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This study aimed to compare the cost-effectiveness of manual therapy and usual care for patients with chronic neck pain. A cost-utility analysis alongside a pragmatic randomized controlled trial was conducted in five South Korean hospitals. Data were procured from surveys and nationally representative data. Participants were 108 patients aged between 19 and 60 years, with chronic neck pain persisting for at least 3 months and a pain intensity score of ≥5 on the numerical rating scale in the last 3 days. The study was conducted for 1 year, including 5 weeks of intervention and additional observational periods. Participants were divided into a manual therapy (Chuna) group and a usual care group, and quality-adjusted life-years, costs, and the incremental cost-effectiveness ratio were calculated. The quality-adjusted life-years of the manual therapy group were 0.024 higher than that of the usual care group. From the societal perspective, manual therapy incurred a lower cost—at $2,131—and was, therefore, the more cost-effective intervention. From a healthcare system perspective, the cost of manual therapy was higher, with an incremental cost-effectiveness ratio amount of $11,217. Manual therapy is more cost-effective for non-specific chronic neck pain management from both a healthcare system and societal perspective.

Abstract Identities of symmetry in two variables for Bernoulli polynomials and power sums had been investigated by considering suitable symmetric identities. T. Kim used a completely different tool, namely the p-adic Volkenborn integrals, to find the same identities of symmetry in two variables. Not much later, it was observed that this p-adic approach can be generalized to the case of three variables and shown that it gives some new identities of symmetry even in the case of two variables upon specializing one of the three variables. In this paper, we generalize the results in three variables to those in an arbitrary number of variables in a suitable setting and illustrate our results with some examples.

Abstract Dedekind sums occur in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. In 1892, Dedekind showed a reciprocity relation for the Dedekind sums. Apostol generalized Dedekind sums by replacing the first Bernoulli function appearing in them by any Bernoulli functions and derived a reciprocity relation for the generalized Dedekind sums. In this paper, we consider the poly-Dedekind sums obtained from the Dedekind sums by replacing the first Bernoulli function by any type 2 poly-Bernoulli functions of arbitrary indices and prove a reciprocity relation for the poly-Dedekind sums.

Abstract The aim of this paper is to study the unsigned degenerate r-Stirling numbers of the first kind as degenerate versions of the r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind as those of the r-Stirling numbers of the second kind. For the degenerate r-Stirling numbers of both kinds, we derive recurrence relations, generating functions, explicit expressions, and some identities involving them.

Abstract Recently, the nth Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for any nonnegative integer n. Further, as natural extensions of the Lah–Bell numbers, Lah–Bell polynomials are defined. We study Lah–Bell polynomials with and without the help of umbral calculus. Notably, we use three different formulas in order to express various known families of polynomials such as higher-order Bernoulli polynomials and poly-Bernoulli polynomials in terms of the Lah–Bell polynomials. In addition, we obtain several properties of Lah–Bell polynomials.

Abstract Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials. In recent years, studying degenerate versions regained lively interest of some mathematicians. The purpose of this paper is to study degenerate Bell polynomials by using umbral calculus and generating functions. We derive several properties of the degenerate Bell polynomials including recurrence relations, Dobinski-type formula, and derivatives. In addition, we represent various known families of polynomials such as Euler polynomials, modified degenerate poly-Bernoulli polynomials, degenerate Bernoulli polynomials of the second kind, and falling factorials in terms of degenerate Bell polynomials and vice versa.

Abstract Background Conventional therapeutic approaches for tumor angiogenesis, which are primarily focused on the inhibition of active angiogenesis to starve cancerous cells, target the vascular endothelial growth factor signaling pathway. This aggravates hypoxia within the tumor core and ultimately leads to increased tumor proliferation and metastasis. To overcome this limitation, we developed nanoparticles with antiseptic activity that target tumor vascular abnormalities. Methods Ferritin-based protein C nanoparticles (PCNs), known as TFG and TFMG, were generated and tested in Lewis lung carcinoma (LLC) allograft and MMTV-PyMT spontaneous breast cancer models. Immunohistochemical analysis was performed on tumor samples to evaluate the tumor vasculature. Western blot and permeability assays were used to explore the role and mechanism of the antitumor effects of PCNs in vivo. For knocking down proteins of interest, endothelial cells were transfected with siRNAs. Statistical analysis was performed using one-way ANOVA followed by post hoc Dunnett’s multiple comparison test. Results PCNs significantly inhibited hypoxia and increased pericyte coverage, leading to the inhibition of tumor growth and metastasis, while increasing survival in LLC allograft and MMTV-PyMT spontaneous breast cancer models. The coadministration of cisplatin with PCNs induced a synergistic suppression of tumor growth by improving drug delivery as evidenced by increased blood prefusion and decreased vascular permeability. Moreover, PCNs altered the immune cell profiles within the tumor by increasing cytotoxic T cells and M1-like macrophages with antitumor activity. PCNs induced PAR-1/PAR-3 heterodimerization through EPCR occupation and PAR-1 activation, which resulted in Gα13-RhoA-mediated-Tie2 activation and stabilized vascular tight junctions via the Akt-FoxO3a signaling pathway. Conclusions Cancer treatment targeting the tumor vasculature by inducing antitumor immune responses and enhancing the delivery of a chemotherapeutic agent with PCNs resulted in tumor regression and may provide an effective therapeutic strategy.

