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The normal ordering of an integral power of the number operator a\(^\dagger\)a in terms of boson annihilation a and creation a\(^\dagger\) operators is expressed with the help of the Stirling numbers of the second kind. The normal ordering problems directly links the problems to combinatorics. Whit this in mind, in this paper, we define the \(\alpha\)-analogues of r-Whitney numbers of the first kind and those of second kind, which are different from degenerate r-Whitney numbers. We show that \(\alpha\)-analogues falling factorial of the number operator is expressed in terms of the \(\alpha\)-analogues of r-Whitney numbers of the first kind and its inverse formula is expressed as those of the second kind. We also derived some properties, recurrence relations and several identities on those numbers arising from Boson annihilation a and creation operators a\(^\dagger\), number operators \(\hat{h}\) and coherent states.

Abstract. Applying disposition theory to narrative persuasion, this study examined how audience members’ enjoyment of a narrative promotes persuasion differently than transportation and identification. In a 2 (affective disposition: liked vs. disliked story character) × 2 (framing: gain vs. loss framed story) between-subject experiment, participants ( N = 295) read a story in which a liked or disliked character has either a positive outcome (a gain frame) or a negative outcome (a loss frame) dependent on the story character’s engagement in sun protection behaviors. Consistent with disposition theory, participants enjoyed the story more when a liked character was in a gain-framed (vs. loss-framed) narrative; however, no framing effect was found for a disliked character. This interactive effect on enjoyment, in turn, mediated participants’ intentions to engage in sun protection behaviors. Affective disposition and framing independently influenced transportation and identification. Transportation mediated the effect of affective disposition on behavioral intention, but identification did not. This study demonstrates distinctive narrative conditions that prompt enjoyment, transportation, and identification in different ways and, in turn, lead to persuasive effects.

In this paper, we introduce a new type degenerate Stirling numbers of the second kind and their degenerate Bell polynomials, which is different from degenerate Stirling numbers of the second kind studied so far. We investigate the explicit formula, recurrence relation and Dobinski-like formula of a new type degenerate Stirling numbers of the second kind. We also derived several interesting expressions and identities for bell polynomials of these new type degenerate Stirling numbers of the second kind including the generating function, recurrence relation, differential equation with Bernoulli number as coefficients, the derivative and Riemann integral, so on.

Activating brown adipose tissue (BAT) and stimulating white adipose tissue (WAT) browning is a prospective obesity treatment method. Dietary components derived from plants are the most effective approach to activate BAT and promote WAT browning in rodents. This study investigated the synergistic effects of Panax ginseng (PG) and Diospyros kaki leaf (DKL) extract on adipocyte differentiation and browning, as well as the molecular mechanism underlying their beneficial effects. The administration of PG and DKL to HFD-induced obese mice significantly decreased body weight and epididymal and abdominal adipose tissue mass. In in vitro, PG inhibited the adipogenesis of 3T3-L1 adipocytes by regulating the expression of key adipogenic regulators, such as peroxisome proliferator-activated receptor (PPAR)γ and CCAAT/enhancer-binding protein (C/EBP)-α. In contrast, DKL negligibly influenced the adipogenesis of 3T3-L1 adipocytes but greatly increased the protein expression of UCP-1, PGC-1α, and PPARα in BAT and/or WAT. Moreover, PG and DKL inhibited adipogenesis synergistically and activated white adipocyte browning via AMP-activated protein kinase (AMPK) and sirtuin 1 (SIRT1) pathways. These results suggest that a combination of PG and DKL regulates adipogenesis in white adipocytes and browning in brown adipocytes by activating AMPK/SIRT1 axis. The potential use of PG and DKL may represent an important strategy in obesity management that will be safer and more effective.

Recently, the λ-analogues of r-Stirling numbers of the first kind were studied by Kim-Kim. The aim of this paper is to introduce the λ-analogues of r-Stirling numbers of the second kind and to investigate some properties, recurrence relations and certain identities on those numbers. We also introduce the λ-analogues of Whitney-type r-Stirling numbers of the second and derive similar results to the case of the λ-analogues of r-Stirling numbers of the second kind. In addition, we consider the λ-analogues of Dowling polynomials and deduce a Dobinski-like formula.

Background We investigated the change of coronary atherosclerosis with long-term exposure to fine particulate matter of aerodynamic diameter Methods Subjects undergoing serial CCTAs between January 2007 and December 2017 (n = 3,127) were analyzed. Each individual's cumulative amount of PM2.5 exposure between the two CCTAs was evaluated by Kriging interpolation and zonal analysis, considering the time interval between the two CCTAs. The main outcome was progression of coronary artery calcium (CAC) with additional semiquantitative analysis on the changes in the severity and composition of atherosclerotic plaques. Results The CAC scores increased by 30.8 Agatston units per-year under a median PM2.5 concentration 24.9μg/m3 and tended to increase with the cumulative amount of PM2.5 exposure (r = 0.321, p Conclusions Cumulative exposure to air pollution is associated with the progression of diffuse coronary calcification, the importance of which may be more significant than other traditional cardiovascular risk factors. Further investigations into the causality between PM2.5 and coronary atherosclerosis are warranted to improve global cardiovascular health.

