• Macromolecular Research
• /
• 제9권1호
• /
• pp.37-44
• /
• 2001

A premixing effect for the properties of carbon black-filled rubber compounds was investigated using biblends of natural rubber (NR), styrene-butadiene rubber (SBR), and butadiene rubber (BR). Degree of mixing of the biblends was controlled by preblending time of 0.0, 2.5, and 5.0 min. Mooney viscosities of the compounds decreased by increasing the preblending time. Of three carbon black-filled compounds of NR/SBR, NR/BR, and SBR/BR compounds, only the SBR/BR blends showed a specific cure characteristics depending on the preblending time. For the bound rubber composition, the NR content was higher than SBR and BR. The difference in the rubber composition ratio of the bound rubber became smaller with increasing the preblending time. Physical properties of the vulcanizates such as hardness, modulus, tensile property, abrasion loss, and tans were also compared. Differences in properties of the compounds were discussed with miscibility of the dissimilar rubbers and degree of mixing.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1323-1330
• /
• 2017

For a nondegenerate projective irreducible variety $X{\subset}{\mathbb{P}}^r$, it is a natural problem to find an upper bound for the value of $${\ell}_{\beta}(X)=max\{length(X{\cap}L){\mid}L={\mathbb{P}}^{\beta}{\subset}{\mathbb{P}}^r,\;{\dim}(X{\cap}L)=0\}$$ for each $1{\leq}{\beta}{\leq}e$. When X is locally Cohen-Macaulay, A. Noma in [10] proves that ${\ell}_{\beta}(X)$ is at most $d-e+{\beta}$ where d and e are respectively the degree and the codimension of X. In this paper, we construct some surfaces $S{\subset}{\mathbb{P}}^5$ of degree $d{\in}\{7,{\ldots},12\}$ which satisfies the inequality $${\ell}_2(S){\geq}d-3+{\lfloor}{\frac{d}{2}}{\rfloor}$$. This shows that Noma's bound is no more valid for locally non-Cohen-Macaulay varieties.

• Journal of applied mathematics & informatics
• /
• 제27권3_4호
• /
• pp.865-873
• /
• 2009

Goodman([3]) presented the question of finding a best possible upper bound of the form $t(G)\;+\;t(G^c)$, where t(G) denote the number of triangles in given graph G. In this, the form of squares of degrees is appeared and many researches have been pursued as an application related to this. Here, we would like to deal with corollary related to the results of Nikiforov([6]).

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 1995년도 추계학술대회 논문집
• /
• pp.195-198
• /
• 1995

In Semi-Solid Forging, it is necessary to control the forming variables accurately in order to make near-net-shape products. Generally, the defects of products may occur due to liquid segregation which can be caused by the degree of deformation and condition of friction in Semi-Solid Forging, where the segregation is to be predicted by flow analysis. This paper presents the feasibility of theoretical analysis model using the new yield function which is proposed by Doraivelu et al. to the flow analysis of the semi-solid dendritic Sn-15%Pb alloys instead of adopting the yield criterion of Shima & Oyane which is used by Charreyron and usefulness of the adopted yield function. The distribution of the liquid fraction at various strains in radial direction and the influence of friction are estimated by Upper Bound Method.

• 대한수학회논문집
• /
• 제33권2호
• /
• pp.631-638
• /
• 2018

Chellai et al. [3] gave an upper bound on the [1, 2]-domination number of tree and posed an open question "how to classify trees satisfying the sharp bound?". Yang and Wu [5] gave a partial solution for tree of order n with ${\ell}$-leaves such that every non-leaf vertex has degree at least 4. In this paper, we give a new upper bound on the [1, 2]-domination number of tree which extends the result of Yang and Wu. In addition, we design a polynomial time algorithm for solving the open question. By using this algorithm, we give a characterization on the [1, 2]-domination number for trees of order n with ${\ell}$ leaves satisfying $n-{\ell}$. Thereby, the open question posed by Chellai et al. is solved.

• 대한수학회지
• /
• 제57권5호
• /
• pp.1119-1133
• /
• 2020

In this paper, we derive an upper bound for the distance from a point in the immediate basin of a root of a complex polynomial to the root itself. We establish that if z is a point in the immediate basin of a root α of a polynomial p of degree d ≥ 12, then ${\mid}z-{\alpha}{\mid}{\leq}{\frac{3}{\sqrt{d}}\(6{\sqrt{310}}/35\)^d{\mid}N_p(z)-z{\mid}$, where N_p is the Newton map induced by p. This bound leads to a new bound of the expected total number of iterations of Newton's method required to reach all roots of every polynomial p within a given precision, where p is normalized so that its roots are in the unit disk.

• 한국정밀공학회지
• /
• 제15권6호
• /
• pp.139-144
• /
• 1998

In Semi-Solid Forging, it is necessary to control the forming variables accurately in order to make near-net-shape products. Generally, the defects of products may occur due to liquid segregation which can be caused by the degree of deformation and strain rate, and condition of friction in Semi-Solid Forging, where the segregation is to be predicted by flow analysis. This paper presents the feasibility of theoretical analysis model using the new yield function for compressible P/M materials which is proposed by Doraivelu et at. to the flow analysis of the semi-solid dendritic Sn-15％Pb alloys instead of adopting the yield criterion of Shima and Oyane which is used by Charreyron and Flemings. The simple compression process is taken into consideration as the model to confirm the usefulness of the adopted yield function. The distribution of the liquid fraction at various strains and strain rates in radial direction, and the influence of friction are estimated by upper-bound method.

• Elastomers and Composites
• /
• 제54권2호
• /
• pp.142-148
• /
• 2019

In this study, the effects of filler particle size and shape on the physical properties of silicone rubber composites were investigated using inorganic fillers (Minusil 5, Celite 219, and Nyad 400) except silica, which was already present as a reinforcing filler of silicone rubber. Fillers with small particle sizes are known to facilitate the formation of the bound rubber by increasing the contact area with the polymer. However, in this experiment, the bound rubber content of Celite 219-added silicone composite was higher than that of Minusil 5-added silicone composite. This was attributed to the porous structure of Celite 219, which led to an increase in the internal surface area of the filler. When the inorganic fillers were added, both thermal decomposition temperature and thermal stability were improved. The bound rubber formed between the silicone rubber and inorganic filler affected the degree of crosslinking of the silicone composite. It is well-known that as the size of the reinforcing filler decreases, the reinforcing effect increases. However, in this experiment, the hardness of the composite material filled with Celite 219 was the highest compared to the other three composites. Furthermore, the highest value of 2.19 MPa was observed for 100% modulus, and the fracture elongation was the lowest at 469%. This was a result of excellent interaction between Celite 219 filler and silicone rubber.

• Journal of applied mathematics & informatics
• /
• 제34권3_4호
• /
• pp.221-225
• /
• 2016

For a connected graph G = (V, E), its inverse degree is defined as $\sum_{{\upsilon}{\in}{V}}^{}\frac{1}{d(\upsilon)}$. Using an upper bound for the inverse degree of a graph obtained by Cioabă in [4], we in this note present sufficient conditions for some Hamiltonian properties and k-connectivity of a graph.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1635-1646
• /
• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.