDBI while improving the THD of the inverter. The modified SPWM control can reduce the duty ratio of the SSDBI and the stress on the components to improve the AC voltage output waveform and reduce the THD value about 2.654%.

Image segmentation and classification still represent an active area of research since no universal solution can be identified. Established segmentation algorithms like thresholding are problem specific, treat well the easy cases and mostly relied on single parameter i.e intensity. Machine learning approaches offer alternatives where predefined features are combined into different classifiers. On the other hand, the outcome of machine learning is only as good as the underlying feature space. Differential geometry can substantially improve the outcome of machine learning since it can enrich the underlying feature space with new geometrical objects, called invariants. In this way, the geometrical features form a high-dimensional feature space for each pixel, where original objects can be resolved. Alternatives based on the geometry of the image scale-invariant interest points have been exploited successfully in the field of computer vision. Here, we integrate geometrical feature extraction based on signal processing, machine learning, and input relying on domain knowledge. The approach is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application, we demonstrate powerful image classification functionality based on the same principles, which was applied to the HeLa and HEp-2 data sets. Obtained results demonstrate that feature space enrichment properly balanced with feature selection functionality can achieve performance comparable to deep learning approaches.

Background: Traditional omic analysis relies on p-value and fold change as selection criteria. There is an ongoing debate on their effectiveness in delivering systemic and robust interpretation, due to their dependence on assumptions of conformity with various parametric distributions.Here, we propose a threshold-free selection method based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques based on fixed thresholds. Methods: Our work extends the Rank Products methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP distribution’s entropy to isolate the features of interest by their contribution to the distribution’s information content. The aim is a methodology performing threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under scrutiny. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterisations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and information-rich, indicating phenotypic aspects specific to the tissue and biological phenomenon i nvestigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresholding, thus facilitating the full automation of the analysis.

An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.

In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.

Perilla frutescens leaves are expected to exhibit antioxidant activity and amyloid-β (Aβ) aggregation inhibitory activity due to the presence of polyphenol-type compounds, etc. These activities fluctuate daily; however, measuring the contents of constituents and functionalities is cumbersome and unsuitable for instantaneous measurements in the field. In this study, we developed a facile method to analyze the activity and content of the components in leaves on-site based on the fluorescence spectra obtained by irradiating the perilla leaves with excitation light. The constituent contents (Chlorophyl (Chl), Total polyphenol content (TPC), Total flavonoid content (TFC), rosmarinic acid (RA) and functional properties DPPH radical scavenging activity, ferric reducing antioxidant power (FRAP), oxygen radical absorbance capacity (ORAC), Aβ aggregation inhibitory activity) were evaluated using established analytical techniques. The correlation between the fluorescence spectrum and the contents and activities was calculated using normalized difference spectral index (NDSI), ratio spectral index (RSI), and difference spectral index (DSI) analyses. We identified a predictive model with a high coefficient of determination R² ≥ 0.57 for content of the constituents, and R² ≥ 0.49 for functional properties. This allows convenient, simultaneous, and non-destructive monitoring of the constituent contents and the functionalities of perilla leave and a simple harvest-time diagnosis. The model established using this method is simple and suggesting that it can simultaneously infer the constituents and functionalities of perilla leaves.

The (numerical) solution of Ordinary Differential Equations (ODEs) problems is of paramount relevance, ODEs system being an ubiquitous mathematical formulation of many physical phenomena (such as those involved in fluid dynamics, chemistry, biology, evolutionary-anthropology, ...): almost every dynamici phenomenon can be modeled by means of an ODEs system. The present paper is the first manifesto of FOODIE, a library aimed to numerically solve ODEs problems by means of a clear, concise and efficient abstract interface. FOODIE, meaning Fortran Object oriented Ordinary Differential Equations integration library, has manifolds aims: to provide a set to built-in numerical schemes that are accurate, robust, validated and efficient and to allow easy application of these schemes to (almost) all ODEs problems by means of an effective Abstract Calculus Pattern. The key idea is to allow the same solver-implementation to be applied to all ODEs problems thus avoiding the re-implementation of the ODEs solver for each different ODEs problem: code re-usability is consequently maximized, FOODIE being a general robust framework. Besides, the same framework also allows rapid development of new ODEs solvers due to the high abstraction level of the library itself. The present paper is the first announcement of FOODIE project: the current implementation is extensively discussed and its capabilities are proved by means of tests and examples.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically, the K-BKZ-PSM (Kaye–Bernstein, Kearsley, Zapas - Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation, and the marker-particle method (known as \emph{Marker-and-Cell}) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.

