The purpose of this study was to investigate the effect of chitosan (CS) and Alginate (Alg) polymers concentrations and CaCl2 concentration on metronidazole (MET) drug loading (LE), size particles and zeta potential. Nanocomposites were prepared by ionotropic pregelation method. A (21 *31 *21) *3= 36 full factorial design (FFD) was used to predict statistical equation and responses. The MET-CS-AlgNPs nanocomposites were characterized by X-ray diffraction, Fourier-transform infrared spectroscopy, thermal gravimetric analysis, scanning electron microscope and in vitro drug release studies. All data indicated the presence of drug into MET-CS-AlgNPs nanocomposites. The release profile of MET-CS-AlgNPs nanocomposites was found to be sustained

This paper presents a theorem in factorial functions with the sum of any two nonnegative integers that is equal to multiple of the product of factorial of the same two nonnegative integers.

The current study aimed to assess the components of the intervention program “Aquatic”, targeted at the reduction of bottled water use in adolescence. The Comprehensive Action Determination Model was chosen as a theory of change for the development and evaluation of pro-environmental behavior intervention. We examined the impact of five experimental intervention factors (water bottles, promo video, prompts, goal setting, and feedback) on eight intervention program outcomes: Perceived behavioral control, Social norm, Habit, Awareness of need, Awareness of consequence, Personal norm, Intention, and Behavior. The study sample consisted of 419 adolescents (52.8% girls, Mage = 15.21, SDage = .64) from Lithuania. A factorial experimental study design was used, and a Latent change modeling approach was applied for the evaluation of individual and combined effects of intervention components. Promo video, Prompts, and Goal setting had a positive effect on Awareness of consequence, Social norm, and Awareness of need, respectively. Receiving a Water bottle in combination with the Promo video had a positive effect on Perceived behavioral control and in combination with Prompts as well as Goals – on Awareness of need. Water bottles, Promo-video, Prompts, and Goals, but not Feedback, had value in the promotion of targeted pro-environmental outcomes.

Education for Sustainable Development (ESD) is considered vital to the success of the United Nations’ Sustainable Development Goals. Systems Thinking has been identified as a core competency necessary to incorporate into ESD. Systems Thinking orientated ESD learning tools, established methods of assessment of sustainability skills, and studies to demonstrate effectiveness of such learning tools, are all lacking. There is a wealth of experience in the System Dynamics field regarding the application of Systems Thinking and simulation to environmental problems, sustainability and systems education. Many System Dynamicists regard simulation as essential for teaching Systems Thinking. The substantial body of research into the design of effective simulation-based learning environments (SBLEs) can also inform ESD initiatives. This research describes a randomised controlled trial (n=106) to investigate whether an online sustainability learning tool that incorporates Systems Thinking and System Dynamics simulation increases understanding of a specific problem and supports transfer of knowledge to a second problem with a similar systemic structure. The effects of Systems Thinking and simulation were tested separately and in combination. The learning tool was designed for a single online learning session. Simulation was found to increase ESD learning outcomes significantly, and also to support transfer of skills, although less significantly.

In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2. We also derive more representations of the p-adic (ρ,q)-gamma function in general case. Moreover, we consider the p-adic (ρ,q)-Euler constant derived from the derivation of p-adic (ρ,q)-gamma function at x = 1. Furthermore, we provide a limit representation of aforementioned Euler constant based on (ρ,q)-numbers. Finally, we consider (ρ,q)-extension of the p-adic beta function via the p-adic (ρ,q)-gamma function and we then investigate various formulas and identities.

A multilevel factorial design of 23 with 12 experiments was developed for the preparation of cellulose nanocrystals (CNC) from Agave tequilana Weber var. Azul bagasse. The studied parameters were acid type (H2SO4 and HCl), acid concentration (60 and 65 wt% for H2SO4, 2 and 8N for HCl) temperature (40 and 60°C for H2SO4, 50 and 90°C for HCl), and hydrolysis time (40, 55 and 70 min for H2SO4, 30, 115 and 200 min for HCl). The obtained CNC were physical and chemically characterized using dynamic light scattering (DLS), atomic force microscopy (AFM), Fourier-transform infrared spectroscopy (FT-IR), X-ray photoelectron spectroscopy (XPS), and X-ray diffraction (XDR) techniques. The size and morphology of A. tequilana CNC strongly depend on the acid type and hydrolysis parameters. The shortest CNC were obtained with H2SO4 (65 wt%, 40 °C, and 70 min) had a length of 137 ± 68 nm, width 33 ± 7 nm, and height 9.1 nm, whereas the shortest CNC obtained with HCl (2 N, 50 °C and 30 min) had a length of 216 ± 73 nm, width 69 ± 17 nm, and height 8.9 nm. CNC prepared from H2SO4 resulted shorter and thinner than those obtained with HCl. The total sulfate groups content in CNC obtained with H2SO4 increase with time agree to CSG=aebt, and increases with temperature and acid concentration.

In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive several correlations for the fully degenerate central Bell polynomials associated with the degenerate Bernstein polynomials and the degenerate Bernoulli, Euler and Genocchi numbers.

