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Extracellular matrix proteins are associated with metabolically healthy adipose tissue and regulate inflammation, fibrosis, angiogenesis, and subsequent metabolic deterioration. In this study, we demonstrated that transforming growth factor-beta (TGFBI), an extracellular matrix (ECM) component, plays an important role in adipose metabolism and browning during high-fat diet-induced obesity. TGFBI KO mice were resistant to adipose tissue hypertrophy, liver steatosis, and insulin resistance. Furthermore, adipose tissue from TGFBI KO mice contained a large population of CD11b+ and CD206+ M2 macrophages, which possibly control adipokine secretion through paracrine mechanisms. Mechanistically, we showed that inhibiting TGFBI-stimulated release of adipsin by Notch-1-dependent signaling resulted in adipocyte browning. TGFBI was physiologically bound to Notch-1 and stimulated its activation in adipocytes. Our findings revealed a novel protective effect of TGFBI deficiency in obesity that is realized via the activation of the Notch-1 signaling pathway.

The ferritin nanocage is an endogenous protein that exists in almost all mammals. Its hollow spherical structure that naturally stores iron ions has been diversely exploited by researchers in biotherapeutics. Ferritin has excellent biosafety profiles, and the nanosized particles exhibit rapid dispersion and controlled/sustained release pharmacokinetics. Moreover, the large surface-to-volume ratio and the disassembly/reassembly behavior of the 24 monomer subunits into a sphere allow diverse modifications by chemical and genetic methods on the surface and inner cage of ferritin. Here, we critically review ferritin and its applications. We (i) introduce the application of ferritin in drug delivery; (ii) present an overview of the use of ferritin in imaging and diagnosis for biomedical purposes; (iii) discuss ferritin-based vaccines; and (iv) review ferritin-based agents currently in clinical trials. Although there are no currently approved drugs based on ferritin, this multifunctional protein scaffold shows immense potential in drug development in diverse categories, and ferritin-based drugs have recently entered phase I clinical trials. This golden shortlist of recent developments will be of immediate benefit and interest to researchers studying ferritin and other protein-based biotherapeutics.

Antigen-presenting cells (APCs), including macrophages and dendritic cells (DCs), play a crucial role in bridging innate and adaptive immunity; thereby, innate immune checkpoint blockade-based therapy is an attractive approach for the induction of sustainable tumor-specific immunity. The interaction between the cluster of differentiation 47 (CD47) on tumor and signal-regulatory protein alpha (SIRPα) on phagocytic cells inhibits the phagocytic function of APCs, acting as a "don't eat me" signal. Accordingly, CD47 blockade is known to increase tumor cell phagocytosis, eliciting tumor-specific CD8+ T-cell immunity. Here, we introduced a nature-derived nanocage to deliver SIRPγ for blocking of antiphagocytic signaling through binding to CD47 and combined it with prophagocytic stimuli using a metabolic reprogramming reagent for APCs (CpG-oligodeoxynucleotides). Upon delivering the clustered SIRPγ variant, the nanocage showed enhanced CD47 binding profiles on tumor cells, thereby promoting active engulfment by phagocytes. Moreover, combination with CpG potentiated the prophagocytic ability, leading to the establishment of antitumorigenic surroundings. This combination treatment could competently inhibit tumor growth by invigorating APCs and CD8+ T-cells in TMEs in B16F10 orthotopic tumor models, known to be resistant to CD47-targeting therapeutics. Collectively, enhanced delivery of an innate immune checkpoint antagonist with metabolic modulation stimuli of immune cells could be a promising strategy for arousing immune responses against cancer.

We examine the effect of the broadband wake on the longitudinal and transverse beam distributions in the low-emittance Hybrid Multi-bend Achromat (HMBA) storage ring. We utilize the Vlasov equation and a multi-particle tracking method to examine the equilibrium longitudinal beam distributions due to the broadband wake. The beam distributions from the Vlasov method is shown to agree well with the multi-particle tracking results. Multi-particle tracking simulations are also performed to investigate the longitudinal and transverse beam instabilities due to the broadband wake in the ring. In view of our results, our designed ring with $$Z/n=0.1\Omega$$ is shown to make the producion of a beams possible.