Klotho (KL) is a glycosyl hydrolase and aging-suppressor gene. Stress is a risk factor for depression and anxiety that are highly comorbid with each other. The aim of this study was to determine KL is regulated by estrogen and plays an important role in sex differences in stress resilience. Our results showed that KL was regulated by estrogen in rat hippocampal neurons in vivo and in vitro and was essential for estrogen-mediated increase in the number of presynaptic vesicular glutamate transporter 1 (Vglut1) positive clusters on the dendrites of hippocampal neurons. The role of KL in sex differences in stress responses was examined in rats using three-week chronic unpredictable mild stress (CUMS). CUMS produced a deficit in spatial learning and memory, anhedonic-like and anxiety-like behaviors in male but not female rats, which was accompanied by a reduction in KL protein levels in the hippocampus of male, but not female rats. This demonstrated the resilience of female rats to CUMS. Interestingly, knockdown of KL protein levels in the rat hippocampus of both sexes caused a decrease in stress resilience in both sexes, especially in female rats. These results suggest that regulation of KL by estrogen plays an important role in estrogen-mediated synapse formation, and KL plays a critical role in the sex differences in cognitive deficit, anhedonic-like and anxiety-like behaviors induced by chronic stress in rats, highlighting an important role of KL in sex differences in stress resilience.

Oleraceins are a class of indoline amide glycosides found in Portulaca oleracea L. (Portulacaceae), or purslane. These compounds are characterized with 5,6-dihydroxyindoline-2-carboxylic acid N-acylated with cinnamic acid derivatives, and many are glucosylated. Herein, hydromethanolic extracts of the aerial parts of purslane were subjected to UHPLC-Orbitrap-HRMS analysis, conducted in negative ionization mode. Diagnostic ion filtering (DIF), followed by diagnostic difference filtering (DDF), were utilized to automatically filter out MS data and select plausible oleracein structures. After an in-depth MS2 analysis, a total of 51 oleracein compounds were tentatively identified. Of them, 26 had structure matching one of already known oleraceins and the other 25 are new, undescribed in the literature structures, belonging to the oleracein class. Moreover, diagnostic fragment ions were selected, based on which clustering algorithms and visualizations were employed. As we demonstrate, clustering methods can provide valuable insights into the mass fragmentation elucidation of natural compounds in complex mixtures.

Steel is one of the essential materials in the world's civilization. It is essential to produce many products such as pipelines, mechanical elements in machines, vehicles, profiles, and beam sections for buildings in many industries. Until the '50s of the 20th century, steel products required a complex process known as ingot casting; for years, steelmakers focused on developing and simplifying this process. The result was the con-tinuous casting process (CCP); it is the most productive method to produce steel. The CCP allows producing significant volumes of steel sections without interruption and is more productive than the formal ingot casting process. The CCP begins by transferring the liquid steel from the steel-ladle to a tundish. This tundish or vessel distributes the liquid steel, by flowing through its volume, to one or more strands having wa-ter-cooled copper molds. The mold is the primary cooling system, PCS, solidifying a steel shell to withstand a liquid core and its friction forces with the mold wall. Further down the mold, the rolls drive the steel section in the SCS. Here the steel section is cooled, solidifying the remaining liquid core, by sprays placed in every cooling segment all around the billet and along the curved section of the machine. Finally, the steel strand goes towards a horizontal-straight free-spray zone, losing heat by radiation mechanism, where the billet cools down further to total solidification. A moving torch cutting-scissor splits the billet to the desired length at the end of this heat-radiant zone.

Our aim is to implement and test some less known numerical methods that might be used to solve an advection equation. The description is restricted to information necessary to implement and test the presented methods and it is given only for one-dimensional case.

Background: We attempted to find if there were gender differences in different types of Negative life events and Suicidal ideation among Chinese adolescents, then analyze the relationship between different types of Negative life events and Suicidal ideation among these young students. Methods: Based on the data from 6 middle-schools and 3 universities in 3 cities of Western China, the gender difference in different types of Negative life events and Suicidal ideation and their related factors were investigated and analyzed in the study. Results: Gender differences were found during different types of Negative life events and Suicidal ideation; Negative life events could predict the intensity of Suicidal ideation by gender, to some specific types. Conclusions: Negative life events were proved to be risk factors of adolescents’ Suicidal ideation regardless of different gender stereotypes, but the specific classification of negative life events which had significant impact on adolescents’ Suicidal ideation also indicated significant gender divisions. For males, negative life events of punishment and adaptation had a significant and boosting impact on their Suicidal ideation, the higher the scores of punishment and adaptation negative life events had, the greater intensity of male adolescents were to have Suicidal ideation. Thus, the above two types of negative life events may be the main stressors predicting male adolescents' Suicidal ideation; For females, in addition to punishment, other types of negative life events all had significant impacts on their Suicidal ideation, which can be treated as the main stressors to trigger female adolescents' Suicidal ideation; Additionally, parents’ marital status of remarriage and divorce were proved to be significant indicators to adolescents’ Suicidal ideation, the age variable was proved to be strongly correlated with Suicidal ideation among female adolescents.