For the in-house validation of a droplet digital PCR method, a factorial experimental design was implemented. This design serves different purposes. On the one hand, it is an efficient design in relation to the workload involved in achieving a desirable level of reliability of variance estimates. On the other hand, it allows a partitioning of total variance into different components, thus providing information regarding the dominant sources of random variation. The statistical modelling reflects the actual measurement mechanism, establishing relationships between nominal target DNA copies per well, the range of variation of copy numbers per droplet, probability of detection values, and estimated numbers of copies.

Let be a power function $f_{r,M}(s)$ defined for every $s$ within the finite set $M$ as follows $$f_{r,M}(s)= \begin{cases} s^r, \ &s\in M,\\ 0, \ &\mathrm{otherwise}. \end{cases} $$ Let a discrete convolution of $f_{r,M}(s)$ be denoted as follows $\mathrm{Conv}_{r,M}[n]=(f_{r,M}*f_{r,M})[n]$. Let a real coefficients $A_{m,j}$ be given by the following recurrence $$ A_{m,j} = \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \end{cases} $$ In this paper we show that for every $n>0$ the following odd-power identities involving coefficients $A_{m,j}$ and convolution transform $\mathrm{Conv}_{r,M}[n]$ hold $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

The prevalence of internet gaming disorders (IGD) is considerably high among youth, especially with social isolation imposed by the ongoing COVID-19 pandemic. IGD adversely affects mental health, quality of life, and academic performance. The Internet Gaming Disorder Scale (IGDS9-SF) is designed to detect IGD according to DSM-IV diagnostic criteria. However, inconsistent results are reported on its capacity to diagnose IGD evenly across different cultures. To ensure the suitability of the IGDS9-SF as a global measure of IGD, this study examined the psychometric properties of the IGDS9-SF in a sample of Sri Lankan university students (N = 322, mean age =17.2 ± 0.6, range = 16-18 years, 56.5% males) and evaluated its measurement invariance across samples from Sri Lanka, Turkey, Australia, and the USA. Among Sri Lankan students, a unidimensional structure expressed good fit, invariance across different groups (e.g., gender, ethnicity, and income), adequate criterion validity (strong correlation with motives of internet gaming, daily gaming duration, and sleep quality), and good reliability (alpha = 0.81). Males and online multiplayers expressed higher IGD levels, greater time spent gaming, and more endorsement of gaming motives (e.g., Social and Coping) than females and offline players. Across countries, the IGDS9-SF was invariant at the configural, metric, and scalar levels, albeit strict invariance was not maintained. The lowest and highest IGD levels were reported among Turkish and American respondents, respectively. In conclusion, the IGDS9-SF can be reliably used to measure IGD among Sri Lankan youth. Because the scale holds scalar invariance across countries, its scores can be used to compare IGD levels in the studied countries.

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k; 0 ≤ k ≤ n−1 or 1 ≤ k ≤ n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m = 5; 7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^2m+1; m ≥ 0 as sum of row terms of corresponding triangle. In other words, in this manuscript are found and discussed the polynomials D_m(n,k) and U_m(n,k), such that, when being summed up over k in some range with respect to m and n returns the monomial n^2m+1.

Despite extensive investigations of the Depression Anxiety Stress Scales-21 (DASS-21) since its development in 1995, its factor structure and other psychometric properties still need to be firmly established, with several calls for revising its item structure. Employing confirmatory factor analysis (CFA), this study examined the factor structure of the DASS-21 and five shortened versions of the DASS-21 among psychiatric patients (N = 168) and the general public (N = 992) during the COVID-19 confinement period in Saudi Arabia. Multigroup CFA, Mann Whitney W test, Spearman’s correlation, and coefficient alpha were used to examine the shortened versions of the DASS-21 (DASS-13, DASS-12, DASS-9 (two versions), and DASS-8) for invariance across age and gender groups, discriminant validity, predictive validity, item coverage, and internal consistency, respectively. Compared with the DASS-21, all three-factor structures of the shortened versions expressed good fit, with the DASS-8 demonstrating the best fit and highest item loadings on the corresponding factors in both samples (χ2(16, 15) = 16.5, 67.0; p = 0.420, 0.000; CFI= 1.000, 0.998; TLI = 0.999, 0.997; RMSEA = 0.013, 0.059, SRMR = 0.0186, 0.0203). It expressed configural, metric, and scalar invariance across age and gender groups. Its internal consistency was comparable to other versions (α = 0.94). Strong positive correlations of the DASS-8 and its subscales with the DASS-21 and its subscales (r = 0.97 to 0.81) suggest adequate item coverage and good predictive validity of this version. The DASS-8 and its subscales distinguished the clinical sample from the general public at the same level of significance expressed by the DASS-21 and other shortened versions, supporting its discriminant validity. Neither the DASS-21 nor the shortened versions distinguished patients diagnosed with depression and anxiety from other conditions. The DASS-8 represents a valid short version of the DASS-21, which may be useful in research and clinical practice for quick identification of individuals with potential psychopathologies. Diagnosing depression/anxiety disorders may be further confirmed in a next step by clinician-facilitated examinations. Brevity of the DASS-21 would save time and effort used for filling the questionnaire and support comprehensive assessments by allowing the inclusion of more measures on test batteries.