• Title/Summary/Keyword: property (E.A)

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HIGH DIMENSION PRUFER DOMAINS OF INTEGER-VALUED POLYNOMIALS

  • Cahen, Paul-Jean;Chabert, Jean-Luc;K.Alan Loper
    • Journal of the Korean Mathematical Society
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    • v.38 no.5
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    • pp.915-935
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    • 2001
  • Let V be any valuation domain and let E be a subset of the quotient field K of V. We study the ring of integer-valued polynomials on E, that is, Int(E, V)={f$\in$K[X]|f(E)⊆V}. We show that, if E is precompact, then Int(E, V) has many properties similar to those of the classical ring Int(Z).In particular, Int(E, V) is dense in the ring of continuous functions C(E, V); each finitely generated ideal of Int(E, V) may be generated by two elements; and finally, Int(E, V) is a Prufer domain.

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COMMON FIXED POINTS UNDER LIPSCHITZ TYPE CONDITION

  • Pant, Vyomesh
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.467-475
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    • 2008
  • The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

THE LEFSCHETZ CONDITION ON PROJECTIVIZATIONS OF COMPLEX VECTOR BUNDLES

  • Nishinobu, Hirokazu;Yamaguchi, Toshihiro
    • Communications of the Korean Mathematical Society
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    • v.29 no.4
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    • pp.569-579
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    • 2014
  • We consider a condition under which the projectivization $P(E^k)$ of a complex k-bundle $E^k{\rightarrow}M$ over an even-dimensional manifold M can have the hard Lefschetz property, affected by [10]. It depends strongly on the rank k of the bundle $E^k$. Our approach is purely algebraic by using rational Sullivan minimal models [5]. We will give some examples.

GENERALIZED FRÉCHET-URYSOHN SPACES

  • Hong, Woo-Chorl
    • Journal of the Korean Mathematical Society
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    • v.44 no.2
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    • pp.261-273
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    • 2007
  • In this paper, we introduce some new properties of a topological space which are respectively generalizations of $Fr\'{e}chet$-Urysohn property. We show that countably AP property is a sufficient condition for a space being countable tightness, sequential, weakly first countable and symmetrizable, to be ACP, $Fr\'{e}chet-Urysohn$, first countable and semimetrizable, respectively. We also prove that countable compactness is a sufficient condition for a countably AP space to be countably $Fr\'{e}chet-Urysohn$. We then show that a countably compact space satisfying one of the properties mentioned here is sequentially compact. And we show that a countably compact and countably AP space is maximal countably compact if and only if it is $Fr\'{e}chet-Urysohn$. We finally obtain a sufficient condition for the ACP closure operator $[{\cdot}]_{ACP}$ to be a Kuratowski topological closure operator and related results.

A CHARACTERIZATION OF FINITE FACTORIZATION POSITIVE MONOIDS

  • Polo, Harold
    • Communications of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.669-679
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    • 2022
  • We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

Fundamental Investigation of Functional Property of Concrete Mixed with Functional Materials

  • Lee, Jong-Chan;Lee, Moon-Hwan;Lee, Sae-Hyun;Park, Young-Sin;Park, Jae-Myung
    • International Journal of Concrete Structures and Materials
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    • v.18 no.3E
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    • pp.165-171
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    • 2006
  • Environment-friendly materials are increasingly used as building construction materials nowadays, and the market share of those is growing. Accordingly, the research and developments in terms of environmental value are progressing steadily now. The main characteristics of environmental products are far-infrared radiation, negative-ion emission, electromagnetic wave shielding, and antimicrobial property. These products are often used in mortar and as spray on the finishing material. Nevertheless, there are hardly any research on the functional properties of concrete, the main material in construction field. Thus, we evaluated such basic properties of concrete as slump, compressive strength and air content while using such functional materials as sericite, wood-pattern sandstone, carbon black and nano-metric silver solution to focus on their functional properties like far-infrared radiation, negative ion emission, electro magnetic wave shielding, and antimicrobial activity in this research. The results indicated that the most useful material in the functional materials was carbon black. Sericite and nano-metric silver solution had a little effect on the functional property. Moreover, although wood-pattern sandstone had very high functional property, it exhibited too low compressive strength to be applied, to concrete as a factory product. Antimicrobial property of nano-metric silver solution in the concrete was not clear demonstrated, but if these specimens were to be aged in $CO_2$ gas for a long time, it might be apparent.

INJECTIVE PROPERTY OF LAURENT POWER SERIES MODULE

  • Park, Sang-Won
    • East Asian mathematical journal
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    • v.17 no.2
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    • pp.367-374
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    • 2001
  • Northcott and McKerrow proved that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-1}]$ is an injective left R[x]-module. Park generalized Northcott and McKerrow's result so that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-S}]$ is an injective left $R[x^S]$-module, where S is a submonoid of $\mathbb{N}$($\mathbb{N}$ is the set of all natural numbers). In this paper we extend the injective property to the Laurent power series module so that if R is a ring and E is an injective left R-module, then $E[[x^{-1},x]]$ is an injective left $R[x^S]$-module.

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COMMON FIXED POINT THEOREMS FOR TWO SELF MAPS SATISFYING ξ-WEAKLY EXPANSIVE MAPPINGS IN DISLOCATED METRIC SPACE

  • Kim, Jong Kyu;Kumar, Manoj;Preeti, Preeti;Poonam, Poonam;Lim, Won Hee
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.2
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    • pp.271-287
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    • 2022
  • In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d*) satisfying the following ξ-weakly expansive condition: d*(𝒫c, 𝒫d) ≥ d* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.

Almost derivations on the banach algebra $C^n$[0,1]

  • Jun, Kil-Woung;Park, Dal-Won
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.359-366
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    • 1996
  • A linear map T from a Banach algebra A into a Banach algebra B is almost multiplicative if $\left\$\mid$ T(fg) - T(f)T(g) \right\$\mid$ \leq \in\left\$\mid$ f \right\$\mid$\left\$\mid$ g \right\$\mid$(f,g \in A)$ for some small positive $\in$. B.E.Johnson [4,5] studied whether this implies that T is near a multiplicative map in the norm of operators from A into B. K. Jarosz [2,3] raised the conjecture : If T is an almost multiplicative functional on uniform algebra A, there is a linear and multiplicative functional F on A such that $\left\$\mid$ T - F \right\$\mid$ \leq \in', where \in' \to 0$ as $\in \to 0$. B. E. Johnson [4] gave an example of non-uniform commutative Banach algebra which does not have the property described in the above conjecture. He proved also that C(K) algebras and the disc algebra A(D) have this property [5]. We extend this property to a derivation on a Banach algebra.

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