This article described the technology of determining earthquake epicenter with radar remote sensing on the example of Sentinel-1A/B. To determine the epicenter of the earthquake, the Earth's crust displacements were analyzed using radar remote sensing data obtained for the ascending and descending flight orbits. Coordinates of Earthquake epicenters were found according to line-of-sight displacement images via its maximum value. Displacement of the Earth's crust was obtained by processing in the GMTSAR package in the VirtualBox virtual machine of the Linux Ubuntu 16.04 operation system. Two earthquakes that occurred in 2020 were studied to determine the accuracy of finding epicenters using the ascending and descending orbits Sentinel-1A/B. These earthquakes occurred in Western Xizang, China, and Doganyol, Turkey. The maximum deviation from the officially registered epicenter coordinates was 15.38 km for Doganyol and 3.2 km for the Western Xizang earthquake. The negative displacement was 90 mm for Doganyol and 50 mm for Western Xizang.

In this paper, we investigate the dynamics of following higher order difference equation x_{n+1}=A+B((x_{n})/(x_{n-m}²)) with A,B and initial conditions are positive numbers, and m∈{2,3,⋯}. Especially we study the boundedness, periodicity, semi-cycles, global asymptotically stability and rate of convergence of solutions of related higher order difference equations.

The application of Virtual Reality in a driving simulation is not novel, yet little is known about the use of this technology by senior populations. The effects of age, sex, control device (joystick or handlebar), and task type on wayfinding proficiency using a virtual reality (VR) driving simulation were explored. The driving experimental model involved 96 randomly recruited participants, including 48 young people and 48 seniors (split evenly by gender in each group). The experimental results and statistical analyses indicate that in a VR driving scenario task type significantly affected VR driving performance. Navigational scores were significantly higher for the straight (easy) task than for the curved (difficult) task. The aging effect was the main reason for significant and interacting effects of sex and control device. It was found that interactions between age and sex difference indicated that the young group exhibited better wayfinding performance than the senior group, and in the young group males had better performance than females. Similarly, interactions between age and control device indicated that the handlebar control device type resulted in better performance than the joystick device in the young group, but no difference was found in the senior group due to age or learning effects. Findings provide an understanding of the evaluation of the interface designs of navigational support systems, taking into consideration any effects of age, sex, control device, and task type within three-dimensional VR games and driving systems. With a VR driving simulator, seniors can test drive inaccessible products, such as electric bicycles or cars, using a computer at home.

Nutrient estimation in forest ecosystems through satellite images allows us to obtain accurate data, starting with data transformation from forest stands and the existing relationship with the spectral information of the image through modeling. The objective of the study was to quantify and validate the content of C, N, H in aboveground tree biomass in managed stands using spatial modeling and satellite images. This study was conducted during 2017-2018 in managed forest stands in San Juan Lachao, Oaxaca, Mexico. Fifteen 400 m2 experimental sites were selectively established, using a completely randomized experimental design of five silvicultural treatments with three replications. As part of data preprocessing, normality and homogeneity of variances assumptions were checked using the Shapiro-Wilk and Bartlett tests, respectively. From the pixels, data of the average of Normalized Difference Vegetation Index (NDVI) that surrounded the sampling sites were contrasted against the data obtained from forest inventory and the regression models to estimate C, N, H and biomass were generated. Models were validated by NDVI. With the models we estimated 0.95 t ha-1 biomass, which contains between 0.61 and 0.63 of C, 0.44-0.46 of N and 0.24 of H. The models generated had coefficients of determination (R2) of 0.85 to 0.87, which are significant parameters (p ≤ 0.0001). These results confirm that the use of Sentinel satellite images in the estimation of these elements in forest ecosystems based on the relationship between data inventory and the NDVI is highly reliable.