p-adic analysis and their applications is used p-adic distributions, p-adic measure, p-adic integrals, p-adic L-function and other generalized functions. In addition, among the many ways to investigate and construct generating functions for special polynomials and numbers, one of the most important techniques is the p-adic Fermionic integral over \(\mathbb{Z}\)p. In this paper, we introduce new numbers and polynomials arising from the Fermionic p-adic integral on \(\mathbb{Z}\)p. First, we introduce new numbers and polynomials as one of generalizations of Changhee numbers and polynomials of order r (r \(\epsilon\) \(\mathbb{N}\)), which are called the generalized Changhee numbers and polynomials. We explore some interesting identities and explicit formulas of these numbers and polynomials. Second, we define new numbers and polynomials as one of generalizations of Catalan numbers and polynomials of order r (r \(\epsilon\) \(\mathbb{N}\)), which are called the generalized Catalan numbers and polynomials. We also study some combinatorial identities and explicit formulas of these numbers and polynomials.

Recently, Kim-Kim [J. Math. Anal. Appl. 493 (2021), no. 1] introduced the degenerate Sheffer sequence and λ-Sheffer sequence. The purpose of this article is to study λ-q-Sheffer sequence and the degenerate q-Sheffer sequence, which are derived from the view point of degenerate umbral calculus and investigate some properties related to those sequences. In addition, we give some new identities associated with q-special polynomials arising from our investigation.

Many mathematicians have studied degenerate versions of some special polynomials and numbers that can take into account the surrounding environment or a person's psychological burden in recent years, and they've discovered some interesting results. Furthermore, one of the most important approaches for finding the combinatorial identities for the degenerate version of special numbers and polynomials is the umbral calculus. The Catalan numbers and the Daehee numbers play important role in connecting relationship between special numbers. In this paper, we first define the degenerate Catalan-Daehee numbers and polynomials and aim to study the relation between well-known special polynomials and degenerate Catalan-Daehee polynomials of order r as one of the generalizations of the degenerate Catalan-Daehee polynomials by using the degenerate Sheffer sequences. Some of them include the degenerate and other special polynomials and numbers such as the degenerate falling factorials, the degenerate Bernoulli polynomials and numbers of order r, the degenerate Euler polynomials and numbers of order r, the degenerate Daehee polynomials of order r, the degenerate Bell polynomials, and so on.

The $ r $-Lah numbers generalize the Lah numbers to the $ r $-Stirling numbers in the same sense. The Stirling numbers and the central factorial numbers are one of the important tools in enumerative combinatorics. The $ r $-Lah number counts the number of partitions of a set with $ n+r $ elements into $ k+r $ ordered blocks such that $ r $ distinguished elements have to be in distinct ordered blocks. In this paper, the $ r $-central Lah numbers and the $ r $-central Lah-Bell numbers ($ r\in \mathbb{N} $) are introduced parallel to the $ r $-extended central factorial numbers of the second kind and $ r $-extended central Bell polynomials. In addition, some identities related to these numbers including the generating functions, explicit formulas, binomial convolutions are derived. Moreover, the $ r $-central Lah numbers and the $ r $-central Lah-Bell numbers are shown to be represented by Riemann integral, respectively.

The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and polynomials. The aim of this article is to further study some identities and properties related to the degenerate Stirling numbers of the second kind, in connection with the degenerate Bell polynomials, the degenerate Fubini polynomials, the degenerate Bernoulli polynomials, and the degenerate Euler polynomials.

In this paper, we derive some identities and recurrence relations for the degenerate Stirling numbers of the first kind and of the second kind, which are degenerate versions of the ordinary Stirling numbers of the first kind and of the second kind. They are deduced from the normal orderings of degenerate integral powers of the number operator and their inversions, certain relations of boson operators and the recurrence relations of the Stirling numbers themselves. Here we note that, while the normal ordering of an integral power of the number operator is expressed with the help of the Stirling numbers of the second kind, that of a degenerate integral power of the number operator is represented by means of the degenerate Stirling numbers of the second kind.

In a public health crisis, communication plays a vital role in making sure policies and recommendations from the government level get disseminated accurately to its people and is only considered as effective when the public accepts, supports, complies to, and engages in policies or behaves as per governments’ recommendations. Adopting the multivariate audience segmentation strategy for health communication, this study uses a data-driven analytical method to (1) identify audience segments of public health crisis communication in Singapore based on knowledge, risk perception, emotional responses, and preventive behaviors; and (2) characterize each audience segment according to demographic factors, personality traits, information processing styles, and health information preferences. Results (N = 2033) from a web-based questionnaire executed in August 2021 have identified three audience segments: the less-concerned (n = 650), the risk-anxious (n = 142), and the risk-majority (n = 1,241). This study offers insights to how audiences of public health crisis communication perceive, process, and respond to information directed to them during the pandemic, thereby informing policy makers to tailor more targeted public health communication interventions in promoting positive attitude and behavior change.