We consider the unambiguous discrimination of multipartite quantum states and provide an upper bound for the maximum success probability of optimal local discrimination. We also provide a necessary and sufficient condition to realize the upper bound. We further establish a necessary and sufficient condition for this upper bound to be saturated. Finally, we illustrate our results using examples in multidimensional multipartite quantum systems., Comment: 12 pages, no figure

In semiconductor manufacturing, detecting defect patterns is important because they are directly related to the root causes of failures in the wafer process. The rapid advancement of the integrated circuit technology has recently led to more frequent occurrences of mixed-type defect patterns, wherein two or more defect patterns simultaneously occur in a wafer bin map. The detection of these mixed patterns is more difficult than that of single patterns. To detect these mixed patterns, binary relevance approaches based on convolutional neural networks have been proposed. However, as the manufacturing process has been advanced and integrated, various failure types are newly detected, thus the number of single models can be continuously increased following the diversification of defect types. Therefore, we propose an effective framework for detecting mixed-type patterns in which a simple single model, called the single shot detector, is employed. By applying the proposed model to the WM-811K dataset, we show that our framework outperforms existing CNN-based methods and also provides defect location information.

Apoptosis plays an essential role in the pathophysiologic processes of rheumatoid arthritis. A molecular probe that allows spatiotemporal observation of apoptosis in vitro, in vivo, and ex vivo concomitantly would be useful to monitoring or predicting pathophysiologic stages. In this study we investigated whether cyclic apoptosis-targeting peptide-1 (CApoPep-1) can be used as an apoptosis imaging probe in inflammatory arthritis. We tested the utility of CApoPep-1 for detecting apoptotic immune cells in vitro and ex vivo using flow cytometry and immunofluorescence. The feasibility of visualizing and quantifying apoptosis using this probe was evaluated in a murine collagen-induced arthritis (CIA) model, especially after treatment. CApoPep-1 peptide may successfully replace Annexin V for in vitro and terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) assay for ex vivo in the measurement of apoptotic cells, thus function as a sensitive probe enough to be used clinically. In vivo imaging in CIA mice revealed that CApoPep-1 had 42.9 times higher fluorescence intensity than Annexin V for apoptosis quantification. Furthermore, it may be used as an imaging probe for early detection of apoptotic response in situ after treatment. The CApoPep-1 signal was mostly co-localized with the TUNEL signal (69.6% of TUNEL+ cells) in defined cell populations in joint tissues of CIA mice. These results demonstrate that CApoPep-1 is sufficiently sensitive to be used as an apoptosis imaging probe for multipurpose applications which could detect the same target across in vitro, in vivo, to ex vivo in inflammatory arthritis.

In the last five years, towing to increasing demand for liquefied natural gas (LNG), researchers have actively analyzed and conducted studies on the sloshing phenomenon. However, there are limitations in the 1:1 model experimental method for LNG tanks installed in actual vessels. This study verified the validity of the average pressure prediction according to the scale ratio of a prismatic LNG tank that was developed through a correlation analysis between the sloshing analysis and model test. We then presented an average pressure prediction for the tank of a full-scale vessel. In addition, to ensure the safety of the tank, this study investigated the degree of cumulative fatigue damage that could be caused by cyclic loading through a fatigue analysis.

Precise and selective removal of silicon nitride (SiNx) over silicon oxide (SiOy) in a oxide/nitride stack is crucial for a current three dimensional NOT-AND type flash memory fabrication process. In this study, fast and selective isotropic etching of SiNx over SiOy has been investigated using a ClF3/H2 remote plasma in an inductively coupled plasma system. The SiNx etch rate over 80 nm/min with the etch selectivity (SiNx over SiOy) of ~ 130 was observed under a ClF3 remote plasma at a room temperature. Furthermore, the addition of H2 to the ClF3 resulted in an increase of etching selectivity over 200 while lowering the etch rate of both oxide and nitride due to the reduction of F radicals in the plasma. The time dependent-etch characteristics of ClF3, ClF3 & H2 remote plasma showed little loading effect during the etching of silicon nitride on oxide/nitride stack wafer with similar etch rate with that of blank nitride wafer.