It is shown that if a non-constant meromorphic function f(z) is of finite order and shares certain values with its shifts/difference operators then f(z) coincides with that particular shift/difference operator.

The early-season area estimation of the winter wheat crop as a strategic product is important for decision makers. Classification of multi-temporal images is an approach which is affected by many factors like appropriate training sample size, proper frequency and acquisition times, vegetation indices (VIs) type, temporal gradient of spectral bands and VIs, appropriate classifier and missed values because of cloudy conditions. This paper addresses the impact of appropriate frequency and acquisition times and VIs type along with the spectral and VI gradient on random forest (RF) classifier when missed values exist in multi-temporal images. To investigate the appropriate temporal resolution for image acquisition, the study area was selected on an overlapping area between two LDCM paths. In our developed method, the miss values of cloudy bands for each pixel are retrieved by the mean of k-nearest ordinary pixels. Then the multi-temporal image analysis is performed by considering different scenarios provided by decision makers in terms of desired crop types that should be extracted at early-season in the study areas. The classification results obtained by the RF decrease by 1.6% when temporally missed values retrieved by the proposed method, which is an acceptable result. Moreover, the experimental results demonstrated that if temporal resolution of Landsat 8 increased to one week the classification task can be conducted earlier with almost better results in terms of OA and kappa. The impact of incorporating VIs along with the temporal gradients of spectral bands and VIs as new features in RF demonstrated that the OA and Kappa are improved 3.1% and 6.6%, respectively. Furthermore, the obtained result showed that if only one image from seasonal changes of crops is available, the temporal gradient of VIs and spectral bands play the main role to discriminate remarkably wheat from barley. The experiments also demonstrated that if both wheat and barley merge to a single class the crop area can be estimated two months earlier with 97.1 and 93.5 in terms of OA and kappa, respectively.

This experimental research presents an easier model for fitting experimental results that can be simulate the dynamical behaviour of a single degree freedom system, SDFS, subjected in a forced vibration in a shaking table. The fractional damping using a Kelvin-Voigt fractional derivative rheological model, KVFRdm, to represent a fractional oscillator and compare with the experimental model.

We present a differentially private extension of the block coordinate descent based on objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, the algorithm also offers a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from an analysis without differential privacy. The algorithm’s performance is compared with the standard block coordinate descent algorithm and the trade-off between utility and privacy is studied. The performance is studied using both artificial test data and the forest fires data set. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.

Alfalfa, an important legume forage, is an ideal crop for sustainable agriculture and a potential bioenergy plant. Drought, one of the most common environmental stresses, substantially affects plants’ growth, development and productivity. MicroRNAs (miRNAs) are newly discovered gene expression regulators that have been linked to several plant stress responses. To elucidate the role of miRNAs in drought stress regulation of alfalfa, a high-throughput sequencing approach was used to analyze 12 small RNA libraries comprising of 4 samples, each with 3 biological replicates. We identified 348 known miRNAs, belonging to 80 miRNA families, from the 12 libraries and 281 novel miRNAs using Mireap software. 18 known miRNAs in roots and 12 known miRNAs in leaves were screened out as drought-responsive miRNAs. Except for miR319d and miR157a which were upregulated under drought stress, the expression pattern of drought-responsive miRNAs were different between roots and leaves in alfalfa. This is the first study discovering miR157a, miR1507, miR3512, miR3630, miR5213, miR5294, miR5368 and miR6173 are drought-responsive miRNAs. Target transcripts of drought-responsive miRNAs were computationally predicted. All 447 target genes for the known miRNAs were predicted using an online tool. This study provides a significant insight on understanding drought-responsive mechanisms of alfalfa.

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

A complete model was developed to simulate the behavior of a circular clamped axisymmetric fluid-coupled Piezoelectric Micromachined Ultrasonic Transducer (PMUT). Combining Finite Difference and Boundary Element Matrix (FD-BEM), this model is based on the discretization of the partial differential equation used to translate the mechanical behavior of a PMUT. In the model, both the axial and the transverse displacements are preserved in the equation of motion and used to properly define the neutral line position. To introduce fluid coupling, a Green’s function dedicated to axisymmetric circular radiating sources is employed. The resolution of the behavioral equations is used to establish the equivalent electroacoustic circuit of a PMUT that preserves the average particular velocity, the mechanical power, and the acoustic power. Particular consideration is given to verifying the validity of certain assumptions that are usually made across various steps of previously reported analytical models. In this framework, the advantages of the membrane discretization performed in the FD-BEM model are highlighted through accurate simulations of the first vibration mode and especially the cutoff frequency that many other models do not predict. This high cutoff frequency corresponds to cases where the spatial average velocity of the plate is null and is of great importance for PMUT design because it defines the upper limit above which the device is considered to be mechanically blocked. These modeling results are compared with electrical and dynamic membrane displacement measurements of AlN-based PMUTs in air and fluid. This complete PMUT model using the FD-BEM approach is shown to be very efficient in terms of computation time and accuracy.