Purpose: In a previous study, we identified the skin-whitening effect of the ethanolic extract of Padina gymnospora. The present study was performed to confirm the safety of the extract in animal replacement tests.Methods: To evaluate the safety of the extract of Padina gymnospora, the photosensitivity test (Harber test), in vitro 3T3 neutral red uptake (3T3 NRU) phototoxicity test, local lymph node assay (5-bromo-2'-deoxyuridine enzyme-linked immunosorbent assay), acute oral toxicity test, and reconstructed human epidermis (RHE) test were used. All experiments followed the guidelines of the Korean Ministry of Food and Drug Safety and were conducted by a GLP-certified organization (Chemon Inc.).Results: The extract of Padina gymnospora was not photosensitive: 0% photosensitization was detected (I grade: very weak). In the 3T3 NRU phototoxicity test, the relative viability of the extract-treated cells was higher than the guideline level; thus, the extract was classified as non-phototoxic. Treatment with the extract did not trigger skin irritation in the RHE test model and did not cause skin sensitization in the local lymph node assay. Finally, oral administration of the extract to rats indicated that it was not a harmful material as the LD50 was estimated at >2,000 mg/kg.Conclusion: The ethanolic extract of Padina gymnospora was demonstrated to be safe when applied to the skin. Taken together with our previous study of its efficacy, we conclude that this extract has the potential for use as a cosmetic ingredient.

In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. The aim of this paper is to study several relations among those three numbers. In more detail, we represent the multi-Bernoulli numbers in terms of the multi-Stirling numbers of the first kind and vice versa, and the multi-Lah numbers in terms of multi-Stirling numbers. In addition, we deduce a recurrence relation for multi-Lah numbers, Comment: 8 pages

The derangement number [Formula: see text] is the number of fixed point free permutations on a set of [Formula: see text] elements and the derangement polynomial [Formula: see text]) is a natural extension of the derangement number [Formula: see text]. The aim of this paper is to introduce [Formula: see text]-derangement numbers and polynomials, which are [Formula: see text]-analogs of the derangement numbers and polynomials, and to investigate their connection with some other [Formula: see text]-special numbers and polynomials. In more detail, we derive explicit expressions and recurrence relations for the [Formula: see text]-derangement numbers and polynomials. Further, we obtain some identities involving such polynomials and numbers and other special [Formula: see text]-polynomials and numbers, which include [Formula: see text]-Bell polynomials, [Formula: see text]-analogs of Fubini polynomials and [Formula: see text]-Stirling numbers of the second kind.

This study capitalizes on the unique capability of virtual reality (VR) to examine the efficacy of self- versus other-embodied perspective taking in promoting kidney donation in Singapore. The study used a 2 (self- vs other-embodied) × 2 (mirror vs photo presentation) between-subjects VR experiment (N = 128), wherein participants played the role of a patient needing a kidney donation, either as themselves or as a typical organ-failure patient. Our findings showed that self-embodied perspective taking triggered self-oriented emotions (i.e. personal distress) and subsequently egoistic motivations that resulted in alternative prosocial behaviors (e.g. monetary donation, volunteering) than kidney donation. We found that embodying the other, rather than the self, had the practical benefit of inducing other-oriented emotions (i.e. empathy) and hence altruistic motivations that promoted kidney donation. This study clarified the conditions under which embodied perspective taking promoted different prosocial outcomes, and the specific mechanisms through which it achieved those outcomes. Ministry of Education (MOE) This research was supported by an Academic Research Fund Tier 1 Grant from the Singapore Ministry of Education and a Start-Up Grant from Nanyang Technological University.

Nosema ceranae infection in Apis mellifera acts as a virulent pathogenic factor of honeybee colony collapse. Fumagillin is the only effective antimicrobial agent currently used against the microsporidial parasite N. ceranae. However, the toxicity of fumagillin is a concern. Therefore, in the present study, the screening of potent alternatives for fumagillin was performed for a total of 21 compounds, including 15 phenolics and 6 monoterpenes, based on their structure–activity correlation. The anti-nosemosis activity of each compound was determined by the relative inhibition level against the expression of the N. ceranae virulence factor encoding the polar tube protein 3 (ptp3) mRNA of the ptp3 gene. Each compound was preliminarily evaluated at 100 and 200 µM treatment concentrations. Then, the activity of 12 compounds showing activity at 200 µM was additionally determined at 40 µM, a concentration generally used in apiaries. At this concentration, gallol (benzene-1,2,3-triol) and 3-pentylcatechol (PC) showed higher activities than fumagillin, and 4-pentylgallol (PG) exhibited activity at a similar level to fumagillin. All three compounds selected in this study were low-molecular-weight phenolics. Among them, PC and PG, chemically synthesized compounds, commonly possess a hydrocarbon side chain of the pentyl group (-C5H11) in catechol and gallol, respectively. That is, the three treatment compounds were selected as potential beneficial alternatives for fumagillin and were markedly different from fumagillin in terms of their chemical structure. These results may trigger further extensive research on the biological mechanism for the prevention of nosemosis.