One of the most important design parameters for the inkjet printing device is the inkjet drop velocity, which changes along the falling path from the ejection out of a nozzle to the impact on a substrate. Therefore, in this study, the droplet velocity of the piezoelectric drop-on-demand inkjet was measured. The nozzle diameter was 70 µm and polyethylene glycol aqueous solution was used as ink. The inkjet droplets were generated within a range from 500 to 10000 Hz of frequencies at a reference piezoelectric input voltage. The successive inkjet droplets were captured by the high-speed camera with 100000 fps, then the inkjet droplet velocities were analyzed visually at each falling location. The velocity change of a drop up to its terminal velocity was calculated theoretically to be compared with the experimental results. This study found that the velocity of the continuously ejected droplets depended on the interval of the droplets, as well as the density and diameter of the droplet which are essential factors of the general velocity change of a falling drop. The inkjet droplets with the long interval can be considered as an independent droplet so that it can follow the terminal velocity curve of the general drop. However, the inkjet droplets with short interval have the higher velocity than the general terminal velocity curve. It is considered that each droplet gets into the wake field of the former droplet so that its drag force can decrease and the velocity can increase.

Predicting remaining useful life (RUL) is crucial for system maintenance. Condition monitoring makes not only degradation data available for RUL estimation but also categorized health status data for health state identification. However, RUL prediction has been treated as an independent process in most cases even though potential relevance exists with health status detection process. In this paper, we propose a convolution neural network based multi-task learning method to reflect the relatedness of RUL estimation with health status detection process. The proposed method applied to the C-MAPSS dataset for aero-engine unit prognostics supported superior performances to existing baseline models.

The aim of this paper is to determine the λ-linear functionals sending any given polynomial $p(x)$ p ( x ) with coefficients in $\mathbb{C}_{p}$ C p to the p-adic invariant integral of $P(x)$ P ( x ) on $\mathbb{Z}_{p}$ Z p and also to that of $P(x_{1}+\cdots +x_{r})$ P ( x 1 + ⋯ + x r ) on $\mathbb{Z}_{p}^{r}$ Z p r . We show that the former is given by the generating function of degenerate Bernoulli polynomials and the latter by that of degenerate Bernoulli polynomials of order r. For this purpose, we use the λ-umbral algebra which has been recently introduced by Kim and Kim (J. Math. Anal. Appl. 493(1):124521 2021).

The aim of this paper is to study the complete and incomplete degenerate Bell polynomials, which are degenerate versions of the complete and incomplete Bell polynomials, and to derive some properties and identities for those polynomials. In particular, we introduce some new polynomials associated with the incomplete degenerate Bell polynomials. In fact, they are the coefficients of the reciprocal of the power series given by 1 plus the one appearing as the exponent of the generating function of the complete degenerate Bell polynomials.

In recent years, many authors have studied Changhee and Dae- hee polynomials in connection with many special numbers and polynomials. In this paper, we investigate type 2 Changhee and Daehee numbers and polynomials and give some identities for these numbers and polynomials in relation to type 2 Euler and Bernoulli numbers and polynomials. In addition, we express the central factorial numbers of the second kind in terms of type 2 Bernoulli, type 2 Changhee and type 2 Daehee numbers of negative integral orders., 10 pages

Here we study the degenerate central Bell numbers and polynomials as a degenerate version of the recently introduced central Bell numbers and polynomials, which are motivated by Zhang’s work ‘Some identities involving the Euler and the central factorial numbers’ (Zhang in Fibonacci Quart 36(2):154–157, 1998) and we derive some properties, identities, and recurrence relations for these numbers and polynomials. In particular, we find various expressions for the degenerate central Bell numbers and polynomials.

In this paper, we study degenerate complete and partial Bell polynomials and establish some new identities for those polynomials. In addition, we investigate the connections between modified degenerate complete and partial Bell polynomials, which are closely related to the degenerate complete and partial Bell polynomials, and the joint distribution of weighted sums of independent degenerate Poisson random variables.

Several studies have suggested that extracellular matrix (ECM) remodeling and the microenvironment are tightly associated with adipogenesis and adipose angiogenesis. In the present study, we demonstrated that transforming growth factor-beta induced (TGFBI) suppresses angiogenesis stimulated by adipocyte-conditioned medium (Ad-CM), both in vitro and in vivo. TGFBI knockout (KO) mice exhibited increased numbers of blood vessels in adipose tissue, and blood vessels from these mice showed enhanced infiltration into Matrigel containing Ad-CM. The treatment of Ad-CM-stimulated SVEC-10 endothelial cells with TGFBI protein reduced migration and tube-forming activity. TGFBI protein suppressed the activation of the Src and extracellular signaling-related kinase signaling pathways of these SVEC-10 endothelial cells. Our findings indicated that TGFBI inhibited adipose angiogenesis by suppressing the activation of Src and ERK signaling pathways, possibly because of the stimulation of the angiogenic activity of endothelial cells.