With the escalating water scarcity in agriculture, a novel water-saving technique has emerged: drip irrigation with plastic-film mulch (DI). Root function is crucial for sustaining rice production, and understanding its response to DI is essential. However, few studies have evaluated root systems in rice varietals and examined which kind of root system contributes to improving rice grain yield and water productivity in DI. To fill this knowledge gap, we conducted a two-year field experiment comparing two irrigation systems: continuous flooding (CF) and DI. We analyzed their effectiveness with four rice varieties, including upland, F1 lowland, animal feed lowland, and lowland varieties. Vertical root distribution, root bleed-ing rate, photosynthetic-associated parameters, water productivity, and yield performance were analyzed. In our study, the average grain yield of varieties in the DI system (6.4t/ha) was equivalent to those in the CF system (6.6 t/ha). Compared to CF, DI demonstrated significant water-saving potential, saving approximately 35% of the total water supplied, resulting in higher water productivity. Among the varieties, the deep-root weight of the upland variety significantly increased by 51%. The deep-root ratio was positively correlated to transpiration rate, grain yield, and water productivity, which suggested that it contributed to high transpiration, thus maintaining a high carbon assimilation rate resulting in high yield and water productivity. Therefore, deep roots deserve consideration as a trait potentially corresponding to high yield under DI.

In this paper, we analyze the convergence of a finite difference method with the implicit forward time central space (FTCS) scheme for solving the three-dimensional advection-diffusion-reaction equation (ADRE). It is proved that the method is unconditionally convergent. We apply the scheme to obtain numerical solutions for the transport of pollutants in street tunnel problems with various reaction coefficients and various rates of change of concentrations of sources or sinks of pollution.

Due to the special terrain of Urumqi (in the valley area), which often triggers strong foehn weather, and causes huge losses to local people's lives and social economy. This study uses in-situ surface meteorological variables (including the hourly temperature, pressure, humidity, wind, etc.) from the Urumqi Meteorological Station (downstream station, DS) and the Dabancheng Meteorological Station (upstream station, US) in the Middle Tianshan Valley and NCEP/NCAR reanalysis data from 2008 to 2022. A dataset of the foehn weather process at DS in the past 15 years is established and the variation patterns of each meteorological variable during the process of foehn is analyzed. Based on the physical mechanism of the occurrence of foehn, a three-element identification standard for foehn in Urumqi is established by comparing and analyzing the variation of wind direction (WD), wind speed (WS), and the difference of potential temperature (Δθ) between DS and US during the period of foehn and non-foehn from 2013 to 2022, namely: 94°≤ 2-minute average WD ≤168°, 2-minute average WS ≥2.0 m/s, and Δθ between DS and US ≥ 0.29 K. According to the test and evaluation, the three-element identification standard has an accuracy of 82.96%, and a hit rate of 89.50% for the occurrence of foehn in Urumqi from 2008 to 2012. Moreover, the hit rate of foehn identification is 100% for strong wind or above (i.e., 2-minute average WS ≥10.8 m/s) WS. In addition, combined with two predictors of sea-level pressure difference (ΔP) and Δθ between DS and US, forecasting foehn can be more accurately predicted than a single forecasting factor. When ΔP ≤ -12 hPa and Δθ≥5 K, the probability of the occurrence of foehn is more than 90%. This study provides certain reference and application value for the weather forecasting operation of foehn.

River renaturation can be an effective management method for restoring the floodplain's natural capacity and minimizing the effects during high flow periods. A 1D-2D HEC-RAS model, in which the flood plain was considered as 2D and the main channel as 1D, was used to simulate flooding in the restored reach of the Spree River. When computing in this model, finite volume and finite difference approximations using the Preissmann approach are used for the 1D and 2D models, respectively. To comprehend the sensitivity of the parameters and model, several scenarios were simulated using different time steps and grid sizes. Additionally, dykes, dredging, and changes to the vegetation pattern have been used to simulate flood mitigation measures. The model predicted that flooding would occur mostly in the downstream portion of the channel in the majority of the scenarios without mitigation measures, whereas with mitigation measures, flooding in the floodplain would be greatly reduced. By preserving the natural balance on the channel's floodplain, the restored area needs to be kept in good condition. Therefore, mitigating measures that balance the area's economic and environmental aspects must be considered in light of the potential for floods.

