Power partitions and saddle-point method

For $k\geqslant 1$, denote by $p_k(n)$ the number of partitions of an integer $n$ into $k$-th powers. In this note, we apply the saddle-point method to provide a new proof for the well-known asymptotic expansion of $p_k(n)$. This approach turns out to significantly simplify those of Wright (1934), Vaughan (2015) and Gafni (2016).Comment: An error in the proof of Lemma 2.3 has been correcte

Wheel and Star-critical Ramsey Numbers for Quadrilateral

The star-critical Ramsey number r∗(H1, H2) is the smallest integer k such that every red/blue coloring of the edges of Kn − K1,n−k−1 contains either a red copy of H1 or a blue copy of H2, where n is the graph Ramsey number R(H1, H2). We study the cases of r∗(C4, Cn) and R(C4, Wn). In particular, we prove that r∗(C4, Cn) = 5 for all n \u3e 4, obtain a general characterization of Ramsey-critical (C4, Wn)-graphs, and establish the exact values of R(C4, Wn) for 9 cases of n between 18 and 44

POWER PARTITIONS AND SADDLE-POINT METHOD

For k 1, denote by p k (n) the number of partitions of an integer n into k-th powers. In this note, we apply the saddle-point method to provide a new proof for the well-known asymptotic expansion of p k (n). This approach turns out to significantly simplify those of Wright (1934), Vaughan (2015) and Gafni (2016)

The influence of motivation, social interaction and space on individual experience: Case m2cell cruise ship concept in three group events

Objectives of the Study The thesis, "The influence of motivation, social interaction and space on individual experience - The m2cell cruise ship concept in three group events", explores consumer behaviour in the context of innovative modular cruise ship concept. The main goal of the research is to investigate what added value m2cell-concept could bring to the participants of three group events, namely family- friends, incentive and conference. The goal is partially achieved by examining factors influencing individual's decision-making and preferences in those events. These elements are motivation, need for social interaction and space experience. Methodology The research is done in three phases: First, a literature review, an observation expedition and expert interviews were conducted to define the background of fairly academically researched area of consumer behaviour on board cruise ships and in the three group events. As a result, a tentative theoretical process map of consumer behaviour was proposed. More clearly, the components of the process map consist of factors such as motivation, social interaction and space experience. Second, an empirical research was done: Five focus group interviews were conducted with interviewees from different backgrounds, to answer the research questions defined in the first stage. Third, an analysis based on empirical findings is produced and conclusions drawn. Results and conclusions The research outcomes indicate that m2cell can be utilised to realise cruise passenger's preferences on space and social interaction in the three group events. Therefore, when designing spaces within m2cell cruise ship concept, the possible motivation and social interaction needs should be consulted. Individual's motivation to participate in an event is found to affect both social interaction and space experience. Moreover, the relationship is mutual and it is found to exist between all three elements studied: they all have interactive relations with each other. Therefore a negative or positive change in one component would reflect on the two others. As a result of the findings, theoretical process model was revised and a new theoretical suggestion formed. Keywords Motivation, social interaction, space, experience, group, conference, incentive, family, friends, event, consumer behaviour, decision-making, modularity, passenger, cruise ship, cruise industr

SYNTHESIS OF PROPYLENE CARBONATE FROM UREA AND 1,2-PROPYLENE GLYCOL OVER METAL CARBONATES

A series of single-metal carbonates and Pb-Zn mixed-metal carbonates were prepared as catalysts for alcoholysis of urea with 1,2-propylene glycol (PG) for the synthesis of propylene carbonate (PC). The mixed carbonates all show much better catalytic activities than the single carbonates, arising from a strong synergistic effect between the two crystalline phases, hydrozincite and lead carbonate. The mixed carbonate with Pb/Zn = 1:2 gives the highest yield of PC, followed by the mixed carbonate with Pb/Zn = 1:3. Furthermore, Taguchi method was used to optimize the synthetic process for improving the yield of PC. It is shown that the reaction temperature is the most significant factor affecting the yield of PC, followed by the reaction time, and that the optimal reaction conditions are the reaction time 5 h, the reaction temperature 180 °C and the catalyst amount 1.8 mass%, resulting in the highest PC yield of 96.3%

Global stability of vaccine-age/staged-structured epidemic models with nonlinear incidence

We consider two classes of infinitely dimensional epidemic models with nonlinear incidence, where one assumes that the rate of a vaccinated individual losing immunity depends on the vaccine-age and another assumes that, before the vaccine begins to wane, there is a period during which the vaccinated individuals have complete immunity against the infection. The first model is given by a coupled ordinary-hyperbolic differential system and the second class is described by a delay differential system. We calculate their respective basic reproduction numbers, and show they characterize the global dynamics by constructing the appropriate Lyapunov functionals

Origin of Difference in Photocatalytic Activity of ZnO (002) Grown on a- and c-Face Sapphire

The oriented (002) ZnO films were grown on a- and c-face sapphire by pulsed laser deposition. The X-ray diffraction analysis revealed that the oriented (002) ZnO films were epitaxially grown on the substrate successfully. The sample on a-face sapphire had higher crystal quality. However, the photocatalytic activity for Rhodamine B degradation of ZnO film on c-face sapphire was higher than that on a-face sapphire. The Raman spectrum and XPS analysis suggested that the sample on a-face sapphire had higher concentration of defects. The result of the contact angle measurement revealed that the sample on c-face sapphire had higher surface energy. And the investigation of the surface conductance implied that the higher light conductance was helpful for the photocatalytic activity

Fluctuating levels of reprogramming factor expression in cultured human undifferentiated keratinocytes

Although human undifferentiated keratinocytes (HUKs) can be reprogrammed to become induced pluripotent stem cells (iPSCs) with high efficiency and rapid kinetics by transducing reprogramming factors (RFs), the endogenous expression of reprogramming factors in cultured HUKs is not clear at different stages. In this study, keratinocytes were isolated from foreskin of adult subject (18 years old) and cultured on collagen type IV-coated culture dishes in a low-calcium, serum-free medium (Epilife, Invitrogen). In order to clarify the expression patterns of RFs and other stem cell markers in cultured human keratinocytes, total RNA was extracted using Trizol reagent, and polymerase chain reaction (PCR) was performed using established GenBank sequences to design primers. The subsequent PCR analysis was carried out by agarose gel electrophoresis. The expression levels of RFs and other stem cell markers in human HUKs clearly fluctuated during culturing, which supports the hypothesis that HUKs might be reprogrammed into a pluripotent state when the maximum levels of RFs expression are maintained by appropriate culture conditions.Keywords: Human undifferentiated keratinocytes, reprogramming factors, expression fluctuationAfrican Journal of Biotechnology Vol. 12(35), pp. 5389-539