Continuity of care is a core dimension of high-quality care in the management of disease. The purpose of this study was to investigate the association between continuity of care and lumbar surgery in patients with moderate disc herniation. The Korean National Sample Cohort was used. The target population consisted of patients who have had disc herniation more than 6 months and didn’t get surgery and red flag signs within 6 months from onset. The population was enrolled from 2004 to 2013. The Bice-Boxerman Continuity of Care was used in measuring continuity of care. The marginal structural model with time dependent survival analysis was used. In total, 29,061 patients were enrolled in the cohort. High level of continuity of care was associated with a lower risk of lumbar surgery (HR, 0.27; 95% CI, 0.20–0.27). When the index was calculated only with outpatient visits to primary care with related specialty, the HR was 0.49 (95% CI: 0.43–0.57). In exploratory analysis, patients with lumbar stenosis and spondylolisthesis had higher risk of having a low level of continuity of care. These results indicate that continuity of care is associated with lower rates of lumbar surgery in patients with moderate disc herniation.

The nth r-extended Lah–Bell number is defined as the number of ways a set with $n+r$ n + r elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks. The aim of this paper is to introduce incomplete r-extended Lah–Bell polynomials and complete r-extended Lah–Bell polynomials respectively as multivariate versions of r-Lah numbers and the r-extended Lah–Bell numbers and to investigate some properties and identities for these polynomials. From these investigations we obtain some expressions for the r-Lah numbers and the r-extended Lah–Bell numbers as finite sums.

Summary We aimed to investigate the association between cadmium levels and the risk of osteopenia and osteoporosis in Korean post-menopausal women. There was a significant positive association between cadmium levels and the risk of osteopenia and osteoporosis, but further studies for dose response are required. Purpose Cadmium exposure can exert detrimental effects on bone health, particularly in post-menopausal women. However, previous studies have failed to report an association in Korean post-menopausal women. We aimed to investigate the association between cadmium levels and the risk of osteopenia and osteoporosis in Korean post-menopausal women. Methods In total, 5432 participants from the 4th and 5th Korean National Health and Nutrition Examination Survey (KNHANES) were randomly sampled for measurements of heavy metal concentrations in the blood, bone mass density (BMD), and nutrient intake. We analyzed data for 1031 post-menopausal women ≥50 years of age. Blood cadmium levels were categorized into quartiles, and a multinomial logistic regression model was used for analysis. Results There was a significant positive association between cadmium levels and the risk of osteopenia and osteoporosis, but the odds ratio (OR) at the 4th level was lower than that at the 3rd level (OR and 95% confidence interval (CI) for osteopenia: 2nd quartile: 1.24, 0.88-1.74; 3rd quartile: 3.22, 2.24-4.64; 4th quartile: 1.27, 0.87-1.85; P for trend P for trend Conclusion Our findings suggest that there is an association between blood cadmium levels and the risk of osteopenia and osteoporosis in Korean post-menopausal women. However, further prospective studies are required to determine whether there is a dose-response relationship and address potential selection bias, especially in patients with femoral neck osteoporosis.

The classical Dedekind sums appear in the transformation behavior of the logarithm of the Dedekind eta-function under substitutions from the modular group. The Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations, and are shown to satisfy some reciprocity relations. In contrast, Dedekind-type DC (Daehee and Changhee) sums and their generalizations are defined in terms of Euler functions and their generalizations. The purpose of this paper is to introduce the poly-Dedekind-type DC sums, which are obtained from the Dedekind-type DC sums by replacing the Euler function by poly-Euler functions of arbitrary indices, and to show that those sums satisfy, among other things, a reciprocity relation.

Apostol considered generalized Dedekind sums by replacing the first Bernoulli function appearing in Dedekind sums by any Bernoulli functions and derived a reciprocity relation for them. Recently, poly-Dedekind sums were introduced by replacing the first Bernoulli function appearing in Dedekind sums by any type 2 poly-Bernoulli functions of arbitrary indices and were shown to satisfy a reciprocity relation. In this paper, we consider other poly-Dedekind sums that are obtained by replacing the first Bernoulli function appearing in Dedekind sums by any poly-Bernoulli functions of arbitrary indices. We derive a reciprocity relation for these poly-Dedekind sums.