Abstract In this paper, by means of p-adic Volkenborn integrals we introduce and study two different degenerate versions of Bernoulli polynomials of the second kind, namely partially and fully degenerate Bernoulli polynomials of the second kind, and also their higher-order versions. We derive several explicit expressions of those polynomials and various identities involving them.

Abstract The aim of this paper is to study Jindalrae and Gaenari numbers and polynomials in connection with Jindalrae–Stirling numbers of the first and second kinds. For this purpose, we first introduce Jindalrae–Stirling numbers of the first and second kinds as extensions of the notions of the degenerate Stirling numbers of the first and second kinds, and deduce several relations involving those special numbers. Then we introduce Jindalrae and Gaenari numbers and polynomials and obtain some explicit expressions and identities associated with those numbers and polynomials. In addition, we interpret our results by using umbral calculus.

Abstract Recently, Dolgy–Jang introduced the poly-Genocchi polynomials and numbers arising from the modified polyexponential function. In this paper, we study the degenerate poly-Genocchi polynomials and numbers constructed from the modified degenerate polyexponential function. We derive explicit expressions for those polynomials and numbers. Also, we obtain identities involving those polynomials and numbers and some other special numbers and polynomials. In addition, we investigate the higher-order degenerate Genocchi polynomials and find identities involving those polynomials and the higher-order Changhee polynomials.

Abstract The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of the polyexponential functions. In this paper, we introduce the degenerate polyexponential functions and the degenerate type 2 poly-Bernoulli numbers and polynomials, as degenerate versions of such functions and numbers and polynomials. We derive several explicit expressions and some identities for those numbers and polynomials.

This present study was conducted to investigate protective effect of discontinuous Percoll gradient containing alpha-linolenic acid (ALA) before freezing process on viability, acrosome damage, mitochondrial activity, and oxidative stress of frozen-thawed boar spermatozoa. The separation of spermatozoa by discontinuous Percoll gradient was performed by different concentration of Percoll solution (45/90%) containing ALA combined with bovine serum albumin (BSA), and collected sperm in each Percoll layer was cryopreserved. To evaluate viability, acrosome damage, mitochondrial activity, and reactive oxygen species (ROS) level of frozen-thawed sperm, flow cytometry was used. Morphological abnormalities were observed under light microscope. In results, viability of sperm from 90% Percoll layer was higher than control and 45% Percoll group (p < 0.05). Separated sperm in 90% Percoll layer had lower acrosome damage and morphological abnormalities than control as well as viability, whereas 45% Percoll group was higher (p < 0.05). Similar with acrosome damage and abnormalities, mitochondrial activity was slightly enhanced and the population of live sperm with high ROS level was decreased by 90% Percoll separation, however, there was no significant difference. Supplementation of 3 ng/mL ALA into Percoll solution increased sperm viability and decreased population of live sperm with high ROS compared to control (p < 0.05). In conclusion, discontinuous Percoll gradient before freezing process could improve efficiency of cryopreservation of boar sperm through selection of sperm with high freezing resistance, and supplement of ALA during Percoll gradient might contribute suppression of ROS generation via stabilizing of plasma membrane during cryopreservation.

One fundamental element of probabilistic safety assessment (PSA) is the initiating event (IE) analysis. Since IE frequencies can change over time, time-trend analysis is required to obtain optimized IE frequencies. Accordingly, such time-trend analyses have been employed to estimate industry-average IE frequencies for use in the PSAs of U.S. nuclear power plants (NPPs); existing PSAs of Korean NPPs, however, neglect such analysis in the estimation of IE frequencies. This article therefore provides the method for and results of estimating Korean industry-average IE frequencies using time-trend analysis. It also examines the effects of the IE frequencies obtained from this study on risk insights by applying them to recently updated internal events Level 1 PSA models (at-power and shutdown) for an OPR-1000 plant. As a result, at-power core damage frequency decreased while shutdown core damage frequency increased, with the related contributions from each IE category changing accordingly. These results imply that the incorporation of time-trend analysis leads to different IE frequencies and resulting risk insights. The IE frequency distributions presented in this study can be used in future PSA updates for Korean NPPs, and should be further updated themselves by adding more recent data. Keywords: Initiating event, Initiating event frequency, Initiating event analysis, Time trend analysis, Probabilistic safety assessment, Probabilistic risk assessment

