• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.239-249
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• 1995

Let $V = (v_1, v_2, \cdots)$ be a sequence of positive integers arranged in nondecreasing order. We define V to be complete if every positive integer n is the sum of some subsequence of V, that is, $$ (1.1) n = \sum_{i=1}^{\infty} a_i v_i where a_i = 0 or 1.

• Honam Mathematical Journal
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• v.46 no.3
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• pp.378-392
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• 2024

In this paper, we study the notion of I-convergence of double sequences in neutrosophic 2-normed spaces which is more generalized version of statistical convergence of double sequences. Also we define I₂-Cauchy sequence and discuss on I₂-completeness with regards to neutrosophic 2-norm.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.93-110
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• 2000

An alternative interpretation of the completeness requirements for the higher order elements is presented. Apart from the familiar condition, $\sum_iN_i=1$, some additional conditions to be satisfied by the shape functions of higher order elements are identified. Elements with their geometry in the natural form, i.e., without any geometrical distortion, satisfy most of these additional conditions inherently. However, the geometrically distorted elements satisfy only fewer conditions. The practical implications of the satisfaction or non-satisfaction of these additional conditions are investigated with respect to a 3-node bar element, and 8- and 9-node quadrilateral elements. The results suggest that non-satisfaction of these additional conditions results in poorer performance of the element when the element is geometrically distorted. Based on the new interpretation of completeness requirements, a 3-node element and an 8-node rectangular element that are insensitive to mid-node distortion under a quadratic displacement field have been developed.

• Korean Journal of Logic
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• v.17 no.2
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• pp.323-349
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• 2014

In this paper, we show that the standard completeness for the extension of UL with compensation-free reinforcement (cfr) $(({\phi}&{\psi}){\rightarrow}({\phi}{\wedge}{\psi})){\vee}(({\phi}{\vee}{\psi}){\rightarrow}({\phi}&{\psi}))$ can be established. More exactly, first, the compensation-freely reinforced uninorm logic $UL_{cfr}$ (the UL with (cfr)) is introduced. The algebraic structures of $UL_{cfr}$ are then defined, and its algebraic completeness is established. Next, standard completeness (i.e. completeness on [0, 1]) is established for $UL_{cfr}$ by using the method introduced in Yang (2009).

• Korean Journal of Logic
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• v.12 no.2
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• pp.115-139
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• 2009

This paper investigates an extension of the uninorm (based) logic UL, which is obtained by adding (t-weakening, $W_t$) (($\phi$ & $\psi$) ${\wedge}$ t) $\rightarrow$ $\phi$ to UL introduced by Metcalfe and Montagna in [8]. First, the t-weakening uninorm logic $UL_{Wt}$ (the UL with $W_t$) is introduced. The algebraic structures corresponding to $UL_{Wt}$ is then defined, and its algebraic completeness is established. Next standard completeness (i.e. completeness on the real unit interval [0, 1]) is established for this logic by using Jenei and Montagna-style approach for proving standard completeness in [3, 6].

• Korean Journal of Logic
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• v.10 no.2
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• pp.125-146
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• 2007

This paper investigates the relevance system R-mingle (RM) as a a fuzzy-relevance logic. It shows that RM is fuzzy in Cintula's sense, i.e., RM is complete with respect to linearly ordered L-matrices (or L-algebras). More exactly, we first introduce RM and its weak versions wwRM and wRM. We next provide algebraic and matrix completeness results for them.

• Korean Journal of Logic
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• v.14 no.1
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• pp.55-76
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• 2011

Fixed-point conjunctive left-continuous idempotent uninorms have been introduced (see e.g. [2, 3]). This paper studies a system for such uninorms. More exactly, one system obtainable from IUML (Involutive uninorm mingle logic) by dropping involution (INV), called here WUML (Weak Uninorm Mingle Logic), is first introduced. This is the system of fixed-point conjunctive left-continuous idempotent uninorms and their residua with weak negation. Algebraic structures corresponding to the system, i.e., WUML-algebras, are then defined, and algebraic completeness is provided for the system. Standard completeness is further established for WUML and IUML in an analogy to that of WNM (Weak nilpotent minimum logic) and NM (Nilpotent minimum logic) in [4].

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.189-200
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• 2012

In this article we introduce the class of I-convergent double sequences of fuzzy real numbers. We have studied different properties like solidness, symmetricity, monotone, sequence algebra etc. We prove that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.

• Kyungpook Mathematical Journal
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• v.54 no.2
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• pp.321-332
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• 2014

In this article we introduce different types of multiplier I-convergent double sequence spaces. We study their different algebraic and topological properties like solidity, symmetricity, completeness etc. The decomposition theorem is established and some inclusion results are proved.

• Journal of the Korean Society of Clothing and Textiles
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• v.21 no.8
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• pp.1261-1274
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• 1997

Contemporary costume by the 'Deconstruction' from the outside has shown disclosure, destruction, poverty and analysis. The conclusion of this thesis as follows, 1. The Deconstruction of disclosure by infra disclosed the underwear and inner structure outside, which has deconstructed a fixed idea i.e.'underwear must be in outwear', modesty versus immodesty and disclosure versus concealment. 2. The Deconstruction of destruction originated in punk look has rejected traditional manners and utility, at the same time, it has shown the ambivalence i.e. completeness versus incompleteness, making versus destructing by slashes, rips, fringes. 3. The Deconstruction of poverty has appeared as French avangarde mode, little black dress by Chanel, second hand style by hippy, blue jean, granny look, especially Rei Kawakubo's poor look influenced by Zen Aesthetics and post punk. It has looked like old and worn out dress by doing patchwork, dye, decolor, rip, fray, which has shown the decentring by concealing the body than disclosing, rejecting snobbery. 4. The Deconstruction of analysis, seemingly partial and patched is a violation only of our expectation of clothing's unbroken entity though it has looked like a fragment. The completeness and coherence of it is made more evident by its breach, void, and bond like a poetic language. As the result, disclosed, destructed, poor, and analytical costumes has expressed as an escape from the appearance which traditional aesthetic concept had pursued.