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.

The demand for high-capacity lithium-ion batteries (LIB) in electric vehicles has increased. In this study, optimization to maximize the specific energy density of a cell is conducted using the LIB electrochemical model and sequential approximate optimization (SAO). First, the design of experiments is performed to analyze the sensitivity of design factors important to the specific energy density, such as electrode and separator thicknesses, porosity, and particle size. Then, the design variables of the cell are optimized for maximum specific energy density using the progressive quadratic response surface method (PQRSM), which is one of the SAO techniques. As a result of optimization, the thickness ratio of the electrode was optimized and the porosity was reduced to keep the specific energy density high, while still maintaining the specific power density performance. This led to an increase in the specific energy density of 56.8% and a reduction in the polarization phenomenon of 11.5%. The specific energy density effectively improved through minimum computation despite the nonlinearity of the electrochemical model in PQRSM optimization.

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.

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.

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.

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.

In this paper, we investigate degenerate versions of the generalized pth order Franel numbers which are certain finite sums involving powers of binomial coefficients. In more detail, we introduce degenerate generalized hypergeometric functions and study degenerate hypergeometric numbers of order p. These numbers involve powers of λ-binomial coefficients and λ-falling sequence, and can be represented by means of the degenerate generalized hypergeometric functions. We derive some explicit expressions and combinatorial identities for those numbers. We also consider several related special numbers like λ-hypergeometric numbers of order p and Apostol type λ-hypergeometric numbers of order p, of which the latter reduce in a limiting case to the generalized pth order Franel numbers.

In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve basic identities for Sheffer polynomials, seven from previous results, to degenerate Bernoulli polynomials and Korobov polynomials of the first kind and get some new identities. In addition, letting $\lambda~\rightarrow~0$ in such identities gives usthose for Bernoulli polynomials and Bernoulli polynomials of the second kind.

The degenerate Changhee numbers of the second kind are a degenerate version of Changhee numbers. Here we derive a family of nonlinear differential equations having the generating function of the degenerate Changhee numbers of the second kind as a solution. As a result, we obtain one identity involving the degenerate Changhee and higher-order degenerate Changhee numbers of the second kind.

In this paper, we study the extended Stirling numbers of the first kind which have close connection with the r-Stirling numbers of the first kind and generalize the usual Stirling numbers of the first kind. We derive recurrence relations for those numbers and show their connections with the Stirling numbers of the first kind, higher-order Daehee polynomials and Bell polynomials. In addition, we introduce Daehee–Stirling numbers of the first kind and deduce their connections with the extended Stirling numbers of the first kind and r-Whitney numbers.

In this paper, we introduce the degenerate Cauchy numbers as a degenerate version of the Cauchy numbers and derive a family of nonlinear differential equations satisfied by the generating function for those numbers.

Older people with several chronic conditions require multiple drugs from different classes to be adequately treated. This study aims to: (i) measure medication adherence across multiple conditions and therapeutic drug groups in older community-dwelling patients, and (ii) examine the effect of multimorbidity on adherence. This is a retrospective cohort study of medication adherence in 855 community-dwelling patients aged ≥ 70 years from 15 practices in Ireland using the Health Service Executive Primary Care Reimbursement Service (HSE-PCRS) pharmacy claims database. Multimorbidity was measured using the RxRisk-V and by the number of different drug classes. The RxRisk-V algorithm classifies prescription drug fills into 45 chronic disease classes for older populations based on the WHO Anatomical Therapeutic Chemical classification system. Adherence to medications was assessed by: (i) calculating the average medication possession ratio (MPR) per patient and (ii) an MPR

Eight basic identities of symmetry in three variables, which are related to degenerate Euler polynomials and alternating generalized falling factorial sums, are derived. These are the degenerate versions of the symmetric identities in three variables obtained in a previous paper. The derivations of identities are based on the p-adic integral expression of the generating function for the degenerate Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating generalized falling factorial sums. Those eight basic identities and most of their corollaries are new, since there have been results only about identities of symmetry in two variables.

In this paper, we study the Carlitz’s degenerate Bernoulli numbers and polynomials, and give some formulae and identities related to those numbers and polynomials.

In this paper, we derive differential equations from the generating function of higher-order Frobenius–Euler numbers. In addition, we give some new and explicit identities for higher-order Frobenius–Euler numbers arising from those differential equations.