Assume that the moment-generating function of the random variable Y exists in a neighborhood of the origin. The aim of this paper is to investigate the probabilistic type 2 Bernoulli polynomials associated with Y and the probabilistic type 2 Euler polynomials associated with Y, along with the probabilistic type 2 cosine-Bernoulli polynomials associated with Y, the probabilistic type 2 sine-Bernoulli polynomials associated with Y, the probabilistic type 2 cosine-Euler polynomials associated with Y, and the probabilistic type 2 sine-Euler polynomials associated with Y. We deal with their properties, related identities and explicit expressions. [ABSTRACT FROM AUTHOR]

Abstract Recently, λ-analogues of Stirling numbers of the first kind were studied. In this paper, we introduce, as natural extensions of these numbers, λ-Stirling polynomials of the first kind and r-truncated λ-Stirling polynomials of the first kind. We give recurrence relations, explicit expressions, some identities, and connections with other special polynomials for those polynomials. Further, as applications, we show that both of them appear in an expression of the probability mass function of a suitable discrete random variable, constructed from λ-logarithmic and negative λ-binomial distributions.

Abstract In this paper, we study some identities on Euler numbers and polynomials, and those on degenerate Euler numbers and polynomials which are derived from the fermionic p-adic integrals on Zp $\mathbb{Z}_{p}$. Specifically, we obtain a recursive formula for alternating integer power sums and representations of alternating integer power sum polynomials in terms of Euler polynomials and Stirling numbers of the second kind, as well as various properties about Euler numbers and polynomials. In addition, we deduce representations of degenerate alternating integer power sum polynomials in terms of degenerate Euler polynomials and degenerate Stirling numbers of the second kind, as well as certain properties on degenerate Euler numbers and polynomials.

Abstract In this paper, we investigate some properties and identities for degenerate Euler polynomials in connection with degenerate Bernstein polynomials by means of fermionic p-adic integrals on Zp $\mathbb{Z}_{p}$ and generating functions. In addition, we study two variable degenerate Bernstein polynomials and the degenerate Bernstein operators.

Abstract As is well known, power sums of consecutive nonnegative integers can be expressed in terms of Bernoulli polynomials. Also, it is well known that alternating power sums of consecutive nonnegative integers can be represented by Euler polynomials. In this paper, we show that power sums of consecutive positive odd q-integers can be expressed by means of type 2 q-Bernoulli polynomials. Also, we show that alternating power sums of consecutive positive odd q-integers can be represented by virtue of type 2 q-Euler polynomials. The type 2 q-Bernoulli polynomials and type 2 q-Euler polynomials are introduced respectively as the bosonic p-adic q-integrals on Zp $\mathbb{Z}_{p}$ and the fermionic p-adic q-integrals on Zp $\mathbb{Z}_{p}$. Along the way, we will obtain Witt type formulas and explicit expressions for those two newly introduced polynomials.

Abstract Recently, the central Fubini polynomials were introduced in connection with central factorial numbers of the second kind. In this paper, we consider two variable higher-order central Fubini polynomials as a ‘central analogue’ of two variable higher-order Fubini polynomials. We investigate some properties, identities, and recurrence relations for these polynomials by making use of generating functions and umbral calculus. In particular, we obtain various expressions for the two variable higher-order central Fubini polynomials and express them in terms of some families of special polynomials and vice versa.

Abstract Recently, extended r-central factorial numbers of the second kind and extended r-central Bell polynomials were introduced and various results of them were investigated. The purpose of this paper is to further derive properties, recurrence relations and identities related to these numbers and polynomials using umbral calculus techniques. Especially, we will represent the extended r-central Bell polynomials in terms of quite a few families of well-known special polynomials.

Abstract Recently, degenerate Bernstein polynomials have been introduced by Kim and Kim. In this paper, we investigate some properties and identities for the degenerate Bernstein polynomials associated with special numbers and polynomials including degenerate Bernstein polynomials and central factorial numbers of the second kind.

Abstract The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials. As a generalization of this, we consider here sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the ones previously studied. We represent each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials. Here, the coefficients involve some terminating hypergeometric functions F12 ${}_{2}F_{1}$, F22 ${}_{2}F_{2}$, and F11 ${}_{1}F_{1}$. These representations are obtained by explicit computations.

