• Kyungpook Mathematical Journal
• /
• 제33권1호
• /
• pp.111-114
• /
• 1993

• Kyungpook Mathematical Journal
• /
• 제45권4호
• /
• pp.455-470
• /
• 2005

This paper introduces compactness notions for frames which are expressed in terms of the convergence of suitably specified general filters. It establishes several preservation properties for them as well as their coreflectiveness in the setting of regular frames. Further, it shows that supercompact, compact, and $Lindel{\ddot{o}}f$ frames can be described by compactness conditions of the present form so that various familiar facts become consequences of these general results. In addition, the Prime Ideal Theorem and the Axiom of Countable Choice are proved to be equivalent to certain conditions connected with the kind of compactness considered here.

• 한국수학사학회지
• /
• 제27권6호
• /
• pp.403-408
• /
• 2014

The interdisciplinary study addresses the G$\ddot{o}$del's ontology from the perspective of the mathematical maximality. We first investigate G$\ddot{o}$del's God having all the positive properties as the intersection of ultrafilters in his own ontological proof(1970). Regarding the axiom of choice and his compactness theorem(1930), the next part discusses the ontological meaning of the maximal rather than the maximum in terms of an episteme space. The results show that G$\ddot{o}$del's ontological arguments imply all the existence of the maximal reality, and all the human's epistemological boundedness as well.

• 충청수학회지
• /
• 제36권1호
• /
• pp.9-11
• /
• 2023

Intuitionistic Zermelo-Fraenkel (IZF) set theory is a set theory without the axiom of choice and the law of excluded middle (LEM). The weak excluded middle law (WEM) states that ¬𝜑∨¬¬𝜑 for any formula 𝜑. In IZF we show that LEM is equivalent to WEM plus the condition that any set not equal to the empty set has an element.

• 한국수학사학회지
• /
• 제14권1호
• /
• pp.47-60
• /
• 2001

The present study develops the given theme “Mathematics and Reality” along two lines. First, we explore the answers, in its various facets, to the following question: How is it possible that mathematics shows such wondrous efficiency when explaining nature\ulcorner In addition to a comparative analysis between empiricism and rationalism, constructivism as a function of idealism is compared with realism within the frame provided by rationalism. The second step involves limiting our discussion to realism. We attempt to explain the various stages of mathematical realism and their points of difficulty. Postulate of parallels, Godel's theorem, continuum hypothesis and choice axiom are typical examples used in demonstrating undecidable propositions. They clearly show that it is necessary to mitigate the mathematical realism which depends on bivalent logic based on an objective exterior world. Lowenheim-Skolem theorem, which states that reality is composed not of one block but rather of diverse domains, also reinforces this line of thought. As we can see the existence of undecidable propositions requires limiting the use of reductio ad absurdum proof which depends on the concept of excluded middle. Consequently, it becomes obvious that bivalent logic must inevitably cede to a trivalent logic since there are three values involved: true, false, and undecidable.

• 한국작물학회:학술대회논문집
• /
• 한국작물학회 2017년도 9th Asian Crop Science Association conference
• /
• pp.145-145
• /
• 2017

Foxglove aphid, Aulacorthum solani (Kaltenbach), is a Hemipteran insect that infected a wide variety of plants worldwide and caused serious yield losses in crops. The objective of this study was to identify the putative genes to foxglove aphid resistance in wild soybean, PI 366121 (Glycine soja Sieb. and Zucc.). One hundred and forty-one F4:8 recombinant inbred lines developed from a cross between susceptible variety, Williams 82 and foxglove aphid resistance wild soybean, PI 366121 were used. The two type of resistance response, antibiosis and antixenosis resistance were evaluated through choice and no-choice test, graded by the degree of total plant damage and primary infestation leaf damage; a genome-wide molecular linkage map was constructed with 29,898 single-nucleotide polymorphism markers utilizing a Axiom(R) 180K soyaSNP array. Using inclusive composite interval mapping analysis for foxglove aphid resistance, one major candidate QTL on chromosome 7 was identified. The major QTL on chromosome 7 showed both antixenosis and antibiosis resistance responses. The newly identified major QTL was consistent with previously reported QTL, Raso2, which showed around 5 times narrow down interval range with 8 candidate genes. Furthermore, total 1,115 soybean varieties including Glycine soja and Glycine max were exposed to germplasm screening, and 31 varieties, which showed significant antibiosis type foxglove aphid resistance were identified. This result could be useful in breeding for new foxglove aphid resistant soybean cultivars and developing novel insecticides.

• 유통과학연구
• /
• 제14권11호
• /
• pp.61-73
• /
• 2016

Purpose - Marketing scholars have developed various types of mathematical models for describing marketing phenomenon, because there is no single model comprehensive enough to incorporate all the relevant marketing phenomena. This study tries to summarize the behavioral foundations and the mathematical derivations of the most widely used marketing models and discusses their strategic implications. This study selected four representative marketing models: multinomial logit(MNL) model, elimination-by-aspects(EBA) model, Hauser and Shugan model and Bass diffusion model. Especially, this study focuses on Hauser and Shugan(1983)'s Defender model and discusses the model's behavioral foundation and its implications. Research design, data, and methodology - Of the four selected model, the multinomial logit model is selected as the basic normative model and the other three models are described as descriptive models in contrast. Starting the discussion from the multinomial logit model, this study explains what important strategic variables are incorporated in each of the four models. The IIA(independence of irrelevant alternatives) axiom and Luce choice model is also discussed in relation to the multinomial logit model. The concept of 'efficient frontier' is discussed in relation to Hauser and Shugan's model. Graphs and tables are used to represent the key implications. No empirical study is included. Results - The analyses of the mathematical marketing models are shown to be very useful in understanding the essence of positioning strategy. The multinomial logit model implies the importance of increasing utility or consumer preference level. The EBA model implies the importance of lowering the inter-brand similarity and dominating the competitors. Hauser and Shugan model implies the importance of considering customer heterogeneity distribution in selecting the target market. Conclusions - It is shown that the concepts of 'efficient frontier' is useful in understanding the effectiveness of positioning strategy. Market positioning can be understood as occupying some place on the efficient frontier. The important strategic implications can be summarized as follows: Always try to increase customer preference by providing what they value, and differentiate from competing alternatives as much as possible. The best positioning strategy is to dominate all the competitors and the worst is to be dominated by the competitors.