Background. We investigated, for the first time, whether there are any sex differences in retrospective self-reported childhood maltreatment (CM) in Italian adult patients with major depressive disorder (MDD) or bipolar disorder (BD). Furthermore, the potential impacts of patients’ age on the CM self-report was investigated. Methods. This retrospective, cross-sectional study used the data documented in the electronic medical records of patients who were hospitalized for a 4-week psychiatric rehabilitation program. The CM was assessed using the 28-item Childhood Trauma Questionnaire (CTQ), which evaluates emotional, physical, and sexual abuse, as well as emotional and physical neglect. The linear and logistic regression models were used (α = 0.01). Results. Three hundred thirty five patients with MDD (255 women and 80 men) and 168 with BD (97 women and 71 men) were included. In both samples, considerable CM rates were identified, but no statistically significant sex differences were detected in the variety of CTQ-based CM aspects. There was a significant association, with no sex differences, between the increasing patients’ age and a decreasing burden of CM. Conclusion. Both women and men with MDD or BD experienced a similar and considerable CM burden. Our findings support the routine CM assessment in psychiatric clinical practice.

To overcome the two-phase flow instability of traditional boiling heat dissipation technologies, a porous wick was used for liquid-vapor isolation, thus realizing efficient and stable boiling heat dissipation. A pump-assisted capillary phase-change loop with methanol as working medium was established to study the effect of liquid-vapor pressure difference and heating power on its start-up and steady-state characteristics. The results indicated that the evaporator undergoes four heat transfer modes including flooded, partial flooded, thin film evaporation and overheating. The thin film evaporation mode was the most efficient one with the shortest start-up period. Besides, the heat transfer modes were determined by liquid-vapor pressure difference and power. The heat transfer coefficient could be significantly improved and the thermal resistance could be reduced by increasing liquid-vapor pressure difference as long as it did not exceed 8 kPa. However, when the liquid-vapor pressure difference exceeded 8kPa, its influence on the heat transfer coefficient weakened. In addition, a two-dimensional heat transfer mode distribution diagram considering both liquid-vapor pressure difference and power was drawn through a great number of experiments. During engineering application, the liquid-vapor pressure difference can be controlled to maintain efficient thin film evaporation in order to achieve the optimum heat dissipation effect.

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on nonlinear generation of a difference frequency in a medium with a second-order susceptibility is considered. The modified SVEA splits a slowly varying amplitude into two factors, which makes it possible to more accurately describe the three-wave mixing process. The theoretical substantiation of the rule of vortex beams topological charges conversion is given – the topological charge of the output radio-vortex beam is equal to the difference between the topological charges of the input optical vortex beams. A numerical simulation model of the processes under consideration has been implemented and analyzed.

In this paper we investigate the global asymptotic stability of following system ofhigher order difference equations with quadratic terms:xn+1=A+Byn/yn−m^2, yn+1=A+Bxn/xn−m^2, where A and B are positive numbers and the initial values are positive numbers.We also study the boundedness, rate of convergence and oscillation behaviour of thesolutions of related system.

This paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}²)),y_{n+1}=A+B((x_{n})/(x_{n-m}²)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

Metasurfaces of gold (Au) nanoparticles on a SiO2-Si substrate were fabricated for the enhancement of second harmonic generation (SHG) using electron beam lithography and lift-off. Triangular Au nanoprisms which are non-centro-symmetric and support the second- order non-linearity were examined for SHG. The thickness of the SiO2 spacer is shown to be an efficient parameter to spectrally tune to maximise SHG. Electrical field enhancement at the fundamental wavelength was shown to define the intensity of the second harmonics. Numerical modeling of light enhancement was verified by experimental measurements of SHG and reflectivity spectra at the normal incidence. At the plasmonic resonance, SHG is enhanced up to ∼3.5×103 times for the optimised conditions.

A second order rational difference equation $$x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$$ with the parameters $p$ and $q$ which lies in $(0,1)$, is studied. The dynamics of the equilibrium is characterized through the trichotomy of the parameter $p<\frac{1}{2}$, $p=\frac{1}{2}$ and $p>\frac{1}{2}$. It is found that there is no periodic solution of period $2$ and $3$ but there exists periodic solutions with only periodic solution $5$ and $10$ are achieved computationally.