Abstract In this paper, we consider the extended central factorial polynomials and numbers of the second kind, and investigate some properties and identities for these polynomials and numbers. In addition, we give some relations between those polynomials and the extended central Bell polynomials. Finally, we present some applications of our results to moments of Poisson distributions.

Following a surge of interest in multi-unit risk in the last few years, many recent studies have suggested methods for multi-unit probabilistic safety assessment (MUPSA) and addressed several related aspects. Most of the existing studies though focused on two-unit nuclear power plant (NPP) sites or used rather simplified probabilistic safety assessment (PSA) models to demonstrate the proposed approaches. When considering an NPP site with three or more units, some approaches are inapplicable or yield very conservative results. Since the number of such sites is increasing, there is a strong need to develop and validate practical approaches to the related MUPSA. This article provides several detailed approaches that are applicable to multi-unit Level 1 PSA for sites with up to six or more reactor units. To validate the approaches, a multi-unit Level 1 PSA model is developed and the site core damage frequency is estimated for each of four representative multi-unit initiators, as well as for the case of a simultaneous occurrence of independent single-unit initiators in multiple units. For this purpose, an NPP site with six identical OPR-1000 units is considered, with full-scale Level 1 PSA models for a specific OPR-1000 plant used as the base single-unit models. Keywords: Inter-unit Dependency, Multi-unit Core Damage Frequency, Multi-unit Probabilistic Safety Assessment, Multi-unit Probabilistic Risk Assessment, Multi-unit Risk, Site Core Damage Frequency

The risk of multi-unit nuclear power plants (NPPs) at a site has received considerable critical attention recently. However, current probabilistic safety assessment (PSA) procedures and computer code do not support multi-unit PSA because the traditional PSA structure is mostly used for the quantification of single-unit NPP risk. In this study, the main purpose is to develop a multi-unit Level 2 PSA method and apply it to full-power operating six-unit OPR1000. Multi-unit Level 2 PSA method consists of three steps: (1) development of single-unit Level 2 PSA; (2) extracting the mapping data from plant damage state to source term category; and (3) combining multi-unit Level 1 PSA results and mapping fractions. By applying developed multi-unit Level 2 PSA method into six-unit OPR1000, site containment failure probabilities in case of loss of ultimate heat sink, loss of off-site power, tsunami, and seismic event were quantified. Keywords: Large Early Release Frequency, Level 2 Probabilistic Safety Assessment Method, Multi-unit Probabilistic Safety Assessment, Seismic Event, Site Containment Failure Probability, Site Risk, Tsunami Event

Site or multi-unit (MU) risk assessment has been a major issue in the field of nuclear safety study since the Fukushima accident in 2011. There have been few methods or experiences for MU risk assessment because the Fukushima accident was the first real MU accident and before the accident, there was little expectation of the possibility that an MU accident will occur. In addition to the lack of experience of MU risk assessment, since an MU nuclear power plant site is usually very complex to analyze as a whole, it was considered that a systematic method such as probabilistic safety assessment (PSA) is difficult to apply to MU risk assessment. This paper proposes a new MU risk assessment methodology by using the conventional PSA methodology which is widely used in nuclear power plant risk assessment. The logical failure structure of a site with multiple units is suggested from the definition of site risk, and a decomposition method is applied to identify specific MU failure scenarios. Keywords: Multi-unit PSA, Multi-unit risk, Site risk, Site CDF, Multi-unit CDF

Abstract In this paper, we study sums of finite products of Chebyshev polynomials of the third and fourth kinds and obtain Fourier series expansions of functions associated with them. Then from these Fourier series expansions we will be able to express those sums of finite products as linear combinations of Bernoulli polynomials and to have some identities from those expressions.

Abstract In this paper, we study sums of finite products of Legendre and Laguerre polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we are going to express those sums of finite products as linear combinations of Bernoulli polynomials. Further, by using a method other than Fourier series expansions, we will be able to express those sums in terms of Euler polynomials.

Abstract In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli polynomials and obtain some identities by using those expressions.

Abstract The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255–258, 1978, Clarke and Sved in Math. Mag. 66(5):299–303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):1–11 2018. A derangement is a permutation that has no fixed points, and the derangement number dn $d_{n}$ is the number of fixed-point-free permutations on an n element set. In this paper, we study the derangement polynomials and investigate some interesting properties which are related to derangement numbers. Also, we study two generalizations of derangement polynomials, namely higher-order and r-derangement polynomials, and show some relations between them. In addition, we express several special polynomials in terms of the higher-order derangement polynomials by using umbral calculus.