The current size of the market for domestic robots is smaller than expected, despite the rapid advance in robotic technologies. On the basis of the previous literature, we attempt to make a distinction between two design approaches for domestic robots: organism- versus object-based robot designs. This research investigates the effects of these domestic robot design approaches on consumer acceptance. Encompassing the theories of Human–Robot Interaction, design, and marketing, we predict that object-based robot design will be more effective than organism-based robot design for consumers’ evaluation of and intent to purchase domestic robots. We also predict that the categorization of robots will mediate the effects of robot design approaches on the evaluation. Two studies using two types of robots were conducted, and the results supported the hypotheses.

Recently, Masjed-Jamei-Beyki-Koepf studied the so called new type Euler polynomials without making use of Euler polynomials of complex variable. Here we study degenerate and type 2 versions of these new type Euler polynomials, namely the type 2 degenerate cosine-Euler and type 2 degenerate sine-Euler polynomials and also the corresponding ones for Bernoulli polynomials, namely the type 2 degenerate cosine-Bernoulli and type 2 degenerate sine-Bernoulli polynomials by considering the degenerate Euler and degenerate Bernoulli polynomials of complex variable and by treating the real and imaginary parts separately. We derive some explicit expressions for those new polynomials and some identities relating to them. Here we note that the idea of separating the real and imaginary parts separately gives an affirmative answer to the question asked by Belbachir., 17 pages

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.

Extended degenerate r-central factorial numbers of the second kind and extended degenerate r-central Bell polynomials were introduced recently, as a degenerate version, a central analogue and an r-extension of Stirling numbers of the second kind and Bell polynomials, respectively, and various properties of them were investigated. The purpose of the present paper is to further derive some properties, recurrence relations and identities concerning those numbers and polynomials. In particular, we will represent the extended degenerate r-central Bell polynomials in terms of a good number of well-known special polynomials.

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 and generating functions. In addition, we study two variable degenerate Bernstein polynomials and the degenerate Bernstein operators., Comment: 11 pages

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.

In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials, and degenerate type 2 Euler polynomials, and their corresponding numbers, as degenerate and type 2 versions of Bernoulli and Euler numbers. Regarding those polynomials and numbers, we derive some identities, distribution relations, Witt type formulas, and analogues for the Bernoulli interpretation of powers of the first m positive integers in terms of Bernoulli polynomials. The present study was done by using the bosonic and fermionic p-adic integrals on $\mathbb{Z}_{p}$ .

The Rare Isotope Science Project (RISP) is a research complex consisting of a heavy-ion accelerator, which contains a front-end system, a super-conducting linear accelerator, an isotope separator online (ISOL) system, and an in-flight system. The original purpose of the post-linear-accelerator (post-linac) section was to accelerate either a stable driver beam derived from an electron cyclotron resonance ion source, or an unstable rare-isotope beam from an ISOL system. The post-linac lattice has now been redesigned using a novel and improved acceleration concept that allows the simultaneous acceleration of both a stable driver beam and a radioisotope beam. To achieve this, the post-linac lattice is set for a mass-to-charge ratio (A/q) that is the average of the two beams. The performance of this simultaneous two-beam acceleration is here assessed using two ion beams: $$^{58}{\mathbf{Ni}}^{8+}$$ and $$^{132}{} {\mathbf{Sn}}^{20+}$$ . A beam dynamics simulation was performed using the TRACK and TraceWin codes. The resultant beam dynamics for the new RISP post-linac lattice design are examined. We also estimate the effects of machine errors and their correction on the post-linac lattice.

In this paper, we investigate sums of finite products of Chebyshev polynomials of the first kind and those of Lucas polynomials. We express each of them as linear combinations of Hermite, extended Laguerre, Legendre, Gegenbauer, and Jacobi polynomials whose coefficients involve some terminating hypergeometric functions ${}_{1}F_{1}$ and ${}_{2}F_{1}$ . These are obtained by means of explicit computations.

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 ${}_{2}F_{1}$ , ${}_{2}F_{2}$ , and ${}_{1}F_{1}$ . These representations are obtained by explicit computations.

In this paper, we consider Catalan type Daehee numbers which are called Catalan–Daehee numbers and study the family of inhomogeneous linear differential equations arising from the generating function of Catalan–Daehee numbers and their applications. From our study of differential equations, we derive some new and explicit identities involving Catalan–Daehee numbers and Catalan numbers.